def add_rotation(cluster, qrot):
"""Add a degree of rotation to an already generated StarCluster
Parameters
----------
cluster : class
StarCluster
qrot : float
fraction of stars with v_phi < 0 that are switched to vphi > 0
Returns
-------
x,y,z,vx,vy,vz : float
stellar positions and velocities (now with rotation)
History
-------
2019 - Written - Webb (UofT)
"""
r, theta, z = bovy_coords.rect_to_cyl(cluster.x, cluster.y, cluster.z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(cluster.vx, cluster.vy,
cluster.vz, cluster.x,
cluster.y, cluster.z)
indx = vtheta < 0.0
rindx = np.random.rand(cluster.ntot) < qrot
vtheta[indx * rindx] = np.sqrt(vtheta[indx * rindx] * vtheta[indx * rindx])
x, y, z = bovy_coords.cyl_to_rect(r, theta, z)
vx, vy, vz = bovy_coords.cyl_to_rect_vec(vr, vtheta, vz, theta)
return x, y, z, vx, vy, vz
def cylindrical_vs(calc_dict):
vRg, vTg, vZg = b_c.rect_to_cyl_vec(calc_dict['vx_gc'], calc_dict['vy_gc'],
calc_dict['vz_gc'], calc_dict['x_gc'],
calc_dict['y_gc'], calc_dict['z_gc'])
return vRg, vTg
def cart_to_cyl(x,y,z,vx,vy,vz):
"""
NAME:
cart_to_cyl
PURPOSE:
Convert cylindrical to spherical coordinates
INPUT:
x,y,z,vx,vy,vz
OUTPUT:
r,theta,z,vr,vtheta,vz
HISTORY:
2018 - Written - Webb (UofT)
"""
r, theta, z = bovy_coords.rect_to_cyl(x, y, z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(
vx, vy, vz, x, y, z
)
return r, theta, z, vr, vtheta, vz
def progenitorOrbit(R0=16.0, V0=230.0, xyz=False):
"""
NAME:
progenitorOrbit
PURPOSE:
return the phase-space point corresponding to the (given) progenitor
INPUT:
R0= (default 16kpc) value of R0 to apply when normalizing
V0= (default 230kpc) value of V0 to apply when normalizing
xyz= (False) if True, return rectangular coordinates
OUTPUT:
Orbit instance with progenitor orbit
HISTORY:
2013-09-16 - Written - Bovy (IAS)
"""
x = 7816.082584 / 1000.0
y = 240.023507 / 1000.0
z = 16640.055966 / 1000.0
vx = -37.456858
vy = -151.794112
vz = -21.609662
if xyz:
return (x, y, z, vx, vy, vz)
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, R, phi, z, cyl=True)
R /= R0
z /= R0
vR /= V0
vT /= V0
vz /= V0
return Orbit([R, vR, vT, z, vz, phi])
def rectangular_to_cylindrical(xv):
R,phi,Z= bovy_coords.rect_to_cyl(xv[:,0],xv[:,1],xv[:,2])
vR,vT,vZ= bovy_coords.rect_to_cyl_vec(xv[:,3],xv[:,4],xv[:,5],
R,phi,Z,cyl=True)
out= numpy.empty_like(xv)
# Preferred galpy arrangement of cylindrical coordinates
out[:,0]= R
out[:,1]= vR
out[:,2]= vT
out[:,3]= Z
out[:,4]= vZ
out[:,5]= phi
return out
def sample_galpy_potential(pot,n,rmin,rmax,ro=8.,vo=220.,coordinates='cartesian'):
ran=np.random.rand(n)
rad=np.linspace(rmin,rmax,n)
try:
menc=pot.mass(rad/ro,z=0,t=0,forceint=False)
except:
vc= potential.vcirc(pot,rad/ro,phi=0,t=0.,ro=ro,vo=vo,use_physical=False)
menc=vc**2.*(rad/ro)
menc*=bovy_conversion.mass_in_msol(ro=ro,vo=vo)
r=np.interp(ran, menc/menc[-1], rad)
phi=2.0*np.pi*np.random.rand(n)
theta=np.arccos(1.0-2.0*np.random.rand(n))
x=r*np.sin(theta)*np.cos(phi)
y=r*np.sin(theta)*np.sin(phi)
z=r*np.cos(theta)
sigma_v_1d=vo*potential.vcirc(pot,rad/ro,phi=0,t=0.,ro=ro,vo=vo,use_physical=False)/np.sqrt(3.)
vx=np.random.normal(0.,sigma_v_1d,n)
vy=np.random.normal(0.,sigma_v_1d,n)
vz=np.random.normal(0.,sigma_v_1d,n)
if coordinates=='spherical':
vr = (vx * np.sin(theta) * np.cos(phi)
+ vy * np.sin(theta) * np.sin(phi)
+ vz * np.cos(theta)
)
vtheta = (
vx * np.cos(theta) * np.cos(phi)
+ vy * np.cos(theta) * np.sin(phi)
- vz * np.sin(theta)
)
vphi = vx * -np.sin(phi) + vy * np.cos(phi)
x,y,z=r,phi,theta
vx,vy,vz=vr,vphi,vtheta
elif coordinates=='cylindrical':
x,y,z=bovy_coords.rect_to_cyl(x,y,z)
vx,vy,vz=bovy_coords.rect_to_cyl_vec(vx,vy,vz,x,y,z,True)
return x,y,z,vx,vy,vz
def rectangular_to_cylindrical(xv):
R, phi, Z = bovy_coords.rect_to_cyl(xv[:, 0], xv[:, 1], xv[:, 2])
vR, vT, vZ = bovy_coords.rect_to_cyl_vec(xv[:, 3],
xv[:, 4],
xv[:, 5],
R,
phi,
Z,
cyl=True)
out = numpy.empty_like(xv)
# Preferred galpy arrangement of cylindrical coordinates
out[:, 0] = R
out[:, 1] = vR
out[:, 2] = vT
out[:, 3] = Z
out[:, 4] = vZ
out[:, 5] = phi
return out
def initialize_orbits(cluster, r0=8.0, v0=220.0):
"""
NAME:
initialize_orbits
PURPOSE:
Initialize a galpy orbit for every stars in the cluster
--> Note currently depends on version of galpy with Orbits, which is soon to be replace by a generic Orbit function
INPUT:
cluster - StarCluster
r0 - galpy distance scale (Default: 8.)
v0 - galpy velocity scale (Default: 220.)
OUTPUT:
orbit instance for each stars
HISTORY:
2018 - Written - Webb (UofT)
"""
units0, origin0 = save_cluster(cluster)
cluster.to_galaxy()
cluster.to_galpy()
x, y, z = cluster.x, cluster.y, cluster.z
vx, vy, vz = cluster.vx, cluster.vy, cluster.vz
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
vxvv = np.column_stack([R, vR, vT, z, vz, phi])
os = Orbit(vxvv, ro=r0, vo=v0, solarmotion=[-11.1, 24.0, 7.25])
return_cluster(cluster, units0, origin0)
return os
def readPal5Data(R0=16.0, V0=230.0, subsample=None, leading=False, trailing=False):
"""
NAME:
readPal5Data
PURPOSE:
Read the Pal 5 data
INPUT:
R0= (default 16kpc) value of R0 to apply when normalizing
V0= (default 230kpc) value of V0 to apply when normalizing
subsample= (None) if set, subsample to this # of stars
leading= (False) if True, only select stars in the leading arm
trailing= (False) if True, only select stars in the trailing arm
OUTPUT:
R,vR,vT,z,vz,phi
HISTORY:
2013-09-16 - Written - Bovy (IAS)
"""
data = numpy.loadtxt(_DATAFILE, comments="#")
# Cut out stars near/in the progenitor
px, py, pz, pvx, pvy, pvz = progenitorOrbit(R0=1.0, V0=1.0, xyz=True)
pindx = (
(px - data[:, 0] / 1000.0) ** 2.0
+ (py - data[:, 1] / 1000.0) ** 2.0
+ (pz - data[:, 2] / 1000.0) ** 2.0
+ (pvx - data[:, 3]) ** 2.0
+ (pvy - data[:, 4]) ** 2.0
+ (pvz - data[:, 5]) ** 2.0
) < 500.0
data = data[True - pindx, :]
if leading:
data = data[data[:, 5] < pvz]
if trailing:
data = data[data[:, 5] > pvz]
if not subsample is None:
indx = numpy.random.permutation(subsample)
data = data[indx, :]
R, phi, z = bovy_coords.rect_to_cyl(data[:, 0] / 1000.0, data[:, 1] / 1000.0, data[:, 2] / 1000.0)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(data[:, 3], data[:, 4], data[:, 5], R, phi, z, cyl=True)
R /= R0
z /= R0
vR /= V0
vT /= V0
vz /= V0
return (R, vR, vT, z, vz, phi)
def aA_prog(ptype):
"""
Parameters
----------------------------------------------------------------------------------
ptype : potential type. It can be either "Log" for logarithmic potential or
"MW" for Milky Way 2014 potential.
Return
----------------------------------------------------------------------------------
action-angle values of the progenitor for GD-1 stream given the potentia type
"""
# setting up the action-angle instance
if ptype == "Log":
lp = potential.LogarithmicHaloPotential(q=0.9, normalize=1.)
aAS = actionAngleIsochroneApprox(pot = lp, b=0.8)
elif ptype == "MW":
aAS = actionAngleIsochroneApprox(pot = MWPotential2014, b=0.6, tintJ=1000,ntintJ=2000)
# current position and velocity of the GD-1 stream progenitor in cartesian coordinates
x, y, z = np.array([12.4, 1.5, 7.1])
vx, vy, vz = np.array([107., -243., -105.])
# current position and velocity in cylindrical coordinate
R, phi, zz = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z, cyl = False)
ro = 8.0
vo = 220.0
# converting to galpy natural units
R /= ro
zz /= ro
vR /= vo
vT /= vo
vz /= vo
# computing the action-angle coordinates
val = aAS.actionsFreqsAngles(R, vR, vT, zz, vz, phi)
return val
def cart_to_cyl(x, y, z, vx, vy, vz):
"""Convert cartesian coordinates to cylindrical coordinates
Parameters
----------
x,y,z,vx,vy,vz : float
positions and velocities in cartesian coordinates
Returns
-------
r, theta, z, vr, vtheta, vz : float
stellar positions and velocities in cylindrical coordinates
History
-------
2018 - Written - Webb (UofT)
"""
r, theta, z = bovy_coords.rect_to_cyl(x, y, z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
return r, theta, z, vr, vtheta, vz
def initialize_orbits(cluster, ro=8.0, vo=220.0):
"""Initialize a galpy orbit for every star in the cluster
Parameters
----------
cluster : class
StarCluster
ro : float
galpy distance scale (default: 8.)
vo : float
galpy velocity scale (default: 220.)
Returns
-------
orbit : class
GALPY orbit
History
-------
2018 - Written - Webb (UofT)
"""
units0, origin0 = save_cluster(cluster)
cluster.to_galaxy()
cluster.to_galpy()
x, y, z = cluster.x, cluster.y, cluster.z
vx, vy, vz = cluster.vx, cluster.vy, cluster.vz
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
vxvv = np.column_stack([R, vR, vT, z, vz, phi])
os = Orbit(vxvv, ro=ro, vo=vo, solarmotion=[-11.1, 24.0, 7.25])
return_cluster(cluster, units0, origin0)
return os
def calc_progenitor_actions(savefilename):
# Setup potential
lp = potential.LogarithmicHaloPotential(normalize=1.0, q=0.9)
# Setup orbit
x, z, y, vx, vz, vy = -11.63337239, -10.631736273934635, -20.76235661, -128.8281653, 79.172383882274971, 42.88727925
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, R, phi, z, cyl=True)
R /= 8.0
z /= 8.0
vR /= 220.0
vT /= 220.0
vz /= 220.0
o = Orbit([R, vR, vT, z, vz, phi])
ts = numpy.linspace(0.0, 5.125 * 220.0 / 8.0, 1313) # times of the snapshots
o.integrate(ts, lp, method="dopr54_c")
if "aas" in savefilename:
aA = actionAngleStaeckel(pot=lp, delta=1.20, c=True)
else:
aA = actionAngleIsochroneApprox(pot=lp, b=0.8)
# Now calculate actions, frequencies, and angles for all positions
Rs = o.R(ts)
vRs = o.vR(ts)
vTs = o.vT(ts)
zs = o.z(ts)
vzs = o.vz(ts)
phis = o.phi(ts)
csvfile = open(savefilename, "wb")
writer = csv.writer(csvfile, delimiter=",")
for ii in range(len(ts)):
acfs = aA.actionsFreqsAngles(Rs[ii], vRs[ii], vTs[ii], zs[ii], vzs[ii], phis[ii])
writer.writerow(
[acfs[0][0], acfs[1][0], acfs[2][0], acfs[3][0], acfs[4][0], acfs[5][0], acfs[6][0], acfs[7][0], acfs[8][0]]
)
csvfile.flush()
csvfile.close()
return None
def orbit_interpolate(
cluster,
dt,
pot=MWPotential2014,
from_centre=False,
do_tails=False,
rmin=None,
rmax=None,
emin=None,
emax=None,
indx=None,
ro=8.0,
vo=220.0,
):
"""
NAME: Interpolate past or future position of cluster and escaped stars
- When moving the cluster centre and stars backwards or forwards along their orbits, stars within the cluster are shifted with the cluster centre.
Tail stars, identified using either rmin/rmax, emin/emax, or indx can be integrated separately in the potential
- Note that this function operates on the cluster and changes the positions and velocities of all stars
Parameters
----------
cluster : class
StarCluster
dt : float
timestep that StarCluster is to be moved to
pot : class
galpy Potential that orbit is to be integrate in (default: MWPotential2014)
from_centre : bool
genrate orbit from cluster's exact centre instead of its assigned galactocentric coordinates (default: False)
do_tails : bool
interpolate the orbits of tail stars separately (default: False)
rmin/rmax : float
radial range corresponding to cluster (needed to identify tail stars)
emin/emax : float
energy range corresponding to cluster (needed to identify tail stars)
indx : bool
specific subset of stars
ro :float
galpy distance scale (Default: 8.)
vo : float
galpy velocity scale (Default: 220.)
Returns
-------
x,y,z : float
interpolated positions of each star
x,y,z : float
interpolated velocities of each star
History
-------
2018 - Written - Webb (UofT)
"""
cluster.tphys += dt
units0, origin0 = save_cluster(cluster)
cluster.to_galaxy()
if do_tails:
cluster.to_cluster()
if from_centre:
cluster.to_centre()
if rmin == None:
rmin = np.min(cluster.r)
if rmax == None:
rmax = np.max(cluster.r)
rindx = (cluster.r >= rmin) * (cluster.r <= rmax)
if len(cluster.etot) == cluster.ntot:
if emin == None:
emin = np.min(cluster.etot)
if emax == None:
emax = np.max(cluster.etot)
eindx = (cluster.etot >= emin) * (cluster.etot <= emax)
else:
eindx = cluster.id > -1
if indx is None:
indx = rindx * eindx
else:
indx *= (rindx * eindx)
tindx = np.invert(indx)
cluster.to_galaxy()
else:
indx = cluster.id > -1
if cluster.orbit is None:
cluster.orbit = initialize_orbit(cluster, from_centre)
ts = np.linspace(0, dt / bovy_conversion.time_in_Gyr(ro=ro, vo=vo), 10)
cluster.orbit.integrate(ts, pot)
cluster.to_kpckms()
x, y, z = cluster.x, cluster.y, cluster.z
vx, vy, vz = cluster.vx, cluster.vy, cluster.vz
if from_centre:
dx = cluster.orbit.x(ts[-1]) - cluster.xc - cluster.xgc
dy = cluster.orbit.y(ts[-1]) - cluster.yc - cluster.ygc
dz = cluster.orbit.z(ts[-1]) - cluster.zc - cluster.zgc
dvx = cluster.orbit.vx(ts[-1]) - cluster.vxc - cluster.vxgc
dvy = cluster.orbit.vy(ts[-1]) - cluster.vyc - cluster.vygc
dvz = cluster.orbit.vz(ts[-1]) - cluster.vzc - cluster.vzgc
else:
dx = cluster.orbit.x(ts[-1]) - cluster.xgc
dy = cluster.orbit.y(ts[-1]) - cluster.ygc
dz = cluster.orbit.z(ts[-1]) - cluster.zgc
dvx = cluster.orbit.vx(ts[-1]) - cluster.vxgc
dvy = cluster.orbit.vy(ts[-1]) - cluster.vygc
dvz = cluster.orbit.vz(ts[-1]) - cluster.vzgc
x[indx] += dx
y[indx] += dy
z[indx] += dz
vx[indx] += dvx
vy[indx] += dvy
vz[indx] += dvz
if from_centre:
xc, yc, zc = 0.0, 0.0, 0.0
vxc, vyc, vzc = 0.0, 0.0, 0.0
else:
xc += dx
yc += dy
zc += dz
vxc += dvx
vyc += dvy
vzc += dvz
xgc, ygc, zgc = (
cluster.orbit.x(ts[-1]),
cluster.orbit.y(ts[-1]),
cluster.orbit.z(ts[-1]),
)
vxgc, vygc, vzgc = (
cluster.orbit.vx(ts[-1]),
cluster.orbit.vy(ts[-1]),
cluster.orbit.vz(ts[-1]),
)
if do_tails:
cluster.to_galaxy()
cluster.to_galpy()
xt, yt, zt = cluster.x[tindx], cluster.y[tindx], cluster.z[tindx]
vxt, vyt, vzt = cluster.vx[tindx], cluster.vy[tindx], cluster.vz[tindx]
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
vxvv = np.column_stack([R, vR, vT, z, vz, phi])
otail = Orbit(vxvv, ro=ro, vo=vo, solarmotion=[-11.1, 24.0, 7.25])
cluster.to_kpckms()
ts = np.linspace(0, dt / bovy_conversion.time_in_Gyr(ro=ro, vo=vo), 10)
otail.integrate(ts, pot)
x[tindx] = np.array(otail.x(ts[-1]))
y[tindx] = np.array(otail.y(ts[-1]))
z[tindx] = np.array(otail.z(ts[-1]))
vx[tindx] = np.array(otail.vx(ts[-1]))
vy[tindx] = np.array(otail.vy(ts[-1]))
vz[tindx] = np.array(otail.vz(ts[-1]))
return_cluster(cluster, units0, origin0)
return x, y, z, vx, vy, vz
def make_sim_movie(proj='xz',comov=False,skippng=False,
includeorbit=True):
#Directories
savedirpng= './movies/oph/pngs/'
timestr= '_1Gyr'
# timestr= ''
# massstr= '_lowmass'
massstr= ''
basefilename= 'oph%s_evol%s_' % (massstr,timestr)
moviefilename= 'oph%s_evol%s' % (massstr,timestr)
#Read data
#datafile= 'oph_evol_hitres.dat'
datafile= 'oph%s_evol%s.dat' % (massstr,timestr)
print "Reading data ..."
data= numpy.loadtxt(datafile,comments='#')
print "Done reading data"
if proj.lower() == 'xz':
includeorbit= False #just to be sure
basefilename+= 'xz_'
moviefilename+= '_xz'
x= data[:,1]
y= data[:,3]
if comov:
basefilename+= 'comov_'
moviefilename+= '_comov'
xrange=[-12.,12.]
yrange=[-10.,10.]
else:
xrange=[-18.,18.]
yrange=[-18.,18.]
xlabel=r'$X\,(\mathrm{kpc})$'
ylabel=r'$Z\,(\mathrm{kpc})$'
elif proj.lower() == 'yz':
includeorbit= False #just to be sure
basefilename+= 'yz_'
moviefilename+= '_yz'
x= data[:,2]
y= data[:,3]
if comov:
basefilename+= 'comov_'
moviefilename+= '_comov'
xrange=[-15.,15.]
yrange=[-15.,15.]
else:
xrange=[-18.,18.]
yrange=[-18.,18.]
xlabel=r'$Y\,(\mathrm{kpc})$'
ylabel=r'$Z\,(\mathrm{kpc})$'
elif proj.lower() == 'orbplane':
basefilename+= 'orbplane_'
moviefilename+= '_orbplane'
x= numpy.zeros_like(data[:,1])
y= numpy.zeros_like(data[:,2])
nx= 20000
nt= len(x)/nx
diff= numpy.empty(nt)
if includeorbit:
npts= 201
pot= potential.MWPotential2014
pts= numpy.linspace(0.,4.,npts)
px= numpy.zeros(nt*(2*npts-1))
py= numpy.zeros(nt*(2*npts-1))
ii= 0
#Calculate median angular momentum at t=0, use this to always go to the orbital plane
Lx= numpy.median(data[ii*nx:(ii+1)*nx,2]*data[ii*nx:(ii+1)*nx,6]\
-data[ii*nx:(ii+1)*nx,3]*data[ii*nx:(ii+1)*nx,5])
Ly= numpy.median(data[ii*nx:(ii+1)*nx,3]*data[ii*nx:(ii+1)*nx,4]\
-data[ii*nx:(ii+1)*nx,1]*data[ii*nx:(ii+1)*nx,6])
Lz= numpy.median(data[ii*nx:(ii+1)*nx,1]*data[ii*nx:(ii+1)*nx,5]\
-data[ii*nx:(ii+1)*nx,2]*data[ii*nx:(ii+1)*nx,4])
L= numpy.sqrt(Lx**2.+Ly**2.+Lz**2.)
Lx/= L
Ly/= L
Lz/= L
Txz= numpy.zeros((3,3))
Tz= numpy.zeros((3,3))
Txz[0,0]= Lx/numpy.sqrt(Lx**2.+Ly**2.)
Txz[1,1]= Lx/numpy.sqrt(Lx**2.+Ly**2.)
Txz[1,0]= Ly/numpy.sqrt(Lx**2.+Ly**2.)
Txz[0,1]= -Ly/numpy.sqrt(Lx**2.+Ly**2.)
Txz[2,2]= 1.
Tz[0,0]= Lz
Tz[1,1]= 1.
Tz[2,2]= Lz
Tz[2,0]= -numpy.sqrt(Lx**2.+Ly**2.)
Tz[0,2]= numpy.sqrt(Lx**2.+Ly**2.)
TL= numpy.dot(Tz,Txz)
for ii in range(nt):
if includeorbit:
#Calculate progenitor orbit around this point
pox= numpy.median(data[ii*nx:(ii+1)*nx,1])
poy= numpy.median(data[ii*nx:(ii+1)*nx,3])
poz= numpy.median(data[ii*nx:(ii+1)*nx,2])
povx= numpy.median(data[ii*nx:(ii+1)*nx,4])
povy= numpy.median(data[ii*nx:(ii+1)*nx,6])
povz= numpy.median(data[ii*nx:(ii+1)*nx,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((3,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec*= 8.
tvec= numpy.empty((3,nx))
tvec[0,:]= data[ii*nx:(ii+1)*nx,1]
tvec[1,:]= data[ii*nx:(ii+1)*nx,2]
tvec[2,:]= data[ii*nx:(ii+1)*nx,3]
x[ii*nx:(ii+1)*nx]= numpy.dot(TL,tvec)[0]
y[ii*nx:(ii+1)*nx]= numpy.dot(TL,tvec)[1]
if includeorbit:
#Also rotate orbit
px[ii*(2*npts-1):(ii+1)*(2*npts-1)]= numpy.dot(TL,pvec)[0]
py[ii*(2*npts-1):(ii+1)*(2*npts-1)]= numpy.dot(TL,pvec)[1]
#print numpy.std(numpy.dot(T,tvec)[2])
#Rotate further to lign up between frames
if not includeorbit:
dist= numpy.sqrt((x[ii*nx:(ii+1)*nx]-numpy.median(x[ii*nx:(ii+1)*nx]))**2.\
+(y[ii*nx:(ii+1)*nx]-numpy.median(y[ii*nx:(ii+1)*nx]))**2.)
largedist= dist > (5.*numpy.std(dist))
A= numpy.ones((numpy.sum(largedist),2))
A[:,1]= x[ii*nx:(ii+1)*nx][largedist]
m= numpy.dot(linalg.inv(numpy.dot(A.T,A)),
numpy.dot(A.T,y[ii*nx:(ii+1)*nx][largedist]))[1]
sint= m/numpy.sqrt(1.+m**2.)
cost= 1./numpy.sqrt(1.+m**2.)
else:
if False:
A= numpy.ones((51,2))
A[:25,1]= px[ii*(2*npts-1)+npts-50:ii*(2*npts-1)+npts-25]
A[25:,1]= px[ii*(2*npts-1)+npts+25:ii*(2*npts-1)+npts+51]
m= numpy.dot(linalg.inv(numpy.dot(A.T,A)),
numpy.dot(A.T,py[ii*(2*npts-1)+npts-25:ii*(2*npts-1)+npts+26]))[1]
sint= m/numpy.sqrt(1.+m**2.)
cost= 1./numpy.sqrt(1.+m**2.)
else:
sint= py[ii*(2*npts-1)+npts+1]/numpy.sqrt(px[ii*(2*npts-1)+npts+1]**2.+py[ii*(2*npts-1)+npts+1]**2.)
cost= px[ii*(2*npts-1)+npts+1]/numpy.sqrt(px[ii*(2*npts-1)+npts+1]**2.+py[ii*(2*npts-1)+npts+1]**2.)
tvec= numpy.empty((2,nx))
tvec[0,:]= x[ii*nx:(ii+1)*nx]-numpy.median(x[ii*nx:(ii+1)*nx])
tvec[1,:]= y[ii*nx:(ii+1)*nx]-numpy.median(y[ii*nx:(ii+1)*nx])
T= numpy.zeros((2,2))
T[0,0]= cost
T[1,1]= cost
T[1,0]= -sint
T[0,1]= sint
tvec= numpy.dot(T,tvec)
if includeorbit:
#Also rotate orbit
pvec2= numpy.empty((2,(2*npts-1)))
pvec2[0,:]= px[ii*(2*npts-1):(ii+1)*(2*npts-1)]-numpy.median(x[ii*nx:(ii+1)*nx])
pvec2[1,:]= py[ii*(2*npts-1):(ii+1)*(2*npts-1)]-numpy.median(y[ii*nx:(ii+1)*nx])
pvec2= numpy.dot(T,pvec2)
T[0,0]= numpy.cos(45./180.*numpy.pi)
T[1,1]= numpy.cos(45./180.*numpy.pi)
T[1,0]= numpy.sin(45./180.*numpy.pi)
T[0,1]= -numpy.sin(45./180.*numpy.pi)
tvec= numpy.dot(T,tvec)
x[ii*nx:(ii+1)*nx]= tvec[0,:]
y[ii*nx:(ii+1)*nx]= tvec[1,:]
if includeorbit:
pvec2= numpy.dot(T,pvec2)
px[ii*(2*npts-1):(ii+1)*(2*npts-1)]= pvec2[0,:]
py[ii*(2*npts-1):(ii+1)*(2*npts-1)]= pvec2[1,:]
if comov:
basefilename+= 'comov_'
moviefilename+= '_comov'
xrange=[-2.,2.]
yrange=[-2.,2.]
# xrange=[-4.,4.]
# yrange=[-4.,4.]
else:
xrange=[-30.,30.]
yrange=[-15.,15.]
xlabel=r'$X_{\mathrm{orb}}\,(\mathrm{kpc})$'
ylabel=r'$Y_{\mathrm{orb}}\,(\mathrm{kpc})$'
if not skippng:
nx= 20000
nt= len(x)/nx
for ii in range(nt):
plotx= x[ii*nx:(ii+1)*nx]
ploty= y[ii*nx:(ii+1)*nx]
if comov:
plotx-= numpy.median(plotx)
ploty-= numpy.median(ploty)
bovy_plot.bovy_print()
bovy_plot.bovy_plot(plotx,ploty,'k.',ms=2.,
xlabel=xlabel,
ylabel=ylabel,
xrange=xrange,
yrange=yrange)
if not comov:
bovy_plot.bovy_plot(numpy.median(plotx),numpy.median(ploty),
'bo',mec='none',overplot=True)
if includeorbit:
bovy_plot.bovy_plot(px[ii*(2*npts-1):(ii+1)*(2*npts-1)],
py[ii*(2*npts-1):(ii+1)*(2*npts-1)],
'b-',
overplot=True)
bovy_plot.bovy_end_print(os.path.join(savedirpng,basefilename+'%s.png' % str(ii).zfill(5)))
#Turn into movie
framerate= 25
bitrate= 1000000
try:
subprocess.check_call(['ffmpeg',
'-i',
os.path.join(savedirpng,basefilename+'%05d.png'),
'-y',
'-r',str(framerate),
'-b', str(bitrate),
moviefilename+'.mpg'])
except subprocess.CalledProcessError:
print "'ffmpeg' failed"
return None
def plot_stream_lb(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPDIR,'gd1_evol_hitres_01312.dat'),
delimiter=',')
aadata= numpy.loadtxt(os.path.join(_STREAMSNAPAADIR,
'gd1_evol_hitres_aa_01312.dat'),
delimiter=',')
thetar= aadata[:,6]
thetar= (numpy.pi+(thetar-numpy.median(thetar))) % (2.*numpy.pi)
sindx= numpy.fabs(thetar-numpy.pi) > (1.5*numpy.median(numpy.fabs(thetar-numpy.median(thetar)))) #stars in the stream
#Transform to (l,b)
XYZ= bovy_coords.galcenrect_to_XYZ(data[:,1],data[:,3],data[:,2],Xsun=8.)
lbd= bovy_coords.XYZ_to_lbd(XYZ[0],XYZ[1],XYZ[2],degree=True)
vXYZ= bovy_coords.galcenrect_to_vxvyvz(data[:,4],data[:,6],data[:,5],
vsun=[0.,30.24*8.,0.])
vlbd= bovy_coords.vxvyvz_to_vrpmllpmbb(vXYZ[0],vXYZ[1],vXYZ[2],
lbd[:,0],lbd[:,1],lbd[:,2],
degree=True)
includeorbit= True
if includeorbit:
npts= 201
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
pts= numpy.linspace(0.,4.,npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((6,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec[3,:npts-1]= -pno.vx(pts)[::-1][:-1]
pvec[4,:npts-1]= -pno.vz(pts)[::-1][:-1]
pvec[5,:npts-1]= -pno.vy(pts)[::-1][:-1]
pvec[3,npts-1:]= ppo.vx(pts)
pvec[4,npts-1:]= ppo.vz(pts)
pvec[5,npts-1:]= ppo.vy(pts)
pvec[:3,:]*= 8.
pvec[3:,:]*= 220.
pXYZ= bovy_coords.galcenrect_to_XYZ(pvec[0,:],pvec[2,:],pvec[1,:],
Xsun=8.)
plbd= bovy_coords.XYZ_to_lbd(pXYZ[0],pXYZ[1],pXYZ[2],degree=True)
pvXYZ= bovy_coords.galcenrect_to_vxvyvz(pvec[3,:],pvec[5,:],pvec[4,:],
vsun=[0.,30.24*8.,0.])
pvlbd= bovy_coords.vxvyvz_to_vrpmllpmbb(pvXYZ[0],pvXYZ[1],pvXYZ[2],
plbd[:,0],plbd[:,1],plbd[:,2],
degree=True)
includetrack= True
if includetrack:
#Setup stream model
lp= potential.LogarithmicHaloPotential(q=0.9,normalize=1.)
aAI= actionAngleIsochroneApprox(b=0.8,pot=lp)
obs= numpy.array([1.56148083,0.35081535,-1.15481504,
0.88719443,-0.47713334,0.12019596])
sdf= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=True,nTrackChunks=_NTRACKCHUNKS,
vsun=[0.,30.24*8.,0.],
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.),
multi=_NTRACKCHUNKS)
sdft= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=False,nTrackChunks=_NTRACKCHUNKS,
vsun=[0.,30.24*8.,0.],
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.),
multi=_NTRACKCHUNKS)
#Plot
bovy_plot.bovy_print(fig_width=8.25,fig_height=3.5)
if 'ld' in plotfilename:
lbindx= 2
ylabel=r'$\mathrm{Distance}\,(\mathrm{kpc})$'
yrange=[0.,30.]
elif 'lvlos' in plotfilename:
lbindx= 0
ylabel=r'$V_\mathrm{los}\,(\mathrm{km\,s}^{-1})$'
yrange=[-500.,500.]
elif 'lpmll' in plotfilename:
lbindx= 1
ylabel=r'$\mu_{l}\cos b\,(\mathrm{mas\,yr}^{-1})$'
yrange=[-2.,13.5]
elif 'lpmbb' in plotfilename:
lbindx= 2
ylabel=r'$\mu_{b}\,(\mathrm{mas\,yr}^{-1})$'
yrange=[-8.,7.]
else:
lbindx= 1
yrange=[-10.,60.]
ylabel=r'$\mathrm{Galactic\ latitude}\,(\mathrm{deg})$'
if 'vlos' in plotfilename or 'pm' in plotfilename:
#Stream
bovy_plot.bovy_plot(lbd[sindx,0],vlbd[sindx,lbindx],'k,',
xlabel=r'$\mathrm{Galactic\ longitude}\,(\mathrm{deg})$',
ylabel=ylabel,
xrange=[0.,290.],
yrange=yrange)
#Progenitor
pindx= copy.copy(True-sindx)
pindx[0:9900]= False
bovy_plot.bovy_plot(lbd[pindx,0],vlbd[pindx,lbindx],'k,',overplot=True)
else:
bovy_plot.bovy_plot(lbd[sindx,0],lbd[sindx,lbindx],'k,',
xlabel=r'$\mathrm{Galactic\ longitude}\,(\mathrm{deg})$',
ylabel=ylabel,
xrange=[0.,290.],
yrange=yrange)
#Progenitor
pindx= copy.copy(True-sindx)
pindx[0:9900]= False
bovy_plot.bovy_plot(lbd[pindx,0],lbd[pindx,lbindx],'k,',overplot=True)
if includeorbit:
if 'vlos' in plotfilename or 'pm' in plotfilename:
bovy_plot.bovy_plot(plbd[npts,0],pvlbd[npts,lbindx],
'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(plbd[:,0],pvlbd[:,lbindx],'k--',overplot=True)
else:
bovy_plot.bovy_plot(plbd[npts,0],plbd[npts,lbindx],
'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(plbd[:,0],plbd[:,lbindx],'k--',overplot=True)
if includetrack:
d1= 'll'
if 'vlos' in plotfilename:
d2= 'vlos'
elif 'pmll' in plotfilename:
d2= 'pmll'
elif 'pmbb' in plotfilename:
d2= 'pmbb'
elif 'ld' in plotfilename:
d2= 'dist'
else:
d2= 'bb'
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Insets
if 'vlos' in plotfilename:
xmin, xmax= 220., 250.
ymin, ymax= 230., 390.
pyplot.plot([xmin,xmin],[ymin,ymax],'k-')
pyplot.plot([xmax,xmax],[ymin,ymax],'k-')
pyplot.plot([xmin,xmax],[ymin,ymin],'k-')
pyplot.plot([xmin,xmax],[ymax,ymax],'k-')
pyplot.plot([xmin,152.],[ymin,-100.],'k:')
pyplot.plot([xmin,152.],[ymax,460.],'k:')
insetAxes= pyplot.axes([0.15,0.42,0.38,0.45])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[:,0],vlbd[:,lbindx],'k,',
overplot=True)
sdf.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([240.,240.],[250.,275.],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(241.,255.,r'$25\,\mathrm{km\,s}^{-1}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin,xmax)
insetAxes.set_ylim(ymin,ymax)
elif 'pmll' in plotfilename:
xmin, xmax= 158.,205.
ymin, ymax= 10.5, 13.
pyplot.plot([xmin,xmin],[ymin,ymax],'k-')
pyplot.plot([xmax,xmax],[ymin,ymax],'k-')
pyplot.plot([xmin,xmax],[ymin,ymin],'k-')
pyplot.plot([xmin,xmax],[ymax,ymax],'k-')
pyplot.plot([xmin,113.],[ymin,6.1],'k:')
pyplot.plot([xmax,227.],[ymin,6.1],'k:')
insetAxes= pyplot.axes([0.43,0.12,0.3,0.4])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[sindx,0],vlbd[sindx,lbindx],'k,',
overplot=True)
bovy_plot.bovy_plot(lbd[pindx,0],vlbd[pindx,lbindx],'k,',
overplot=True)
sdf.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([168.5,168.5],[10.75,11.25],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(169.8,10.875,r'$0.5\,\mathrm{mas\,yr}^{-1}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin,xmax)
insetAxes.set_ylim(ymin,ymax)
elif 'pmbb' in plotfilename:
xmin, xmax= 185., 230.
ymin, ymax= -7.4, -4.7
pyplot.plot([xmin,xmin],[ymin,ymax],'k-')
pyplot.plot([xmax,xmax],[ymin,ymax],'k-')
pyplot.plot([xmin,xmax],[ymin,ymin],'k-')
pyplot.plot([xmin,xmax],[ymax,ymax],'k-')
pyplot.plot([xmin,159.],[ymax,1.],'k:')
pyplot.plot([xmax,287.],[ymax,1.],'k:')
#2nd inset
xmin2, xmax2= 80., 125.
ymin2, ymax2= 4.2, 5.8
pyplot.plot([xmin2,xmin2],[ymin2,ymax2],'k-')
pyplot.plot([xmax2,xmax2],[ymin2,ymax2],'k-')
pyplot.plot([xmin2,xmax2],[ymin2,ymin2],'k-')
pyplot.plot([xmin2,xmax2],[ymax2,ymax2],'k-')
pyplot.plot([xmin2,8.],[ymin2,-1.],'k:')
pyplot.plot([xmax2,155.],[ymin2,-1.],'k:')
insetAxes= pyplot.axes([0.55,0.57,0.34,0.3])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[:,0],vlbd[:,lbindx],'k,',
overplot=True)
sdf.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([200.,200.],[-5.75,-5.25],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(201.25,-5.675,r'$0.5\,\mathrm{mas\,yr}^{-1}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin,xmax)
insetAxes.set_ylim(ymin,ymax)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
#Also make second inset
insetAxes= pyplot.axes([0.14,0.12,0.4,0.35])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[:,0],vlbd[:,lbindx],'k,',
overplot=True)
sdft.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([103.,103.],[4.35,4.85],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(104.,4.5,r'$0.5\,\mathrm{mas\,yr}^{-1}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin2,xmax2)
insetAxes.set_ylim(ymin2,ymax2)
elif 'ld' in plotfilename:
xmin, xmax= 158., 227.
ymin, ymax= 7.7,9.5
pyplot.plot([xmin,xmin],[ymin,ymax],'k-')
pyplot.plot([xmax,xmax],[ymin,ymax],'k-')
pyplot.plot([xmin,xmax],[ymin,ymin],'k-')
pyplot.plot([xmin,xmax],[ymax,ymax],'k-')
pyplot.plot([xmin,70.],[ymax,18.5],'k:')
pyplot.plot([xmax,248.],[ymax,18.5],'k:')
#2nd inset
xmin2, xmax2= 72.,100.
ymin2, ymax2= 11.5, 16.1
pyplot.plot([xmin2,xmin2],[ymin2,ymax2],'k-')
pyplot.plot([xmax2,xmax2],[ymin2,ymax2],'k-')
pyplot.plot([xmin2,xmax2],[ymin2,ymin2],'k-')
pyplot.plot([xmin2,xmax2],[ymax2,ymax2],'k-')
pyplot.plot([xmin2,66.5],[ymax2,15.85],'k:')
pyplot.plot([xmin2,66.5],[ymin2,0.5],'k:')
insetAxes= pyplot.axes([0.31,0.6,0.48,0.27])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[sindx,0],lbd[sindx,lbindx],'k,',
overplot=True)
bovy_plot.bovy_plot(lbd[pindx,0],lbd[pindx,lbindx],'k,',
overplot=True)
sdf.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([168.,168.],[8.7,9.2],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(169.7,8.8,r'$0.5\,\mathrm{kpc}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin,xmax)
insetAxes.set_ylim(ymin,ymax)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
#Also make second inset
insetAxes= pyplot.axes([0.13,0.12,0.17,0.4])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[:,0],lbd[:,lbindx],'k,',
overplot=True)
sdft.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([74.,74.],[11.95,12.45],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(76.,12.01,r'$0.5\,\mathrm{kpc}$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin2,xmax2)
insetAxes.set_ylim(ymin2,ymax2)
else:
xmin, xmax= 90., 165.
ymin, ymax= 47., 59.
pyplot.plot([xmin,xmin],[ymin,ymax],'k-')
pyplot.plot([xmax,xmax],[ymin,ymax],'k-')
pyplot.plot([xmin,xmax],[ymin,ymin],'k-')
pyplot.plot([xmin,xmax],[ymax,ymax],'k-')
pyplot.plot([xmin,70.],[ymin,31.],'k:')
pyplot.plot([xmax,213.],[ymin,31.],'k:')
insetAxes= pyplot.axes([0.31,0.12,0.38,0.45])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(lbd[sindx,0],lbd[sindx,lbindx],'k,',
overplot=True)
bovy_plot.bovy_plot(lbd[pindx,0],lbd[pindx,lbindx],'k,',
overplot=True)
sdft.plotProgenitor(d1=d1,d2=d2,color='k',ls='--',
overplot=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.)
#Plot approximate scale
bovy_plot.bovy_plot([115.,115.],[48.5,49.5],'k-',lw=2.,
overplot=True)
bovy_plot.bovy_text(117.2,48.5,r'$1^\circ$',
size=16.)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(xmin,xmax)
insetAxes.set_ylim(ymin,ymax)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
bovy_plot.bovy_end_print(plotfilename)
def plot_stream_times(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPAADIR,
'gd1_evol_hitres_aa_01312.dat'),
delimiter=',')
#Calculate times at which stars were stripped, angles
thetar= data[:,6]
thetar= (numpy.pi+(thetar-numpy.median(thetar))) % (2.*numpy.pi)
indx= numpy.fabs(thetar-numpy.pi) > (5.*numpy.median(numpy.fabs(thetar-numpy.median(thetar))))
thetar= thetar[indx]
thetap= data[:,7]
thetap= (numpy.pi+(thetap-numpy.median(thetap))) % (2.*numpy.pi)
thetap= thetap[indx]
thetaz= data[:,8]
thetaz= (numpy.pi+(thetaz-numpy.median(thetaz))) % (2.*numpy.pi)
thetaz= thetaz[indx]
#center around 0 (instead of pi)
thetar-= numpy.pi
thetap-= numpy.pi
thetaz-= numpy.pi
#Frequencies
Or= data[:,3]
Op= data[:,4]
Oz= data[:,5]
dOr= Or[indx]-numpy.median(Or)
dOp= Op[indx]-numpy.median(Op)
dOz= Oz[indx]-numpy.median(Oz)
#Times
dangle= numpy.vstack((thetar,thetap,thetaz))
dO= numpy.vstack((dOr,dOp,dOz))*bovy_conversion.freq_in_Gyr(220.,8.)
dts= numpy.sum(dO*dangle,axis=0)/numpy.sum(dO**2.,axis=0)
if 'hist' in plotfilename:
bovy_plot.bovy_print()
bovy_plot.bovy_hist(dts,range=[0.,6.],bins=13,
xlabel=r'$t_s\ (\mathrm{Gyr})$',
histtype='step',color='k',normed=True,lw=2.)
bovy_plot.bovy_hist(dts,range=[0.,6.],bins=61,normed=True,
overplot=True,ls='dotted',histtype='step',
color='0.5',lw=2.)
includeorbit= False #bc pericenter passage doesn't seem to work
if includeorbit:
npts= 10001
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
ts= numpy.linspace(0.,5./bovy_conversion.time_in_Gyr(220.,8.),
npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
o= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
o.integrate(ts,pot)
rs= numpy.sqrt(o.R(ts)**2.+o.z(ts)**2.)
#Find local minima
periIndx= numpy.r_[True, rs[1:] < rs[:-1]] & numpy.r_[rs[:-1] < rs[1:], True]
for ii in range(numpy.sum(periIndx)):
bovy_plot.bovy_plot([ts[periIndx][ii]*bovy_conversion.time_in_Gyr(220.,8.),
ts[periIndx][ii]*bovy_conversion.time_in_Gyr(220.,8.)],
[0.,1.],overplot=True,ls='--',lw=1.,
color='0.5')
elif 'dO' in plotfilename:
bovy_plot.bovy_print()
bovy_plot.bovy_plot(dts,
numpy.sqrt(numpy.sum(dO**2.,axis=0)),
'k.',
xrange=[0.,6.],
yrange=[0.1,0.35],
xlabel=r'$t_s\ (\mathrm{Gyr})$',
ylabel=r'$|\Delta \mathbf{\Omega}|\ (\mathrm{Gyr}^{-1})$')
elif 'da' in plotfilename:
bovy_plot.bovy_print()
bovy_plot.bovy_plot(dts,
numpy.sqrt(numpy.sum(dangle**2.,axis=0)),
'k.',
xrange=[0.,6.],
yrange=[0.,1.5],
xlabel=r'$t_s\ (\mathrm{Gyr})$',
ylabel=r'$|\Delta \boldsymbol\theta|$')
bovy_plot.bovy_end_print(plotfilename)
return None
def sample(self, n, returndt=False, integrate=True, xy=False, lb=False):
"""
NAME:
sample
PURPOSE:
sample from the DF
INPUT:
n - number of points to return
returndt= (False) if True, also return the time since the star was stripped
integrate= (True) if True, integrate the orbits to the present time, if False, return positions at stripping (probably want to combine with returndt=True then to make sense of them!)
xy= (False) if True, return Galactocentric rectangular coordinates
lb= (False) if True, return Galactic l,b,d,vlos,pmll,pmbb coordinates
OUTPUT:
(R,vR,vT,z,vz,phi) of points on the stream in 6,N array
HISTORY:
2018-07-31 - Written - Bovy (IAS)
"""
if xy or lb:
raise NotImplementedError(
"xy=True and lb=True options currently not implemented")
# First sample times
dt = numpy.random.uniform(size=n) * self._tdisrupt
# Build all rotation matrices
rot, rot_inv = self._setup_rot(dt)
# Compute progenitor position in the instantaneous frame
xyzpt = numpy.einsum(
'ijk,ik->ij', rot,
numpy.array([
self._progenitor.x(-dt),
self._progenitor.y(-dt),
self._progenitor.z(-dt)
]).T)
vxyzpt = numpy.einsum(
'ijk,ik->ij', rot,
numpy.array([
self._progenitor.vx(-dt),
self._progenitor.vy(-dt),
self._progenitor.vz(-dt)
]).T)
Rpt, phipt, Zpt = bovy_coords.rect_to_cyl(xyzpt[:, 0], xyzpt[:, 1],
xyzpt[:, 2])
vRpt, vTpt, vZpt = bovy_coords.rect_to_cyl_vec(vxyzpt[:, 0],
vxyzpt[:, 1],
vxyzpt[:, 2],
Rpt,
phipt,
Zpt,
cyl=True)
# Sample positions and velocities in the instantaneous frame
k = self._meankvec + numpy.random.normal(
size=n)[:, numpy.newaxis] * self._sigkvec
try:
rtides = rtide(self._rtpot,
Rpt,
Zpt,
phi=phipt,
t=-dt,
M=self._progenitor_mass,
use_physical=False)
vcs = numpy.sqrt(-Rpt * evaluateRforces(
self._rtpot, Rpt, Zpt, phi=phipt, t=-dt, use_physical=False))
except (ValueError, TypeError):
rtides = numpy.array([
rtide(self._rtpot,
Rpt[ii],
Zpt[ii],
phi=phipt[ii],
t=-dt[ii],
M=self._progenitor_mass,
use_physical=False) for ii in range(len(Rpt))
])
vcs = numpy.array([
numpy.sqrt(-Rpt[ii] * evaluateRforces(self._rtpot,
Rpt[ii],
Zpt[ii],
phi=phipt[ii],
t=-dt[ii],
use_physical=False))
for ii in range(len(Rpt))
])
rtides_as_frac = rtides / Rpt
RpZst = numpy.array([
Rpt + k[:, 0] * rtides, phipt + k[:, 5] * rtides_as_frac,
k[:, 3] * rtides_as_frac
]).T
vRTZst = numpy.array([
vRpt * (1. + k[:, 1]), vTpt + k[:, 2] * vcs * rtides_as_frac,
k[:, 4] * vcs * rtides_as_frac
]).T
# Now rotate these back to the galactocentric frame
xst, yst, zst = bovy_coords.cyl_to_rect(RpZst[:, 0], RpZst[:, 1],
RpZst[:, 2])
vxst, vyst, vzst = bovy_coords.cyl_to_rect_vec(vRTZst[:, 0], vRTZst[:,
1],
vRTZst[:, 2], RpZst[:,
1])
xyzs = numpy.einsum('ijk,ik->ij', rot_inv,
numpy.array([xst, yst, zst]).T)
vxyzs = numpy.einsum('ijk,ik->ij', rot_inv,
numpy.array([vxst, vyst, vzst]).T)
Rs, phis, Zs = bovy_coords.rect_to_cyl(xyzs[:, 0], xyzs[:, 1], xyzs[:,
2])
vRs, vTs, vZs = bovy_coords.rect_to_cyl_vec(vxyzs[:, 0],
vxyzs[:, 1],
vxyzs[:, 2],
Rs,
phis,
Zs,
cyl=True)
out = numpy.empty((6, n))
if integrate:
# Now integrate the orbits
for ii in range(n):
o = Orbit(
[Rs[ii], vRs[ii], vTs[ii], Zs[ii], vZs[ii], phis[ii]])
o.integrate(numpy.linspace(-dt[ii], 0., 10001), self._pot)
o = o(0.)
out[:, ii] = [o.R(), o.vR(), o.vT(), o.z(), o.vz(), o.phi()]
else:
out[0] = Rs
out[1] = vRs
out[2] = vTs
out[3] = Zs
out[4] = vZs
out[5] = phis
if returndt:
return (out, dt)
else:
return out
def indiv_calc_actions(x,aA,snapdir,basefilename,snapaadir):
#Read data
data= numpy.loadtxt(os.path.join(snapdir,
basefilename+'_%s.dat' % str(x).zfill(5)),
delimiter=',')
R,phi,Z= bovy_coords.rect_to_cyl(data[:,1],data[:,3],data[:,2])
vR,vT,vZ= bovy_coords.rect_to_cyl_vec(data[:,4],data[:,6],data[:,5],
R,phi,Z,cyl=True)
R/= 8.
Z/= 8.
vR/= 220.
vT/= 220.
vZ/= 220.
if False: #Used for testing
R= R[0:100]
vR= vR[0:100]
vT= vT[0:100]
Z= Z[0:100]
vZ= vZ[0:100]
phi= phi[0:100]
nx= len(R)
#calculation actions, frequencies, and angles
if isinstance(aA,actionAngleIsochroneApprox):
#Processes in batches to not run out of memory
csvfilename= os.path.join(snapaadir,basefilename+'_aa_%s.dat' % str(x).zfill(5))
if os.path.exists(csvfilename):
#Don't recalculate those that have already been calculated
nstart= int(subprocess.check_output(['wc','-l',csvfilename]).split(' ')[0])
csvfile= open(csvfilename,'ab')
else:
csvfile= open(csvfilename,'wb')
nstart= 0
if nstart >= nx: return 1 #Done already
print "Working on aa %i ..." % x
print "Starting from %i ..." % nstart
nx-= nstart
writer= csv.writer(csvfile,delimiter=',')
nbatch= 20
for ii in range(nx/nbatch):
tR= R[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvR= vR[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvT= vT[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tZ= Z[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvZ= vZ[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tphi= phi[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
try:
tacfs= aA.actionsFreqsAngles(tR,tvR,tvT,tZ,tvZ,tphi)
except numpy.linalg.linalg.LinAlgError:
print x,tR,tvR,tvT,tZ,tvZ,tphi
raise
for jj in range(len(tacfs[0])):
writer.writerow([tacfs[0][jj],tacfs[1][jj],tacfs[2][jj],
tacfs[3][jj],tacfs[4][jj],tacfs[5][jj],
tacfs[6][jj],tacfs[7][jj],tacfs[8][jj]])
csvfile.flush()
csvfile.close()
else:
acfs= aA.actionsFreqsAngles(R,vR,vT,Z,vZ,phi)
csvfile= open(os.path.join(snapaadir,basefilename+'_aa_%s.dat' % str(x).zfill(5)),'wb')
writer= csv.writer(csvfile,delimiter=',')
for jj in range(len(acfs[0])):
writer.writerow([acfs[0][jj],acfs[1][jj],acfs[2][jj],
acfs[3][jj],acfs[4][jj],acfs[5][jj],
acfs[6][jj],acfs[7][jj],acfs[8][jj]])
csvfile.close()
print "Done with aa %i" % x
return 1
def _sample_galpy_potential(pot,
n,
rmin,
rmax,
ro=8.,
vo=220.,
coordinates='cartesian'):
"""Generate positions and velocities from galpy potentail
Parameters
----------
pot : class
galpy potential
N : int
number of stars in the cluster (default: 1000)
rmin : float
minimum stellar radius (default: 0.01)
rmax : float
maximnum stellar radius (default: 100.)
ro : float
galpy distance scaling parameter
vo : float
galpy velocity scaling parameter
coordinates : str
coordinate system to return (default: cartesian)
Returns
-------
x,y,z,vx,vy,vz : float
positions and velocities of generated points
History
-------
2020 - Written - Webb (UofT)
"""
ran = np.random.rand(n)
rad = np.linspace(rmin, rmax, n)
try:
menc = pot.mass(rad / ro, z=0, t=0, forceint=False)
except:
vc = potential.vcirc(pot,
rad / ro,
phi=0,
t=0.,
ro=ro,
vo=vo,
use_physical=False)
menc = vc**2. * (rad / ro)
menc *= bovy_conversion.mass_in_msol(ro=ro, vo=vo)
r = np.interp(ran, menc / menc[-1], rad)
phi = 2.0 * np.pi * np.random.rand(n)
theta = np.arccos(1.0 - 2.0 * np.random.rand(n))
x = r * np.sin(theta) * np.cos(phi)
y = r * np.sin(theta) * np.sin(phi)
z = r * np.cos(theta)
sigma_v_1d = vo * potential.vcirc(
pot, rad / ro, phi=0, t=0., ro=ro, vo=vo,
use_physical=False) / np.sqrt(3.)
vx = np.random.normal(0., sigma_v_1d, n)
vy = np.random.normal(0., sigma_v_1d, n)
vz = np.random.normal(0., sigma_v_1d, n)
if coordinates == 'spherical':
vr = (vx * np.sin(theta) * np.cos(phi) +
vy * np.sin(theta) * np.sin(phi) + vz * np.cos(theta))
vtheta = (vx * np.cos(theta) * np.cos(phi) +
vy * np.cos(theta) * np.sin(phi) - vz * np.sin(theta))
vphi = vx * -np.sin(phi) + vy * np.cos(phi)
x, y, z = r, phi, theta
vx, vy, vz = vr, vphi, vtheta
elif coordinates == 'cylindrical':
x, y, z = bovy_coords.rect_to_cyl(x, y, z)
vx, vy, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z, True)
return x, y, z, vx, vy, vz
def orbit_interpolate(
cluster,
dt,
pot=MWPotential2014,
from_centre=False,
do_tails=False,
rmin=None,
rmax=None,
emin=None,
emax=None,
r0=8.0,
v0=220.0,
):
"""
NAME:
orbit_interpolate
PURPOSE:
Move the cluster centre and stars backwards or forwards along its orbit assuming stars only feel a force from the galaxy
INPUT:
cluster - StarCluster
dt - timestep that StarCluster is to be moved to
pot - Potential orbit is to be integrate in (Default: MWPotential2014)
from_centre - interpolate from cluster's define position (default) or the measured centre of cluster
do_tails - interpolate the orbits of tail stars separately (Default: False)
rmin/rmax - radial range corresponding to cluster (needed to identify tail stars)
emin/emax - energy range corresponding to cluster (needed to identify tail stars)
r0 - galpy distance scale (Default: 8.)
v0 - galpy velocity scale (Default: 220.)
OUTPUT:
None
HISTORY:
2018 - Written - Webb (UofT)
"""
cluster.tphys += dt
units0, origin0 = save_cluster(cluster)
cluster.to_galaxy()
if do_tails:
cluster.to_cluster()
if from_centre:
cluster.to_centre()
if rmin == None:
rmin = np.min(cluster.r)
if rmax == None:
rmax = np.max(cluster.r)
rindx = (cluster.r >= rmin) * (cluster.r <= rmax)
if len(cluster.etot) == cluster.ntot:
if emin == None:
emin = np.min(cluster.etot)
if emax == None:
emax = np.max(cluster.etot)
eindx = (cluster.etot >= emin) * (cluster.etot <= emax)
else:
eindx = cluster.id > -1
indx = rindx * eindx
tindx = np.invert(indx)
cluster.to_galaxy()
else:
indx = cluster.id > -1
cluster.orbit = initialize_orbit(cluster, from_centre)
ts = np.linspace(0, dt / bovy_conversion.time_in_Gyr(ro=r0, vo=v0), 10)
cluster.orbit.integrate(ts, pot)
cluster.to_realkpc()
if from_centre:
dx = cluster.orbit.x(ts[-1]) - cluster.xc - cluster.xgc
dy = cluster.orbit.y(ts[-1]) - cluster.yc - cluster.ygc
dz = cluster.orbit.z(ts[-1]) - cluster.zc - cluster.zgc
dvx = cluster.orbit.vx(ts[-1]) - cluster.vxc - cluster.vxgc
dvy = cluster.orbit.vy(ts[-1]) - cluster.vyc - cluster.vygc
dvz = cluster.orbit.vz(ts[-1]) - cluster.vzc - cluster.vzgc
else:
dx = cluster.orbit.x(ts[-1]) - cluster.xgc
dy = cluster.orbit.y(ts[-1]) - cluster.ygc
dz = cluster.orbit.z(ts[-1]) - cluster.zgc
dvx = cluster.orbit.vx(ts[-1]) - cluster.vxgc
dvy = cluster.orbit.vy(ts[-1]) - cluster.vygc
dvz = cluster.orbit.vz(ts[-1]) - cluster.vzgc
cluster.x[indx] += dx
cluster.y[indx] += dy
cluster.z[indx] += dz
cluster.vx[indx] += dvx
cluster.vy[indx] += dvy
cluster.vz[indx] += dvz
if from_centre:
cluster.xc, cluster.yc, cluster.zc = 0.0, 0.0, 0.0
cluster.vxc, cluster.vyc, cluster.vzc = 0.0, 0.0, 0.0
else:
cluster.xc += dx
cluster.yc += dy
cluster.zc += dz
cluster.vxc += dvx
cluster.vyc += dvy
cluster.vzc += dvz
cluster.xgc, cluster.ygc, cluster.zgc = (
cluster.orbit.x(ts[-1]),
cluster.orbit.y(ts[-1]),
cluster.orbit.z(ts[-1]),
)
cluster.vxgc, cluster.vygc, cluster.vzgc = (
cluster.orbit.vx(ts[-1]),
cluster.orbit.vy(ts[-1]),
cluster.orbit.vz(ts[-1]),
)
if do_tails:
cluster.to_galaxy()
cluster.to_galpy()
x, y, z = cluster.x[tindx], cluster.y[tindx], cluster.z[tindx]
vx, vy, vz = cluster.vx[tindx], cluster.vy[tindx], cluster.vz[tindx]
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
vxvv = np.column_stack([R, vR, vT, z, vz, phi])
otail = Orbit(vxvv, ro=r0, vo=v0, solarmotion=[-11.1, 24.0, 7.25])
cluster.to_realkpc()
ts = np.linspace(0, dt / bovy_conversion.time_in_Gyr(ro=r0, vo=v0), 10)
otail.integrate(ts, pot)
cluster.x[tindx] = np.array(otail.x(ts[-1]))
cluster.y[tindx] = np.array(otail.y(ts[-1]))
cluster.z[tindx] = np.array(otail.z(ts[-1]))
cluster.vx[tindx] = np.array(otail.vx(ts[-1]))
cluster.vy[tindx] = np.array(otail.vy(ts[-1]))
cluster.vz[tindx] = np.array(otail.vz(ts[-1]))
return_cluster(cluster, units0, origin0)
def plot_sat_cluster(sat_galaxy, name_sat, sat_potential, xaxis_dim, yaxis_dim,
sat_mass, sat_size, x_satgal, y_satgal, z_satgal,
vx_satgal, vy_satgal, vz_satgal, tform, tsteady):
# Function plots orbits of satellite galaxy as well as a star cluster within the satellite galaxy - simulates accretion onto MW
#
# Input:
# sat_galaxy: an orbit object for a given satellite galaxy of the MW
# name_sat: string of the satellite galaxy's name
# sat_potential: potential object modelling the satellite's potential
# x and y axis dimensions to plot in (strings)
# x_satgal, y_satgal, z_satgal: x,y,z positions of the star_cluster within the satellite galaxy's frame of reference
# vx_satgal, vy_satgal, vz_satgal: x,y,z velocities of the star_cluster within the satellite galaxy's frame of reference
# mass and size of satellite to model dynamical friction effects (quantities with units attached)
# tform, tsteady: parameters of the potential, models tidal disruption of satellite galaxy (quantities with units attached)
#
# Output:
#
# end_pos_cluster: the coordinates for star cluster at end of integration (@ time tend: tform+5*units.Gyr)
# end_pos_gal: the coordinates for satellite galaxy at tend
# dswp: wrapper potential object that modifies satelltie galaxy to begin disrupting at tform
# cdf: model for dynamical friction force
t_back = 10.
ts = numpy.linspace(0., -t_back, 1000) * units.Gyr
cdf = ChandrasekharDynamicalFrictionForce(GMs=sat_mass,
rhm=sat_size,
dens=mw)
sat_galaxy.integrate(ts, mw + cdf)
'''
R_sat = sat_galaxy.R(-t_back*units.Gyr) #cylindrical radius at time t
vR_sat = sat_galaxy.vR(-t_back*units.Gyr) #radial velocity at time t
vT_sat = sat_galaxy.vT(-t_back*units.Gyr) #tangential velocity at time t
z_sat = sat_galaxy.z(-t_back*units.Gyr) #vertical height at time t
vz_sat = sat_galaxy.vz(-t_back*units.Gyr) #vertical velocity at time t
phi_sat = sat_galaxy.phi(-t_back*units.Gyr) #azimuth at time t
'''
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(-t_back * units.Gyr),
sat_galaxy.y(-t_back * units.Gyr),
sat_galaxy.z(-t_back * units.Gyr)
]
vcoord = [
sat_galaxy.vx(-t_back * units.Gyr),
sat_galaxy.vy(-t_back * units.Gyr),
sat_galaxy.vz(-t_back * units.Gyr)
]
t_fwrd = 15
ts_f = numpy.linspace(-t_back, -t_back + t_fwrd, 1000) * units.Gyr
sat_galaxy = sat_galaxy(-t_back * units.Gyr)
sat_galaxy.integrate(ts_f, mw + cdf)
sat_galaxy.plot(
d1=xaxis_dim,
d2=yaxis_dim,
linestyle=':',
color='black',
label='satellite'
) #plots orbit of the satellite galaxy in MW frame of reference
#!!sat_pot = HernquistPotential(amp = 2*sat_mass, a = sat_size, ro = 8., vo=220.)
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
star_cluster = Orbit(vxvv=[R, vR, vT, z, vz, phi], ro=8., vo=220.)
star_cluster.integrate(ts_f, mw + sat_movingpot)
star_cluster.plot(
d1=xaxis_dim,
d2=yaxis_dim,
linestyle='-',
overplot=True,
color='blue',
alpha=0.6,
label='star cluster'
) #plots orbit of the star_cluster in MW frame of reference
plt.title('Orbit of Star Cluster Within Satellite Galaxy: ' + name_sat +
' in Galactocentric Frame')
plt.legend()
plt.show()
plt.close()
# Implement wrapper potential to simulate tidal disruption of satellite galaxy
# Plot orbit of the satellite galaxy and star cluster within sat galaxy in MW frame of reference:
plt.figure(figsize=(12., 10.))
tstart = tform - 5. * units.Gyr
tend = tform + 5. * units.Gyr
time_int = numpy.linspace(tstart.to_value(units.Gyr),
tend.to_value(units.Gyr), 1000) * units.Gyr
if tstart < -t_back * units.Gyr:
# re-integrate satellite galaxy from current time back to tstart
re_time = numpy.linspace(-t_back, tstart.to_value(units.Gyr),
1000) * units.Gyr
sat_galaxy.integrate(re_time, mw + cdf)
# initialize star cluster on orbit in satellite galaxy at time tstart:
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(tstart),
sat_galaxy.y(tstart),
sat_galaxy.z(tstart)
]
vcoord = [
sat_galaxy.vx(tstart),
sat_galaxy.vy(tstart),
sat_galaxy.vz(tstart)
]
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
# Re-initialize star cluster on orbit at time tstart
star_cluster = Orbit(vxvv=[R, vR, vT, vz, z, phi], ro=8., vo=220.)
else:
# default: star cluster is initialized at -10Gyr in given satellite galaxy
star_cluster = star_cluster(tstart)
sat_galaxy = sat_galaxy(
tstart) #make copy of sat_galaxy orbit at time tstart
sat_galaxy.integrate(time_int,
mw + cdf) # integrate sat_galaxy forward for 10Gyrs
sat_galaxy.plot(d1=xaxis_dim,
d2=yaxis_dim,
linestyle=':',
color='black',
label='satellite galaxy')
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
dswp = DehnenSmoothWrapperPotential(amp=1.0,
pot=sat_movingpot,
tform=tform,
tsteady=tsteady,
decay=True)
star_cluster.integrate(time_int, mw + dswp)
# star cluster in combined potential: MW galaxy & moving potential of satellite galaxy
star_cluster.plot(d1 = xaxis_dim, d2= yaxis_dim, linestyle = '-', overplot = True, color = 'blue', alpha = 0.6,\
label = 'star cluster')
#plots orbit of the star_cluster in MW frame of reference
plt.legend()
plt.title('Star Cluster Orbit Within: ' + name_sat + ' for Tform = ' +
str(tform) + ' & Tsteady = ' + str(tsteady) +
' in Galactocentric Frame')
plt.savefig('WrapperPotential-Decaying Mass.pdf')
plt.show()
plt.close()
# Figure out where star cluster is at end of integration: at tend
end_pos_cluster = [
star_cluster.R(tend),
star_cluster.vR(tend),
star_cluster.vT(tend),
star_cluster.z(tend),
star_cluster.vz(tend),
star_cluster.phi(tend)
]
# [R,vT,vT,z,vz,phi]
end_pos_gal = [
sat_galaxy.R(tend),
sat_galaxy.vR(tend),
sat_galaxy.vT(tend),
sat_galaxy.z(tend),
sat_galaxy.vz(tend),
sat_galaxy.phi(tend)
]
'''
# Used for finding dswp when integrating satellite galaxy backward in previous version of code
time_intb = numpy.linspace(tend.to_value(units.Gyr), tstart.to_value(units.Gyr), 1000)*units.Gyr
star_cluster_b = Orbit(vxvv = end_pos_cluster, ro=8., vo =220.) #full 6 coordinates
sat_galaxy_b = Orbit(vxvv=end_pos_gal, ro=8., vo =220.)
sat_galaxy_b.integrate(time_intb, mw + cdf)
sat_galaxy_b.plot(d1 = xaxis_dim, d2= yaxis_dim,linestyle = ':', color = 'black', label = 'satellite galaxy')
sat_movingpot_b = MovingObjectPotential(sat_galaxy_b, sat_potential)
#new_tform = tform - end_t
#dswp_back = DehnenSmoothWrapperPotential(amp=1.0, pot = sat_movingpot_b, tform=tform, tsteady=tsteady, decay = True)
star_cluster_b.integrate(time_intb, mw + dswp) # star cluster is in combined potential of MW galaxy and the moving potential of satellite galaxy
star_cluster_b.plot(d1 = xaxis_dim, d2= yaxis_dim, linestyle = '-', overplot = True, color = 'blue', alpha = 0.6,\
label = 'star cluster') # galactocentric radius as a function of time
plt.legend()
plt.title('Orbit of Star Cluster Within Satellite Galaxy for Tform = ' + str(tform) + ' & Tsteady = ' + str(tsteady) + ' (in Galactocentric Frame)')
plt.show()
plt.close()
'''
return end_pos_cluster, end_pos_gal, dswp, cdf
def sigv_prof(
cluster,
mmin=None,
mmax=None,
rmin=None,
rmax=None,
nrad=20,
vmin=None,
vmax=None,
emin=None,
emax=None,
kwmin=None,
kwmax=None,
indx=None,
projected=False,
rcustom=None,
coord=None,
normalize=True,
):
"""
NAME:
sigv_prof
PURPOSE:
Measure the radial variation in the velocity dispersion
INPUT:
cluster - StarCluster instance
mmin/mmax - minimum and maximum stellar mass
rmin/rmax - minimum and maximum stellar radii
nrad - number of radial bins
vmin/vmax - minimum and maximum stellar velocity
emin/emax - minimum and maximum stellar energy
kwmin/kwmax - minimum and maximum stellar type (kw)
indx - user defined boolean array from which to extract the subset
projected - use projected values and constraints (Default:False)
rcustom - use custom radius to bin data (not well implemented)
coord - choose what coordinate the velocity dispersion profile is to be returned in (default None returns (sigx**2.+sigy**2.+sigz**2.)^1/2)
normalize - normalize radial bins by cluster's half-mass radius (default: True)
KWARGS:
Same as for ..util.plot.nplot
OUTPUT:
lrprofn - natural log of radius (normalized by half-mass radius)
sigvprof - velocity dispersion
betaprof - anisotropy parameter
HISTORY:
2018 - Written - Webb (UofT)
"""
units0, origin0 = save_cluster(cluster)
cluster.to_centre(do_order=True, do_key_params=True)
lrprofn = []
sigvprof = []
betaprof = []
if projected:
r = cluster.rpro
v = cluster.vpro
else:
r = cluster.r
v = cluster.v
if rmin == None:
rmin = np.min(r)
if rmax == None:
rmax = np.max(r)
if vmin == None:
vmin = np.min(v)
if vmax == None:
vmax = np.max(v)
if mmin == None:
mmin = np.min(cluster.m)
if mmax == None:
mmax = np.max(cluster.m)
# Build subcluster containing only stars in the full radial and mass range:
indx = ((r >= rmin) * (r <= rmax) * (cluster.m >= mmin) *
(cluster.m <= mmax) * (v >= vmin) * (v <= vmax))
if kwmin is not None:
indx *= (cluster.kw >= kwmin)
if kwmax is not None:
indx *= (cluster.kw <= kwmax)
if emin is not None:
indx *= cluster.etot >= emin
if emin is not None:
indx *= cluster.etot <= emax
# Convert to cylindrical or spherical coordinates:
if projected:
r, theta, z = bovy_coords.rect_to_cyl(cluster.x, cluster.y, cluster.z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(cluster.vx, cluster.vy,
cluster.vz, cluster.x,
cluster.y, cluster.z)
else:
r, phi, theta, vr, vp, vt = sphere_coords(cluster)
if rcustom is not None:
r = rcustom
r_lower, r_mean, r_upper, r_hist = nbinmaker(r[indx], nrad)
for i in range(0, len(r_mean)):
rindx = indx * (r >= r_lower[i]) * (r < r_upper[i])
if np.sum(rindx) > 3.0:
sigr = np.std(vr[rindx])
sigt = np.std(vt[rindx])
if projected:
sigp = np.zeros(len(vr))
beta = sigt / sigr - 1.0
else:
sigp = np.std(vp[rindx])
beta = 1.0 - (sigt**2.0 + sigp**2.0) / (2.0 * (sigr**2.0))
if coord is None:
sigv = np.sqrt(sigr**2.0 + sigt**2.0 + sigp**2.0)
elif coord == 'r':
sigv = sigr
elif coord == 'phi':
sigv = sigp
elif coord == 'theta':
sigv = sigt
if normalize:
if projected:
lrprofn.append(np.log(r_mean[i] / cluster.rmpro))
else:
lrprofn.append(np.log(r_mean[i] / cluster.rm))
else:
lrprofn.append(np.log(r_mean[i]))
sigvprof.append(sigv)
betaprof.append(beta)
return_cluster(cluster, units0, origin0, do_order=True, do_key_params=True)
return lrprofn, sigvprof, betaprof
def sample_perturbed_Pal5(N,
barpot,
barpot_invert,
nobarpot,
prog_barpot,
prog_barpot_invert,
prog_nobarpot,
fo='blah_trailing.dat',
trailing=True,
tpal5age=5.,
t_on=2.,
tgrow=2,
pat_speed=40.):
#Sample N points from the smooth model today
tpal5age = tpal5age / bovy_conversion.time_in_Gyr(220., 8.)
if trailing:
sdf_trailing = pal5_util.setup_pal5model(pot=nobarpot)
R, vR, vT, z, vz, phi, dt = sdf_trailing.sample(n=N, returndt=True)
fo = open(fo, 'w')
else:
sdf_leading = pal5_util.setup_pal5model(pot=nobarpot, leading=True)
R, vR, vT, z, vz, phi, dt = sdf_leading.sample(n=N, returndt=True)
fo_lead = fo.replace('trailing', 'leading')
fo = open(fo_lead, 'w')
tage = numpy.linspace(0., tpal5age, 1001)
#integrate Pal 5 progenitor in barpot all the way back to 5 Gyrs,
#from this orbits will be extracted by interpolation in the for loop
pal5_bar = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
solarmotion=[-11.1, 24., 7.25]).flip()
pal5_bar.integrate(tage, prog_barpot_invert)
#integrate Pal 5 progenitor in nobarpot all the way back to 5 Gyrs,
#from this orbits will be extracted by interpolation in the for loop
pal5_nobar = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
solarmotion=[-11.1, 24., 7.25]).flip()
pal5_nobar.integrate(tage, prog_nobarpot)
pal5_bar.turn_physical_off()
pal5_nobar.turn_physical_off()
finalR = numpy.empty(N)
finalvR = numpy.empty(N)
finalvT = numpy.empty(N)
finalvz = numpy.empty(N)
finalphi = numpy.empty(N)
finalz = numpy.empty(N)
tt = numpy.empty(N)
tform = tform_from_t_on(t_on=t_on, pat_speed=pat_speed,
tgrow=tgrow) #in galpy
t_on = t_on / bovy_conversion.time_in_Gyr(220., 8.)
for ii in range(N):
o = Orbit([
R[ii], vR[ii], vT[ii], z[ii], vz[ii], phi[ii]
]).flip() # flip flips the velocities for backwards integration
o.turn_physical_off()
ts = numpy.linspace(0., dt[ii], 1001)
#for integrating in barpot, time starts 5 Gyrs in the past and goes forward
ts_future = numpy.linspace(tpal5age - dt[ii], tpal5age, 1001)
o.integrate(ts, nobarpot)
#unp_orb=o(ts[-1]).flip()._orb.vxvv
#extract the orbit at the stripping time from the above integrated orbit
#pal5_orb_bar = pal5_bar(ts[-1]).flip()._orb.vxvv
#pal5_orb_nobar = pal5_nobar(ts[-1]).flip()._orb.vxvv
unp_orb = numpy.array([
o.x(ts[-1]),
o.y(ts[-1]),
o.z(ts[-1]), -o.vx(ts[-1]), -o.vy(ts[-1]), -o.vz(ts[-1])
])
pal5_orb_bar = numpy.array([
pal5_bar.x(ts[-1]),
pal5_bar.y(ts[-1]),
pal5_bar.z(ts[-1]), -pal5_bar.vx(ts[-1]), -pal5_bar.vy(ts[-1]),
-pal5_bar.vz(ts[-1])
])
pal5_orb_nobar = numpy.array([
pal5_nobar.x(ts[-1]),
pal5_nobar.y(ts[-1]),
pal5_nobar.z(ts[-1]), -pal5_nobar.vx(ts[-1]),
-pal5_nobar.vy(ts[-1]), -pal5_nobar.vz(ts[-1])
])
#print (unp_orb)
#print (pal5_orb_bar)
#print (pal5_orb_nobar)
#subtract Pal 5 orb in nobarpot and add Pal 5 orbit in barpot
#pert_orb=(np.array(unp_orb) - np.array(pal5_orb_nobar)) + np.array(pal5_orb_bar)
#pert_orb=Orbit(list(pert_orb))
pert_orb = unp_orb - pal5_orb_nobar + pal5_orb_bar
print(unp_orb, dt[ii] * bovy_conversion.time_in_Gyr(220., 8.))
print(pert_orb, dt[ii] * bovy_conversion.time_in_Gyr(220., 8.))
#(R,phi,Z)
#vR,vT,vz
#vxvv=[R,vR,vT,z,vz,phi]
pert_orb_RpZ = bovy_coords.rect_to_cyl(pert_orb[0], pert_orb[1],
pert_orb[2])
pert_orb_vRpZ = bovy_coords.rect_to_cyl_vec(pert_orb[3], pert_orb[4],
pert_orb[5], pert_orb[0],
pert_orb[1], pert_orb[2])
pert_orb = Orbit([
pert_orb_RpZ[0], pert_orb_vRpZ[0], pert_orb_vRpZ[1],
pert_orb_RpZ[2], pert_orb_vRpZ[2], pert_orb_RpZ[1]
])
#forward integrate in barred potential
pert_orb.integrate(ts_future, barpot)
finalR[ii] = pert_orb.R(ts_future[-1])
finalphi[ii] = pert_orb.phi(ts_future[-1])
finalz[ii] = pert_orb.z(ts_future[-1])
finalvR[ii] = pert_orb.vR(ts_future[-1])
finalvT[ii] = pert_orb.vT(ts_future[-1])
finalvz[ii] = pert_orb.vz(ts_future[-1])
tt[ii] = dt[ii]
fo.write("#R phi z vR vT vz ts" + "\n")
for jj in range(N):
fo.write(
str(finalR[jj]) + " " + str(finalphi[jj]) + " " +
str(finalz[jj]) + " " + str(finalvR[jj]) + " " +
str(finalvT[jj]) + " " + str(finalvz[jj]) + " " + str(tt[jj]) +
"\n")
fo.close()
return None
def calc_actions(snapfile=None,first=0):
#Setup potential and actionAngle object
lp= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
aA= actionAngleIsochroneApprox(pot=lp,b=0.8)
# Load snapshot and convert to cylindrical coordinates
xvid= numpy.loadtxt(snapfile)
xv= xvid[:,:6]
id= xvid[:,6]
xv= xv[numpy.argsort(id)]
id= id[numpy.argsort(id)].astype(int)
R,phi,Z= bovy_coords.rect_to_cyl(xv[:,0],xv[:,1],xv[:,2])
vR,vT,vZ= bovy_coords.rect_to_cyl_vec(xv[:,3],xv[:,4],xv[:,5],R,phi,Z,
cyl=True)
R/= 8.
Z/= 8.
vR/= 220.
vT/= 220.
vZ/= 220.
if False: #Used for testing
R= R[0:100]
vR= vR[0:100]
vT= vT[0:100]
Z= Z[0:100]
vZ= vZ[0:100]
phi= phi[0:100]
nx= len(R)
if first:
R= R[:nx//2]
vR= vR[:nx//2]
vT= vT[:nx//2]
Z= Z[:nx//2]
vZ= vZ[:nx//2]
phi= phi[:nx//2]
id= id[:nx//2]
else:
R= R[nx//2:]
vR= vR[nx//2:]
vT= vT[nx//2:]
Z= Z[nx//2:]
vZ= vZ[nx//2:]
phi= phi[nx//2:]
id= id[nx//2:]
nx/= 2
#calculation actions, frequencies, and angles
#Processes in batches to not run out of memory
if first:
csvfilename= snapfile.replace('.txt','_aA1.txt')
else:
csvfilename= snapfile.replace('.txt','_aA2.txt')
if os.path.exists(csvfilename):
#Don't recalculate those that have already been calculated
nstart= int(subprocess.check_output(['wc','-l',csvfilename]).split(' ')[0])
csvfile= open(csvfilename,'ab')
else:
csvfile= open(csvfilename,'wb')
nstart= 0
if nstart >= nx: return 1 #Done already
print "Starting from %i ..." % nstart
nx-= nstart
writer= csv.writer(csvfile,delimiter=',')
nbatch= 20
for ii in range(nx//nbatch):
print "Working on batch %i out of %i ..." % (ii+1,nx//nbatch)
tR= R[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvR= vR[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvT= vT[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tZ= Z[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tvZ= vZ[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
tphi= phi[nstart+ii*nbatch:numpy.amin([nstart+(ii+1)*nbatch,nstart+nx])]
try:
tacfs= aA.actionsFreqsAngles(tR,tvR,tvT,tZ,tvZ,tphi)
except numpy.linalg.linalg.LinAlgError:
print tR,tvR,tvT,tZ,tvZ,tphi
raise
for jj in range(len(tacfs[0])):
writer.writerow([tacfs[0][jj],tacfs[1][jj],tacfs[2][jj],
tacfs[3][jj],tacfs[4][jj],tacfs[5][jj],
tacfs[6][jj],tacfs[7][jj],tacfs[8][jj],
id[nstart+ii*nbatch+jj]])
csvfile.flush()
csvfile.close()
return None
def initialize_orbit(cluster, from_centre=False, ro=8.0, vo=220.0):
""" Initialize a galpy orbit instance for the cluster
Parameters
----------
cluster : class
StarCluster
from_centre : bool
genrate orbit from cluster's exact centre instead of its assigned galactocentric coordinates (default: False)
ro : float
galpy distance scale (default: 8.)
vo : float
galpy velocity scale (default: 220.)
Returns
-------
orbit : class
GALPY orbit
History
-------
2018 - Written - Webb (UofT)
"""
if cluster.units == "radec":
o = Orbit(
[
cluster.ra_gc,
cluster.dec_gc,
cluster.dist_gc,
cluster.pmra_gc,
cluster.pmdec_gc,
cluster.vlos_gc,
],
radec=True,
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
)
else:
units0, origin0 = save_cluster(cluster)
cluster.to_galpy()
if from_centre:
x, y, z = (
cluster.xgc + cluster.xc,
cluster.ygc + cluster.yc,
cluster.zgc + cluster.zc,
)
vx, vy, vz = (
cluster.vxgc + cluster.vxc,
cluster.vygc + cluster.vyc,
cluster.vzgc + cluster.vzc,
)
else:
x, y, z = cluster.xgc, cluster.ygc, cluster.zgc
vx, vy, vz = cluster.vxgc, cluster.vygc, cluster.vzgc
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
o = Orbit([R, vR, vT, z, vz, phi],
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25])
return_cluster(cluster, units0, origin0)
return o
def orbital_path(cluster,
dt=0.1,
nt=100,
pot=MWPotential2014,
from_centre=False,
skypath=False,
initialize=False,
ro=8.0,
vo=220.0,
plot=False):
"""Calculate the cluster's orbital path
Parameters
----------
cluster : class
StarCluster
dt : float
timestep that StarCluster is to be moved to
nt : int
number of timesteps
pot : class
galpy Potential that orbit is to be integrate in (default: MWPotential2014)
from_centre : bool
genrate orbit from cluster's exact centre instead of its assigned galactocentric coordinates (default: False)
sky_path : bool
return sky coordinates instead of cartesian coordinates (default: False)
initialize : bool
Initialize and return Orbit (default: False)
ro :float
galpy distance scale (Default: 8.)
vo : float
galpy velocity scale (Default: 220.)
plot : bool
plot a snapshot of the cluster in galactocentric coordinates with the orbital path (defualt: False)
Returns
-------
t : float
times for which path is provided
x,y,z : float
orbit positions
vx,vy,vz : float
orbit velocity
o : class
galpy orbit (if initialize==True)
History
-------
2018 - Written - Webb (UofT)
"""
o = initialize_orbit(cluster, from_centre=from_centre)
ts = np.linspace(0, -1.0 * dt / bovy_conversion.time_in_Gyr(ro=ro, vo=vo),
nt)
o.integrate(ts, pot)
R, phi, z = bovy_coords.rect_to_cyl(o.x(ts[-1]), o.y(ts[-1]), o.z(ts[-1]))
vR, vT, vz = bovy_coords.rect_to_cyl_vec(o.vx(ts[-1]), o.vy(ts[-1]),
o.vz(ts[-1]), o.x(ts[-1]),
o.y(ts[-1]), o.z(ts[-1]))
o = Orbit(
[R / ro, vR / vo, vT / vo, z / ro, vz / vo, phi],
ro=ro,
vo=vo,
solarmotion=[-11.1, 24.0, 7.25],
)
ts = np.linspace(
-1.0 * dt / bovy_conversion.time_in_Gyr(ro=ro, vo=vo),
dt / bovy_conversion.time_in_Gyr(ro=ro, vo=vo),
nt,
)
o.integrate(ts, pot)
if skypath:
ra = np.array(o.ra(ts))
dec = np.array(o.dec(ts))
dist = np.array(o.dist(ts))
pmra = np.array(o.pmra(ts))
pmdec = np.array(o.pmdec(ts))
vlos = np.array(o.vlos(ts))
if cluster.units == "pckms":
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo)
elif cluster.units == "nbody":
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo) / cluster.tstar
elif cluster.units == "galpy":
t = ts
else:
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo)
if plot:
filename = kwargs.pop("filename", None)
overplot = kwargs.pop("overplot", False)
skyplot(cluster)
plt.plot(ra, dec)
if filename != None:
plt.savefig(filename)
if initialize:
cluster.orbit = o
return t, ra, dec, dist, pmra, pmdec, vlos, o
else:
return t, ra, dec, dist, pmra, pmdec, vlos
else:
x = np.array(o.x(ts))
y = np.array(o.y(ts))
z = np.array(o.z(ts))
vx = np.array(o.vx(ts))
vy = np.array(o.vy(ts))
vz = np.array(o.vz(ts))
if cluster.units == "pckms":
x *= 1000.0
y *= 1000.0
z *= 1000.0
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo)
elif cluster.units == "nbody":
x *= 1000.0 / cluster.rbar
y *= 1000.0 / cluster.rbar
z *= 1000.0 / luster.rbar
vx /= cluster.vstar
vy /= cluster.vstar
vz /= cluster.vstar
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo) / cluster.tstar
elif cluster.units == "galpy":
x /= ro
y /= ro
z /= ro
vx /= vo
vy /= vo
vz /= vo
t = ts
else:
t = ts * bovy_conversion.time_in_Gyr(ro=ro, vo=vo)
if plot:
filename = kwargs.pop("filename", None)
overplot = kwargs.pop("overplot", False)
starplot(cluster, coord='xy', overplot=overplot)
_lplot(x, y, overplot=True)
if filename != None:
plt.savefig(filename)
if initialize:
return t, x, y, z, vx, vy, vz, o
else:
return t, x, y, z, vx, vy, vz
def v_prof(
cluster,
mmin=None,
mmax=None,
rmin=None,
rmax=None,
nrad=20,
vmin=None,
vmax=None,
emin=None,
emax=None,
kwmin=0,
kwmax=15,
indx=None,
projected=False,
plot=False,
):
"""Measure the radial variation in the mean velocity
Parameters
----------
cluster : class
StarCluster
mmin/mmax : float
minimum and maximum stellar mass
rmin/rmax : float
minimum and maximum stellar radii
nrad : int
number of radial bins
vmin/vmax : float
minimum and maximum stellar velocity
emin/emax : float
minimum and maximum stellar energy
kwmin/kwmax : float
minimum and maximum stellar type (kw)
indx : float
user defined boolean array from which to extract the subset
projected : bool
use projected values and constraints (default:False)
plot : bool
plot the velocity disperions profile (default: False)
Returns
-------
lrprofn : float
natural log of radius (normalized by half-mass radius)
vprof : float
mean velocity
Other Parameters
----------------
kwrags : str
key word arguments for plotting
History
-------
2018 - Written - Webb (UofT)
"""
units0, origin0 = save_cluster(cluster)
cluster.to_centre(do_order=True, do_key_params=True)
lrprofn = []
sigvprof = []
if projected:
r = cluster.rpro
v = cluster.vpro
else:
r = cluster.r
v = cluster.v
if rmin == None:
rmin = np.min(r)
if rmax == None:
rmax = np.max(r)
if vmin == None:
vmin = np.min(v)
if vmax == None:
vmax = np.max(v)
if mmin == None:
mmin = np.min(cluster.m)
if mmax == None:
mmax = np.max(cluster.m)
if indx is None:
indx = cluster.id > -1
# Build subcluster containing only stars in the full radial and mass range:
indx *= ((r >= rmin) * (r <= rmax) * (cluster.m >= mmin) *
(cluster.m <= mmax) * (v >= vmin) * (v <= vmax) *
(cluster.kw >= kwmin) * (cluster.kw <= kwmax))
if emin != None:
indx *= cluster.etot >= emin
if emin != None:
indx *= cluster.etot <= emax
# Convert to cylindrical or spherical coordinates:
if projected:
r, theta, z = bovy_coords.rect_to_cyl(cluster.x, cluster.y, cluster.z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(cluster.vx, cluster.vy,
cluster.vz, cluster.x,
cluster.y, cluster.z)
else:
r, phi, theta, vr, vp, vt = sphere_coords(cluster)
r_lower, r_mean, r_upper, r_hist = nbinmaker(r[indx], nrad)
for i in range(0, len(r_mean)):
rindx = indx * (r >= r_lower[i]) * (r < r_upper[i])
if np.sum(rindx) > 3.0:
vrmean = np.mean(vr[rindx])
vtmean = np.mean(vt[rindx])
if projected:
vpmean = np.zeros(len(vr))
else:
vpmean = np.mean(vp[rindx])
vmean = np.sqrt(vrmean**2.0 + vtmean**2.0 + vpmean**2.0)
if projected:
lrprofn.append(np.log(r_mean[i] / cluster.rmpro))
else:
lrprofn.append(np.log(r_mean[i] / cluster.rm))
vprof.append(vmean)
return_cluster(cluster, units0, origin0, do_order=True, do_key_params=True)
if plot:
filename = kwargs.pop("filename", None)
overplot = kwargs.pop("overplot", False)
_plot(lrprofn,
vprof,
xlabel=r"$\ln(r/r_m)$",
ylabel=r"$<v>$",
overplot=overplot,
**kwargs)
if filename != None:
plt.savefig(filename)
return lrprofn, vprof
def plot_tidalstreams(sat_galaxy,
name_sat,
sat_potential,
xaxis,
yaxis,
sat_mass,
sat_size,
x_satgal,
y_satgal,
z_satgal,
vx_satgal,
vy_satgal,
vz_satgal,
tform,
tsteady,
cluster_mass,
pre_tform=5 * units.Gyr,
post_tform=5 * units.Gyr,
xlim=None,
ylim=None):
# Function plots tidal streams formed from GC initially bound to MW satellite and later accreted onto galaxy (ex-situ) & plots corresponding in-situ streams to compare
#
# Input:
# sat_galaxy: an orbit object for a given satellite galaxy of the MW
# name_sat: string of the satellite galaxy's name
# sat_potential: potential object modelling the satellite's potential
# x and y axis dimensions to plot in (strings)
# x_satgal, y_satgal, z_satgal: x,y,z positions of the star_cluster within the satellite galaxy's frame of reference
# vx_satgal, vy_satgal, vz_satgal: x,y,z velocities of the star_cluster within the satellite galaxy's frame of reference
# mass and size of satellite to model dynamical friction effects (quantities with units attached)
# tform, tsteady: parameters of the potential, models tidal disruption of satellite galaxy (quantities in units of Gyr)
# cluster_mass: mass of globular cluster being tidally disrupted
# pre_tform: time quantity (w/ units) before tform to integrate to, default: 5Gyr
# post_tform: time quantity (w/ units) after tform to integrate to, default: 5Gyr
# xlim: (smaller, larger) limits of x-axis for tidal streams plot, optional
# ylim: (smaller, larger) limits of y-axis for tidal streams plot, optional
#
# Output:
#
# RvR: streamspraydf sampled points [(R,vR,vT,z,vz,phi) of sampled points on the stream in 6,N array], trailing = False
# RvRt: streamspraydf sampled points[(R,vR,vT,z,vz,phi) of sampled points on the stream in 6,N array], trailing = True
# dt: time since stripping for streamspraydf sampled points, trailing = False
# dtt: time since stripping for streamspraydf sampled points, trailing = True
# cluster_orbit: orbit of globular cluster integrated forward for 100Myr
# cluster_orbitb: orbit of globular cluster integrated backwards for 100Myr
# tstart: time quantity (in units of Gyr) at which stripping begins (= tform-pre_tform)
# tend: time quantity (in units of Gyr) at which stripping ends (= tform+post_tform)
#
# 1) Integrate orbit of satellite galaxy back in time given dynamical friction effects for t_back
t_back = 10.
ts = numpy.linspace(0., -t_back, 1000) * units.Gyr
cdf = ChandrasekharDynamicalFrictionForce(GMs=sat_mass,
rhm=sat_size,
dens=mw)
sat_galaxy.integrate(ts, mw + cdf)
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(-t_back * units.Gyr),
sat_galaxy.y(-t_back * units.Gyr),
sat_galaxy.z(-t_back * units.Gyr)
]
vcoord = [
sat_galaxy.vx(-t_back * units.Gyr),
sat_galaxy.vy(-t_back * units.Gyr),
sat_galaxy.vz(-t_back * units.Gyr)
]
# 2) Initialize star cluster on some orbit within the satellite galaxy
# (specific orbit is determined by cluster's x,y,z positions & vx,vy,vz velocities)
# Integrate orbits of star cluster and satellite galaxy forward for t_fwdr
t_fwrd = 15.
ts = numpy.linspace(-t_back, -t_back + t_fwrd, 1000) * units.Gyr
sat_galaxy = sat_galaxy(-t_back * units.Gyr)
# !! sat_galaxy = Orbit(vxvv = [R_sat, vR_sat, vT_sat, z_sat, vz_sat, phi_sat],ro = 8., vo=220.)
sat_galaxy.integrate(ts, mw + cdf)
'''
# Plot orbit of the satellite galaxy in MW frame of reference:
plt.figure(figsize=(12.,10.))
sat_galaxy.plot(d1 = xaxis, d2= yaxis,linestyle = ':', color = 'black', label = 'satellite galaxy')
'''
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference
# (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
star_cluster = Orbit(vxvv=[R, vR, vT, z, vz, phi], ro=8., vo=220.)
star_cluster.integrate(ts, mw + sat_movingpot)
'''
# Plot orbit of the star cluster in MW frame of reference:
star_cluster.plot(d1 = xaxis, d2= yaxis, linestyle = '-', overplot = True, color = 'blue', alpha=0.6,\
label = 'star cluster')
plt.title('Orbit of Star Cluster Within ' + name_sat + ' in Galactocentric Frame')
plt.legend()
plt.show()
plt.close()
'''
# 3) Implement wrapper potential to simulate tidal disruption of satellite galaxy's potential
# Re-integrate orbit of star cluster within modified sat_galaxy potential
# Plot orbit of the satellite galaxy and star cluster within sat galaxy in MW frame of reference:
plt.figure(figsize=(12., 10.))
tstart = tform - pre_tform
tend = tform + post_tform
time_int = numpy.linspace(tstart.to_value(units.Gyr),
tend.to_value(units.Gyr), 1000) * units.Gyr
if tstart < -t_back * units.Gyr:
# re-integrate satellite galaxy from current time back to tstart
re_time = numpy.linspace(-t_back, tstart.to_value(units.Gyr),
1000) * units.Gyr
sat_galaxy.integrate(re_time, mw + cdf)
# initialize star cluster on orbit in satellite galaxy at time tstart:
# Rectangular coordinates and velocities
coord = [
sat_galaxy.x(tstart),
sat_galaxy.y(tstart),
sat_galaxy.z(tstart)
]
vcoord = [
sat_galaxy.vx(tstart),
sat_galaxy.vy(tstart),
sat_galaxy.vz(tstart)
]
# Transform from satellite galaxy's frame of reference to Milky Way Galaxy's frame of reference (using Cartesian coordinates)
# Rectangular coordinates of the star cluster in galactocentric frame
x_gal = coord[0] + x_satgal
y_gal = coord[1] + y_satgal
z_gal = coord[2] + z_satgal
# Velocity of the star cluster in galactocentric frame
vx_gal = vcoord[0] + vx_satgal
vy_gal = vcoord[1] + vy_satgal
vz_gal = vcoord[2] + vz_satgal
# Transform to cylindrical coordinate system: R, phi, z
R, phi, z = rect_to_cyl(x_gal, y_gal, z_gal)
vR, vT, vz = rect_to_cyl_vec(vx_gal,
vy_gal,
vz_gal,
x_gal,
y_gal,
z_gal,
cyl=False)
# Re-initialize star cluster on orbit at time tstart
star_cluster = Orbit(vxvv=[R, vR, vT, vz, z, phi], ro=8., vo=220.)
else:
# default: star cluster is initialized at -10Gyr in given satellite galaxy
star_cluster = star_cluster(tstart)
sat_galaxy = sat_galaxy(
tstart) # make copy of sat_galaxy orbit at time tstart
sat_galaxy.integrate(time_int,
mw + cdf) # integrate sat_galaxy forward for 10Gyrs
sat_galaxy.plot(d1=xaxis,
d2=yaxis,
linestyle=':',
color='black',
label='satellite galaxy')
sat_movingpot = MovingObjectPotential(sat_galaxy, sat_potential)
dswp = DehnenSmoothWrapperPotential(amp=1.0,
pot=sat_movingpot,
tform=tform,
tsteady=tsteady,
decay=True)
star_cluster.integrate(time_int, mw + dswp)
# star cluster in combined potential: MW galaxy & moving potential of satellite galaxy
star_cluster.plot(d1=xaxis, d2=yaxis, linestyle='-', overplot=True, color='blue', alpha=0.6, \
label='star cluster')
# plots orbit of the star_cluster in MW frame of reference
plt.legend()
plt.title("Globular Cluster's Orbit Within Satellite Galaxy: " + name_sat)
label = 'wrappedpot_orbit_' + name_sat + '.pdf'
#plt.savefig(label, bbox_inches="tight")
plt.show()
plt.close()
# Figure out where star cluster is at end of integration: at tend
end_pos_cluster = [
star_cluster.R(tend),
star_cluster.vR(tend),
star_cluster.vT(tend),
star_cluster.z(tend),
star_cluster.vz(tend),
star_cluster.phi(tend)
]
# [R,vT,vT,z,vz,phi]
end_pos_gal = [
sat_galaxy.R(tend),
sat_galaxy.vR(tend),
sat_galaxy.vT(tend),
sat_galaxy.z(tend),
sat_galaxy.vz(tend),
sat_galaxy.phi(tend)
]
# 4) Model tidal streams formed by disruption of globular cluster with given cluster_mass and cluster orbit from #3
cluster_orbit = Orbit(vxvv=end_pos_cluster, ro=8., vo=220.)
# Integrate orbit of star cluster (progenitor) both forwards and backwards for 100 Myr
ts = numpy.linspace(0., 100., 1000) * units.Myr
cluster_orbit.integrate(ts, mw + dswp)
cluster_orbitb = cluster_orbit()
cluster_orbitb.integrate(-ts, mw + dswp)
cluster_orbit.turn_physical_off()
# Re-integrate orbit of sat galaxy to match disruption time and re-implement moving potential to model satellite galaxy
t_disrupt = tend - tstart
ts = numpy.linspace(0., -t_disrupt.to_value(units.Gyr), 1000) * units.Gyr
sat_galaxy_tidal = Orbit(vxvv=end_pos_gal)
sat_galaxy_tidal.integrate(ts, mw + cdf)
sat_movingpot = MovingObjectPotential(sat_galaxy_tidal, sat_potential)
tform_new = tform - tend
dswp_new = DehnenSmoothWrapperPotential(amp=1.0,
pot=sat_movingpot,
tform=tform_new,
tsteady=tsteady,
decay=True)
# Model leading part of the stream
spdf = streamspraydf(cluster_mass,
progenitor=cluster_orbit,
pot=dswp_new + mw,
rtpot=mw,
leading=True,
tdisrupt=t_disrupt)
# Model trailing part of the tidal stream
spdft = streamspraydf(cluster_mass,
progenitor=cluster_orbit,
pot=dswp_new + mw,
rtpot=mw,
leading=False,
tdisrupt=t_disrupt)
'''
# Comparing streamspraydf progenitor's orbit to cluster orbit integrated with: wrapped potential of sat_galaxy + milkyway
o = copy.deepcopy(spdf._progenitor)
o.turn_physical_on()
o.plot(d1='t',d2='r', color = 'pink', label= 'Progenitor Orbit from Streamspray')
ts = numpy.linspace(0.,-t_disrupt.to_value(units.Gyr),1000)*units.Gyr
cluster_o = Orbit(vxvv=end_pos_cluster, ro=8., vo=220.)
cluster_o.integrate(ts, dswp_new+mw)
cluster_o.plot(d1='t',d2='r',linestyle = ':', overplot = True, color = 'black',\
label='Manually Integrated Cluster Orbit')
plt.legend()
plt.title('Comparing Orbit from Streamspray to Manually Integrated Orbit of Star Cluster')
plt.show()
plt.close()
o.plot(color = 'pink', label='Progenitor Orbit from Streamspray')
cluster_o.plot(linestyle=':', color='black',overplot=True, label='Manually Integrated Cluster Orbit')
plt.legend()
plt.title('Comparing Orbit from Streamspray to Manually Integrated Orbit of Star Cluster')
plt.show()
plt.close()
'''
# Plot orbit of progenitor
plt.figure(figsize=(16., 12.))
cluster_orbit.turn_physical_on()
cluster_orbitb.turn_physical_on()
cluster_orbit.plot(d1='R', d2='z', color='k', label='_Hidden label')
cluster_orbitb.plot(d1='R',
d2='z',
color='k',
overplot=True,
label='_Hidden label')
# spdf.sample returns: (R,vR,vT,z,vz,phi) of sampled points on the stream in 6,N array
sample_num = 500
RvR, dt = spdf.sample(n=sample_num, returndt=True, integrate=True)
RvRt, dtt = spdft.sample(n=sample_num, returndt=True, integrate=True)
# Convert from natural units to physical units
d = 8.
plt.plot(cluster_orbit.R(),
cluster_orbit.z(),
'o',
color='orange',
ms=5.,
label='globular cluster')
plt.plot(RvR[0] * d, RvR[3] * d, 'r.', label='leading', alpha=0.6)
plt.plot(RvRt[0] * d, RvRt[3] * d, 'b.', label='trailing', alpha=0.6)
plt.legend()
'''
xmin = [min(RvR[0]*d), min(RvRt[0]*d)]
xmax = [max(RvR[0]*d), max(RvRt[0]*d)]
xlim = (min(xmin), max(xmax))
ymin = [min(RvR[3]*d), min(RvRt[3]*d)]
ymax = [max(RvR[3]*d), max(RvRt[3]*d)]
ylim = (min(ymin), max(ymax))
plt.xlim(xlim)
plt.ylim(ylim)
'''
if (xlim != None):
plt.xlim(xlim)
if (ylim != None):
plt.ylim(ylim)
plt.title('Tidal Disruption of Ex-situ GC Initially Bound to: ' + name_sat)
# plt.title('Tidal Disruption for '+ str(t_disrupt)+' of GC Initially Bound to: ' + name_sat )
label = 'tidalstream_' + name_sat + '.pdf'
#plt.savefig(label, bbox_inches="tight")
plt.show()
plt.close()
# 5) Create a streamspraydf object to model tidal disruption of in-situ cluster in potential of MW only
insitu_cluster = Orbit(
vxvv=end_pos_cluster, ro=8.,
vo=220.) # end position is pos of cluster at time tform+post_tform
# Integrate orbit of in-situ star cluster (progenitor) both forwards and backwards for 100 Myr
ts = numpy.linspace(0., 100., 1000) * units.Myr
insitu_cluster.integrate(ts, mw)
insitu_clusterb = cluster_orbit()
insitu_clusterb.integrate(-ts, mw)
insitu_cluster.turn_physical_off()
# Model leading part of the stream
spdf_insitu = streamspraydf(cluster_mass,
progenitor=insitu_cluster,
pot=mw,
rtpot=mw,
leading=True,
tdisrupt=t_disrupt)
# Model trailing part of the tidal stream
spdft_insitu = streamspraydf(cluster_mass,
progenitor=insitu_cluster,
pot=mw,
rtpot=mw,
leading=False,
tdisrupt=t_disrupt)
# Plot orbit of progenitor
plt.figure(figsize=(16., 12.))
insitu_cluster.turn_physical_on()
insitu_clusterb.turn_physical_on()
insitu_cluster.plot(d1='R', d2='z', color='k', label='_Hidden label')
insitu_clusterb.plot(d1='R',
d2='z',
color='k',
overplot=True,
label='_Hidden label')
# spdf.sample returns: (R,vR,vT,z,vz,phi) of sampled points on the stream in 6,N array
sample_num = 500
RvR_insitu, dt_insitu = spdf_insitu.sample(n=sample_num,
returndt=True,
integrate=True)
RvRt_insitu, dtt_insitu = spdft_insitu.sample(n=sample_num,
returndt=True,
integrate=True)
# Convert from natural units to physical units
d = 8.
plt.plot(insitu_cluster.R(),
insitu_cluster.z(),
'o',
color='orange',
ms=5.,
label='globular cluster')
plt.plot(RvR_insitu[0] * d,
RvR_insitu[3] * d,
'r.',
label='leading',
alpha=0.6)
plt.plot(RvRt_insitu[0] * d,
RvRt_insitu[3] * d,
'b.',
label='trailing',
alpha=0.6)
plt.legend()
if (xlim != None):
plt.xlim(xlim)
if (ylim != None):
plt.ylim(ylim)
plt.title('Tidal Disruption of In-situ GC Counterpart')
label = 'tidalstream_insitu_' + name_sat + '.pdf'
#plt.savefig(label, bbox_inches="tight")
plt.show()
plt.close()
return RvR, RvRt, dt, dtt, cluster_orbit, cluster_orbitb, tstart, tend
def _interpolate_stream_track_kick(self):
"""Build interpolations of the stream track near the kick"""
if hasattr(self,'_kick_interpolatedThetasTrack'): #pragma: no cover
return None #Already did this
# Setup the trackpoints where the kick will be computed, covering the
# full length of the stream
self._kick_interpolatedThetasTrack= \
numpy.linspace(self._gap_thetasTrack[0],
self._gap_thetasTrack[-1],
self._nKickPoints)
TrackX= self._gap_ObsTrack[:,0]*numpy.cos(self._gap_ObsTrack[:,5])
TrackY= self._gap_ObsTrack[:,0]*numpy.sin(self._gap_ObsTrack[:,5])
TrackZ= self._gap_ObsTrack[:,3]
TrackvX, TrackvY, TrackvZ=\
bovy_coords.cyl_to_rect_vec(self._gap_ObsTrack[:,1],
self._gap_ObsTrack[:,2],
self._gap_ObsTrack[:,4],
self._gap_ObsTrack[:,5])
#Interpolate
self._kick_interpTrackX=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackX,k=3)
self._kick_interpTrackY=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackY,k=3)
self._kick_interpTrackZ=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackZ,k=3)
self._kick_interpTrackvX=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackvX,k=3)
self._kick_interpTrackvY=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackvY,k=3)
self._kick_interpTrackvZ=\
interpolate.InterpolatedUnivariateSpline(self._gap_thetasTrack,
TrackvZ,k=3)
#Now store an interpolated version of the stream track
self._kick_interpolatedObsTrackXY= numpy.empty((len(self._kick_interpolatedThetasTrack),6))
self._kick_interpolatedObsTrackXY[:,0]=\
self._kick_interpTrackX(self._kick_interpolatedThetasTrack)
self._kick_interpolatedObsTrackXY[:,1]=\
self._kick_interpTrackY(self._kick_interpolatedThetasTrack)
self._kick_interpolatedObsTrackXY[:,2]=\
self._kick_interpTrackZ(self._kick_interpolatedThetasTrack)
self._kick_interpolatedObsTrackXY[:,3]=\
self._kick_interpTrackvX(self._kick_interpolatedThetasTrack)
self._kick_interpolatedObsTrackXY[:,4]=\
self._kick_interpTrackvY(self._kick_interpolatedThetasTrack)
self._kick_interpolatedObsTrackXY[:,5]=\
self._kick_interpTrackvZ(self._kick_interpolatedThetasTrack)
#Also in cylindrical coordinates
self._kick_interpolatedObsTrack= \
numpy.empty((len(self._kick_interpolatedThetasTrack),6))
tR,tphi,tZ= bovy_coords.rect_to_cyl(self._kick_interpolatedObsTrackXY[:,0],
self._kick_interpolatedObsTrackXY[:,1],
self._kick_interpolatedObsTrackXY[:,2])
tvR,tvT,tvZ=\
bovy_coords.rect_to_cyl_vec(self._kick_interpolatedObsTrackXY[:,3],
self._kick_interpolatedObsTrackXY[:,4],
self._kick_interpolatedObsTrackXY[:,5],
tR,tphi,tZ,cyl=True)
self._kick_interpolatedObsTrack[:,0]= tR
self._kick_interpolatedObsTrack[:,1]= tvR
self._kick_interpolatedObsTrack[:,2]= tvT
self._kick_interpolatedObsTrack[:,3]= tZ
self._kick_interpolatedObsTrack[:,4]= tvZ
self._kick_interpolatedObsTrack[:,5]= tphi
# Also store (x,v) for the point of closest approach
self._kick_ObsTrackXY_closest= numpy.array([\
self._kick_interpTrackX(self._impact_angle),
self._kick_interpTrackY(self._impact_angle),
self._kick_interpTrackZ(self._impact_angle),
self._kick_interpTrackvX(self._impact_angle),
self._kick_interpTrackvY(self._impact_angle),
self._kick_interpTrackvZ(self._impact_angle)])
return None
def plot_stream_xz(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPDIR,'gd1_evol_hitres_01312.dat'),
delimiter=',')
includeorbit= True
if includeorbit:
npts= 201
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
pts= numpy.linspace(0.,4.,npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((3,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec*= 8.
includetrack= True
if includetrack:
#Setup stream model
lp= potential.LogarithmicHaloPotential(q=0.9,normalize=1.)
aAI= actionAngleIsochroneApprox(b=0.8,pot=lp)
obs= numpy.array([1.56148083,0.35081535,-1.15481504,
0.88719443,-0.47713334,0.12019596])
sdf= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=True,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.))
sdft= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=False,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.))
#Plot
bovy_plot.bovy_print()
bovy_plot.bovy_plot(data[:,1],data[:,2],'k,',
xlabel=r'$X\,(\mathrm{kpc})$',
ylabel=r'$Z\,(\mathrm{kpc})$',
xrange=[0.,16.],
yrange=[-0.5,11.])
if includeorbit:
bovy_plot.bovy_plot(pox,poz,'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.)
if includetrack:
d1= 'x'
d2= 'z'
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
#Also create inset
pyplot.plot([12.,12.],[0.5,7.5],'k-')
pyplot.plot([14.5,14.5],[0.5,7.5],'k-')
pyplot.plot([12.,14.5],[0.5,0.5],'k-')
pyplot.plot([12.,14.5],[7.5,7.5],'k-')
pyplot.plot([12.,8.8],[7.5,7.69],'k:')
pyplot.plot([12.,8.8],[0.5,-0.21],'k:')
insetAxes= pyplot.axes([0.15,0.12,0.4,0.55])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(data[:,1],data[:,2],'k,',
overplot=True)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(12.,14.5)
insetAxes.set_ylim(.5,7.5)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
bovy_plot.bovy_end_print(plotfilename)
def impulse_deltav_general_orbitintegration(v,x,b,w,x0,v0,pot,tmax,galpot,
tmaxfac=10.,nsamp=1000,
integrate_method='symplec4_c'):
"""
NAME:
impulse_deltav_general_orbitintegration
PURPOSE:
calculate the delta velocity to due an encounter with a general spherical potential NOT in the impulse approximation by integrating each particle in the underlying galactic potential; allows for arbitrary velocity vectors and arbitrary shaped streams.
INPUT:
v - velocity of the stream (nstar,3)
x - position along the stream (nstar,3)
b - impact parameter
w - velocity of the subhalo (3)
x0 - position of closest approach (3)
v0 - velocity of stream at closest approach (3)
pot - Potential object or list thereof (should be spherical)
tmax - maximum integration time
galpot - galpy Potential object or list thereof
nsamp(1000) - number of forward integration points
integrate_method= ('symplec4_c') orbit integrator to use (see Orbit.integrate)
OUTPUT:
deltav (nstar,3)
HISTORY:
2015-08-17 - SANDERS
"""
if len(v.shape) == 1: v= numpy.reshape(v,(1,3))
if len(x.shape) == 1: x= numpy.reshape(x,(1,3))
nstar,ndim=numpy.shape(v)
b0 = numpy.cross(w,v0)
b0 *= b/numpy.sqrt(numpy.sum(b0**2))
times = numpy.linspace(0.,tmax,nsamp)
xres = numpy.zeros(shape=(len(x),nsamp*2-1,3))
R, phi, z= bovy_coords.rect_to_cyl(x[:,0],x[:,1],x[:,2])
vR, vp, vz= bovy_coords.rect_to_cyl_vec(v[:,0],v[:,1],v[:,2],
R,phi,z,cyl=True)
for i in range(nstar):
o = Orbit([R[i],vR[i],vp[i],z[i],vz[i],phi[i]])
o.integrate(times,galpot,method=integrate_method)
xres[i,nsamp:,0]=o.x(times)[1:]
xres[i,nsamp:,1]=o.y(times)[1:]
xres[i,nsamp:,2]=o.z(times)[1:]
oreverse = o.flip()
oreverse.integrate(times,galpot,method=integrate_method)
xres[i,:nsamp,0]=oreverse.x(times)[::-1]
xres[i,:nsamp,1]=oreverse.y(times)[::-1]
xres[i,:nsamp,2]=oreverse.z(times)[::-1]
times = numpy.concatenate((-times[::-1],times[1:]))
nsamp = len(times)
X = b0+xres-x0-numpy.outer(times,w)
r = numpy.sqrt(numpy.sum(X**2,axis=-1))
acc = (numpy.reshape(evaluateRforces(r.flatten(),0.,pot),(nstar,nsamp))/r)[:,:,numpy.newaxis]*X
return integrate.simps(acc,x=times,axis=1)
def initialize_orbit(cluster, from_centre=False, r0=8.0, v0=220.0):
"""
NAME:
initialize_orbit
PURPOSE:
Initialize a galpy orbit instance for the cluster
INPUT:
cluster - StarCluster
from_centre - genrate orbit from cluster's assigned galactocentric coordinates (default) or from its centre
r0 - galpy distance scale (Default: 8.)
v0 - galpy velocity scale (Default: 220.)
OUTPUT:
orbit instance
HISTORY:
2018 - Written - Webb (UofT)
"""
if cluster.units == "radec":
o = Orbit(
[
cluster.ra_gc,
cluster.dec_gc,
cluster.dist_gc,
cluster.pmra_gc,
cluster.pmdec_gc,
cluster.vlos_gc,
],
radec=True,
ro=r0,
vo=v0,
solarmotion=[-11.1, 24.0, 7.25],
)
else:
units0, origin0 = save_cluster(cluster)
cluster.to_galpy()
if from_centre:
x, y, z = (
cluster.xgc + cluster.xc,
cluster.ygc + cluster.yc,
cluster.zgc + cluster.zc,
)
vx, vy, vz = (
cluster.vxgc + cluster.vxc,
cluster.vygc + cluster.vyc,
cluster.vzgc + cluster.vzc,
)
else:
x, y, z = cluster.xgc, cluster.ygc, cluster.zgc
vx, vy, vz = cluster.vxgc, cluster.vygc, cluster.vzgc
R, phi, z = bovy_coords.rect_to_cyl(x, y, z)
vR, vT, vz = bovy_coords.rect_to_cyl_vec(vx, vy, vz, x, y, z)
o = Orbit(
[R, vR, vT, z, vz, phi], ro=r0, vo=v0, solarmotion=[-11.1, 24.0, 7.25]
)
return_cluster(cluster, units0, origin0)
cluster.orbit = o
return o
def v_prof(
cluster,
mmin=None,
mmax=None,
rmin=None,
rmax=None,
nrad=20,
vmin=None,
vmax=None,
emin=None,
emax=None,
kwmin=0,
kwmax=15,
indx=None,
projected=False,
):
"""
NAME:
v_prof
PURPOSE:
Measure the radial variation in the mean velocity
INPUT:
cluster - StarCluster instance
mmin/mmax - minimum and maximum stellar mass
rmin/rmax - minimum and maximum stellar radii
nrad - number of radial bins
vmin/vmax - minimum and maximum stellar velocity
emin/emax - minimum and maximum stellar energy
kwmin/kwmax - minimum and maximum stellar type (kw)
indx - user defined boolean array from which to extract the subset
projected - use projected values and constraints (Default:False)
plot - plot the density profile (Default: False)
KWARGS:
Same as for ..util.plot.nplot
OUTPUT:
lrprofn - natural log of radius (normalized by half-mass radius)
vprof - mean velocity
HISTORY:
2018 - Written - Webb (UofT)
"""
units0, origin0 = save_cluster(cluster)
cluster.to_centre(do_order=True, do_key_params=True)
lrprofn = []
sigvprof = []
if projected:
r = cluster.rpro
v = cluster.vpro
else:
r = cluster.r
v = cluster.v
if rmin == None:
rmin = np.min(r)
if rmax == None:
rmax = np.max(r)
if vmin == None:
vmin = np.min(v)
if vmax == None:
vmax = np.max(v)
if mmin == None:
mmin = np.min(cluster.m)
if mmax == None:
mmax = np.max(cluster.m)
if indx is None:
indx = cluster.id > -1
# Build subcluster containing only stars in the full radial and mass range:
indx *= ((r >= rmin) * (r <= rmax) * (cluster.m >= mmin) *
(cluster.m <= mmax) * (v >= vmin) * (v <= vmax) *
(cluster.kw >= kwmin) * (cluster.kw <= kwmax))
if emin != None:
indx *= cluster.etot >= emin
if emin != None:
indx *= cluster.etot <= emax
# Convert to cylindrical or spherical coordinates:
if projected:
r, theta, z = bovy_coords.rect_to_cyl(cluster.x, cluster.y, cluster.z)
vr, vtheta, vz = bovy_coords.rect_to_cyl_vec(cluster.vx, cluster.vy,
cluster.vz, cluster.x,
cluster.y, cluster.z)
else:
r, phi, theta, vr, vp, vt = sphere_coords(cluster)
r_lower, r_mean, r_upper, r_hist = nbinmaker(r[indx], nrad)
for i in range(0, len(r_mean)):
rindx = indx * (r >= r_lower[i]) * (r < r_upper[i])
if np.sum(rindx) > 3.0:
vrmean = np.mean(vr[rindx])
vtmean = np.mean(vt[rindx])
if projected:
vpmean = np.zeros(len(vr))
else:
vpmean = np.mean(vp[rindx])
vmean = np.sqrt(vrmean**2.0 + vtmean**2.0 + vpmean**2.0)
if projected:
lrprofn.append(np.log(r_mean[i] / cluster.rmpro))
else:
lrprofn.append(np.log(r_mean[i] / cluster.rm))
vprof.append(vmean)
return_cluster(cluster, units0, origin0, do_order=True, do_key_params=True)
return lrprofn, vprof
def plot_stream_xz(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPDIR,'gd1_evol_hitres_00800.dat'),
delimiter=',')
aadata= numpy.loadtxt(os.path.join(_STREAMSNAPAADIR,
'gd1_evol_hitres_aa_00800.dat'),
delimiter=',')
thetar= aadata[:,6]
thetar= (numpy.pi+(thetar-numpy.median(thetar))) % (2.*numpy.pi)
if 'sim' in plotfilename:
sindx= numpy.fabs(thetar-numpy.pi) > (4.*numpy.median(numpy.fabs(thetar-numpy.median(thetar))))
else:
sindx= numpy.fabs(thetar-numpy.pi) > (1.5*numpy.median(numpy.fabs(thetar-numpy.median(thetar))))
includeorbit= True
if includeorbit:
npts= 201
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
pts= numpy.linspace(0.,4.,npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((3,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec*= 8.
includetrack= True
if includetrack:
#Setup stream model
lp= potential.LogarithmicHaloPotential(q=0.9,normalize=1.)
aAI= actionAngleIsochroneApprox(b=0.8,pot=lp)
obs= numpy.array([1.56148083,0.35081535,-1.15481504,
0.88719443,-0.47713334,0.12019596])
#Obs is at time 1312, need to go back 2 Gyr to time 800
obs[1]*= -1.
obs[2]*= -1.
obs[4]*= -1.
o= Orbit(obs)
ts= numpy.linspace(0.,2.*977.7922212082034/1000./bovy_conversion.time_in_Gyr(220.,8.),1001)
o.integrate(ts,lp)
obs= o(ts[-1])._orb.vxvv
obs[1]*= -1.
obs[2]*= -1.
obs[4]*= -1.
tdisrupt= 4.5-2.*977.7922212082034/1000.
sdf= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=True,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=tdisrupt/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=1.5*3./5.,multi=_NTRACKCHUNKS)
sdft= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=False,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=tdisrupt/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=1.5*3./5.,multi=_NTRACKCHUNKS)
if 'sim' in plotfilename:
#Replace data with simulated data
forwardXY= sdf.sample(int(round(numpy.sum(sindx)/2.)),
xy=True)
backwardXY= sdft.sample(int(round(numpy.sum(sindx)/2.)),
xy=True)
data= numpy.empty((forwardXY.shape[1]+backwardXY.shape[1],7))
data[:forwardXY.shape[1],1]= forwardXY[0]*8.
data[:forwardXY.shape[1],2]= forwardXY[2]*8.
data[:forwardXY.shape[1],3]= forwardXY[1]*8.
data[:forwardXY.shape[1],4]= forwardXY[3]*220.
data[:forwardXY.shape[1],5]= forwardXY[5]*220.
data[:forwardXY.shape[1],6]= forwardXY[4]*220.
data[forwardXY.shape[1]:,1]= backwardXY[0]*8.
data[forwardXY.shape[1]:,2]= backwardXY[2]*8.
data[forwardXY.shape[1]:,3]= backwardXY[1]*8.
data[forwardXY.shape[1]:,4]= backwardXY[3]*220.
data[forwardXY.shape[1]:,5]= backwardXY[5]*220.
data[forwardXY.shape[1]:,6]= backwardXY[4]*220.
sindx= numpy.ones(data.shape[0],dtype='bool')
#Plot
bovy_plot.bovy_print()
bovy_plot.bovy_plot(data[sindx,1],data[sindx,2],'k,',ms=2.,
xlabel=r'$X\,(\mathrm{kpc})$',
ylabel=r'$Z\,(\mathrm{kpc})$',
xrange=[-12.5,-3.],
yrange=[-12.5,-7.])
if numpy.sum(True-sindx) > 0:
#Also plot progenitor
pindx= copy.copy(True-sindx)
pindx[0:9900]= False #subsample
bovy_plot.bovy_plot(data[pindx,1],data[pindx,2],
'k,',overplot=True)
if includeorbit:
bovy_plot.bovy_plot(pox,poz,'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.)
if 'sim' in plotfilename:
bovy_plot.bovy_text(r'$\mathrm{mock\ stream}$',
bottom_left=True,size=16.)
else:
bovy_plot.bovy_text(r'$N\!\!-\!\!\mathrm{body\ stream}$',
bottom_left=True,size=16.)
if includetrack:
d1= 'x'
d2= 'z'
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
#Also create inset
pyplot.plot([-9.,-9.],[-11.75,-10.3],'k-')
pyplot.plot([-6.,-6.],[-11.75,-10.3],'k-')
pyplot.plot([-9.,-6.],[-11.75,-11.75],'k-')
pyplot.plot([-9.,-6.],[-10.3,-10.3],'k-')
pyplot.plot([-6.,-3.4],[-10.3,-10.],'k:')
pyplot.plot([-9.,-8.85],[-10.3,-10.],'k:')
insetAxes= pyplot.axes([0.42,0.47,0.45,0.42])
pyplot.sca(insetAxes)
bovy_plot.bovy_plot(data[sindx,1],data[sindx,2],'k.',ms=2.,zorder=0.,
overplot=True)
if numpy.sum(True-sindx) > 0:
pindx= copy.copy(True-sindx)
pindx[0:9700]= False #subsample
bovy_plot.bovy_plot(data[pindx,1],data[pindx,2],'k,',
zorder=0.,
overplot=True)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.,
zorder=1)
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True,zorder=2)
nullfmt = NullFormatter() # no labels
insetAxes.xaxis.set_major_formatter(nullfmt)
insetAxes.yaxis.set_major_formatter(nullfmt)
insetAxes.set_xlim(-9.,-6.)
insetAxes.set_ylim(-11.75,-10.3)
pyplot.tick_params(\
axis='both', # changes apply to the x-axis
which='both', # both major and minor ticks are affected
bottom='off', # ticks along the bottom edge are off
top='off', # ticks along the top edge are off
left='off', # ticks along the bottom edge are off
right='off') # ticks along the top edge are off
bovy_plot.bovy_end_print(plotfilename)
def orbital_path(
cluster,
dt=0.1,
nt=100,
pot=MWPotential2014,
from_centre=False,
skypath=False,
initialize=False,
r0=8.0,
v0=220.0,
):
"""
NAME:
orbital_path
PURPOSE:
Calculate orbital path +/- dt Gyr around the cluster
INPUT:
cluster - StarCluster
dt - timestep that StarCluster is to be moved to
nt - number of timesteps
pot - Potential orbit is to be integrate in (Default: MWPotential2014)
from_centre - interpolate from cluster's define position (default) or the measured centre of cluster
sky_path - return sky coordinates instead of cartesian coordinates (Default: False)
initialize - Initialize and return Orbit (Default: False)
r0 - galpy distance scale (Default: 8.)
v0 - galpy velocity scale (Default: 220.)
OUTPUT:
t,x,y,z,vx,vy,vz
HISTORY:
2018 - Written - Webb (UofT)
"""
o = initialize_orbit(cluster, from_centre=from_centre)
ts = np.linspace(0, -1.0 * dt / bovy_conversion.time_in_Gyr(ro=r0, vo=v0), nt)
o.integrate(ts, pot)
R, phi, z = bovy_coords.rect_to_cyl(o.x(ts[-1]), o.y(ts[-1]), o.z(ts[-1]))
vR, vT, vz = bovy_coords.rect_to_cyl_vec(
o.vx(ts[-1]), o.vy(ts[-1]), o.vz(ts[-1]), o.x(ts[-1]), o.y(ts[-1]), o.z(ts[-1])
)
o = Orbit(
[R / r0, vR / v0, vT / v0, z / r0, vz / v0, phi],
ro=r0,
vo=v0,
solarmotion=[-11.1, 24.0, 7.25],
)
ts = np.linspace(
-1.0 * dt / bovy_conversion.time_in_Gyr(ro=r0, vo=v0),
dt / bovy_conversion.time_in_Gyr(ro=r0, vo=v0),
nt,
)
o.integrate(ts, pot)
if skypath:
ra = np.array(o.ra(ts))
dec = np.array(o.dec(ts))
dist = np.array(o.dist(ts))
pmra = np.array(o.pmra(ts))
pmdec = np.array(o.pmdec(ts))
vlos = np.array(o.vlos(ts))
if cluster.units == "realpc":
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0)
elif cluster.units == "nbody":
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0) / cluster.tstar
elif cluster.units == "galpy":
t = ts
else:
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0)
if initialize:
cluster.orbit = o
return t, ra, dec, dist, pmra, pmdec, vlos, o
else:
return t, ra, dec, dist, pmra, pmdec, vlos
else:
x = np.array(o.x(ts))
y = np.array(o.y(ts))
z = np.array(o.z(ts))
vx = np.array(o.vx(ts))
vy = np.array(o.vy(ts))
vz = np.array(o.vz(ts))
if cluster.units == "realpc":
x *= 1000.0
y *= 1000.0
z *= 1000.0
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0)
elif cluster.units == "nbody":
x *= 1000.0 / cluster.rbar
y *= 1000.0 / cluster.rbar
z *= 1000.0 / luster.rbar
vx /= cluster.vstar
vy /= cluster.vstar
vz /= cluster.vstar
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0) / cluster.tstar
elif cluster.units == "galpy":
x /= r0
y /= r0
z /= r0
vx /= v0
vy /= v0
vz /= v0
t = ts
else:
t = ts * bovy_conversion.time_in_Gyr(ro=r0, vo=v0)
if initialize:
cluster.orbit = o
return t, x, y, z, vx, vy, vz, o
else:
return t, x, y, z, vx, vy, vz
def impulse_deltav_general_fullplummerintegration(v,x,b,w,x0,v0,galpot,GM,rs,
tmaxfac=10.,N=1000,
integrate_method='symplec4_c'):
"""
NAME:
impulse_deltav_general_fullplummerintegration
PURPOSE:
calculate the delta velocity to due an encounter with a moving Plummer sphere and galactic potential relative to just in galactic potential
INPUT:
v - velocity of the stream (nstar,3)
x - position along the stream (nstar,3)
b - impact parameter
w - velocity of the subhalo (3)
x0 - position of closest approach (3)
v0 - velocity of stream at closest approach (3)
galpot - Galaxy Potential object
GM - mass of Plummer
rs - scale of Plummer
tmaxfac(10) - multiple of rs/|w-v0| to use for time integration interval
N(1000) - number of forward integration points
integrate_method('symplec4_c') - orbit integrator to use (see Orbit.integrate)
OUTPUT:
deltav (nstar,3)
HISTORY:
2015-08-18 - SANDERS
"""
if len(v.shape) == 1: v= numpy.reshape(v,(1,3))
if len(x.shape) == 1: x= numpy.reshape(x,(1,3))
nstar,ndim=numpy.shape(v)
b0 = numpy.cross(w,v0)
b0 *= b/numpy.sqrt(numpy.sum(b0**2))
X = x0-b0
# Setup Plummer orbit
R, phi, z= bovy_coords.rect_to_cyl(X[0],X[1],X[2])
vR, vp, vz= bovy_coords.rect_to_cyl_vec(w[0],w[1],w[2],R,phi,z,cyl=True)
tmax = tmaxfac*rs/numpy.sqrt(numpy.sum((w-v0)**2))
times = numpy.linspace(0.,tmax,N)
dtimes = numpy.linspace(-tmax,tmax,2*N)
o = Orbit(vxvv=[R,-vR,-vp,z,-vz,phi])
o.integrate(times,galpot,method=integrate_method)
oplum = Orbit(vxvv=[o.R(times[-1]),-o.vR(times[-1]),-o.vT(times[-1]),o.z(times[-1]),-o.vz(times[-1]),o.phi(times[-1])])
oplum.integrate(dtimes,galpot,method=integrate_method)
plumpot = MovingObjectPotential(orbit=oplum, GM=GM, softening_model='plummer', softening_length=rs)
# Now integrate each particle backwards in galaxy potential, forwards in combined potential and backwards again in galaxy and take diff
deltav = numpy.zeros((nstar,3))
R, phi, z= bovy_coords.rect_to_cyl(x[:,0],x[:,1],x[:,2])
vR, vp, vz= bovy_coords.rect_to_cyl_vec(v[:,0],v[:,1],v[:,2],
R,phi,z,cyl=True)
for i in range(nstar):
ostar= Orbit(vxvv=[R[i],-vR[i],-vp[i],z[i],-vz[i],phi[i]])
ostar.integrate(times,galpot,method=integrate_method)
oboth = Orbit(vxvv=[ostar.R(times[-1]),-ostar.vR(times[-1]),-ostar.vT(times[-1]),ostar.z(times[-1]),-ostar.vz(times[-1]),ostar.phi(times[-1])])
oboth.integrate(dtimes,[galpot,plumpot],method=integrate_method)
ogalpot = Orbit(vxvv=[oboth.R(times[-1]),-oboth.vR(times[-1]),-oboth.vT(times[-1]),oboth.z(times[-1]),-oboth.vz(times[-1]),oboth.phi(times[-1])])
ogalpot.integrate(times,galpot,method=integrate_method)
deltav[i][0] = -ogalpot.vx(times[-1]) - v[i][0]
deltav[i][1] = -ogalpot.vy(times[-1]) - v[i][1]
deltav[i][2] = -ogalpot.vz(times[-1]) - v[i][2]
return deltav
def _determine_deltaOmegaTheta_kick(self):
# Propagate deltav(angle) -> delta (Omega,theta) [angle]
# Cylindrical coordinates of the perturbed points
vXp= self._kick_interpolatedObsTrackXY[:,3]+self._kick_deltav[:,0]
vYp= self._kick_interpolatedObsTrackXY[:,4]+self._kick_deltav[:,1]
vZp= self._kick_interpolatedObsTrackXY[:,5]+self._kick_deltav[:,2]
vRp,vTp,vZp=\
bovy_coords.rect_to_cyl_vec(vXp,vYp,vZp,
self._kick_interpolatedObsTrack[:,0],
self._kick_interpolatedObsTrack[:,5],
self._kick_interpolatedObsTrack[:,3],
cyl=True)
# We will abuse streamdf functions for doing the (O,a) -> (R,vR)
# coordinate transformation, to do this, we assign some of the
# attributes related to the track near the impact to the equivalent
# attributes related to the track at the present time, carefully
# removing this again to avoid confusion (as much as possible)
self._interpolatedObsTrack= self._kick_interpolatedObsTrack
self._ObsTrack= self._gap_ObsTrack
self._interpolatedObsTrackXY= self._kick_interpolatedObsTrackXY
self._ObsTrackXY= self._gap_ObsTrackXY
self._alljacsTrack= self._gap_alljacsTrack
self._interpolatedObsTrackAA= self._kick_interpolatedObsTrackAA
self._ObsTrackAA= self._gap_ObsTrackAA
Oap= self._approxaA(self._kick_interpolatedObsTrack[:,0],
vRp,vTp,
self._kick_interpolatedObsTrack[:,3],
vZp,
self._kick_interpolatedObsTrack[:,5],interp=True,
cindx=range(len(self._kick_interpolatedObsTrackAA)))
# Remove attributes again to avoid confusion later
delattr(self,'_interpolatedObsTrack')
delattr(self,'_ObsTrack')
delattr(self,'_interpolatedObsTrackXY')
delattr(self,'_ObsTrackXY')
delattr(self,'_alljacsTrack')
delattr(self,'_interpolatedObsTrackAA')
delattr(self,'_ObsTrackAA')
# Generate (dO,da)[angle_offset] and interpolate
self._kick_dOap= Oap.T-self._kick_interpolatedObsTrackAA
self.__kick_interpdOr=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,0],k=3)
self.__kick_interpdOp=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,1],k=3)
self.__kick_interpdOz=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,2],k=3)
self.__kick_interpdar=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,3],k=3)
self.__kick_interpdap=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,4],k=3)
self.__kick_interpdaz=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOap[:,5],k=3)
# Also interpolate parallel and perpendicular frequencies
self._kick_dOaparperp=\
numpy.dot(self._kick_dOap[:,:3],
self._sigomatrixEig[1][:,self._sigomatrixEigsortIndx])
self.__kick_interpdOpar=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,
numpy.dot(self._kick_dOap[:,:3],self._dsigomeanProgDirection),k=3)
self.__kick_interpdOperp0=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOaparperp[:,0],k=3)
self.__kick_interpdOperp1=\
interpolate.InterpolatedUnivariateSpline(\
self._kick_interpolatedThetasTrack,self._kick_dOaparperp[:,1],k=3)
return None
def sample_perturbed_pal5_new(N,
barpot,
nobarpot,
fo='blah_trailing.dat',
trailing=True,
tpal5age=5.):
tage = np.linspace(0., -tpal5age, 1001) / bovy_conversion.time_in_Gyr(
220., 8.)
if trailing:
sdf_trailing = pal5_util.setup_pal5model(pot=nobarpot)
R, vR, vT, z, vz, phi, dt = sdf_trailing.sample(n=N, returndt=True)
fo = open(fo, 'w')
else:
sdf_leading = pal5_util.setup_pal5model(pot=nobarpot, leading=True)
R, vR, vT, z, vz, phi, dt = sdf_leading.sample(n=N, returndt=True)
fo_lead = fo.replace('trailing', 'leading')
fo = open(fo_lead, 'w')
#integrate Pal 5 progenitor in barpot all the way back to 5 Gyrs,
#from this orbits will be extracted by interpolation in the for loop
pal5_bar = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
solarmotion=[-11.1, 24., 7.25])
pal5_bar.integrate(tage, barpot)
#integrate Pal 5 progenitor in nobarpot all the way back to 5 Gyrs,
#from this orbits will be extracted by interpolation in the for loop
pal5_nobar = Orbit([229.018, -0.124, 23.2, -2.296, -2.257, -58.7],
radec=True,
solarmotion=[-11.1, 24., 7.25])
pal5_nobar.integrate(tage, nobarpot)
pal5_bar.turn_physical_off()
pal5_nobar.turn_physical_off()
finalR = numpy.empty(N)
finalvR = numpy.empty(N)
finalvT = numpy.empty(N)
finalvz = numpy.empty(N)
finalphi = numpy.empty(N)
finalz = numpy.empty(N)
tt = numpy.empty(N)
for ii in range(N):
o = Orbit([R[ii], vR[ii], vT[ii], z[ii], vz[ii], phi[ii]])
o.turn_physical_off()
ts = numpy.linspace(0., -dt[ii], 1001)
o.integrate(ts, nobarpot)
#extract the orbit at the stripping time from the above integrated orbit
unp_orb = numpy.array([
o.x(ts[-1]),
o.y(ts[-1]),
o.z(ts[-1]),
o.vx(ts[-1]),
o.vy(ts[-1]),
o.vz(ts[-1])
])
pal5_orb_bar = numpy.array([
pal5_bar.x(ts[-1]),
pal5_bar.y(ts[-1]),
pal5_bar.z(ts[-1]),
pal5_bar.vx(ts[-1]),
pal5_bar.vy(ts[-1]),
pal5_bar.vz(ts[-1])
])
pal5_orb_nobar = numpy.array([
pal5_nobar.x(ts[-1]),
pal5_nobar.y(ts[-1]),
pal5_nobar.z(ts[-1]),
pal5_nobar.vx(ts[-1]),
pal5_nobar.vy(ts[-1]),
pal5_nobar.vz(ts[-1])
])
#print (unp_orb)
#print (pal5_orb_bar)
#print (pal5_orb_nobar)
#subtract Pal 5 orb in nobarpot and add Pal 5 orbit in barpot
pert_orb = (unp_orb - pal5_orb_nobar) + pal5_orb_bar
#print (unp_orb,dt[ii]*bovy_conversion.time_in_Gyr(220.,8.))
#print (pert_orb,dt[ii]*bovy_conversion.time_in_Gyr(220.,8.))
#(R,phi,Z)
#vR,vT,vz
#vxvv=[R,vR,vT,z,vz,phi]
pert_orb_RpZ = bovy_coords.rect_to_cyl(pert_orb[0], pert_orb[1],
pert_orb[2])
pert_orb_vRpZ = bovy_coords.rect_to_cyl_vec(pert_orb[3], pert_orb[4],
pert_orb[5], pert_orb[0],
pert_orb[1], pert_orb[2])
pert_orb = Orbit([
pert_orb_RpZ[0], pert_orb_vRpZ[0], pert_orb_vRpZ[1],
pert_orb_RpZ[2], pert_orb_vRpZ[2], pert_orb_RpZ[1]
])
ts_future = numpy.linspace(-dt[ii], 0., 1001)
#forward integrate in barred potential
pert_orb.integrate(ts_future, barpot)
finalR[ii] = pert_orb.R(ts_future[-1])
finalphi[ii] = pert_orb.phi(ts_future[-1])
finalz[ii] = pert_orb.z(ts_future[-1])
finalvR[ii] = pert_orb.vR(ts_future[-1])
finalvT[ii] = pert_orb.vT(ts_future[-1])
finalvz[ii] = pert_orb.vz(ts_future[-1])
tt[ii] = dt[ii]
fo.write("#R phi z vR vT vz ts" + "\n")
for jj in range(N):
fo.write(
str(finalR[jj]) + " " + str(finalphi[jj]) + " " +
str(finalz[jj]) + " " + str(finalvR[jj]) + " " +
str(finalvT[jj]) + " " + str(finalvz[jj]) + " " + str(tt[jj]) +
"\n")
fo.close()
return None
def plot_stream_xz(plotfilename):
#Read stream
data= numpy.loadtxt(os.path.join(_STREAMSNAPDIR,'gd1-hisigv_evol_00041.dat'),
delimiter=',')
includeorbit= True
if includeorbit:
npts= 201
pot= potential.LogarithmicHaloPotential(normalize=1.,q=0.9)
pts= numpy.linspace(0.,17.,npts)
#Calculate progenitor orbit around this point
pox= numpy.median(data[:,1])
poy= numpy.median(data[:,3])
poz= numpy.median(data[:,2])
povx= numpy.median(data[:,4])
povy= numpy.median(data[:,6])
povz= numpy.median(data[:,5])
pR,pphi,pZ= bovy_coords.rect_to_cyl(pox,poy,poz)
pvR,pvT,pvZ= bovy_coords.rect_to_cyl_vec(povx,povy,povz,pR,
pphi,pZ,cyl=True)
ppo= Orbit([pR/8.,pvR/220.,pvT/220.,pZ/8.,pvZ/220.,pphi])
pno= Orbit([pR/8.,-pvR/220.,-pvT/220.,pZ/8.,-pvZ/220.,pphi])
ppo.integrate(pts,pot)
pno.integrate(pts,pot)
pvec= numpy.zeros((3,npts*2-1))
pvec[0,:npts-1]= pno.x(pts)[::-1][:-1]
pvec[1,:npts-1]= pno.z(pts)[::-1][:-1]
pvec[2,:npts-1]= pno.y(pts)[::-1][:-1]
pvec[0,npts-1:]= ppo.x(pts)
pvec[1,npts-1:]= ppo.z(pts)
pvec[2,npts-1:]= ppo.y(pts)
pvec*= 8.
includetrack= True
if includetrack:
#Setup stream model
lp= potential.LogarithmicHaloPotential(q=0.9,normalize=1.)
aAI= actionAngleIsochroneApprox(b=0.8,pot=lp)
obs= numpy.array([1.56148083,0.35081535,-1.15481504,
0.88719443,-0.47713334,0.12019596])
sdf= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=True,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=13.5,multi=_NTRACKCHUNKS)
sdft= streamdf(_SIGV/220.,progenitor=Orbit(obs),pot=lp,aA=aAI,
leading=False,nTrackChunks=_NTRACKCHUNKS,
tdisrupt=4.5/bovy_conversion.time_in_Gyr(220.,8.),
deltaAngleTrack=13.5,multi=_NTRACKCHUNKS)
#Plot
bovy_plot.bovy_print()
bovy_plot.bovy_plot(data[:,1],data[:,2],'k,',
xlabel=r'$X\,(\mathrm{kpc})$',
ylabel=r'$Z\,(\mathrm{kpc})$',
xrange=[-30.,30.],
yrange=[-20.,20])
if includeorbit:
bovy_plot.bovy_plot(pox,poz,'o',color='0.5',mec='none',overplot=True,ms=8)
bovy_plot.bovy_plot(pvec[0,:],pvec[1,:],'k--',overplot=True,lw=1.)
if includetrack:
d1= 'x'
d2= 'z'
sdf.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
sdft.plotTrack(d1=d1,d2=d2,interp=True,color='k',spread=0,
overplot=True,lw=1.,scaleToPhysical=True)
bovy_plot.bovy_text(r'$M^p = 2\times 10^7\,M_\odot$'+'\n'+
r'$\sigma_v^p = 14\,\mathrm{km\,s}^{-1}$',
top_left=True,size=16.)
bovy_plot.bovy_end_print(plotfilename)
