def calAcc(r, v) :
N = r.shape[0]
a = np.zeros([N,3])
dt_min = np.ones(N)*1e5*yrs
dr = r
dx = r[:,0]
dy = r[:,1]
dz = r[:,2]
dv = v
dr_gp = np.sqrt(dx*dx + dy*dy)/(r0*kpc) # galpy units
dz_gp = dz/(r0*kpc)
drNorm = np.linalg.norm(dr, axis = 1)
acc = None
if useNFW :
m, rho, sigma = NFWmass( drNorm)
acc = -G*m/(drNorm*drNorm)[:,np.newaxis]*dr/drNorm[:,np.newaxis]
elif useHernquist:
m, rho, sigma = hernquistmass( drNorm)
acc = -G*m/(drNorm*drNorm)[:,np.newaxis]*dr/drNorm[:,np.newaxis]
else :
acc = np.zeros([dr_gp.size,3])
conv = 1e-13*1e5
for i, x_gp, y_gp, r_gp, z_gp in zip(range(dr_gp.size), dx/(r0*kpc), dy/(r0*kpc), dr_gp, dz_gp) :
a = gp.evaluateRforces(MWpot,r_gp,z_gp)*bovy_conversion.force_in_10m13kms2(v0,r0)*conv
acc[i,0] = a*x_gp/r_gp
acc[i,1] = a*y_gp/r_gp
acc[i,2] = gp.evaluatezforces(MWpot,r_gp,z_gp)*bovy_conversion.force_in_10m13kms2(v0,r0)*conv
dt_rmin = np.min(drNorm/np.linalg.norm(dv, axis=1))
dt_amin = np.min(np.linalg.norm(dv,axis=1)/np.maximum(np.linalg.norm(acc,axis=1), TINY))
dt_min = min(dt_rmin, dt_amin)
if(args.use_DF) :
acc = acc + accDF( r, v)
return acc, dt_min
def accmaps(npix=200):
#First setup the potential, the following are the best-fit parameters from the Sec. 5 of our paper
#params= numpy.array([-1.33663190049,0.998420232634,-3.49031638164,0.31949840593,-1.63965169376])
params= numpy.array([-1.33663190049,0.998420232634,-3.0736938150237028,0.31949840593,-1.63965169376]) #this has a scale height of 360 pc
try:
pot= setup_potential(params)
except RuntimeError: #if this set of parameters gives a nonsense potential
raise
#Setup grid and output
Rs= numpy.linspace(0.01,20.,npix)/_REFR0
Zs= numpy.linspace(0.,20.,npix)/_REFR0
accR_dm= numpy.empty((len(Rs),len(Zs)))
accZ_dm= numpy.empty((len(Rs),len(Zs)))
accR_baryon= numpy.empty((len(Rs),len(Zs)))
accZ_baryon= numpy.empty((len(Rs),len(Zs)))
#Calculate accelerations
for ii in range(len(Rs)):
for jj in range(len(Zs)):
accR_dm[ii,jj]= potential.evaluateRforces(Rs[ii],Zs[jj],[pot[0]])
accZ_dm[ii,jj]= potential.evaluatezforces(Rs[ii],Zs[jj],[pot[0]])
accR_baryon[ii,jj]= potential.evaluateRforces(Rs[ii],Zs[jj],pot[1:])
accZ_baryon[ii,jj]= potential.evaluatezforces(Rs[ii],Zs[jj],pot[1:])
accR_dm*= bovy_conversion.force_in_10m13kms2(_REFV0*params[1],_REFR0)
accZ_dm*= bovy_conversion.force_in_10m13kms2(_REFV0*params[1],_REFR0)
accR_baryon*= bovy_conversion.force_in_10m13kms2(_REFV0*params[1],_REFR0)
accZ_baryon*= bovy_conversion.force_in_10m13kms2(_REFV0*params[1],_REFR0)
return (accR_dm,accZ_dm,accR_baryon,accZ_baryon,Rs,Zs)
def test_force_in_10m13kms2():
#Test the scaling, as a 1st derivative of the potential, should scale as velocity^2/position
vofid, rofid = 200., 8.
assert numpy.fabs(
4. * bovy_conversion.force_in_10m13kms2(vofid, rofid) /
bovy_conversion.force_in_10m13kms2(2. * vofid, rofid) -
1.) < 10.**-10., 'force_in_10m13kms2 did not work as expected'
assert numpy.fabs(
.5 * bovy_conversion.force_in_10m13kms2(vofid, rofid) /
bovy_conversion.force_in_10m13kms2(vofid, 2 * rofid) -
1.) < 10.**-10., 'force_in_10m13kms2 did not work as expected'
return None
def calAcc(r, v):
N = r.shape[0]
a = np.zeros([N, 3])
dt_min = np.ones(N) * 1e5 * yrs
dr = r
dx = r[:, 0]
dy = r[:, 1]
dz = r[:, 2]
dv = v
dr_gp = np.sqrt(dx * dx + dy * dy) / (r0 * kpc) # galpy units
dz_gp = dz / (r0 * kpc)
drNorm = np.linalg.norm(dr, axis=1)
acc = None
if useNFW:
m, rho, sigma = NFWmass(drNorm)
acc = -G * m / (drNorm *
drNorm)[:, np.newaxis] * dr / drNorm[:, np.newaxis]
elif useHernquist:
m, rho, sigma = hernquistmass(drNorm)
acc = -G * m / (drNorm *
drNorm)[:, np.newaxis] * dr / drNorm[:, np.newaxis]
else:
acc = np.zeros([dr_gp.size, 3])
conv = 1e-13 * 1e5
for i, x_gp, y_gp, r_gp, z_gp in zip(range(dr_gp.size),
dx / (r0 * kpc), dy / (r0 * kpc),
dr_gp, dz_gp):
a = gp.evaluateRforces(MWpot, r_gp,
z_gp) * bovy_conversion.force_in_10m13kms2(
v0, r0) * conv
acc[i, 0] = a * x_gp / r_gp
acc[i, 1] = a * y_gp / r_gp
acc[i, 2] = gp.evaluatezforces(
MWpot, r_gp, z_gp) * bovy_conversion.force_in_10m13kms2(
v0, r0) * conv
dt_rmin = np.min(drNorm / np.linalg.norm(dv, axis=1))
dt_amin = np.min(
np.linalg.norm(dv, axis=1) /
np.maximum(np.linalg.norm(acc, axis=1), TINY))
dt_min = min(dt_rmin, dt_amin)
if (args.use_DF):
acc = acc + accDF(r, v)
return acc, dt_min
def calAcc(r, v) :
N = r.shape[0]
dr = r
dx = r[:,0]
dy = r[:,1]
dz = r[:,2]
dv = v
dr_gp = np.sqrt(dx*dx + dy*dy)/(r0*kpc) # galpy units
dz_gp = dz/(r0*kpc)
drNorm = np.linalg.norm(dr, axis = 1)
acc = None
if useNFW :
m, rho, sigma = NFWmass( drNorm)
acc = -G*m/(drNorm*drNorm)[:,np.newaxis]*dr/drNorm[:,np.newaxis]
elif useHernquist:
m, rho, sigma = hernquistmass( drNorm)
acc = (-G*m/(drNorm*drNorm*drNorm))[:,np.newaxis]*dr#[:,np.newaxis]*dr
else :
acc = np.zeros([dr_gp.size,3])
conv = 1e-13*1e5
for i, x_gp, y_gp, r_gp, z_gp in zip(range(dr_gp.size), dx/(r0*kpc), dy/(r0*kpc), dr_gp, dz_gp) :
a = gp.evaluateRforces(MWpot,r_gp,z_gp)*bovy_conversion.force_in_10m13kms2(v0,r0)*conv
acc[i,0] = a*x_gp/r_gp
acc[i,1] = a*y_gp/r_gp
acc[i,2] = gp.evaluatezforces(MWpot,r_gp,z_gp)*bovy_conversion.force_in_10m13kms2(v0,r0)*conv
dt_rmin = np.min(drNorm/np.linalg.norm(dv, axis=1))
dt_amin = np.min(np.linalg.norm(dv,axis=1)/np.maximum(np.linalg.norm(acc,axis=1), TINY))
dt_min = min(dt_rmin, dt_amin)
if(useDF) :
acc[:Nsat,:] = acc[:Nsat,:] + accDF( r[:Nsat,:], v[:Nsat,:])
if(useTestParticles and Nsat < N and runSat) :
# include accelerations from other satellites for test particles
for i in range(Nsat) :
rsat = r[i]
dr = r[Nsat:,:] - rsat[np.newaxis,:]
drNorm = np.linalg.norm( dr, axis=1)
m, rho, sigma = hernquistmass( drNorm, m0=msat[i], vc200=vc200sat[i], r200=r200sat[i], c0=c0sat[i])
acc[Nsat:,:] = acc[Nsat:,:] - (G*m/(drNorm*drNorm*drNorm))[:,np.newaxis]*dr
return acc, dt_min
def test_force_in_10m13kms2():
#Test the scaling, as a 1st derivative of the potential, should scale as velocity^2/position
vofid, rofid= 200., 8.
assert numpy.fabs(4.*bovy_conversion.force_in_10m13kms2(vofid,rofid)/bovy_conversion.force_in_10m13kms2(2.*vofid,rofid)-1.) < 10.**-10., 'force_in_10m13kms2 did not work as expected'
assert numpy.fabs(.5*bovy_conversion.force_in_10m13kms2(vofid,rofid)/bovy_conversion.force_in_10m13kms2(vofid,2*rofid)-1.) < 10.**-10., 'force_in_10m13kms2 did not work as expected'
return None