def estimateDeltaStaeckel(R,z,pot=None):
"""
NAME:
estimateDeltaStaeckel
PURPOSE:
Estimate a good value for delta using eqn. (9) in Sanders (2012)
INPUT:
R,z = coordinates (if these are arrays, the median estimated delta is returned, i.e., if this is an orbit)
pot= Potential instance or list thereof
OUTPUT:
delta
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
if pot is None:
raise IOError("pot= needs to be set to a Potential instance or list thereof")
if isinstance(R,nu.ndarray):
delta2= nu.array([(z[ii]**2.-R[ii]**2. #eqn. (9) has a sign error
+(3.*R[ii]*evaluatezforces(R[ii],z[ii],pot)
-3.*z[ii]*evaluateRforces(R[ii],z[ii],pot)
+R[ii]*z[ii]*(evaluateR2derivs(R[ii],z[ii],pot)
-evaluatez2derivs(R[ii],z[ii],pot)))/evaluateRzderivs(R[ii],z[ii],pot)) for ii in range(len(R))])
indx= (delta2 < 0.)*(delta2 > -10.**-10.)
delta2[indx]= 0.
delta2= nu.median(delta2[True-nu.isnan(delta2)])
else:
delta2= (z**2.-R**2. #eqn. (9) has a sign error
+(3.*R*evaluatezforces(R,z,pot)
-3.*z*evaluateRforces(R,z,pot)
+R*z*(evaluateR2derivs(R,z,pot)
-evaluatez2derivs(R,z,pot)))/evaluateRzderivs(R,z,pot))
if delta2 < 0. and delta2 > -10.**-10.: delta2= 0.
return nu.sqrt(delta2)
def estimateDeltaStaeckel(pot,R,z):
"""
NAME:
estimateDeltaStaeckel
PURPOSE:
Estimate a good value for delta using eqn. (9) in Sanders (2012)
INPUT:
pot - Potential instance or list thereof
R,z- coordinates (if these are arrays, the median estimated delta is returned, i.e., if this is an orbit)
OUTPUT:
delta
HISTORY:
2013-08-28 - Written - Bovy (IAS)
2016-02-20 - Changed input order to allow physical conversions - Bovy (UofT)
"""
if isinstance(R,nu.ndarray):
delta2= nu.array([(z[ii]**2.-R[ii]**2. #eqn. (9) has a sign error
+(3.*R[ii]*_evaluatezforces(pot,R[ii],z[ii])
-3.*z[ii]*_evaluateRforces(pot,R[ii],z[ii])
+R[ii]*z[ii]*(evaluateR2derivs(pot,R[ii],z[ii],
use_physical=False)
-evaluatez2derivs(pot,R[ii],z[ii],
use_physical=False)))/evaluateRzderivs(pot,R[ii],z[ii],use_physical=False)) for ii in range(len(R))])
indx= (delta2 < 0.)*(delta2 > -10.**-10.)
delta2[indx]= 0.
delta2= nu.median(delta2[True-nu.isnan(delta2)])
else:
delta2= (z**2.-R**2. #eqn. (9) has a sign error
+(3.*R*_evaluatezforces(pot,R,z)
-3.*z*_evaluateRforces(pot,R,z)
+R*z*(evaluateR2derivs(pot,R,z,use_physical=False)
-evaluatez2derivs(pot,R,z,use_physical=False)))/evaluateRzderivs(pot,R,z,use_physical=False))
if delta2 < 0. and delta2 > -10.**-10.: delta2= 0.
return nu.sqrt(delta2)
def fdotdotSB1cal(ldeg, bdeg, dkpc, mul, mub, Rpkpc, zkpc, vrad, coslam, alpha,
appl, apz, aspl, aT, MWPot):
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
yrts = par.yrts
c = par.c
kpctom = par.kpctom
Rs = Rskpc * kpctom
mastorad = par.mastorad
normpottoSI = par.normpottoSI
normForcetoSI = par.normForcetoSI
normjerktoSI = par.normjerktoSI
b = bdeg * par.degtorad
l = ldeg * par.degtorad
muT = (mub**2. + mul**2.)**0.5
zdot = (1000.0 * vrad) * math.sin(b) + (mastorad / yrts) * mub * (
dkpc * kpctom) * math.cos(b)
Rpdot = (1. / (Rpkpc * kpctom)) * (
((dkpc * kpctom) *
(math.cos(b)**2.) - Rs * math.cos(b) * math.cos(l)) *
(1000.0 * vrad) + (Rs * (dkpc * kpctom) * math.sin(b) * math.cos(l) -
((dkpc * kpctom)**2.) * math.cos(b) * math.sin(b)) *
((mastorad / yrts) * mub) + Rs * (dkpc * kpctom) * math.sin(l) *
((mastorad / yrts) * mul))
#phiR2a = evaluateR2derivs(MWPot,Rpkpc/Rskpc,zkpc/Rskpc)
phiR2 = normjerktoSI * evaluateR2derivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiz2 = normjerktoSI * evaluatez2derivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiRz = normjerktoSI * evaluateRzderivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiR2sun = normjerktoSI * evaluateR2derivs(MWPot, Rskpc / Rskpc,
0.0 / Rskpc)
phiRzsun = normjerktoSI * evaluateRzderivs(MWPot, Rskpc / Rskpc,
0.0 / Rskpc)
aspldot = phiR2sun * Rpdot + phiRzsun * zdot
appldot = phiR2 * Rpdot + phiRz * zdot
apzdot = phiRz * Rpdot + phiz2 * zdot
#if coslam != 0.0 and Rpkpc != 0.0 and math.cos(b) != 0.0:
lamdot = (1. / coslam) * ((Rs * math.cos(l) * ((mastorad / yrts) * mul)) /
((Rpkpc * kpctom) * math.cos(b)) -
(Rs * math.sin(l) /
((Rpkpc * kpctom)**2.)) * Rpdot)
ardot1 = math.sin(b) * (appl * coslam + aspl * math.cos(l)) * (
(mastorad / yrts) * mub)
ardot2 = math.cos(b) * (appldot * coslam + aspldot * math.cos(l))
ardot3 = apzdot * math.sin(b)
ardot4 = appl * math.cos(b) * (Rskpc * math.sin(l) / Rpkpc) * lamdot
ardot5 = aspl * math.sin(l) * ((mastorad / yrts) * mul)
ardot6 = apz * math.cos(b) * ((mastorad / yrts) * mub)
ardot = ardot1 - ardot2 - ardot3 + ardot4 + ardot5 - ardot6
jerkt = (1. / c) * (ardot - aT *
((mastorad / yrts) * muT) * math.cos(alpha))
return jerkt
def gamma(R, z):
if not isinstance(R, u.Quantity):
R = R * u.kpc
if not isinstance(z, u.Quantity):
z = z * u.kpc
r = numpy.sqrt(R**2. + z**2.)
return numpy.sqrt(3. + r**2. / (220. * u.km / u.s)**2.
* evaluateR2derivs(MWPotential2014, R, z, ro=8., vo=220.)) / 1.9 * 1.5
def estimateDeltaStaeckel(pot, R, z, no_median=False):
"""
NAME:
estimateDeltaStaeckel
PURPOSE:
Estimate a good value for delta using eqn. (9) in Sanders (2012)
INPUT:
pot - Potential instance or list thereof
R,z- coordinates (if these are arrays, the median estimated delta is returned, i.e., if this is an orbit)
no_median - (False) if True, and input is array, return all calculated values of delta (useful for quickly
estimating delta for many phase space points)
OUTPUT:
delta
HISTORY:
2013-08-28 - Written - Bovy (IAS)
2016-02-20 - Changed input order to allow physical conversions - Bovy (UofT)
"""
if isinstance(R, nu.ndarray):
delta2 = nu.array([
(
z[ii]**2. - R[ii]**2. #eqn. (9) has a sign error
+
(3. * R[ii] * _evaluatezforces(pot, R[ii], z[ii]) - 3. *
z[ii] * _evaluateRforces(pot, R[ii], z[ii]) + R[ii] * z[ii] *
(evaluateR2derivs(pot, R[ii], z[ii], use_physical=False) -
evaluatez2derivs(pot, R[ii], z[ii], use_physical=False))) /
evaluateRzderivs(pot, R[ii], z[ii], use_physical=False))
for ii in range(len(R))
])
indx = (delta2 < 0.) * (delta2 > -10.**-10.)
delta2[indx] = 0.
if not no_median:
delta2 = nu.median(delta2[True ^ nu.isnan(delta2)])
else:
delta2 = (
z**2. - R**2. #eqn. (9) has a sign error
+ (3. * R * _evaluatezforces(pot, R, z) -
3. * z * _evaluateRforces(pot, R, z) + R * z *
(evaluateR2derivs(pot, R, z, use_physical=False) -
evaluatez2derivs(pot, R, z, use_physical=False))) /
evaluateRzderivs(pot, R, z, use_physical=False))
if delta2 < 0. and delta2 > -10.**-10.: delta2 = 0.
return nu.sqrt(delta2)
def gamma(R, z):
if not isinstance(R, u.Quantity):
R = R * u.kpc
if not isinstance(z, u.Quantity):
z = z * u.kpc
r = numpy.sqrt(R**2. + z**2.)
#not sure if the value thing here is right
return numpy.sqrt(
3. + (r**2. / (220. * u.km / u.s)**2.).value *
evaluateR2derivs(MWPotential2014, R, z, ro=8., vo=220.)) / 1.9 * 1.5
def estimateDeltaStaeckel(R, z, pot=None):
"""
NAME:
estimateDeltaStaeckel
PURPOSE:
Estimate a good value for delta using eqn. (9) in Sanders (2012)
INPUT:
R,z = coordinates (if these are arrays, the median estimated delta is returned, i.e., if this is an orbit)
pot= Potential instance or list thereof
OUTPUT:
delta
HISTORY:
2013-08-28 - Written - Bovy (IAS)
"""
if pot is None: #pragma: no cover
raise IOError(
"pot= needs to be set to a Potential instance or list thereof")
if isinstance(R, nu.ndarray):
delta2 = nu.array([
(
z[ii]**2. - R[ii]**2. #eqn. (9) has a sign error
+ (3. * R[ii] * evaluatezforces(R[ii], z[ii], pot) - 3. *
z[ii] * evaluateRforces(R[ii], z[ii], pot) + R[ii] * z[ii] *
(evaluateR2derivs(R[ii], z[ii], pot) -
evaluatez2derivs(R[ii], z[ii], pot))) /
evaluateRzderivs(R[ii], z[ii], pot)) for ii in range(len(R))
])
indx = (delta2 < 0.) * (delta2 > -10.**-10.)
delta2[indx] = 0.
delta2 = nu.median(delta2[True - nu.isnan(delta2)])
else:
delta2 = (
z**2. - R**2. #eqn. (9) has a sign error
+ (3. * R * evaluatezforces(R, z, pot) -
3. * z * evaluateRforces(R, z, pot) + R * z *
(evaluateR2derivs(R, z, pot) - evaluatez2derivs(R, z, pot))) /
evaluateRzderivs(R, z, pot))
if delta2 < 0. and delta2 > -10.**-10.: delta2 = 0.
return nu.sqrt(delta2)
def fdotdotSB1cal(ldeg, bdeg, dkpc, mul, mub, vrad):
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
yrts = par.yrts
c = par.c
kpctom = par.kpctom
Rs = Rskpc * kpctom
mastorad = par.mastorad
normpottoSI = par.normpottoSI
normForcetoSI = par.normForcetoSI
normjerktoSI = par.normjerktoSI
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rpkpc = par.Rpkpc(ldeg, bdeg, dkpc)
zkpc = par.z(ldeg, bdeg, dkpc)
fex_pl = excGal.Expl(ldeg, bdeg, dkpc)
fex_z = excGal.Exz(ldeg, bdeg, dkpc)
fex_shk = Shk.Exshk(dkpc, mul, mub)
fex_tot = fex_pl + fex_z + fex_shk
#mub = mu_alpha #mas/yr
#mul = mu_delta
muT = (mub**2. + mul**2.)**0.5
#MWPotential2014= [MWPotential2014,KeplerPotential(amp=4*10**6./bovy_conversion.mass_in_msol(par.Vs,par.Rskpc))]
MWPot = MWPotential2014
appl = -evaluateRforces(MWPot, Rpkpc / Rskpc, zkpc / Rskpc) * normForcetoSI
aspl = -evaluateRforces(MWPot, Rskpc / Rskpc, 0.0 / Rskpc) * normForcetoSI
apz = evaluatezforces(MWPot, Rpkpc / Rskpc, zkpc / Rskpc) * normForcetoSI
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
coslam = be * (Rskpc / Rpkpc)
coslpluslam = math.cos(l) * coslam - (Rskpc * math.sin(l) /
Rpkpc) * math.sin(l)
aTl1 = -(appl * (Rskpc * math.sin(l) / Rpkpc) - aspl * math.sin(l))
aTb1 = appl * coslam * math.sin(b) + apz * math.cos(b) + aspl * math.cos(
l) * math.sin(b)
aTnet1 = (aTl1**2. + aTb1**2.)**(0.5)
alphaV1 = math.atan2(mub, mul) / par.degtorad
alphaA1 = math.atan2(aTb1, aTl1) / par.degtorad
if alphaV1 < 0.:
alphaV = 360. + alphaV1
else:
alphaV = alphaV1
if alphaA1 < 0.:
alphaA = 360. + alphaA1
else:
alphaA = alphaA1
alpha = abs(alphaA - alphaV)
aT1 = 2. * appl * aspl * coslpluslam
aT2 = (c * (fex_pl + fex_z))**2.
aTsq = appl**2. + aspl**2. + aT1 + apz**2. - aT2
#if aTsq < 0.0:
aT = (appl**2. + aspl**2. + aT1 + apz**2. - aT2)**0.5
zdot = (1000.0 * vrad) * math.sin(b) + (mastorad / yrts) * mub * (
dkpc * kpctom) * math.cos(b)
Rpdot = (1. / (Rpkpc * kpctom)) * (
((dkpc * kpctom) *
(math.cos(b)**2.) - Rs * math.cos(b) * math.cos(l)) *
(1000.0 * vrad) + (Rs * (dkpc * kpctom) * math.sin(b) * math.cos(l) -
((dkpc * kpctom)**2.) * math.cos(b) * math.sin(b)) *
((mastorad / yrts) * mub) + Rs * (dkpc * kpctom) * math.sin(l) *
((mastorad / yrts) * mul))
phiR2 = normjerktoSI * evaluateR2derivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiz2 = normjerktoSI * evaluatez2derivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiRz = normjerktoSI * evaluateRzderivs(MWPot, Rpkpc / Rskpc, zkpc / Rskpc)
phiR2sun = normjerktoSI * evaluateR2derivs(MWPot, Rskpc / Rskpc,
0.0 / Rskpc)
phiRzsun = normjerktoSI * evaluateRzderivs(MWPot, Rskpc / Rskpc,
0.0 / Rskpc)
aspldot = phiR2sun * Rpdot + phiRzsun * zdot
appldot = phiR2 * Rpdot + phiRz * zdot
if b > 0:
apzdot = phiRz * Rpdot + phiz2 * zdot
else:
apzdot = -(phiRz * Rpdot + phiz2 * zdot)
#if coslam != 0.0 and Rpkpc != 0.0 and math.cos(b) != 0.0:
lamdot = (1. / coslam) * ((Rs * math.cos(l) * ((mastorad / yrts) * mul)) /
((Rpkpc * kpctom) * math.cos(b)) -
(Rs * math.sin(l) /
((Rpkpc * kpctom)**2.)) * Rpdot)
ardot1 = math.sin(b) * (appl * coslam + aspl * math.cos(l)) * (
(mastorad / yrts) * mub)
ardot2 = math.cos(b) * (appldot * coslam + aspldot * math.cos(l))
ardot3 = apzdot * math.sin(abs(b))
ardot4 = appl * math.cos(b) * (Rskpc * math.sin(l) / Rpkpc) * lamdot
ardot5 = aspl * math.sin(l) * ((mastorad / yrts) * mul)
ardot6 = abs(apz) * math.cos(b) * ((mastorad / yrts) * mub) * (b / abs(b))
ardot = ardot1 - ardot2 - ardot3 + ardot4 + ardot5 - ardot6
jerkt = (1. / c) * (ardot - aT *
((mastorad / yrts) * muT) * math.cos(alpha))
return jerkt
def plhalo_from_dlnvcdlnr(dlnvcdlnr,diskpot,bulgepot,fh):
"""Calculate the halo's shape corresponding to this rotation curve derivative"""
#First calculate the derivatives dvc^2/dR of disk and bulge
dvcdr_disk= -potential.evaluateRforces(1.,0.,diskpot)+potential.evaluateR2derivs(1.,0.,diskpot)
dvcdr_bulge= -potential.evaluateRforces(1.,0.,bulgepot)+potential.evaluateR2derivs(1.,0.,bulgepot)
return 2.-(2.*dlnvcdlnr-dvcdr_disk-dvcdr_bulge)/fh