def aplold(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b0dt91 = par.b0dt91
c = par.c
Rskpc = par.Rskpc
Rs = Rskpc * par.kpctom
Vs = par.Vs
Vsms = 1000.0 * Vs
l = ldeg * par.degtorad
b = bdeg * par.degtorad
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
t0 = math.sin(l) * math.sin(l) + be * be
vp = Vs + b0dt91 * (Rpkpc - Rskpc) # in km s^-1
vp_rat_square = (vp * vp) / (Vs * Vs)
t2 = (-1.0) * (math.cos(l) + vp_rat_square * (be / t0)) #dimensionless
t3 = (Vsms * Vsms) / (Rs) #in SI
adr = t2 * t3 #m sec^-2 (divide by c to get in s^-1)
adrc = adr / c #sec^-1
return adrc
def MWpl(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b = bdeg * par.degtorad
l = ldeg * par.degtorad
c = par.c
Rskpc = par.Rskpc
kpctom = par.kpctom
Vs = par.Vs
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
Vprat = VpratioMW(Rpkpc)
Vp = Vprat * Vs
zkpc = dkpc * math.sin(b)
Vsms = 1000.0 * Vs #m/s
Rs = Rskpc * kpctom
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
t0 = math.sin(l) * math.sin(l) + be * be
t2 = (-1.0) * (math.cos(l) + Vprat * Vprat * (be / t0)) #dimensionless
t3 = (Vsms * Vsms) / (Rs) #in SI
adr = t2 * t3 * math.cos(b) #m sec^-2 (divide by c to get in s^-1)
Excpl = adr / c #sec^-1
return Excpl
def aplmod(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b0reid14 = par.b0reid14
c = par.c
Rskpc = par.Rskpc
Rs = Rskpc * par.kpctom
Vs = par.Vs
Vsms = 1000.0 * Vs
l = ldeg * par.degtorad
b = bdeg * par.degtorad
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
t0 = math.sin(l) * math.sin(l) + be * be
Vpratio = Vprat(Rpkpc)
vp_rat_square = Vpratio * Vpratio
t2 = (-1.0) * (math.cos(l) + vp_rat_square * (be / t0)) #dimensionless
t3 = (Vsms * Vsms) / (Rs) #in SI
adr = t2 * t3 #m sec^-2 (divide by c to get in s^-1)
adrc = adr / c #sec^-1
return adrc
def MWBHZfo(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
zkpc = dkpc * math.sin(b)
'''
bp= PowerSphericalPotentialwCutoff(alpha=1.8,rc=1.9/8.,normalize=0.05)
mp= MiyamotoNagaiPotential(a=3./8.,b=0.28/8.,normalize=.6)
np= NFWPotential(a=16./8.,normalize=.35)
kp = KeplerPotential(amp=4*10**6./bovy_conversion.mass_in_msol(par.Vs,par.Rskpc))
MWBH = [bp,mp,np,kp]
zf1 = evaluatezforces(MWBH, Rpkpc/Rskpc,zkpc/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
'''
MWPotential2014wBH = [
MWPotential2014,
KeplerPotential(amp=4 * 10**6. /
bovy_conversion.mass_in_msol(par.Vs, par.Rskpc))
]
zf1 = evaluatezforces(MWPotential2014wBH, Rpkpc / Rskpc, zkpc /
Rskpc) * bovy_conversion.force_in_kmsMyr(Vs, Rskpc)
#MWPotential2014.append(KeplerPotential(amp=4*10**6./bovy_conversion.mass_in_msol(Vs,Rskpc)))
#zf1 = evaluatezforces(MWPotential2014, Rpkpc/Rskpc,zkpc/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
Excz = zf1 * conversion * math.sin(b) #s-1
return Excz
def MWZfo(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b = bdeg*par.degtorad
l = ldeg*par.degtorad
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
zkpc = dkpc*math.sin(b)
zf1 = evaluatezforces(MWPotential2014, Rpkpc/Rskpc,zkpc/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
Excz = zf1*conversion*math.sin(b)#s-1
return Excz;
def MWBHRfo(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
zkpc = dkpc * math.sin(b)
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
coslam = be * (Rskpc / Rpkpc)
'''
bp= PowerSphericalPotentialwCutoff(alpha=1.8,rc=1.9/8.,normalize=0.05)
mp= MiyamotoNagaiPotential(a=3./8.,b=0.28/8.,normalize=.6)
np= NFWPotential(a=16./8.,normalize=.35)
kp = KeplerPotential(amp=4*10**6./bovy_conversion.mass_in_msol(par.Vs,par.Rskpc))
MWBH = [bp,mp,np,kp]
rforce1 = evaluateRforces(MWBH, Rpkpc/Rskpc,zkpc/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
rfsun = evaluateRforces(MWBH, Rskpc/Rskpc,0.0/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
'''
#MWPotential2014.append(KeplerPotential(amp=4*10**6./bovy_conversion.mass_in_msol(Vs,Rskpc)))
#rforce1 = evaluateRforces(MWPotential2014, Rpkpc/Rskpc,zkpc/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
#rfsun = evaluateRforces(MWPotential2014, Rskpc/Rskpc,0.0/Rskpc)*bovy_conversion.force_in_kmsMyr(Vs,Rskpc)
MWPotential2014wBH = [
MWPotential2014,
KeplerPotential(amp=4 * 10**6. /
bovy_conversion.mass_in_msol(par.Vs, par.Rskpc))
]
rforce1 = evaluateRforces(MWPotential2014wBH, Rpkpc / Rskpc,
zkpc / Rskpc) * bovy_conversion.force_in_kmsMyr(
Vs, Rskpc)
rfsun = evaluateRforces(MWPotential2014wBH, Rskpc / Rskpc,
0.0 / Rskpc) * bovy_conversion.force_in_kmsMyr(
Vs, Rskpc)
#rf = (rforce1-rfsun)*conversion*math.cos(b) # s-1
rf0 = rforce1 * coslam + rfsun * math.cos(l)
rf = rf0 * conversion * math.cos(b) # s-1
return rf
def MWRfo(ldeg, sigl, bdeg, sigb, dkpc, sigd):
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rskpc = par.Rskpc
Vs = par.Vs
conversion = par.conversion
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
zkpc = dkpc * math.sin(b)
be = (dkpc / Rskpc) * math.cos(b) - math.cos(l)
coslam = be * (Rskpc / Rpkpc)
rforce1 = evaluateRforces(MWPotential2014, Rpkpc / Rskpc,
zkpc / Rskpc) * bovy_conversion.force_in_kmsMyr(
Vs, Rskpc)
rfsun = evaluateRforces(MWPotential2014, Rskpc / Rskpc,
0.0 / Rskpc) * bovy_conversion.force_in_kmsMyr(
Vs, Rskpc)
rf0 = rforce1 * coslam + rfsun * math.cos(l)
rf = rf0 * conversion * math.cos(b) # s-1
return rf
def err_DT91(ldeg, sigl, bdeg, sigb, dkpc, sigd):
sigVs = par.sigVs * 1000.0 #SI
sigRs = par.sigRs * par.kpctom #SI
sigb0dt = par.sigb0dt #Dimensionless
b0dt91 = par.b0dt91 #Dimensionless
c = par.c
Rskpc = par.Rskpc
Rs = Rskpc * par.kpctom #SI
Vs = par.Vs
Vsms = 1000.0 * Vs #SI
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
Vp = Vs * (1.0 - b0dt91 * (Rpkpc - Rskpc) / Rskpc) # in km s^-1
Vpms = 1000.0 * Vp #SI
Rp = Rpkpc * par.kpctom #SI
d = dkpc * par.kpctom #SI
beta = (dkpc * math.cos(b) / Rskpc) - math.cos(l)
t0 = math.sin(l) * math.sin(l) + beta * beta
def betabyd():
a = math.cos(b) / Rs
return a
def betabyb():
a = -d * math.sin(b) / Rs
return a
def betabyl():
a = math.sin(l)
return a
def betabyRs():
a = -d * math.cos(b) / (Rs * Rs)
return a
def Rpbyd():
a = (Rs * beta * betabyd()) / pow(t0, 0.5)
return a
def Rpbyb():
a = (Rs * beta * betabyb()) / pow(t0, 0.5)
return a
def Rpbyl():
a = (Rs *
(math.sin(l) * math.cos(l) + beta * betabyl())) / pow(t0, 0.5)
return a
def RpbyRs():
a = pow(t0, 0.5) + (Rs * beta * betabyRs()) / pow(t0, 0.5)
return a
def Vpbyb():
a = -(Vsms / Rs) * b0dt91 * Rpbyb()
return a
def Vpbyl():
a = -(Vsms / Rs) * b0dt91 * Rpbyl()
return a
def Vpbyd():
a = -(Vsms / Rs) * b0dt91 * Rpbyd()
return a
def VpbyRs():
a = (Vsms * b0dt91 * Rp /
(Rs * Rs)) - ((Vsms / Rs) * b0dt91 * RpbyRs())
return a
def VpbyVs():
a = 1.0 - b0dt91 * (Rp - Rs) / Rs
return a
def Vpbyb0dt():
a = -Vsms * (Rp - Rs) / Rs
return a
def diffbyb():
term1 = math.cos(l) * math.sin(b) * Vsms * Vsms / (c * Rs)
term2 = math.sin(b) * beta * Vpms * Vpms / (c * Rs * t0)
term3 = -math.cos(b) * Vpms * Vpms * betabyb() / (c * Rs * t0)
term4 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyb() / (
c * Rs * t0 * t0)
term5 = -2.0 * math.cos(b) * beta * Vpms * Vpbyb() / (c * Rs * t0)
a = term1 + term2 + term3 + term4 + term5
return a
def diffbyl():
term1 = math.sin(l) * math.cos(b) * Vsms * Vsms / (c * Rs)
term2 = -math.cos(b) * Vpms * Vpms * betabyl() / (c * Rs * t0)
term3 = -2.0 * math.cos(b) * beta * Vpms * Vpbyl() / (c * Rs * t0)
t4a = math.sin(l) * math.cos(l)
t4b = beta * betabyl()
term4 = 2.0 * math.cos(b) * beta * Vpms * Vpms * (t4a + t4b) / (
c * Rs * t0 * t0)
a = term1 + term2 + term3 + term4
return a
def diffbyd():
term1 = -math.cos(b) * Vpms * Vpms * betabyd() / (c * Rs * t0)
term2 = -2.0 * math.cos(b) * beta * Vpms * Vpbyd() / (c * Rs * t0)
term3 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyd() / (
c * Rs * t0 * t0)
a = term1 + term2 + term3
return a
def diffbyRs():
term1 = math.cos(l) * math.cos(b) * Vsms * Vsms / (c * Rs * Rs)
term2 = math.cos(b) * beta * Vpms * Vpms / (c * Rs * Rs * t0)
term3 = -math.cos(b) * Vpms * Vpms * betabyRs() / (c * Rs * t0)
term4 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyRs() / (
c * Rs * t0 * t0)
term5 = -2.0 * math.cos(b) * beta * Vpms * VpbyRs() / (c * Rs * t0)
a = term1 + term2 + term3 + term4 + term5
return a
def diffbyVs():
term1 = -2.0 * math.cos(b) * math.cos(l) * Vsms / (c * Rs)
term2 = -2.0 * math.cos(b) * beta * Vpms * VpbyVs() / (c * Rs * t0)
a = term1 + term2
return a
def diffbyb0dt():
a = -2.0 * math.cos(b) * beta * Vpms * Vpbyb0dt() / (c * Rs * t0)
return a
err_plsq = pow(diffbyb(), 2.0) * pow(sigb, 2.0) + pow(diffbyl(
), 2.0) * pow(sigl, 2.0) + pow(diffbyd(), 2.0) * pow(sigd, 2.0) + pow(
diffbyVs(), 2.0) * pow(sigVs, 2.0) + pow(diffbyRs(), 2.0) * pow(
sigRs, 2.0) + pow(diffbyb0dt(), 2.0) * pow(sigb0dt, 2.0)
err_pl = pow(err_plsq, 0.5)
return err_pl
def err_Reid14(ldeg, sigl, bdeg, sigb, dkpc, sigd):
sigVs = par.sigVs * 1000.0 #SI
sigRs = par.sigRs * par.kpctom #SI
sigb0r = par.sigb0r * 1000.0 / par.kpctom #SI
b0reid14 = par.b0reid14 * 1000.0 / par.kpctom #SI
c = par.c
Rskpc = par.Rskpc
Rs = Rskpc * par.kpctom #SI
Vs = par.Vs
Vsms = 1000.0 * Vs #SI
b = bdeg * par.degtorad
l = ldeg * par.degtorad
Rpkpc = par.Rpkpc(ldeg, sigl, bdeg, sigb, dkpc, sigd)
Vp = Vs + par.b0reid14 * (Rpkpc - Rskpc) # in km s^-1
Vpms = 1000.0 * Vp #SI
Rp = Rpkpc * par.kpctom #SI
d = dkpc * par.kpctom #SI
beta = (dkpc * math.cos(b) / Rskpc) - math.cos(l)
t0 = math.sin(l) * math.sin(l) + beta * beta
def betabyd():
a = math.cos(b) / Rs
return a
def betabyb():
a = -d * math.sin(b) / Rs
return a
def betabyl():
a = math.sin(l)
return a
def betabyRs():
a = -d * math.cos(b) / (Rs * Rs)
return a
def Rpbyd():
a = (Rs * beta * betabyd()) / pow(t0, 0.5)
return a
def Rpbyb():
a = (Rs * beta * betabyb()) / pow(t0, 0.5)
return a
def Rpbyl():
a = (Rs *
(math.sin(l) * math.cos(l) + beta * betabyl())) / pow(t0, 0.5)
return a
def RpbyRs():
a = pow(t0, 0.5) + (Rs * beta * betabyRs()) / pow(t0, 0.5)
return a
def Vpbyd():
a = b0reid14 * Rpbyd()
return a
def Vpbyb():
a = b0reid14 * Rpbyb()
return a
def Vpbyl():
a = b0reid14 * Rpbyl()
return a
def VpbyRs():
a = b0reid14 * (RpbyRs() - 1.0)
return a
def VpbyVs():
a = 1.0
return a
def Vpbyb0reid():
a = Rp - Rs
return a
def diffbyb():
term1 = math.cos(l) * math.sin(b) * Vsms * Vsms / (c * Rs)
term2 = math.sin(b) * beta * Vpms * Vpms / (c * Rs * t0)
term3 = -math.cos(b) * Vpms * Vpms * betabyb() / (c * Rs * t0)
term4 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyb() / (
c * Rs * t0 * t0)
term5 = -2.0 * math.cos(b) * beta * Vpms * Vpbyb() / (c * Rs * t0)
a = term1 + term2 + term3 + term4 + term5
return a
def diffbyl():
term1 = math.sin(l) * math.cos(b) * Vsms * Vsms / (c * Rs)
term2 = -math.cos(b) * Vpms * Vpms * betabyl() / (c * Rs * t0)
term3 = -2.0 * math.cos(b) * beta * Vpms * Vpbyl() / (c * Rs * t0)
t4a = math.sin(l) * math.cos(l)
t4b = beta * betabyl()
term4 = 2.0 * math.cos(b) * beta * Vpms * Vpms * (t4a + t4b) / (
c * Rs * t0 * t0)
a = term1 + term2 + term3 + term4
return a
def diffbyd():
term1 = -math.cos(b) * Vpms * Vpms * betabyd() / (c * Rs * t0)
term2 = -2.0 * math.cos(b) * beta * Vpms * Vpbyd() / (c * Rs * t0)
term3 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyd() / (
c * Rs * t0 * t0)
a = term1 + term2 + term3
return a
def diffbyRs():
term1 = math.cos(l) * math.cos(b) * Vsms * Vsms / (c * Rs * Rs)
term2 = math.cos(b) * beta * Vpms * Vpms / (c * Rs * Rs * t0)
term3 = -math.cos(b) * Vpms * Vpms * betabyRs() / (c * Rs * t0)
term4 = 2.0 * math.cos(b) * beta * beta * Vpms * Vpms * betabyRs() / (
c * Rs * t0 * t0)
term5 = -2.0 * math.cos(b) * beta * Vpms * VpbyRs() / (c * Rs * t0)
a = term1 + term2 + term3 + term4 + term5
return a
def diffbyVs():
term1 = -2.0 * math.cos(b) * math.cos(l) * Vsms / (c * Rs)
term2 = -2.0 * math.cos(b) * beta * Vpms * VpbyVs() / (c * Rs * t0)
a = term1 + term2
return a
def diffbyb0reid():
a = -2.0 * math.cos(b) * beta * Vpms * Vpbyb0reid() / (c * Rs * t0)
return a
err_plsq = pow(diffbyb(), 2.0) * pow(sigb, 2.0) + pow(diffbyl(
), 2.0) * pow(sigl, 2.0) + pow(diffbyd(), 2.0) * pow(sigd, 2.0) + pow(
diffbyVs(), 2.0) * pow(sigVs, 2.0) + pow(diffbyRs(), 2.0) * pow(
sigRs, 2.0) + pow(diffbyb0reid(), 2.0) * pow(sigb0r, 2.0)
err_pl = pow(err_plsq, 0.5)
return err_pl