def Findlt_King62(l, sp, potential, xv):
"""
Auxiliary function for 'ltidal', which returns the
left-hand side - right-hand side
of the King62 equation for tidal radius, as in eq.(12.21) of
Mo, van den Bosch, White 10
Syntax:
Findlt_King62(l,sp,potential,xv)
where
l: radius in the satellite [kpc] (float)
sp: satellite potential (an object define in profiles.py)
potential: host potential (a density profile object, or a list of
such objects that constitute a composite potential)
xv: phase-space coordinates [R,phi,z,VR,Vphi,Vz] in units of
[kpc,radian,kpc,kpc/Gyr,kpc/Gyr,kpc/Gyr] (float array)
"""
r = np.sqrt(xv[0]**2. + xv[2]**2.)
r1 = r * (1. - cfg.eps)
r2 = r * (1. + cfg.eps)
Om = Omega(xv)
m = sp.M(l)
M = pr.M(potential, r)
M1 = pr.M(potential, r1)
M2 = pr.M(potential, r2)
dlnMdlnr = (np.log(M2) - np.log(M1)) / (np.log(r2) - np.log(r1))
return l - r * (m / M /
(2. + Om**2. * r**3 / cfg.G / M - dlnMdlnr))**(1. / 3.)
def get_T(r,
params,
m=0.,
add_params=[],
Ttype='jeans-alpha',
do_smooth=False,
polyorder=3,
sigma=21,
mode='interp',
rlim=[-2, 0]):
alpha, beta, gamma, p = params
if Ttype[-5:] == 'Mreal':
M = array(add_params) + array(m)
else:
M = prf.M(r, p, model='an') + m
Rvir = p[-2]
if Ttype == 'jeans-alpha' or Ttype == 'jeans' or Ttype == 'jeans-Mreal' or Ttype == 'alpha-p-Mreal':
denominator = get_denominator(r, params, Ttype=Ttype)
T = 0.5 * (3. - 2 * beta) / denominator * G * M / r
elif Ttype == 'alpha' or Ttype == 'alpha-Mreal' or Ttype == 'betazero' or Ttype == 'gamma-Treal':
denominator = get_denominator(r, params, Ttype=Ttype)
T = 1.5 / denominator * G * M / r
elif Ttype == 'zero':
T = zeros_like(r)
elif Ttype == 'virial' or Ttype == 'virial-Mreal':
T = 0.5 * G * M / r
elif Ttype == 'jeans-smooth':
T = 0.5 * (3. - 2 * beta) / denominator * G * M / r
do_smooth = True
elif Ttype == 'Tdekel':
# T from hydrostatic equilibrum (sigmar)
(c, a, b, g, Rvir, Mvir) = p
x = r / Rvir * c
sigmar2 = prf.sigmar2_dekel_m(x, Mvir, Rvir, c, a, m=m, mtype='center')
T = 1.5 * sigmar2
elif Ttype == 'Tmulti':
(c, a, b, g, Rvir, Mvir) = p
[Mratio, n] = add_params
x = r / Rvir * c
T = prf.K_Mratio(x, Mvir, Rvir, c, a, Mratio, n, m)
if do_smooth:
r_range = where((log10(r / Rvir) >= rlim[0])
& (log10(r / Rvir) < rlim[1]))
T_smooth = nan * ones(size(T))
T_smooth[r_range] = savgol_filter(T[r_range],
sigma,
polyorder,
deriv=0,
mode=mode,
delta=diff(log10(r))[0])
T = T_smooth
return T
def fit_prof_constrained(r,
data,
params,
constraint=(),
w=1,
model='an',
y='brho',
xi1=0.015,
xi2=1.000):
#least squares fitting
result = minimize(min_res,
params,
args=(r, data, w, model, y),
method='SLSQP',
constraints=constraint)
p = result2p(result, model)
Rvir = p[-2]
Mvir = p[-1]
brho = prf.brho(r, p, model)
rho = prf.rho(r, p, model)
bs = prf.bs(r, p, model)
s = prf.s(r, p, model)
M = prf.M(r, p, model)
V = prf.V(r, p, model)
if y == 'brho':
rms = rmslog(brho, data)
if y == 'rho':
rms = rmslog(rho, data)
try:
c2 = Rvir / r[bisect(bs, 2) - 1]
except:
c2 = 0
return {
'p': p,
'brho': brho,
'rho': rho,
'bs': bs,
's': s,
'M': M,
'V': V,
's1': prf.s(xi1 * Rvir, p, model),
's2': prf.s(xi2 * Rvir, p, model),
'bs1': prf.bs(xi1 * Rvir, p, model),
'bs2': prf.bs(xi2 * Rvir, p, model),
'c2': c2,
'rms': rms,
'Merr': (prf.calc_total_mass(r, rho, Rvir) - Mvir) / Mvir
}
def E_diff(ri,
pi,
pf,
m,
alphai=0.,
alphaf=0.,
gammai=0.,
gammaf=0.,
betai=0.,
betaf=0.,
Ttype='jeans',
model='an',
method='halo',
add_params=[],
do_smooth=False):
#returns the energy difference of the mass enclosing shell between the before and after states. the difference should be ideally zero according to the model
if Ttype[-5:] == 'Mreal':
Mi = array(add_params)
else:
Mi = prf.M(ri, pi, model)
rf = prf.inv_M(Mi, pf, model) #the new radii that enclose the same masses
Ui = prf.U(ri, pi, model)
Uf = prf.U(rf, pf, model)
if Ttype == 'gamma-Treal':
Treal = add_params
gammai = 1.5 * G * Mi / ri / Treal - prf.alpha_Dekel(ri, pi)
gammaf = gammai
Ti = get_T(ri, [alphai, betai, gammai, pi],
m=0.,
add_params=add_params,
Ttype=Ttype,
do_smooth=do_smooth)
Tf = get_T(rf, [alphaf, betaf, gammaf, pf],
m=m,
add_params=add_params,
Ttype=Ttype,
do_smooth=do_smooth)
Ei = Ui - G * m / ri + Ti #0.5*G*Mi/ri
Ef = Uf - G * m / rf + Tf #0.5*G*Mi/rf
return array([Ef - Ei, (Ef - Ei) / abs(Ei)], dtype=float)
def evolve(r,
ri,
Mi,
pi,
m,
alphai=0.,
alphaf=0.,
gammai=0.,
gammaf=0.,
betai=0.,
betaf=0.,
Ttype='jeans',
Mcen=0,
w=1,
model='an',
method='halo',
add_params=[],
Rvirf=0.,
Mvirf=0.,
component='d'):
gamma = 0.
if method == 'halo' or method == 'halo_noUex':
if model == 'an':
(ci, ai, bi, gi, Rviri, Mviri) = pi
if Rvirf == 0.: Rvirf = Rviri
if Mvirf == 0.: Mvirf = Mviri
paramsf = Parameters()
paramsf.add('c', value=ci, min=1e-16, vary=True)
paramsf.add('a', value=ai, vary=True)
paramsf.add('b', value=bi, vary=False)
paramsf.add('g', value=gi, vary=False)
paramsf.add('Rvir', value=float(Rvirf), vary=False)
if component == 'd':
paramsf.add('Mvir', value=float(Mvirf), vary=False)
else:
paramsf.add('Mvir', value=float(Mvirf), vary=True)
if Ttype == 'jeans-gamma':
paramsf.add('gamma',
value=float(gamma),
min=-1.,
max=1.,
vary=True)
result = minimize(min_E_diff,
paramsf,
args=(r, pi, m, alphai, alphaf, gammai, gammaf,
betai, betaf, Ttype, w, model, method,
add_params))
if Ttype == 'jeans-gamma':
gamma = result.values['gamma']
pf = fit.result2p(result, model)
#energy error calc
ere = E_diff(r, pi, pf, m, alphai, alphaf, gammai, gammaf, betai,
betaf, Ttype, model, method, add_params)[1]
errterms = [
log10(r / Rviri) < -1.33, #inner region
(log10(r / Rviri) >= -1.33) &
(log10(r / Rviri) <= -0.67), #middle region
log10(r / Rviri) > -0.67, #outer region
r == r
] #all
ererms = [sqrt(mean(ere[errterm]**2)) for errterm in errterms]
#cosider mass bath at center - important for a sequence
Mcenf = Mcen + m
rf = r
rf0 = prf.inv_M(Mi, pf)
Mf = prf.M(rf, pf, model)
return {
'ri': ri, #initial radii
'rf0': rf0, #final radii
'rf': rf, #final radii, sorted
'Mf': Mf, #final mass profile
'Mcenf': Mcenf, #final mass at center
'pi': pi, #initial profile parameters
'pf': pf, #final profile parameters
'gammaf': gamma, # gamma
'm': m, #added mass
'model': model, #profile model used
'method': method, #evolution method used
'ere': ere, #energy relative error array
'ererms': ererms
} #rms of energy relative error