def disc_mock(gp):
global K,C,D,F, zth, zp_kz, zmin, zmax, z0, z02
# Set up simple population here using analytic formulae:
zmin = 100. # [pc], first bin center
zmax = 1300. # [pc], last bin center
# get Stuetzpunkte for theoretical profiles (not yet stars, finer spacing in real space)
nth = 3*gp.nipol
zth = 1.* np.arange(nth) * (zmax-zmin)/(nth-1.) + zmin
z0 = 240. # [pc], scaleheight of first population
z02 = 200. # [pc], scaleheight of second population
D = 250. # [pc], scaleheight of all stellar tracers
K = 1.65
F = 1.65e-4
C = 17.**2. # [km/s] integration constant in sig
# Draw mock data:
nu_zth = np.exp(-zth/z0) # [1]
Kz_zth = -(K*zth/np.sqrt(zth**2.+D**2.) + 2.0 * F * zth)
if gp.adddarkdisc:
DD = 600 # [pc]
KD = 0.15 * 1.650
Kz_zth = Kz_zth - KD*zth/np.sqrt(zth**2. + DD**2.)
# calculate sig_z^2
inti = np.zeros(nth)
for i in range(1, nth):
inti[i] = simps(Kz_zth[:i]*nu_zth[:i], zth[:i])
sigzth = np.sqrt((inti + C) / nu_zth)
# project back to positions of stars
ran = npr.uniform(size=int(gp.ntracer[1-1])) # [1]
zstar = -z0 * np.log(1.0 - ran) # [pc] stellar positions
sigzstar = gh.ipol(zth, sigzth, zstar)
# > 0 ((IDL, Justin)) stellar velocity dispersion
# assign [0,1] * maxsig
ran2 = npr.normal(size=int(gp.ntracer[1-1])) # [1]
vzstar = ran2 * sigzstar # [km/s]
# Add second population [thick-disc like]:
if gp.pops == 2:
nu_zth2 = gp.ntracer[2-1]/gp.ntracer[1-1]*np.exp(-zth/z02)
# no normalization to 1
inti = np.zeros(nth)
for i in range(1, nth):
inti[i] = simps(Kz_zth[:i]*nu_zth2[:i], zth[:i])
sigzth2 = np.sqrt((inti + C) / nu_zth2) # same integration constant
ran = npr.uniform(-1., 1., gp.ntracer[2-1]) # [1]
zstar2 = -z02 * np.log(1.0 - ran) # [pc]
zstarobs = np.hstack([zstar, zstar2]) # concat pop1, pop2 for all stars
sigzstar2 = gh.ipol(zth, sigzth2, zstar2)
ran2 = npr.normal(-1., 1, gp.ntracer[2-1]) # [1]
vzstar2 = ran2 * sigzstar2 # [(km/2)^2]
# enforce observational cut on zmax:
sel = (zstar < zmax)
print('fraction of z<zmax selected elements: ', 1.*sum(sel)/(1.*len(sel)))
z_dat = zstar[sel]
vz_dat = vzstar[sel]
# throw away velocities of value zero (unstable?):
sel = (abs(vz_dat) > 0)
print('fraction of vz_dat>0 selected elements: ', 1.*sum(sel)/(1.*len(sel)))
z_dat = z_dat[sel]
vz_dat = vz_dat[sel]
# Calulate binned data (for plots/binned anal.). old way, linear spacings, no const #particles/bin
binmin, binmax, z_dat_bin, sig_dat_bin, count_bin = gh.binsmooth(z_dat, vz_dat, \
zmin, zmax, gp.nipol, 0.)
sig_dat_err_bin = sig_dat_bin / np.sqrt(count_bin)
nu_dat_bin, count_bin = gh.bincount(z_dat, binmax)
nu_dat_err_bin = nu_dat_bin / np.sqrt(count_bin)
renorm = max(nu_dat_bin)
nu_dat_bin = nu_dat_bin / renorm
nu_dat_err_bin = nu_dat_err_bin / renorm
# if only 1 pop, use 0 for all components
binmin0 = binmin; binmax0 = binmax; z_dat_bin0 = z_dat_bin
sig_dat_bin0 = sig_dat_bin; sig_dat_err_bin0 = sig_dat_err_bin
nu_dat_bin0 = nu_dat_bin; nu_dat_err_bin0 = nu_dat_err_bin
if gp.pops == 2:
# enforce observational constraint on z<z_max
sel = (zstar2 < zmax)
z_dat2 = zstar2[sel]
vz_dat2 = vzstar2[sel]
# cut zero velocities:
sel = (abs(vz_dat2) > 0)
z_dat2 = z_dat2[sel]
vz_dat2 = vz_dat2[sel]
# Calulate binned data (for plots/binned analysis):
binmin2, binmax2, z_dat_bin2, sig_dat_bin2, count_bin2 = gh.binsmooth(z_dat2, vz_dat2, \
zmin, zmax, gp.nipol, 0.)
sig_dat_err_bin2 = sig_dat_bin2 / np.sqrt(count_bin2)
nu_dat_bin2, count_bin2 = gh.bincount(z_dat2, binmax2)
nu_dat_err_bin2 = nu_dat_bin2 / np.sqrt(count_bin2)
renorm2 = max(nu_dat_bin2) # normalize by max density of first bin, rather
nu_dat_bin2 = nu_dat_bin2 / renorm2
nu_dat_err_bin2 = nu_dat_err_bin2 / renorm2
# CALCULATE PROPERTIES FOR ALL POP TOGETHER
z_dat0 = np.hstack([z_dat, z_dat2])
vz_dat0 = np.hstack([vz_dat, vz_dat2])
# Calulate binned data (for plots/binned anal.). old way, linear spacings, no const #particles/bin
binmin0, binmax0, z_dat_bin0, sig_dat_bin0, count_bin0 = gh.binsmooth(z_dat0, vz_dat0, \
zmin, zmax, gp.nipol, 0.)
sig_dat_err_bin0 = sig_dat_bin0 / np.sqrt(count_bin0)
# binmin, binmax, z_dat_bin = gh.bin_r_const_tracers(z_dat, gp.nipol)
nu_dat_bin0, count_bin0 = gh.bincount(z_dat0, binmax0)
nu_dat_err_bin0 = nu_dat_bin0 / np.sqrt(count_bin0)
renorm0 = max(nu_dat_bin0)
nu_dat_bin0 = nu_dat_bin0 / renorm0
nu_dat_err_bin0 = nu_dat_err_bin0 / renorm0
xip = np.copy(z_dat_bin0) # [pc]
gp.dat.binmin = binmin0
gp.dat.rbin = xip
gp.xipol = gp.dat.rbin
gp.Rscale.append(D) # [pc]
gp.Rscale.append(z0) # [pc]
maxr = max(gp.dat.rbin)
gp.xepol = np.hstack([gp.dat.rbin, 2*maxr, 4*maxr, 8*maxr])
gp.dat.binmax = binmax0
gp.dat.Mrdat = K*xip/np.sqrt(xip**2.+D**2.) / (2.0*np.pi*gu.G1__pcMsun_1km2s_2)
gp.dat.Mrerr = gp.dat.Mrdat*nu_dat_err_bin/nu_dat_bin
gp.dat.nu.append(nu_dat_bin0) # [Msun/pc^3], normalized to 1 at center
gp.dat.nuerr.append(nu_dat_err_bin0) # [Msun/pc^3], normalized
gp.dat.sig.append(sig_dat_bin0) # [km/s]
gp.dat.sigerr.append(sig_dat_err_bin0)# [km/s]
gp.dat.nu.append(nu_dat_bin) # [Msun/pc^3], normalized to 1
gp.dat.nuerr.append(nu_dat_err_bin) # [Msun/pc^3], normalized
gp.dat.sig.append(sig_dat_bin) # [km/s]
gp.dat.sigerr.append(sig_dat_err_bin) # [km/s]
if gp.pops == 2:
gp.Rscale.append(z02) # [pc]
gp.dat.nu.append(nu_dat_bin2) # [Msun/pc^3], normalized to 1
gp.dat.nuerr.append(nu_dat_err_bin2) # [Msun/pc^3], normalized
gp.dat.sig.append(sig_dat_bin2) # [km/s]
gp.dat.sigerr.append(sig_dat_err_bin2)# [km/s]
return gp.dat
def run(gp):
global K, C, D, F, zth, zp_kz, zmin, zmax, z0, z02
# Set up simple population here using analytic formulae:
zmin = 100.0 # [pc], first bin center
zmax = 1300.0 # [pc], last bin center
# get Stuetzpunkte for theoretical profiles (not yet stars, finer spacing in real space)
nth = gp.nipol # [1] number of bins
zth = 1.0 * np.arange(nth) * (zmax - zmin) / (nth - 1.0) + zmin # [pc] bin centers
z0 = 240.0 # [pc], scaleheight of first population
z02 = 200.0 # [pc], scaleheight of second population
D = 250.0 # [pc], scaleheight of all stellar tracers
K = 1.65
F = 1.65e-4
C = 17.0 ** 2.0 # [km/s] integration constant in sig
# Draw mock data from exponential disk:
nu_zth = np.exp(-zth / z0) # [nu0] = [Msun/A/pc] 3D tracer density
Kz_zth = -(K * zth / np.sqrt(zth ** 2.0 + D ** 2.0) + 2.0 * F * zth)
if gp.adddarkdisc:
DD = 600 # [pc] scaleheight of dark disc
KD = 0.15 * 1.650
Kz_zth = Kz_zth - KD * zth / np.sqrt(zth ** 2.0 + DD ** 2.0)
# calculate sig_z^2
inti = np.zeros(nth)
for i in range(1, nth):
inti[i] = simps(Kz_zth[:i] * nu_zth[:i], zth[:i])
sigzth = np.sqrt((inti + C) / nu_zth)
# project back to positions of stars
ran = npr.uniform(size=int(gp.ntracer[1 - 1])) # [1]
zstar = -z0 * np.log(1.0 - ran) # [pc] stellar positions, exponential falloff
sigzstar = gh.ipol(zth, sigzth, zstar)
# > 0 ((IDL, Justin)) stellar velocity dispersion
# assign [0,1] * maxsig
ran2 = npr.normal(size=int(gp.ntracer[1 - 1])) # [1]
vzstar = ran2 * sigzstar # [km/s]
# Add second population [thick-disc like]:
if gp.pops == 2:
nu_zth2 = gp.ntracer[2 - 1] / gp.ntracer[1 - 1] * np.exp(-zth / z02)
# [nu0,2] = [Msun/A/pc], 3D tracer density, exponentially falling
# no normalization to 1 done here
inti = np.zeros(nth)
for i in range(1, nth):
inti[i] = simps(Kz_zth[:i] * nu_zth2[:i], zth[:i])
sigzth2 = np.sqrt((inti + C) / nu_zth2) # same integration constant
ran = npr.uniform(-1.0, 1.0, gp.ntracer[2 - 1]) # [1]
zstar2 = -z02 * np.log(1.0 - ran) # [pc]
# zstarobs = np.hstack([zstar, zstar2]) # concat pop1, pop2 for all stars
sigzstar2 = gh.ipol(zth, sigzth2, zstar2)
ran2 = npr.normal(-1.0, 1, gp.ntracer[2 - 1]) # [1]
vzstar2 = ran2 * sigzstar2 # [(km/2)^2]
# enforce observational cut on zmax:
sel = zstar < zmax
print("fraction of z<zmax selected elements: ", 1.0 * sum(sel) / (1.0 * len(sel)))
z_dat1 = zstar[sel]
vz_dat1 = vzstar[sel]
# throw away velocities of value zero (unstable?):
sel = abs(vz_dat1) > 0
print("fraction of vz_dat>0 selected elements: ", 1.0 * sum(sel) / (1.0 * len(sel)))
z_dat1 = z_dat1[sel]
vz_dat1 = vz_dat1[sel]
# Calulate binned data (for plots/binned anal.). old way, linear spacings, no const #particles/bin
binmin1, binmax1, z_dat_bin1, sig_dat_bin1, count_bin1 = gh.binsmooth(z_dat1, vz_dat1, zmin, zmax, gp.nipol, 0.0)
sig_dat_err_bin1 = np.sqrt(sig_dat_bin1) # Poisson errors
nu_dat_bin1, nu_dat_err_bin1 = gh.bincount(z_dat1, binmax1)
nu_dat_bin1 /= binmax1 - binmin1
nu_dat_err_bin1 /= binmax1 - binmin1
import gr_params
gpr = gr_params.grParams(gp)
if gpr.showplots:
nuscaleb = nu_zth[np.argmin(np.abs(zth - z0))]
plt.loglog(zth, nu_zth / nuscaleb, "b.-")
nuscaler = nu_dat_bin1[np.argmin(np.abs(zth - z0))]
plt.loglog(zth, nu_dat_bin1 / nuscaler, "r.-")
# pdb.set_trace()
Sig_dat_bin1 = np.cumsum(nu_dat_bin1)
Sig_dat_err_bin1 = np.sqrt(Sig_dat_bin1)
Mrdat1 = np.cumsum(Sig_dat_bin1)
Mrerr1 = Mrdat1 * Sig_dat_err_bin1 / Sig_dat_bin1
scales = [[], [], []]
scales[1].append(z0) # [pc]
scales[1].append(Sig_dat_bin1[0])
scales[1].append(Mrdat1[-1])
scales[1].append(nu_dat_bin1[0])
scales[1].append(max(sig_dat_bin1))
# start analysis of "all stars" with only component 1,
# append to it later if more populations required
z_dat0 = z_dat1 # [pc]
vz_dat0 = vz_dat1 # [km/s]
if gp.pops == 2:
# enforce observational constraints on z<z_max
sel = zstar2 < zmax
z_dat2 = zstar2[sel]
vz_dat2 = vzstar2[sel]
# cut zero velocities:
sel = abs(vz_dat2) > 0
z_dat2 = z_dat2[sel]
vz_dat2 = vz_dat2[sel]
# Calulate binned data (for plots/binned analysis):
binmin2, binmax2, z_dat_bin2, sig_dat_bin2, count_bin2 = gh.binsmooth(
z_dat2, vz_dat2, zmin, zmax, gp.nipol, 0.0
)
sig_dat_err_bin2 = np.sqrt(sig_dat_bin2) # Poissonian errors
nu_dat_bin2, nu_dat_err_bin2 = gh.bincount(z_dat2, binmax2)
nu_dat_bin2 /= binmax2 - binmin2
nu_dat_err_bin2 /= binmax2 - binmin2
Sig_dat_bin2 = np.cumsum(nu_dat_bin2)
Sig_dat_err_bin2 = np.sqrt(Sig_dat_bin2)
Mrdat2 = np.cumsum(nu_dat_bin2)
Mrerr2 = np.sqrt(Mrdat2)
scales[2].append(z02) # [pc]
scales[2].append(Sig_dat_bin2[0])
scales[2].append(Mrdat2[-1])
scales[2].append(nu_dat_bin2[0]) # normalize by max density of first bin, rather
scales[2].append(max(sig_dat_bin2))
# calculate properties for all pop together with stacked values
z_dat0 = np.hstack([z_dat1, z_dat2])
vz_dat0 = np.hstack([vz_dat1, vz_dat2])
# Calulate binned data (for plots/binned anal.). old way, linear spacings, no const #particles/bin
binmin0, binmax0, z_dat_bin0, sig_dat_bin0, count_bin0 = gh.binsmooth(z_dat0, vz_dat0, zmin, zmax, gp.nipol, 0.0)
sig_dat_err_bin0 = np.sqrt(sig_dat_bin0)
# binmin, binmax, z_dat_bin = gh.bin_r_const_tracers(z_dat, gp.nipol)
nu_dat_bin0, nu_dat_err_bin0 = gh.bincount(z_dat0, binmax0)
nu_dat_bin0 /= binmax0 - binmin0
nu_dat_err_bin0 /= binmax0 - binmin0
Sig_dat_bin0 = np.cumsum(nu_dat_bin0)
Sig_dat_err_bin0 = np.sqrt(Sig_dat_bin0)
# renorm0 = max(nu_dat_bin0)
xip = np.copy(z_dat_bin0) # [pc]
Mrdat0 = K * xip / np.sqrt(xip ** 2.0 + D ** 2.0) / (2.0 * np.pi * gu.G1__pcMsun_1km2s_2)
Mrerr0 = Mrdat0 * nu_dat_err_bin0 / nu_dat_bin0
scales[0].append(D) # [pc]
scales[0].append(Sig_dat_bin0[0])
scales[0].append(Mrdat0[-1])
scales[0].append(nu_dat_bin0[0])
scales[0].append(max(sig_dat_bin0))
rmin = binmin0 / scales[0][0] # [pc]
rbin = xip / scales[0][0] # [pc]
rmax = binmax0 / scales[0][0] # [pc]
# store parameters for output
# normalized by scale values
nudat = []
nudat.append(nu_dat_bin0 / scales[0][3]) # [Msun/pc^3]
nudat.append(nu_dat_bin1 / scales[1][3])
if gp.pops == 2:
nudat.append(nu_dat_bin2 / scales[2][3])
nuerr = []
nuerr.append(nu_dat_err_bin0 / scales[0][3]) # [Msun/pc^3]
nuerr.append(nu_dat_err_bin1 / scales[1][3])
if gp.pops == 2:
nuerr.append(nu_dat_err_bin2 / scales[2][3])
Mrdat = []
Mrdat.append(Mrdat0 / scales[0][2]) # [Msun]
Mrdat.append(Mrdat1 / scales[1][2])
if gp.pops == 2:
Mrdat.append(Mrdat2 / scales[2][2])
Mrerr = []
Mrerr.append(Mrerr0 / scales[0][2]) # [Msun]
Mrerr.append(Mrerr1 / scales[1][2])
if gp.pops == 2:
Mrerr.append(Mrerr2 / scales[2][2])
Sigdat = []
Sigdat.append(Sig_dat_bin0 / scales[0][1])
Sigdat.append(Sig_dat_bin1 / scales[1][1])
if gp.pops == 2:
Sigdat.append(Sig_dat_bin2 / scales[2][1])
Sigerr = []
Sigerr.append(Sig_dat_err_bin0 / scales[0][1])
Sigerr.append(Sig_dat_err_bin1 / scales[1][1])
if gp.pops == 2:
Sigerr.append(Sig_dat_err_bin2 / scales[2][1])
sigdat = []
sigdat.append(sig_dat_bin0 / scales[0][4]) # [km/s]
sigdat.append(sig_dat_bin1 / scales[1][4])
if gp.pops == 2:
sigdat.append(sig_dat_bin2 / scales[2][4])
sigerr = []
sigerr.append(sig_dat_err_bin0 / scales[0][4]) # [km/s]
sigerr.append(sig_dat_err_bin1 / scales[1][4])
if gp.pops == 2:
sigerr.append(sig_dat_err_bin2 / scales[2][4])
write_disc_output_files(rbin, rmin, rmax, nudat, nuerr, Sigdat, Sigerr, Mrdat, Mrerr, sigdat, sigerr, scales, gp)
return gp.dat
