/
vcorrect.py
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/
vcorrect.py
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# semianalytics.py
# created 2017.05.25 by stacy kim
from sys import *
from numpy import *
from numpy.random import normal
from scipy.interpolate import interp1d
from scipy.optimize import minimize_scalar
from scipy.integrate import quad
import os
hostname = os.uname()[1]
if hostname == 'CLWS00081':
RDIST_DATDIR = '/home/stacykim/research/pyutils/radial_distributions/'
else:
RDIST_DATDIR = '/Users/hgzxbprn/Documents/research/pyutils/radial_distributions/' # '/projects/msp/semianalytics/'
# for instances where radial and angular are separable
#C_OMEGA = 5.
mMW = 1e12 ## HERE 1.5 vs 1
# MW dwarf data, from Jethwa+2017's compilation, who got mags and dist from
# McConnachie 2012, and M* from Woo+ 2008 or assuming M*/L = 2 MSUN/LSUN
# name v-band Mabs MSUN kpc velocity disp, error (km/s) reff (pc) ueff (M/arcsec^2)
dwarfs = {'LMC' : {'type': 'classical', 'mv': -18.1, 'mstar': 1.1e9, 'dsun': 51.0, 'sigma': 20.2, 'sigerr': 0.5, 'reff': None, 'ueff': None},
'SMC' : {'type': 'classical', 'mv': -16.8, 'mstar': 3.7e8, 'dsun': 64.0, 'sigma': 27.6, 'sigerr': 0.5, 'reff': None, 'ueff': None},
'Sagittarius' : {'type': 'classical', 'mv': -13.5, 'mstar': 3.4e7, 'dsun': 26.0, 'sigma': 11.4, 'sigerr': 0.7, 'reff': 2587., 'ueff': 26.0},
'Fornax' : {'type': 'classical', 'mv': -13.4, 'mstar': 3.3e7, 'dsun': 147., 'sigma': 11.7, 'sigerr': 0.9, 'reff': 710., 'ueff': 24.0},
'Leo I' : {'type': 'classical', 'mv': -12.0, 'mstar': 8.8e6, 'dsun': 254., 'sigma': 9.2, 'sigerr': 1.4, 'reff': 251., 'ueff': 23.3},
'Sculptor' : {'type': 'classical', 'mv': -11.1, 'mstar': 3.7e6, 'dsun': 86.0, 'sigma': 9.2, 'sigerr': 1.4, 'reff': 283., 'ueff': 24.3},
'Leo II' : {'type': 'classical', 'mv': -9.8, 'mstar': 1.2e6, 'dsun': 233., 'sigma': 6.6, 'sigerr': 0.7, 'reff': 176., 'ueff': 24.8},
'Sextans I' : {'type': 'classical', 'mv': -9.3, 'mstar': 7.0e5, 'dsun': 86.0, 'sigma': 7.9, 'sigerr': 1.3, 'reff': 695., 'ueff': 28.0},
'Carina' : {'type': 'classical', 'mv': -9.1, 'mstar': 6.0e5, 'dsun': 105., 'sigma': 6.6, 'sigerr': 1.2, 'reff': 250., 'ueff': 26.0},
'Draco' : {'type': 'classical', 'mv': -8.8, 'mstar': 4.5e5, 'dsun': 76.0, 'sigma': 9.1, 'sigerr': 1.2, 'reff': 221., 'ueff': 26.1},
'Ursa Minor' : {'type': 'classical', 'mv': -8.8, 'mstar': 4.5e5, 'dsun': 76.0, 'sigma': 9.5, 'sigerr': 1.2, 'reff': 181., 'ueff': 25.2},
'Canes Venatici I' : {'type': 'ufd' , 'mv': -8.6, 'mstar': 1.2e5, 'dsun': 218., 'sigma': 7.6, 'sigerr': 0.4, 'reff': 564., 'ueff': 28.2},
'Hercules' : {'type': 'ufd tidal', 'mv': -6.6, 'mstar': 1.9e4, 'dsun': 132., 'sigma': 3.7, 'sigerr': 0.9, 'reff': 330., 'ueff': 28.3},
'Bootes I' : {'type': 'ufd' , 'mv': -6.3, 'mstar': 1.4e4, 'dsun': 66.0, 'sigma': 2.4, 'sigerr': [0.5,0.9], 'reff': 242., 'ueff': 28.7}, # technically +0.9 -0.5
'Leo IV' : {'type': 'ufd' , 'mv': -5.8, 'mstar': 9.0e3, 'dsun': 154., 'sigma': 3.3, 'sigerr': 1.7, 'reff': 206., 'ueff': 28.6},
'Ursa Major I' : {'type': 'ufd' , 'mv': -5.5, 'mstar': 6.8e3, 'dsun': 97.0, 'sigma': 7.6, 'sigerr': 1.0, 'reff': 319., 'ueff': 28.8},
'Leo V' : {'type': 'ufd tidal', 'mv': -5.2, 'mstar': 5.1e3, 'dsun': 178., 'sigma': 3.7, 'sigerr': [1.4,2.3], 'reff': 135., 'ueff': 28.2}, # techinically +2.3 -1.4
'Pisces II' : {'type': 'ufd' , 'mv': -5.0, 'mstar': 4.3e3, 'dsun': 182., 'sigma': None, 'sigerr': None, 'reff': 58., 'ueff': 26.8},
'Canes Venatici II': {'type': 'ufd' , 'mv': -4.9, 'mstar': 3.9e3, 'dsun': 160., 'sigma': 4.6, 'sigerr': 1.0, 'reff': 74., 'ueff': 27.2},
'Ursa Major II' : {'type': 'ufd' , 'mv': -4.2, 'mstar': 2.1e3, 'dsun': 32.0, 'sigma': 6.7, 'sigerr': 1.4, 'reff': 149., 'ueff': 29.1},
'Coma Berenices' : {'type': 'ufd' , 'mv': -4.1, 'mstar': 1.9e3, 'dsun': 44.0, 'sigma': 4.6, 'sigerr': 0.8, 'reff': 77., 'ueff': 28.4},
#'Bootes II' : {'type': 'ufd' , 'mv': -2.7, 'mstar': 5.1e2, 'dsun': 42.0, 'sigma': 10.5, 'sigerr': 7.4, 'reff': 51., 'ueff': 29.1}, # AM
'Bootes II' : {'type': 'ufd' , 'mv': -2.7, 'mstar': 5.1e2, 'dsun': 42.0, 'sigma': 4.4, 'sigerr': 1.0, 'reff': 51., 'ueff': 29.1}, # MG
'Willman 1' : {'type': 'ufd tidal', 'mv': -2.7, 'mstar': 5.1e2, 'dsun': 38.0, 'sigma': 4.3, 'sigerr': [1.3,2.3], 'reff': 25., 'ueff': 27.2},
'Segue II' : {'type': 'ufd tidal', 'mv': -2.5, 'mstar': 4.3e2, 'dsun': 35.0, 'sigma': 3.4, 'sigerr': [1.2,2.5], 'reff': 35., 'ueff': 28.6},
'Segue I' : {'type': 'ufd' , 'mv': -1.5, 'mstar': 1.7e2, 'dsun': 23.0, 'sigma': 3.9, 'sigerr': 0.8, 'reff': 29., 'ueff': 28.7}} # AM
#'Segue I' : {'type': 'ufd' , 'mv': -1.5, 'mstar': 1.7e2, 'dsun': 23.0, 'sigma': 3.7, 'sigerr': [1.1,1.4], 'reff': 29., 'ueff': 28.7}} # MANOJ
# 'Tucana III' : {'type': 'tidal' , 'mv': },}}
# M31 dwarfs (from McConnachie+ 2012)
# name v-band Mabs MSUN kpc velocity disp, error (km/s) reff (pc) ueff (M/arcsec^2)
dwarfsM31 = {'M32' : {'type': 'm31', 'mv': -16.4, 'mstar': 3.2e8, 'dm31': 23.0, 'sigma': 92.0, 'sigerr': 5.0, 'reff': 110., 'ueff': 17.0},
'And IX' : {'type': 'm31', 'mv': -8.1, 'mstar': 1.5e5, 'dm31': 40.0, 'sigma': 4.5, 'sigerr': 3.6, 'reff': 557., 'ueff': 29.2},
'NGC 205' : {'type': 'm31', 'mv': -16.5, 'mstar': 3.3e8, 'dm31': 42.0, 'sigma': 35.0, 'sigerr': 5.0, 'reff': 590., 'ueff': 20.3},
'And XVII' : {'type': 'm31', 'mv': -8.7, 'mstar': 2.6e5, 'dm31': 45.0, 'sigma': None, 'sigerr': None, 'reff': 286., 'ueff': 26.8},
'And I' : {'type': 'm31', 'mv': -11.7, 'mstar': 3.9e6, 'dm31': 58.0, 'sigma': 10.6, 'sigerr': 1.1, 'reff': 672., 'ueff': 25.8},
'And XXVII' : {'type': 'm31', 'mv': -7.9, 'mstar': 1.2e5, 'dm31': 75.0, 'sigma': None, 'sigerr': None, 'reff': 434., 'ueff': 28.3},
'And III' : {'type': 'm31', 'mv': -10.0, 'mstar': 8.3e5, 'dm31': 75.0, 'sigma': 4.7, 'sigerr': 1.8, 'reff': 479., 'ueff': 26.2},
'And XXV' : {'type': 'm31', 'mv': -9.7, 'mstar': 6.8e5, 'dm31': 88.0, 'sigma': None, 'sigerr': None, 'reff': 709., 'ueff': 27.8},
'And XXVI' : {'type': 'm31', 'mv': -7.1, 'mstar': 6.0e4, 'dm31': 103.0, 'sigma': None, 'sigerr': None, 'reff': 222., 'ueff': 27.9},
'And XI' : {'type': 'm31', 'mv': -6.9, 'mstar': 4.9e4, 'dm31': 104.0, 'sigma': 4.6, 'sigerr': None, 'reff': 157., 'ueff': 27.6}, # sigma upper limit
'And V' : {'type': 'm31', 'mv': -9.1, 'mstar': 3.9e5, 'dm31': 110.0, 'sigma': 11.5, 'sigerr': [4.4,5.3], 'reff': 315., 'ueff': 26.7},
'And X' : {'type': 'm31', 'mv': -7.6, 'mstar': 9.6e4, 'dm31': 110.0, 'sigma': 3.9, 'sigerr': 1.2, 'reff': 265., 'ueff': 27.4},
'And XXIII' : {'type': 'm31', 'mv': -10.2, 'mstar': 1.1e6, 'dm31': 127.0, 'sigma': None, 'sigerr': None, 'reff': 1029., 'ueff': 27.8},
'And XX' : {'type': 'm31', 'mv': -6.3, 'mstar': 2.9e4, 'dm31': 129.0, 'sigma': None, 'sigerr': None, 'reff': 124., 'ueff': 27.3},
'And XII' : {'type': 'm31', 'mv': -6.4, 'mstar': 3.1e4, 'dm31': 133.0, 'sigma': 2.6, 'sigerr': [2.6,5.1], 'reff': 304., 'ueff': 29.6},
'NGC 147' : {'type': 'm31', 'mv': -14.6, 'mstar': 6.2e7, 'dm31': 142.0, 'sigma': 16.0, 'sigerr': 1.0, 'reff': 623., 'ueff': 22.3},
'And XXI' : {'type': 'm31', 'mv': -9.9, 'mstar': 7.6e5, 'dm31': 150.0, 'sigma': None, 'sigerr': None, 'reff': 875., 'ueff': 28.2},
'And XIV' : {'type': 'm31', 'mv': -8.4, 'mstar': 2.0e5, 'dm31': 162.0, 'sigma': 5.4, 'sigerr': 1.3, 'reff': 363., 'ueff': 27.5},
'And XV' : {'type': 'm31', 'mv': -9.4, 'mstar': 4.9e5, 'dm31': 174.0, 'sigma': 11.0, 'sigerr': [5.,7.], 'reff': 222., 'ueff': 25.9},
'And XIII' : {'type': 'm31', 'mv': -6.7, 'mstar': 4.1e4, 'dm31': 180.0, 'sigma': 9.7, 'sigerr': [4.5,8.9], 'reff': 207., 'ueff': 28.4},
'And II' : {'type': 'm31', 'mv': -12.4, 'mstar': 7.6e6, 'dm31': 184.0, 'sigma': 7.3, 'sigerr': 0.8, 'reff': 1176., 'ueff': 26.3},
'NGC 185' : {'type': 'm31', 'mv': -14.8, 'mstar': 6.8e7, 'dm31': 187.0, 'sigma': 24.0, 'sigerr': 1.0, 'reff': 458., 'ueff': 21.9},
'And XXIX' : {'type': 'm31', 'mv': -8.3, 'mstar': 1.8e5, 'dm31': 188.0, 'sigma': None, 'sigerr': None, 'reff': 361., 'ueff': 27.6},
'And XIX' : {'type': 'm31', 'mv': -9.2, 'mstar': 4.3e5, 'dm31': 189.0, 'sigma': None, 'sigerr': None, 'reff': 1683., 'ueff': 30.2},
'Triangulum' : {'type': 'm31', 'mv': -18.8, 'mstar': 2.9e9, 'dm31': 206.0, 'sigma': None, 'sigerr': None, 'reff': None, 'ueff': None},
'And XXIV' : {'type': 'm31', 'mv': -7.6, 'mstar': 9.3e4, 'dm31': 208.0, 'sigma': None, 'sigerr': None, 'reff': 367., 'ueff': 28.5},
'And VII' : {'type': 'm31', 'mv': -12.6, 'mstar': 9.5e6, 'dm31': 218.0, 'sigma': 9.7, 'sigerr': 1.6, 'reff': 776., 'ueff': 25.3},
'And XXII' : {'type': 'm31', 'mv': -6.5, 'mstar': 3.4e4, 'dm31': 221.0, 'sigma': None, 'sigerr': None, 'reff': 217., 'ueff': 27.9},
'IC 10' : {'type': 'm31', 'mv': -15.0, 'mstar': 8.6e7, 'dm31': 252.0, 'sigma': None, 'sigerr': None, 'reff': 612., 'ueff': 22.3},
'LGS 3' : {'type': 'm31', 'mv': -10.1, 'mstar': 9.6e5, 'dm31': 269.0, 'sigma': 7.9, 'sigerr': [2.9,5.3], 'reff': 470., 'ueff': 26.6},
'And VI' : {'type': 'm31', 'mv': -11.3, 'mstar': 2.8e6, 'dm31': 269.0, 'sigma': 9.4, 'sigerr': [2.4,3.2], 'reff': 524., 'ueff': 25.3},
'And XVI' : {'type': 'm31', 'mv': -9.2, 'mstar': 4.1e5, 'dm31': 279.0, 'sigma': 10.0, 'sigerr': None, 'reff': 136., 'ueff': 25.0}} # sigma upper limit
# 'Isolated' Local Group dwarfs (from McConnachie+ 2012)
# name v-band Mabs MSUN kpc velocity disp, error (km/s) reff (pc)
isolatedLG = {'And XXVIII' : {'type': 'LG' , 'mv': -8.5, 'mstar': 2.1e5, 'dsun': 661., 'sigma': None, 'sigerr': None, 'reff': 213.},
'IC 1613' : {'type': 'LG' , 'mv': -15.2, 'mstar': 1.0e8, 'dsun': 755., 'sigma': None, 'sigerr': None, 'reff': 1496.},
'Phoenix' : {'type': 'LG' , 'mv': -9.9, 'mstar': 7.7e5, 'dsun': 415., 'sigma': None, 'sigerr': None, 'reff': 454.},
'NGC 6822' : {'type': 'LG' , 'mv': -15.2, 'mstar': 1.0e8, 'dsun': 459., 'sigma': None, 'sigerr': None, 'reff': 354.},
'Cetus' : {'type': 'LG' , 'mv': -11.2, 'mstar': 2.6e6, 'dsun': 755., 'sigma': 17.0, 'sigerr': 2.0, 'reff': 703.},
'Pegasus dIrr' : {'type': 'LG' , 'mv': -12.2, 'mstar': 6.61e6, 'dsun': 920., 'sigma': None, 'sigerr': None, 'reff': 562.},
'Leo T' : {'type': 'LG' , 'mv': -8.0, 'mstar': 1.4e5, 'dsun': 417., 'sigma': 7.5, 'sigerr': 1.6, 'reff': 120.},
'WLM' : {'type': 'LG' , 'mv': -14.2, 'mstar': 4.3e7, 'dsun': 933., 'sigma': 17.5, 'sigerr': 2.0, 'reff': 2111.},
'Leo A' : {'type': 'LG' , 'mv': -12.1, 'mstar': 6.0e6, 'dsun': 798., 'sigma': 9.3, 'sigerr': 1.3, 'reff': 499.},
'And XVIII' : {'type': 'LG' , 'mv': -9.7, 'mstar': 6.3e5, 'dsun': 1355., 'sigma': None, 'sigerr': None, 'reff': 363.},
'Aquarius' : {'type': 'LG' , 'mv': -10.6, 'mstar': 1.6e6, 'dsun': 1072., 'sigma': None, 'sigerr': None, 'reff': 458.},
'Tucana' : {'type': 'LG' , 'mv': -9.5, 'mstar': 5.6e5, 'dsun': 887., 'sigma': 15.8, 'sigerr': [3.1,4.1], 'reff': 284.},
'Sag dIrr' : {'type': 'LG' , 'mv': -11.5, 'mstar': 3.5e6, 'dsun': 1067., 'sigma': None, 'sigerr': None, 'reff': 282.},
'UGC 4879' : {'type': 'LG' , 'mv': -12.5, 'mstar': 8.3e6, 'dsun': 1361., 'sigma': None, 'sigerr': None, 'reff': 162.},
'NGC 3109' : {'type': 'LG' , 'mv': -14.9, 'mstar': 7.6e7, 'dsun': 1300., 'sigma': None, 'sigerr': None, 'reff': 1626.},
'Sextans B' : {'type': 'LG' , 'mv': -14.5, 'mstar': 5.2e7, 'dsun': 1426., 'sigma': None, 'sigerr': None, 'reff': 440.},
'Antila' : {'type': 'LG' , 'mv': -10.4, 'mstar': 1.3e6, 'dsun': 1349., 'sigma': None, 'sigerr': None, 'reff': 471.},
'Sextans A' : {'type': 'LG' , 'mv': -14.3, 'mstar': 4.4e7, 'dsun': 1432., 'sigma': None, 'sigerr': None, 'reff': 1029.},
'KKR 25' : {'type': 'LG' , 'mv': -10.5, 'mstar': 1.4e6, 'dsun': 1905., 'sigma': None, 'sigerr': None, 'reff': 222.},
'ESO 410-G005' : {'type': 'LG' , 'mv': -11.5, 'mstar': 3.5e6, 'dsun': 1923., 'sigma': None, 'sigerr': None, 'reff': 280.},
'NGC 55' : {'type': 'LG' , 'mv': -18.5, 'mstar': 2.2e9, 'dsun': 1932., 'sigma': None, 'sigerr': None, 'reff': 2900.},
'ESO 294-G010' : {'type': 'LG' , 'mv': -11.2, 'mstar': 2.7e6, 'dsun': 2032., 'sigma': None, 'sigerr': None, 'reff': 248.},
'NGC 300' : {'type': 'LG' , 'mv': -18.5, 'mstar': 2.1e9, 'dsun': 2080., 'sigma': None, 'sigerr': None, 'reff': 3025.},
'IC 5152' : {'type': 'LG' , 'mv': -15.6, 'mstar': 2.7e8, 'dsun': 1950., 'sigma': None, 'sigerr': None, 'reff': 550.},
'KKH 98' : {'type': 'LG' , 'mv': -11.8, 'mstar': 4.5e6, 'dsun': 2523., 'sigma': None, 'sigerr': None, 'reff': 470.},
'UKS 2323-326' : {'type': 'LG' , 'mv': -13.2, 'mstar': 1.7e7, 'dsun': 2208., 'sigma': None, 'sigerr': None, 'reff': 578.},
'KKR 3' : {'type': 'LG' , 'mv': -9.5, 'mstar': 5.4e5, 'dsun': 2188., 'sigma': None, 'sigerr': None, 'reff': 229.},
'GR 8' : {'type': 'LG' , 'mv': -12.2, 'mstar': 6.4e6, 'dsun': 2178., 'sigma': None, 'sigerr': None, 'reff': 203.},
'UGC 9128' : {'type': 'LG' , 'mv': -12.4, 'mstar': 7.8e6, 'dsun': 2291., 'sigma': None, 'sigerr': None, 'reff': 427.},
'UGC 8508' : {'type': 'LG' , 'mv': -13.4, 'mstar': 1.9e7, 'dsun': 2582., 'sigma': None, 'sigerr': None, 'reff': 315.},
'IC 3104' : {'type': 'LG' , 'mv': -14.0, 'mstar': 6.2e7, 'dsun': 2270., 'sigma': None, 'sigerr': None, 'reff': 1327.},
'DDO 125' : {'type': 'LG' , 'mv': -14.4, 'mstar': 4.7e7, 'dsun': 2582., 'sigma': None, 'sigerr': None, 'reff': 781.},
'UGCA 86' : {'type': 'LG' , 'mv': -13.2, 'mstar': 1.6e7, 'dsun': 2965., 'sigma': None, 'sigerr': None, 'reff': 811.},
'DDO 99' : {'type': 'LG' , 'mv': -13.2, 'mstar': 1.6e7, 'dsun': 2594., 'sigma': None, 'sigerr': None, 'reff': 679.},
'IC 4662' : {'type': 'LG' , 'mv': -15.8, 'mstar': 1.9e8, 'dsun': 2443., 'sigma': None, 'sigerr': None, 'reff': 341.},
'DDO 190' : {'type': 'LG' , 'mv': -14.4, 'mstar': 5.1e7, 'dsun': 2783., 'sigma': None, 'sigerr': None, 'reff': 520.},
'KKH 86' : {'type': 'LG' , 'mv': -10.0, 'mstar': 8.2e5, 'dsun': 2582., 'sigma': None, 'sigerr': None, 'reff': 210.},
'NGC 4163' : {'type': 'LG' , 'mv': -14.1, 'mstar': 3.7e7, 'dsun': 2858., 'sigma': None, 'sigerr': None, 'reff': 374.},
'DDO 113' : {'type': 'LG' , 'mv': -11.0, 'mstar': 2.1e6, 'dsun': 2951., 'sigma': None, 'sigerr': None, 'reff': 601.}}
NCLASSICAL = 11
MLIMIT_SDSS = 22.0
MLIMIT_LSST1 = 23.8
MLIMIT_LSSTC = 26.8
MLIMIT_DES = 24.7
def dmax(mobs,mlimit,algorithm='walsh',router=300.):
"""
Returns maximum distance a dwarf of magnitude 'mobs' could be detected in a survey
with limiting magnitude 'mlimit' based on the detection limit 'algorithm'
(default 'walsh') in a halo of radius 'router' kpc (default 300).
mlimit = a number or 'full'
"""
if mlimit == 'full':
return router
else:
mlimit = float(mlimit)
if algorithm == 'walsh':
return 10**( -0.204*mobs + 1.164 + (mlimit-MLIMIT_SDSS)/5. )
if algorithm == 'kopos':
return 10**( (-0.6/3.)*mobs + log10(1071.6) + (-5.23/3) + (mlimit-MLIMIT_SDSS)/5. )
C = 9.0 # duffy08(mMW) # 12.
RVIR = 300. # kpc
rs = RVIR/C
print('--> NOTE: for completeness corrections, hard-coding MW NFW parameters to C =',C,' RS',rs,'kpc RVIR',RVIR,'kpc')
AREA_DR5 = 8000. # area of SDSS DR5
AREA_DR8 = 12000. # area of SDSS DR8 (actually 14,500 but need to cut out low Galactic latitudes)
AREA_LSST = 20000.
AREA_DES = 5000.
AREA_SKY = 41253. # total area of the sky (sq. deg)
# ------------------------------------------------------------------------------
# radial correction functions
def correct(profiles):
menc_fxns = []
rdist_names = []
interp_fxns = []
ifxn = 0
r = arange(10,300)
for profile in profiles:
base,mod = (profile,None) if ',' not in profile else profile.split(',')
if base == 'nfw' :
menc_fxns += [ lambda rc,t: (log(1.+rc/rs)-1./(rs/rc+1.)) / (log(1.+C) - 1./(1/C + 1)) ]
rdist_names += ['NFW']
elif base == 'sis' :
menc_fxns += [ lambda rc,t: rc/RVIR ]
rdist_names += ['SIS']
elif base == 'hern':
menc_fxns += [ lambda rc,t: ( (1./C+1) / (rs/rc+1) )**2 ]
rdist_names += ['Hernquist']
elif base == 'ein':
C200 = 4.9
ALPHA = 0.24
rho = lambda rr: exp(-2./ALPHA * (C200*rr)**ALPHA)
menc = array([ quad(lambda rr: rho(rr)*rr**2, 0,rend)[0] for rend in r/RVIR ])
menc /= menc[-1]
menc = concatenate([[0],menc,[1]])
interp_fxns += [ interp1d(concatenate([[0],r,[300]]),menc) ] #,fill_value=[0,1],bounds_error=False) ]
menc_fxns += [ lambda rc,t,i=ifxn: interp_fxns[i](rc) ]
ifxn += 1
rdist_names += ['Einasto']
else: # we'll try to read menc profile from a data file
datfn = RDIST_DATDIR+base+'-menc.dat'
if 'tidal' not in base:
rr,mm = loadtxt(datfn,unpack=True)
rr *= 300 if rr[-1]/100 < 1 else 1
interp_fxns += [ interp1d(rr,mm/mm[-1]) ]
menc_fxns += [ lambda rc,t,i=ifxn: interp_fxns[i](rc) ]
ifxn += 1
else:
rr,mm = loadtxt(datfn,unpack=True,usecols=(0,3)) # assume they're all severely tidally stripped
rr *= 300 if rr[-1]/100 < 1 else 1
interp_fxns += [ interp1d(rr,mm/mm[-1]) ]
menc_fxns += [ lambda rc,t,i=ifxn: interp_fxns[i](rc) ]
ifxn += 1
"""
rts,rnts, mts,mnts = loadtxt(datfn,unpack=True,usecols=(0,1,3,4))
rts *= 300 if rts[-1] /100 < 1 else 1
rnts *= 300 if rnts[-1]/100 < 1 else 1
interp_fxns += [ interp1d(rts ,mts /mts [-1]) ] # tidally stripped
interp_fxns += [ interp1d(rnts,mnts/mnts[-1]) ] # not tidally stripped
menc_fxns += [ lambda rc,t,i=ifxn,j=(ifxn+1): (interp_fxns[i] if 'tidal' in t else interp_fxns[j])(rc) ]
ifxn += 2
"""
rdist_names += [ base[:].upper() ]
# read in modification to profile, if provided
if mod != None:
datfn = RDIST_DATDIR+mod+'-mod.dat'
print('reading modification from',datfn)
rr,mm = loadtxt(datfn,unpack=True)
rr *= 300 if rr[-1]/100 < 1 else 1
interp_fxns += [ menc_fxns[len(menc_fxns)-1] ]
interp_fxns += [ interp1d(rr,mm/mm[-1]) ]
menc_fxns[-1] = lambda rc,t,i=ifxn: interp_fxns[i](rc,t)*interp_fxns[i+1](rc)
ifxn += 2
rdist_names[-1] += '+'+mod
# solve for radius that encloses half the satellites
result = minimize_scalar(lambda rr: abs(menc_fxns[-1](rr,1)-0.5), bounds=(10,300), method='Bounded')
print('for',rdist_names[-1],'r1/2 =',result.x,'kpc')
# -------------------------------------------------------------------------
# correction calculation
crs_tot = [[],[],[]]
for dwarf_name,dwarf in dwarfs.items():
if 'classical' in dwarf['type']: continue
rc = dmax(dwarf['mv'],MLIMIT_SDSS)
rc = RVIR if rc > RVIR else rc
print('{0:<20} {1:>7} kpc'.format(dwarf_name,round(rc,2)),end=' ')
for im,maglim in enumerate(['full', MLIMIT_DES, MLIMIT_LSST1]):
rout = dmax(dwarf['mv'],maglim)
rout = RVIR if rout > RVIR else rout
print('| {0:>7} kpc '.format(round(rout,2)),end='')
crs_tot[im] += [ [ menc(rout,dwarf['type'])/menc(rc,dwarf['type']) for menc in menc_fxns ] ]
#crs_tot[im] += [ [ crfxn(rc,dwarf['type'])/crfxn(rout,dwarf['type']) for crfxn in crfxns ] ]
print(' '.join(['{0:<7}'.format(round(cr,3)) for cr in crs_tot[im][-1]]),end=' ')
print()
# and print the results
for iml,maglim in enumerate(['full','DES', 'LSST']):
print()
print('MAGLIM',maglim,end=' ')
if maglim == 'full': C_OMEGA = AREA_SKY / AREA_DR8
if maglim == 'DES' : C_OMEGA = AREA_DES / AREA_DR8
if maglim == 'LSST': C_OMEGA = AREA_LSST / AREA_DR8
for ird,name in enumerate(rdist_names):
crs = [crs_tot[iml][i][ird] for i in range(len(crs_tot[0]))]
print(name+':',int(round(sum(crs)*C_OMEGA,2)),'total satellites (not including classicals)') # + NCLASSICAL
return crs_tot, menc_fxns, rdist_names # crs_tot[maglims][dwarfs][profiles]
# -----------------------------------------------------------------------------
# velocity function, completeness corrected, for full sky
def vcorrect(profiles,bootstrap=True,nboot=1000,obs_uncertainty=None):
"""
Returns a list of the velocities of a completeness-corrected sample of galaxies.
obs_uncertainty = None, 'sigdiv2' to divide all uncertainties by a factor of 2, or
'BooIIAM' to use the McConnachie+ 2012 values/uncertainties for Boo II, or
'strip' to use 2*sig for unobserved analogs of likely stripped dwarfs
"""
nprofiles = len(profiles)
id = -1 # UFD dwarf index
# do radial completeness correction
crs_tot, menc_fxns, rdist_names = correct(profiles)
if bootstrap:
sigmas = [ [ [] for ib in range(nboot) ] for ird in range(nprofiles) ]
else:
sigmas = [ [] for ird in range(nprofiles) ]
for dwarf_name,dwarf in dwarfs.items():
if dwarf['type'] == 'classical':
nsigmas = ones(nprofiles)
else:
id += 1
if dwarf['sigma'] == None: continue
nsigmas = array(crs_tot[0][id])*(AREA_SKY/AREA_DR8) # for all profiles, full volume + full sky correction
if not bootstrap:
for ip in range(nprofiles): sigmas[ip] += [ [dwarf['sigma']]*int(round(nsigmas[ip])) ]
else:
for ip in range(nprofiles):
for ib in range(nboot):
if dwarf_name=='Bootes II' and obs_uncertainty=='BooIIAM':
sigmas[ip][ib] += [ normal(loc=10.5,scale=7.4,
size=int(round(nsigmas[ip] * (1 if nsigmas[ip]==1 else normal(loc=5.15,scale=1.)/5.15) ))) ] # anisotropy if completeness-corrected
elif dwarf['type']=='ufd tidal' and obs_uncertainty=='strip': # dwarf_name=='Segue I' dwarf_name=='Hercules'
sigmas[ip][ib] += [ normal(loc=dwarf['sigma']*2,scale=mean(dwarf['sigerr']),
size=int(round(nsigmas[ip] * (1 if nsigmas[ip]==1 else normal(loc=5.15,scale=1.)/5.15) ))) ]
else:
sigmas[ip][ib] += [ normal(loc=dwarf['sigma'],scale=mean(dwarf['sigerr'])*(0.5 if obs_uncertainty=='sigdiv2' else 1.), ## modify all sigmas
size=int(round(nsigmas[ip] * (1 if nsigmas[ip]==1 else normal(loc=5.15,scale=1.)/5.15) ))) ]
if bootstrap:
for ip in range(nprofiles):
for ib in range(nboot): sigmas[ip][ib] = concatenate(sigmas[ip][ib])
return array(sigmas), rdist_names, nboot
# ==============================================================================
# MAIN
if __name__ == '__main__':
if len(argv) < 2:
print('usage: {0} [menc1](,mod1) .. [mencN](,modN)'.format(argv[0]))
print(" mencX and modX can be nfw, sis, hern, or point to file [mencX]-menc.dat or [modX]-mod.dat")
exit()
profiles = argv[1:]
vcorrect(profiles)