In [13]:
import time

import numpy as np
from scipy import integrate

from astropy import units as u
from astropy.table import Table
from astropy.coordinates import SkyCoord, Distance, Galactocentric, CartesianRepresentation, SphericalRepresentation

In [2]:
%matplotlib inline
import matplotlib
from matplotlib import pyplot as plt
from matplotlib import rcParams

rcParams['figure.figsize'] = (16, 10)
rcParams['image.interpolation'] = 'none'
rcParams['image.origin'] = 'lower'

In [3]:
# This changes the current directory to the base saga directory - make sure to run this first!
# This is necessary to be able to import the py files and use the right directories,
# while keeping all the notebooks in their own directory.
import os
import sys

import numpy as np

if 'saga_base_dir' not in locals():
    saga_base_dir = os.path.abspath('..')
if saga_base_dir not in sys.path:
    os.chdir(saga_base_dir)
    
from utils import get_mcconn_table

In [4]:
mcconndat = get_mcconn_table()

#the MW sats
sample = mcconndat['distance']<420
sample[mcconndat['name']=='Canis Major'] = False
sample[mcconndat['name']=='Phoenix'] = False
sample[mcconndat['name']=='Phoenix'] = False
sample[mcconndat['name']=='Sagittarius dSph'] = False  # disrupting

#special-case including some of the bright M31 objects
sample[mcconndat['name']=='M32'] = True
sample[mcconndat['name']=='NGC 147'] = True
sample[mcconndat['name']=='NGC 185'] = True
sample[mcconndat['name']=='NGC 205'] = True

ldat = mcconndat[sample]
ldat


Out[4]:
<Table length=30>
namecenterEBmVdistmoddistmod+distmod-vhvh+vh-VmagVmag+Vmag-PAPA+PA-ee+e-muV0muV0+muV0-rhrh+rh-sigma_ssigma_s+sigma_s-vrot_svrot_s+vrot_s-MHIsigma_gsigma_g+sigma_g-vrot_gvrot_g+vrot_g-[Fe/H][Fe/H]+[Fe/H]-FReferencesVabslogLVdistancedistance+distance-rh_physradegdecdegx [106]y [106]z [106]and_number
magsolLumkpckpckpckpcdegdegkpckpckpc
str19objectfloat64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64float64int64str40float64float64float64float64float64float64float64float64float64float64float64int64
Segue (I)<ICRS Coordinate: (ra, dec) in deg (151.76666667, 16.08194444)>0.03116.80.20.2208.50.90.915.30.80.885.08.08.00.480.130.1327.61.01.04.41.20.63.90.80.80.00.00.00.00.00.00.00.00.00.0-2.720.40.42(5)(6)(98)(130)(178)-1.52.53222.90867652772.109967082912.109967082910.0293210010634151.76666666716.0819444444-6.10454009929 .. -2498.348108383.27779965593 .. 1341.474449651.99755331472 .. 817.519987428-99
Ursa Major II<ICRS Coordinate: (ra, dec) in deg (132.875, 63.13)>0.09417.50.30.3-116.51.91.913.30.50.598.04.04.00.630.050.0527.90.60.616.01.01.06.71.41.40.00.00.00.00.00.00.00.00.00.0-2.470.060.062(7)(8)(98)(130)(179)(180)-4.23.61231.62277660174.368848040134.368848040130.147179085419132.87563.13-2.21754506878 .. -907.5539578292.38845178607 .. 977.4993537026.43252606578 .. 2632.57986141-99
Bootes II<ICRS Coordinate: (ra, dec) in deg (209.5, 12.85)>0.03118.10.060.06-117.05.25.215.40.90.9145.055.055.00.210.210.2128.11.61.64.21.41.410.57.47.499.999.999.90.00.00.00.00.00.00.0-1.790.050.053(9)(10)(98)(130)-2.73.01241.6869383471.151852673731.151852673730.0509302030462-150.512.85-6.11901664063 .. -2504.27278724-3.46197304455 .. -1416.849372181.60373864575 .. 656.347136196-99
Segue II<ICRS Coordinate: (ra, dec) in deg (34.81666667, 20.17527778)>0.18517.70.10.1-39.22.52.515.20.30.3182.017.017.00.150.10.127.40.40.43.40.20.23.42.51.299.999.999.999.999.999.999.9999.999.999.9-2.220.130.132(11)(214)-2.52.93234.67368504531.596782206091.596782206090.034292964844234.816666666720.17527777785.55692068545 .. 2274.229025793.86455823779 .. 1581.611653962.48705081888 .. 1017.85205892-99
Willman 1<ICRS Coordinate: (ra, dec) in deg (162.3375, 51.05)>0.01417.90.40.4-12.32.52.515.20.70.777.05.05.00.470.080.0826.10.90.92.30.40.44.32.31.399.999.999.90.00.00.00.00.00.00.0-2.19.999.992(12)(13)(98)(130)(181)-2.73.01238.01893963217.003347491867.003347491860.0254363008634162.337551.05-4.31949112113 .. -1767.797785931.3754110679 .. 562.9016410485.60801573662 .. 2295.14022014-99
Coma Berenices<ICRS Coordinate: (ra, dec) in deg (186.74583333, 23.90416667)>0.01718.20.20.298.10.90.914.10.50.5115.010.010.00.380.140.1427.30.70.76.00.60.64.60.80.80.00.00.00.00.00.00.00.00.00.0-2.60.050.052(5)(8)(98)(130)(179)(180)-4.13.57243.6515832244.020459392694.020459392690.0761863850967-173.25416666723.9041666667-6.54690102446 .. -2679.38903246-0.774394030261 .. -316.9290117162.9219857144 .. 1195.8538012-99
Bootes III<ICRS Coordinate: (ra, dec) in deg (209.3, 26.8)>0.02118.350.10.1197.53.83.812.60.50.590.099.999.90.59.999.9931.30.30.399.999.999.9914.03.23.299.999.999.999.999.999.999.9999.999.999.9-2.10.20.22(14)(15)(99)-5.754.23246.77351412872.153999927592.153999927591.36045031515-150.726.8-5.61307657105 .. -2297.21142058-3.14991166531 .. -1289.134926243.25131166787 .. 1330.63395818-99
LMC<ICRS Coordinate: (ra, dec) in deg (80.89375, -69.75611111)>0.92618.520.090.09262.23.43.40.40.10.1999.999.999.99.999.999.9999.99.99.999.999.999.9920.20.50.549.815.915.9460.015.80.20.263.03.03.0-0.59.999.993(16)(17)(41)(131)(132)(182)-18.129.1850.58246620032.096467787512.096467787511.4712371598680.89375-69.75611111110.394897545897 .. 161.616030162.46370682644 .. 1008.29828117-6.76563406156 .. -2768.90785953-99
SMC<ICRS Coordinate: (ra, dec) in deg (13.18666667, -72.82861111)>0.41919.030.120.12145.60.60.62.20.20.2999.999.999.99.999.999.9999.99.99.999.999.999.9927.60.50.50.00.00.0460.022.02.02.060.05.05.0-1.00.020.023(18)(19)(41)(133)(132)(184)-16.838.66463.97348354833.535305349563.535305349561.8607271118313.1866666667-72.82861111112.07279706589 .. 848.3142946720.485661292603 .. 198.762061016-6.88964767502 .. -2819.66175278-99
..................................................................................................................................................................
Leo V<ICRS Coordinate: (ra, dec) in deg (172.79, 2.22)>0.02721.250.120.12173.33.13.116.00.40.496.013.013.00.50.150.1527.10.80.82.60.60.63.72.31.499.999.999.90.00.00.00.00.00.00.0-2.00.20.25(34)(34)(101)(139)(130)-5.254.032177.8279410049.827135185769.827135185760.134492933144172.792.22-7.1486860278 .. -2925.675959940.904356683526 .. 370.1176129310.279332630121 .. 114.319856487-99
Pisces II<ICRS Coordinate: (ra, dec) in deg (344.62916667, 5.9525)>0.06521.39.999.99999.99.99.916.30.50.577.012.012.00.40.10.125.70.60.61.10.10.199.999.999.999.999.999.999.999.999.999.9999.999.999.9-1.99.999.995(35)-5.03.932181.970085861837.165210935837.1652109350.0582262475375-15.37083333335.95256.91564812364 .. 2830.30271354-1.90109985066 .. -778.0453790940.747816850005 .. 306.05201739-99
Canes Venatici (I)<ICRS Coordinate: (ra, dec) in deg (202.01458333, 33.55583333)>0.01421.690.10.130.90.60.613.10.20.270.04.04.00.390.030.0327.10.20.28.90.40.47.60.40.499.999.999.90.00.00.00.00.00.00.0-1.980.010.012(36)(8)(98)(130)(179)(180)-8.595.368217.77097723510.028724117410.02872411740.56378838426-157.98541666733.5558333333-5.57118217935 .. -2280.0656942-2.25255336951 .. -921.8814780823.98591671957 .. 1631.27890628-99
Leo II<ICRS Coordinate: (ra, dec) in deg (168.37, 22.15166667)>0.01721.840.130.1378.00.10.112.00.30.312.010.010.00.130.050.0524.20.30.32.60.60.66.60.70.799.999.999.90.00.00.00.00.00.00.0-1.620.010.012(37)(22)(100)(130)(180)-9.845.868233.34580622813.969762948313.96976294830.176481613291168.3722.1516666667-6.5417008345 .. -2677.260799291.34638826973 .. 551.0237515232.71900505192 .. 1112.78180136-99
Leo I<ICRS Coordinate: (ra, dec) in deg (152.11708333, 12.30638889)>0.03622.020.130.13282.50.10.110.00.30.379.03.03.00.210.030.0322.60.30.33.40.30.39.21.41.40.00.00.00.00.00.00.00.00.00.0-1.430.010.012(38)(39)(100)(130)(180)-12.026.74253.5128630515.177108422915.17710842290.250729268861152.11708333312.3063888889-6.22744505505 .. -2548.648271663.29488549474 .. 1348.467011311.53696366784 .. 629.018764682-99
M32<ICRS Coordinate: (ra, dec) in deg (10.67416667, 40.86527778)>0.15424.530.210.21-199.06.06.08.10.10.1159.02.02.00.250.020.0211.19.99.90.470.050.0592.05.05.055.03.03.00.00.00.00.00.00.00.0-0.259.999.995(42)(43)(41)(102)(140)(130)(195)-16.438.504805.37844119977.887000502877.88700050280.11010929326710.674166666740.86527777785.35901314887 .. 2193.233256811.01009373821 .. 413.391629694.71808100436 .. 1930.9249445-1
NGC 205<ICRS Coordinate: (ra, dec) in deg (10.09208333, 41.68527778)>0.08524.580.070.07-246.01.01.08.10.10.128.05.05.00.430.10.119.29.99.92.460.10.135.05.05.011.05.05.00.416.199.999.90.00.00.0-0.80.20.25(40)(45)(41)(102)(142)-16.488.524824.13811501326.567073934826.56707393480.58974086752410.092083333341.68527777785.30197167213 .. 2169.888424410.943669188958 .. 386.206674844.79564224094 .. 1962.66770736-1
NGC 147<ICRS Coordinate: (ra, dec) in deg (8.30041667, 48.50888889)>0.17224.150.090.09-193.10.80.89.50.10.125.03.03.00.410.020.0221.29.99.93.179.999.9916.01.01.017.02.02.00.00.00.00.00.00.00.0-1.10.10.13(40)(52)(41)(130)-14.657.792676.08297539228.021294453828.02129445380.6234266730198.3004166666748.50888888894.72732064851 .. 1934.706367360.689676609997 .. 282.2575044085.40151694556 .. 2210.62838868-1
NGC 185<ICRS Coordinate: (ra, dec) in deg (9.74166667, 48.3375)>0.18423.950.090.09-203.81.11.19.20.10.135.03.03.00.150.010.0120.89.99.92.559.999.9924.01.01.015.05.05.00.1115.30.80.80.00.00.0-1.30.10.13(40)(52)(41)(142)-14.757.832616.59500186125.555724274625.55572427460.4573685496879.7416666666748.33754.72438192606 .. 1933.503663880.811089883091 .. 331.9471806545.38720226756 .. 2204.76995412-1
Leo T<ICRS Coordinate: (ra, dec) in deg (143.7225, 17.05138889)>0.03123.10.10.138.12.02.015.10.50.50.099.999.90.09.999.9924.80.60.60.990.060.067.51.61.699.999.999.90.286.91.01.00.00.00.0-2.020.050.052(70)(8)(111)(153)(179)(180)-8.05.132416.8693834719.197544562119.19754456210.120049764323143.722517.0513888889-5.55774556029 .. -2274.566614624.07921075017 .. 1669.460482792.11449842661 .. 865.381021071-99

Trial distances for SAGA-like hosts


In [5]:
sagadists = [5, 10, 20, 30, 35, 42] * u.Mpc
distmods = 5*np.log10(sagadists/(10*u.pc))

Try basic LG dSph-like things


In [6]:
data = ldat[ldat['Vabs']<-10]
data = data[np.argsort(data['Vabs'])]

plt.figure(figsize=(12,5))
plt.subplot(1,2,1)
for gal in data:
    plt.plot(sagadists.value, gal['Vabs']+distmods.value,'-o',label=gal['name'])
plt.xlabel('d[Mpc]')
plt.ylabel('V')

plt.subplot(1,2,2)
for gal in data:
    plt.plot(sagadists.value, ((gal['rh_phys']/sagadists.to(u.kpc).value)*u.rad).to(u.arcsec).value,'-o',label=gal['name'])
plt.xlabel('d[Mpc]')
plt.ylabel('apparent size [arcsec]')
plt.legend(loc=0)
plt.ylim(0,20)
plt.axhline(2, c='k', ls='--')
plt.axhline(0.7, c='k', ls=':')

plt.tight_layout()



In [7]:
def plummer_prof(r, totflux=1, Reff=1):
    a = Reff*(2**(2/3)-1)**-0.5
    return 2*a*(3 * totflux / (4*np.pi*a**3))*(1+(r/a)**2)**-2.5
def exp_prof(r, totflux=1, Reff=1):
    from scipy.special import lambertw
    #the parenthetical below is non-trivial, but it's ~1.67835
    rs = Reff / -(lambertw(-1/2/np.exp(1),-1).real+1)
    return totflux*np.exp(-r/rs)/np.pi/2./rs/rs
                                     
r = np.linspace(0,3,101)[1:]
plt.figure(figsize=(6,5))

#test that the integrals behave correctly
print integrate.quad(lambda x:plummer_prof(x,1,2.123)*x*np.pi*2,0,np.inf)[0] # should be 1
print integrate.quad(lambda x:plummer_prof(x,1,2.123)*x*np.pi*2,0,2.123)[0] # should be 0.5
print integrate.quad(lambda x:exp_prof(x,1,2.123)*x*np.pi*2,0,np.inf)[0] # should be 1
print integrate.quad(lambda x:exp_prof(x,1,2.123)*x*np.pi*2,0,2.123)[0] # should be 0.5

plt.plot(r, plummer_prof(r,1,1),'b-')
plt.plot(r, exp_prof(r,1,1),'g-');
plt.plot(r, r*plummer_prof(r,1,1),'b--')
plt.plot(r, r*exp_prof(r,1,1),'g--');
plt.axvline(1, c='k')
None


1.0
0.5
1.0
0.5

In [8]:
def frac_inside(gal, radius, dist, prof):
    """
    Compute the magnitude inside the given angular `radius` for the
    table entry `gal` at a distance of `dist`, assuming a profile
    `prof` ('plummer' or 'exp')
    """    
    if prof == 'plummer':
        prof_func = plummer_prof
    elif prof == 'exp':
        prof_func = exp_prof
    else:
        raise ValueError('invalid profile type '+ str(prof))
        
    rh_at_distance = (u.arcmin*gal['rh'] * (gal['distance']*u.kpc)/dist).to(u.arcmin)
    return integrate.quad(lambda x:prof_func(x, 1, rh_at_distance.value)*x*np.pi*2, 0, radius.to(u.arcmin).value)[0]

def gal_mag_frac(gal, frac, dist):
    """
    determine the V magnitude for `frac` of the flux from `gal` at distance `dist`
    """
    flux = 10**((gal['Vabs'])/-2.5)
    fluxd = flux * ((10*u.pc/dist)**2).decompose().value
    return -2.5*np.log10(frac*fluxd)

In [9]:
data = ldat[(ldat['Vabs']<-8)&(ldat['distance']<500)]
data = data[np.argsort(data['Vabs'])]
rad = 3*u.arcsec/2 #3" diam = fibermag
Vmr=0.3

plt.figure(figsize=(12,6))

cc = []
for _ in range(5):
    cc.extend(matplotlib.rcParams['axes.color_cycle'])

#first do plummer
for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'plummer') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    plt.subplot(1,2,1)
    plt.plot(sagadists.value, totmags,'-o',color=cc[i],label=gal['name'])
    
    plt.subplot(1,2,2)
    plt.plot(sagadists.value, fibmags,'-o',color=cc[i],label=gal['name'])
    
plt.subplot(1,2,1)
plt.legend(loc=0)
    
#now exp
for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'exp') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    #plt.subplot(1,2,1)
    #plt.plot(sagadists.value, totmags,'-o',color=cc[i],label=gal['name'])
    
    plt.subplot(1,2,2)
    plt.plot(sagadists.value, fibmags,'--o',color=cc[i],label=gal['name'])
    
plt.subplot(1,2,1)
plt.xlabel('d[Mpc]')
plt.ylabel('Total r mag (assuming V-r={1})'.format(rad*2, Vmr))
plt.xlim(4,43)
plt.axhline(21, c='k', ls=':')

plt.subplot(1,2,2)
plt.xlabel('d[Mpc]')
plt.ylabel('r mag w/i diam={0} (assuming V-r={1})'.format(rad*2, Vmr))
plt.xlim(4,43)
plt.axhline(22, c='k', ls=':')
plt.axhline(23, c='k', ls=':')
plt.title('Solid=Plummer, Dashed=Exponential')

plt.tight_layout()


/Users/erik/miniconda3/envs/anaconda2/lib/python2.7/site-packages/matplotlib/__init__.py:892: UserWarning: axes.color_cycle is deprecated and replaced with axes.prop_cycle; please use the latter.
  warnings.warn(self.msg_depr % (key, alt_key))

In [15]:
#matched to similar plot in 2014May-MMTHecto
data = ldat[(ldat['Vabs']<-8)&(ldat['distance']<5000)]
data = data[np.argsort(data['Vabs'])]
rad = 3*u.arcsec/2 #3" diam = fibermag
Vmr=0.3

fiblim = (16, 24)
totlim = (14, 24)

cc = []
for _ in range(5):
    cc.extend(matplotlib.rcParams['axes.color_cycle'])

#first do plummer
for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'plummer') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    plt.plot(fibmags, totmags,'-o',color=cc[i],label=gal['name'])
    
    f0 = fiblim[0] < fibmags[0] < fiblim[1]
    fm1 = fiblim[0] < fibmags[-1] < fiblim[1]
    t0 = totlim[0] < totmags[0] < totlim[1]
    tm1 = totlim[0] < totmags[-1] < totlim[1]
    fi = ti = None
    if f0:
        fi=0
        if t0:
            ti=0
        elif tm1:
            ti=-1
    elif fm1:
        fi=-1
        if t0:
            ti=0
        elif tm1:
            ti=-1
    if fi is not None and ti is not None:
        plt.text(fibmags[fi], totmags[ti], gal['name'],color=cc[i])
#plt.legend(loc=0)

for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'exp') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    plt.plot(fibmags, totmags,'--o',color=cc[i],label=gal['name'])
    
x1t1 = [min(fiblim[0], totlim[0]), max(fiblim[1], totlim[1])]
plt.fill_between(x1t1,x1t1, totlim[1],facecolor=[0.6]*3)
plt.axhline(21, c='k', ls=':')
    
plt.xlabel('Approximate fibermag_r (assuming V-r={0})'.format(Vmr))
plt.ylabel('r')
plt.title('Solid=Plummer, Dashed=Exponential. Points at distances: {0}'.format(sagadists))
plt.xlim(fiblim[0], fiblim[1]+.25) #tweak for text
plt.ylim(*totlim)
plt.tight_layout()


Now try similar plots, but with SAGA data on them


In [14]:
clean = Table.read('SAGADropbox/data/saga_spectra_clean_jan15.fits.gz')
dirty = Table.read('SAGADropbox/data/saga_spectra_dirty_jan15.fits.gz')
sats = clean[clean['SATS']==1]
sats.show_in_notebook(display_length=5)


Out[14]:
<Table masked=True length=131>
OBJIDRADECPHOTPTYPEPHOT_SGFLAGSSATURATEDBAD_COUNTS_ERRORBINNED1ugrizu_errg_errr_erri_errz_errMODELMAGERR_UMODELMAGERR_GMODELMAGERR_RMODELMAGERR_IMODELMAGERR_ZEXTINCTION_UEXTINCTION_GEXTINCTION_REXTINCTION_IEXTINCTION_ZDERED_UDERED_GDERED_RDERED_IDERED_ZPETRORAD_UPETRORAD_GPETRORAD_RPETRORAD_IPETRORAD_ZPETRORADERR_UPETRORADERR_GPETRORADERR_RPETRORADERR_IPETRORADERR_ZDEVRAD_UDEVRADERR_UDEVRAD_GDEVRADERR_GDEVRAD_RDEVRADERR_RDEVRAD_IDEVRADERR_IDEVRAD_ZDEVRADERR_ZDEVAB_UDEVAB_GDEVAB_RDEVAB_IDEVAB_ZCMODELMAG_UCMODELMAGERR_UCMODELMAG_GCMODELMAGERR_GCMODELMAG_RCMODELMAGERR_RCMODELMAG_ICMODELMAGERR_ICMODELMAG_ZCMODELMAGERR_ZPSFMAG_UPSFMAGERR_UPSFMAG_GPSFMAGERR_GPSFMAG_RPSFMAGERR_RPSFMAG_IPSFMAGERR_IPSFMAG_ZPSFMAGERR_ZFIBERMAG_UFIBERMAGERR_UFIBERMAG_GFIBERMAGERR_GFIBERMAG_RFIBERMAGERR_RFIBERMAG_IFIBERMAGERR_IFIBERMAG_ZFIBERMAGERR_ZFRACDEV_UFRACDEV_GFRACDEV_RFRACDEV_IFRACDEV_ZQ_UU_UQ_GU_GQ_RU_RQ_IU_IQ_ZU_ZEXPAB_UEXPRAD_UEXPPHI_UEXPAB_GEXPRAD_GEXPPHI_GEXPAB_REXPRAD_REXPPHI_REXPAB_IEXPRAD_IEXPPHI_IEXPAB_ZEXPRAD_ZEXPPHI_ZFIBER2MAG_RFIBER2MAGERR_REXPMAG_REXPMAGERR_RColumn1PETROR50_RPETROR90_RPETROMAG_RSB_EXP_RSB_PETRO_RJJERRHHERRKKERRSPEC_ZSPEC_Z_ERRSPEC_Z_WARNPHOTOZPHOTOZ_ERRW1W1ERRW2W2ERRHOST_RAHOST_DECHOST_DISTHOST_VHOSTHOST_MKHOST_NSAIDHOST_FLAGHOST_SAGA_NAMERHOST_ARCMRHOST_KPCOBJ_NSAIDSATSPROBABILITY_CLASS1RESCALED_PROBABILITY_CLASS1REMOVETELNAMEMASKNAMEZQUALITYSPECOBJIDSPEC_REPEAT
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1237678777399443498348.6966488914.639954870193GALAXY13194893838295200026843545616.258915.411815.146115.15115.07110.01339540.003370960.003725280.005035850.0169960.01339540.003370960.003725280.005035850.0169960.3512280.2584310.1874350.1421270.1007715.907715.153414.958715.008914.97037.8567714.821616.972317.459216.1980.4160850.5923620.5326950.5836271.596426.140380.39312212.9450.14769716.55760.23083821.28750.42844219.27481.184880.5608360.6330220.6529680.6668180.64215616.92740.012595815.76630.0034433415.36670.0038493415.31860.0052521915.38940.017696118.56680.02926618.17650.016765118.01760.015761418.24270.037280618.26840.044452218.91260.020189418.39650.0081589618.27630.011205418.41890.033091218.27890.03297461.00.5979770.5429130.3309330.2788190.1410980.05806110.1534930.03300520.1379070.02165590.1381050.008222530.1176440.005158010.6091363.0603618.4440.6425875.920362.272560.661756.76683-0.1021340.6883677.1676177.6060.7122236.223860.76463419.02830.015108515.70490.0037812nan7.1740220.272515.513921.852230002221.788190453615.789999.016.0410.22614.7069999.00.009556-1.0-10.0096560.006745-1.0-1.0-1.0-1.0348.6834.5340637.0192689.08.3271508870Catch226.405916584268.9813719874-110.719369681440.920132632891-1MMT/Spectra/Final/MMT/spHect-2015.0918_1.zlog4130.0MMT
1237678777399509170348.8741990974.613261474723GALAXY12315585519289200026843545622.315920.624520.091919.815719.85340.3920780.03841790.03807880.04411040.1743270.3920780.03841790.03807880.04411040.1743270.369570.2719260.1972240.1495490.10603221.946320.352619.894719.666219.74741.957971.995652.013212.024831.81491.931420.08130150.09570390.1052370.3585330.2651893.54270.6423170.2048920.7247540.1696960.8110980.2973180.7602092.149110.050.3218010.3499640.4683590.90847822.4440.8879520.64470.038388820.09190.038078819.78840.045260319.81160.38438822.47420.43609620.92670.083239420.42370.081164220.20960.079704220.24210.22499621.89640.21242420.86850.06404720.330.063285220.04460.061354119.81390.1426791.00.00.00.00.0-0.120885-0.08557430.06680410.05706490.06037440.07412860.0356770.0451530.1388970.002169010.08523280.47200537.67510.4499650.83772421.67010.4572910.9124227.60230.5804930.90098223.61420.9997720.72012280.131521.16250.090823320.09190.0380788nan1.149931.7662720.273721.888300434422.57251919469999.09999.09999.09999.09999.09999.00.009029-1.0-10.0522250.046889-1.0-1.0-1.0-1.0348.6834.5340637.0192689.08.3271508870Catch2212.3834987085133.350062655-110.001129836929490.000214772468376-1MMT/Spectra/Final/MMT/spHect-2015.0918_1.zlog3170.0MMT
1237678776862572690348.7769076364.3731970123GALAXY352877198705520026843545617.492316.4115.793615.533315.31040.01654650.003722220.003444890.003773880.008789840.01654650.003722220.003444890.003773880.008789840.3442050.2532630.1836870.1392840.098754417.148116.156715.6115.39415.21167.620938.39588.646948.967638.067840.4536970.2998890.2334560.2244260.2567398.642910.6558249.174820.1546569.476760.15194110.35850.14884412.32240.4775520.6411160.6007250.6353760.6331740.57530317.45340.016863516.35840.0037892915.74220.0034972615.46080.0038404815.30940.0089538419.18390.039578918.27930.018440117.70890.018508817.55380.024288917.41820.023452219.63950.030297618.57690.0064787918.0070.0056222917.7780.0062707917.54370.01567310.2090680.1503570.1071630.103020.05343560.04621940.09529060.1205480.09261420.1114360.07191390.1188290.07120980.1347640.06511880.6731483.6883837.98260.5894484.3689418.34070.6298364.4032216.17590.6303884.4698616.95620.6242884.2350815.965818.80150.0079987215.79360.00344489nan3.958929.487315.770421.007942276220.753706214915.8510.14715.350.19314.7870.1260.008904-1.0-10.0898980.056008-1.0-1.0-1.0-1.0348.6834.5340637.0192689.08.3271508870Catch2211.1674755393120.255527082-110.0002965336609938.08778605097e-05-1MMT/Spectra/Final/MMT/spHect-2015.0918_1.zlog4216.0MMT
1237679005558702536348.5545917394.915003269623GALAXY2817093208637440026843545621.808621.171920.884421.273921.83060.2981880.06268130.07841840.1710631.148790.2981880.06268130.07841840.1710631.148790.3669880.2700260.1958450.1485040.10529121.441620.901920.688621.125421.72530.09191223.734252.505112.602160.2968030.03555740.5123030.2006752.445690.5735814.106677.807635.116081.794234.106011.984313.447673.130929.8934122.99860.050.3863320.2865190.3499380.0521.78120.26121220.88840.086255120.88440.078418421.2290.16929820.57530.53809822.62190.31422422.29870.084245922.17660.10712122.58410.21663422.32920.68621122.46010.29508322.10810.081697121.82150.10653622.15160.22461822.14080.7941240.00.1349920.00.00.05143840.2219750.1805260.144255-0.2084830.140232-0.1714690.27856-0.1264871.7557852.53330.1587491.764483.196970.4314372.24219156.3530.4002151.76425156.3260.4496281.75905173.7020.053.4110550.52222.53290.13587620.88440.0784184nan1.298021.9569321.105724.112657687523.66757364339999.09999.09999.09999.09999.09999.00.009368-1.0-10.0545010.05523-1.0-1.0-1.0-1.0348.6834.5340637.0192689.08.3271508870Catch2224.1118295796259.64347008-110.004823259529290.00156115369126-1MMT/Spectra/Final/MMT/spHect-2015.0918_1.zlog4109.0MMT
1237650372092690464180.29544216-1.29768383193GALAXY13194485816402800026843545614.754913.856913.513313.336313.27120.006161120.002182750.002218780.002977850.005712360.006161120.002182750.002218780.002977850.005712360.187590.1380270.1001090.07590930.053820714.896913.987513.639413.736413.371722.79926.67927.864328.513228.39390.6577160.8176551.006031.143551.2581629.6710.43327829.67080.26279929.6730.12308229.6720.31665729.67850.2250820.973450.8908420.8777470.9826330.70400315.10050.0062107614.16030.0021926213.74040.0022259213.62460.0029276913.37120.0057073518.84730.020726518.51060.020790618.22530.016911618.74040.017192317.94550.028418618.93080.01636218.39250.0086600918.12150.0087814918.03680.011253417.89860.0215550.08330920.04383040.0312610.00.00.01704870.003629030.08510470.006120260.0984430.004162410.1096220.003200810.1036990.004879930.63249216.694650.09440.64703616.774935.39220.64994417.400330.97590.69997119.932426.86130.6216218.798631.028318.83840.011127213.73950.00221878nan13.766129.69213.703221.937774287621.392664250716.4810.20314.6879999.014.3539999.00.00489-1.000.039220.037245-1.0-1.0-1.0-1.0180.098-1.1000823.24871465.07.3211405940Alice16.7327056701113.1590382381715141-1.0-1.0-1GAMAhttp://www.gama-survey.org/dr2/data/spectra/gama41.0GAMA
1237650762927308814179.69172842-1.461941334033GALAXY1153238168554049552262144026843545615.566314.420513.988413.625313.67210.07039090.02602870.01022390.03118840.04389190.07039090.02602870.01022390.03118840.04389190.1338820.09850890.07144690.0541760.038411519.962619.704618.105218.750717.99652.446412.856452.693122.551844.698940.1423180.01859440.02329170.05209322.520933.296751.477615.34941.034931.405930.0789734.106370.4862620.8172250.3147060.3807470.05404440.8772460.2663520.90314219.89470.083679418.69060.017856218.17670.010223918.40460.028506618.20390.043274620.88910.080373920.56571.0854818.90020.045593819.54660.11271418.67190.066837320.5670.069070419.36831.0856818.92690.033005718.60420.041380118.62590.05702570.00.00.00.00.00156207-0.0295862-0.0856345-0.0420412-0.00552304-0.0379529-0.0200157-0.0361029-0.0415385-0.647101-0.1159360.4500031.98032109.4070.2499484.32815100.8920.9229891.13723104.0260.330442.5557687.80650.9796360.762346112.32619.76850.047800818.17670.0102239nan1.468142.356518.289620.45134758321.11887133289999.09999.09999.09999.09999.09999.00.005-1.000.1871210.128613-1.0-1.0-1.0-1.0180.098-1.1000823.24871465.07.3211405940Alice32.6395144778220.7303010414054219.0407076298e-070.0-1GAMAhttp://www.gama-survey.org/dr2/data/spectra/gama41.0GAMA
1237662524159557757195.10556395113.67058584193GALAXY1056242853522080026843545616.32215.43115.144915.010914.97450.1735130.07380120.07986120.1388940.9937910.1735130.07380120.07986120.1388940.9937910.1821450.1340210.09720310.07370620.052258621.443321.157621.184121.351222.79561.366811.419341.39691.443052.969340.2246610.1860380.1471740.197682-1000.00.056814513.290.01029573.604660.2358640.688430.3660840.9065860.01048640.00.1047010.3661440.8162980.6863230.091264121.6910.30936621.36660.072668721.28130.19367921.33670.20648622.84751.2765221.66150.18348521.35140.13185121.460.12951821.64470.2251322.85111.325420.65370.071767219.77710.028854619.55250.02797119.46320.037298919.5410.1911611.01.00.00.00.0-0.0390132-0.00197435-0.02040820.003028420.01807350.01337890.031910.04683461.065780.8009690.1577930.000781397116.1990.4236690.0124015141.9410.8572870.32144520.31160.7454580.46423819.7890.05166990.00609491136.09820.39020.040416121.28130.193679nan0.7288761.314321.429620.812329138322.73836708199999.09999.09999.09999.09999.09999.00.00663794-1.00-1.0-1.0-1.0-1.0-1.0-1.0194.86314.171230.0271988.07.907142722033.1973972389289.95816760316997110.05346433356610.0370897992686-1NSAalfalfa41.23766252416e+18NSA
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In [26]:
plt.figure(figsize=(14,6))

fiblim = (12, 24)
totlim = (12, 24.25)

x1t1 = [min(fiblim[0], totlim[0]), max(fiblim[1], totlim[1])]
plt.fill_between(x1t1,x1t1, totlim[1],facecolor=[0.6]*3)
plt.axhline(21, c='k', ls=':')

cc = []
for _ in range(5):
    cc.extend(matplotlib.rcParams['axes.color_cycle'])

#first do plummer
for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'plummer') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    plt.plot(fibmags, totmags,'-o',color=cc[i],label=gal['name'])
    
    f0 = fiblim[0] < fibmags[0] < fiblim[1]
    fm1 = fiblim[0] < fibmags[-1] < fiblim[1]
    t0 = totlim[0] < totmags[0] < totlim[1]
    tm1 = totlim[0] < totmags[-1] < totlim[1]
    fi = ti = None
    if f0:
        fi=0
        if t0:
            ti=0
        elif tm1:
            ti=-1
    elif fm1:
        fi=-1
        if t0:
            ti=0
        elif tm1:
            ti=-1

for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'exp') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = gal_mag_frac(gal, np.ones_like(fracs), sagadists) - Vmr
    
    plt.plot(fibmags, totmags,'--o',color=cc[i],label=gal['name'])


#real data

plt.scatter(sats['FIBERMAG_R'], sats['r'], color='r',s=10)
plt.xlim(*fiblim)
plt.ylim(*totlim)

plt.xlabel('fibermag_r')
plt.ylabel('r')


Out[26]:
<matplotlib.text.Text at 0x1172af7d0>

In [68]:
# and absolute magnitudes
plt.figure(figsize=(10,5))

fiblim = (15, 24)
totlim = (-20, -6)

#simulated
for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'plummer') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = np.ones_like(fracs)*gal['Vabs'] - Vmr
    
    plt.plot(fibmags, totmags,'-o',color=cc[i],label=gal['name'], ms=3)
    
    f0 = fiblim[0] < fibmags[0] < fiblim[1]
    fm1 = fiblim[0] < fibmags[-1] < fiblim[1]
    t0 = totlim[0] < totmags[0] < totlim[1]
    tm1 = totlim[0] < totmags[-1] < totlim[1]
    fi = ti = None
    if f0:
        fi=0
        if t0:
            ti=0
        elif tm1:
            ti=-1
    elif fm1:
        fi=-1
        if t0:
            ti=0
        elif tm1:
            ti=-1

for i, gal in enumerate(data):
    fracs = np.array([frac_inside(gal, rad, dist, 'exp') for dist in sagadists])
    fibmags = gal_mag_frac(gal, fracs, sagadists) - Vmr
    totmags = np.ones_like(fracs)*gal['Vabs'] - Vmr 
    plt.plot(fibmags, totmags,'--o',color=cc[i],label=gal['name'], ms=3)


# now the actual SAGA data
dists = Distance(sats['HOST_DIST']*u.Mpc)
Mr = sats['r'] - dists.distmod.value

plt.scatter(sats['FIBERMAG_R'], Mr, color='r',s=20, zorder=10)


plt.xlim(*fiblim)
plt.ylim(*totlim)
plt.xlabel('fibermag_r')
plt.ylabel('$M_r$')

plt.tight_layout()


Simulated images with specific LG-dwarf like gals

The data for the LG dwarf stars here are from Ricardo Munoz and are not yet public so the data are not in the repo. If you want to reproduce these feel free to check with Ricardo or Erik.


In [11]:
fnx = Table.read('lg_dwarfs/fornax_erik.erad', format='ascii.commented_header', guess=False, header_start=2)
leoi = Table.read('lg_dwarfs/leoi_erik.erad', format='ascii.commented_header', guess=False, header_start=2)
scl = Table.read('lg_dwarfs/scl_erik.erad', format='ascii.commented_header', guess=False, header_start=2)

fnx.colnames


Out[11]:
['id',
 'ra',
 'dec',
 'g',
 'gerr',
 'r',
 'rerr',
 'chi',
 'sharp',
 'rd',
 'l',
 'b',
 'egr',
 'ag',
 'ar']

In [13]:
def plot_cmd(tab, plkwargs):
    plt.scatter(tab['g']-tab['r']-tab['egr'], tab['r']-tab['ar'], **plkwargs)
    plt.xlim(-2,3)
    plt.ylim(26,15)
    plt.xlabel('$(g-r)_0$')
    plt.ylabel('$r_0$')
    plt.tight_layout()

plkwargs = dict(alpha=.05,edgecolor='none', s=4)
plt.subplot(1,3,1)
plot_cmd(fnx, plkwargs)
plt.title('Fnx')
plt.subplot(1,3,2)
plot_cmd(leoi, plkwargs)
plt.title('Leo I')
plt.subplot(1,3,3)
plot_cmd(scl, plkwargs)
plt.title('Scl')

plt.tight_layout()


Define cython code for computationally-expensive bits


In [17]:
%load_ext Cython

In [18]:
%%cython -a

import cython
import numpy as np
from libc.math cimport exp

cdef double PI = 3.141592653589793

@cython.cdivision(True) 
cdef inline double ngauss2d(double x, double y, double sig):
    cdef double tsigsq = 2.0*sig*sig
    return exp(-(x*x + y*y)/tsigsq)/(tsigsq * PI)

@cython.wraparound(False)
@cython.boundscheck(False)
@cython.nonecheck(False)
cpdef convolve(data, xgrid, ygrid, fluxes, cenx, ceny, fwhm):
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    import time
    
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    cdef double[:, :] xgrid_view = xgrid
    cdef double[:, :] ygrid_view = ygrid
    cdef double[:] fluxes_view = fluxes
    cdef double[:] cenx_view = cenx
    cdef double[:] ceny_view = ceny
    
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    cdef double sig = fwhm/(2*(2*log(2))**0.5)
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    J = data.shape[1]
    S = fluxes.shape[0]
    
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        starflux = fluxes_view[s]
        starx = cenx_view[s]
        stary = ceny_view[s]
        
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                dx = starx + xgrid_view[i, j]
                dy = stary + ygrid_view[i, j]
                data_view[i,j] += starflux * ngauss2d(dx, dy, sig)


Out[18]:

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  if (unlikely(!__pyx_t_3.memview)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 22; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_v_ygrid_view = __pyx_t_3;
  __pyx_t_3.memview = NULL;
  __pyx_t_3.data = NULL;
+23:     cdef double[:] fluxes_view = fluxes
  __pyx_t_4 = __Pyx_PyObject_to_MemoryviewSlice_ds_double(__pyx_v_fluxes);
  if (unlikely(!__pyx_t_4.memview)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 23; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_v_fluxes_view = __pyx_t_4;
  __pyx_t_4.memview = NULL;
  __pyx_t_4.data = NULL;
+24:     cdef double[:] cenx_view = cenx
  __pyx_t_4 = __Pyx_PyObject_to_MemoryviewSlice_ds_double(__pyx_v_cenx);
  if (unlikely(!__pyx_t_4.memview)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 24; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __pyx_v_cenx_view = __pyx_t_4;
  __pyx_t_4.memview = NULL;
  __pyx_t_4.data = NULL;
+25:     cdef double[:] ceny_view = ceny
  __pyx_t_4 = __Pyx_PyObject_to_MemoryviewSlice_ds_double(__pyx_v_ceny);
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  __pyx_t_4.data = NULL;
 26: 
 27:     cdef int I, J, S
+28:     cdef double sig = fwhm/(2*(2*log(2))**0.5)
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  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
  __pyx_v_sig = __pyx_t_5;
/* … */
  __pyx_tuple_ = PyTuple_Pack(1, __pyx_int_2); if (unlikely(!__pyx_tuple_)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 28; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
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 29:     cdef double starflux, starx, stary, dx, dy
 30: 
+31:     I = data.shape[0]
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+32:     J = data.shape[1]
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  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
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+33:     S = fluxes.shape[0]
  __pyx_t_2 = __Pyx_PyObject_GetAttrStr(__pyx_v_fluxes, __pyx_n_s_shape); if (unlikely(!__pyx_t_2)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 33; __pyx_clineno = __LINE__; goto __pyx_L1_error;}
  __Pyx_GOTREF(__pyx_t_2);
  __pyx_t_1 = __Pyx_GetItemInt(__pyx_t_2, 0, long, 1, __Pyx_PyInt_From_long, 0, 0, 0); if (unlikely(__pyx_t_1 == NULL)) {__pyx_filename = __pyx_f[0]; __pyx_lineno = 33; __pyx_clineno = __LINE__; goto __pyx_L1_error;};
  __Pyx_GOTREF(__pyx_t_1);
  __Pyx_DECREF(__pyx_t_2); __pyx_t_2 = 0;
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  __Pyx_DECREF(__pyx_t_1); __pyx_t_1 = 0;
  __pyx_v_S = __pyx_t_6;
 34: 
+35:     for s in range(S):
  __pyx_t_6 = __pyx_v_S;
  for (__pyx_t_7 = 0; __pyx_t_7 < __pyx_t_6; __pyx_t_7+=1) {
    __pyx_v_s = __pyx_t_7;
+36:         starflux = fluxes_view[s]
    __pyx_t_8 = __pyx_v_s;
    __pyx_v_starflux = (*((double *) ( /* dim=0 */ (__pyx_v_fluxes_view.data + __pyx_t_8 * __pyx_v_fluxes_view.strides[0]) )));
+37:         starx = cenx_view[s]
    __pyx_t_9 = __pyx_v_s;
    __pyx_v_starx = (*((double *) ( /* dim=0 */ (__pyx_v_cenx_view.data + __pyx_t_9 * __pyx_v_cenx_view.strides[0]) )));
+38:         stary = ceny_view[s]
    __pyx_t_10 = __pyx_v_s;
    __pyx_v_stary = (*((double *) ( /* dim=0 */ (__pyx_v_ceny_view.data + __pyx_t_10 * __pyx_v_ceny_view.strides[0]) )));
 39: 
+40:         for i in range(I):
    __pyx_t_11 = __pyx_v_I;
    for (__pyx_t_12 = 0; __pyx_t_12 < __pyx_t_11; __pyx_t_12+=1) {
      __pyx_v_i = __pyx_t_12;
+41:             for j in range(J):
      __pyx_t_13 = __pyx_v_J;
      for (__pyx_t_14 = 0; __pyx_t_14 < __pyx_t_13; __pyx_t_14+=1) {
        __pyx_v_j = __pyx_t_14;
+42:                 dx = starx + xgrid_view[i, j]
        __pyx_t_15 = __pyx_v_i;
        __pyx_t_16 = __pyx_v_j;
        __pyx_v_dx = (__pyx_v_starx + (*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_xgrid_view.data + __pyx_t_15 * __pyx_v_xgrid_view.strides[0]) ) + __pyx_t_16 * __pyx_v_xgrid_view.strides[1]) ))));
+43:                 dy = stary + ygrid_view[i, j]
        __pyx_t_17 = __pyx_v_i;
        __pyx_t_18 = __pyx_v_j;
        __pyx_v_dy = (__pyx_v_stary + (*((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_ygrid_view.data + __pyx_t_17 * __pyx_v_ygrid_view.strides[0]) ) + __pyx_t_18 * __pyx_v_ygrid_view.strides[1]) ))));
+44:                 data_view[i,j] += starflux * ngauss2d(dx, dy, sig)
        __pyx_t_19 = __pyx_v_i;
        __pyx_t_20 = __pyx_v_j;
        *((double *) ( /* dim=1 */ (( /* dim=0 */ (__pyx_v_data_view.data + __pyx_t_19 * __pyx_v_data_view.strides[0]) ) + __pyx_t_20 * __pyx_v_data_view.strides[1]) )) += (__pyx_v_starflux * __pyx_f_46_cython_magic_d880b1320534d516f3bee0dfaca900e1_ngauss2d(__pyx_v_dx, __pyx_v_dy, __pyx_v_sig));
      }
    }
  }

Experiment with Fornax


In [15]:
tab = fnx
x = tab['g']-tab['r']-tab['egr']
y = tab['r']-tab['ar']


#first the larger box
maxmag = 17.4
colorrng = (-.5, 1.45)
fnxmsk = (colorrng[0]<x)&(x<colorrng[1])&(y>maxmag)

#now eliminate the MW inset
insetcolor = 1.2
insetmag = 18.5
fnxmsk[(x>insetcolor)&(y>insetmag)] = False


plt.scatter(x[fnxmsk], y[fnxmsk], alpha=.1,edgecolor='none', s=4, color='b')
plt.scatter(x[~fnxmsk], y[~fnxmsk], alpha=.1,edgecolor='none', s=4, color='r')

plt.axhline(maxmag, color='r')
plt.axvline(colorrng[0], color='r')
plt.axvline(colorrng[1], color='r')

plt.axhline(insetmag, color='r')
plt.axvline(insetcolor, color='r')

plt.xlim(-2,3)
plt.ylim(26,15)
plt.tight_layout()



In [14]:
plt.scatter(fnx['ra'], fnx['dec'], alpha=.05, edgecolor='none', s=4)
plt.tight_layout()



In [250]:
pixel_scale = 0.396*u.arcsec/u.pixel # SDSS imager
image_size = 1*u.arcmin #on a side

seeing_fwhm = 1.43*u.arcsec #median for DR7 imaging - http://classic.sdss.org/dr7/products/general/seeing.html

sky_brightness = 20.86 * u.mag * u.arcsec**-2 #SDSS r-band median -  - http://classic.sdss.org/dr7/products/general/seeing.html
inst_zeropoint = 28.2 *u.mag #mag corresponding to 1 DN/sec. this is ~r-band for SDSS DR7 based on .005 NMGYpercount
exposure_time = 59.3*u.second #SDSS
readnoise_cnts = 0

In [251]:
# just assume *all* the stars are members for now
#fnxcoo = SkyCoord.from_name('Fornax dSph')
fnx_coo = SkyCoord(39.99708*u.deg, -34.44917*u.deg)
fnx_dist = u.Quantity(ldat[ldat['name'] == 'Fornax']['distance'])[0]

fnx_galactocentric = Galactocentric(galcen_distance=fnx_dist, galcen_ra=fnx_coo.ra, galcen_dec=fnx_coo.dec,z_sun=0*u.kpc)
fnxstars_coo = SkyCoord(fnx['ra']*u.hourangle, fnx['dec']*u.deg, distance=fnx_dist).transform_to(fnx_galactocentric)
fnxstars_at_sagadists = [SkyCoord(CartesianRepresentation(x=fnxstars_coo.x+dist, y=fnxstars_coo.y, z=fnxstars_coo.z)) for dist in sagadists]

In [252]:
i = -1

imsize = np.ceil((image_size/pixel_scale).to(u.pix).value)
xg, yg = np.mgrid[-image_size/2:image_size/2:imsize*1j, -image_size/2:image_size/2:imsize*1j] * image_size.unit
fakeimagenosky = np.zeros(xg.shape)

rflux = 10**((fnx['r'] - fnx['ar'])/-2.5)
msk = np.random.permutation(np.where(fnxmsk)[0])[:40000]

star_dra = fnxstars_at_sagadists[i].ra.wrap_at(180*u.deg)
star_ddec = fnxstars_at_sagadists[i].dec.wrap_at(180*u.deg)

st = time.time()
convolve(fakeimagenosky, xg, yg, rflux[msk], star_dra.arcmin[msk], star_ddec.arcmin[msk], seeing_fwhm.to('arcmin').value)
print(time.time()-st, 'sec for', np.sum(msk), 'stars')

# correct for distance
distance_factor=((sagadists[i]/fnx_dist)**-2).decompose().value
# and pixel size
dxdy = (np.mean(np.diff(xg[:,0])).value * np.mean(np.diff(yg[0])).value)*xg.unit*yg.unit
fakeimagenosky *= dxdy.value*distance_factor*(np.sum(fnxmsk)/len(msk))

skyflux = u.arcsec**-2*10**(sky_brightness/(u.mag*u.arcsec**-2)/-2.5)
skyfluxperpixel = (skyflux*dxdy).decompose()
fakeimage = fakeimagenosky + skyfluxperpixel.value


(16.249601125717163, 'sec for', 10409377925, 'stars')

In [253]:
imunit = u.arcsec
extent = (xg.to(imunit).value.min(), xg.to(imunit).value.max(), 
          yg.to(imunit).value.min(), yg.to(imunit).value.max())
plt.imshow(fakeimage, extent=extent, cmap='gray')

plt.gca().add_patch(plt.Circle((0, 0), radius=(2*u.arcsec).to(imunit).value, edgecolor='b', facecolor='none'))
plt.gca().add_patch(plt.Circle((0, 0), radius=(3*u.arcsec).to(imunit).value, edgecolor='r', facecolor='none'))

plt.xlabel(str(imunit))
plt.ylabel(str(imunit))
plt.tight_layout()



In [254]:
#poissonified
pfakeimage = np.random.poisson(exposure_time/u.second*fakeimage*10**(inst_zeropoint/(2.5*u.mag)))
pfakeimage += np.random.randn(*fakeimage.shape)*readnoise_cnts # read noise

imunit = u.arcsec
extent = (xg.to(imunit).value.min(), xg.to(imunit).value.max(), 
          yg.to(imunit).value.min(), yg.to(imunit).value.max())
plt.imshow(pfakeimage, extent=extent, cmap='gray')

#plt.gca().add_patch(plt.Circle((0, 0), radius=(2*u.arcsec).to(imunit).value, edgecolor='b', facecolor='none'))
#plt.gca().add_patch(plt.Circle((0, 0), radius=(3*u.arcsec).to(imunit).value, edgecolor='r', facecolor='none'))

plt.xlabel(str(imunit))
plt.ylabel(str(imunit))
plt.tight_layout()



In [255]:
sep = np.hypot(xg, yg).value*xg.unit
totmag = -2.5*np.log10(np.sum(fakeimagenosky))
fibermag2 = -2.5*np.log10(np.sum(fakeimagenosky[sep < 2*u.arcsec]))
fibermag3 = -2.5*np.log10(np.sum(fakeimagenosky[sep < 3*u.arcsec]))
totmag, fibermag2, fibermag3, totmag-fibermag2, totmag-fibermag3


Out[255]:
(20.317312215648183,
 21.608086692009167,
 20.980555437629885,
 -1.2907744763609834,
 -0.66324322198170194)

In [256]:
#double- check that flux is conserved
totmag, -2.5*np.log10(np.sum(rflux[msk]))


Out[256]:
(20.317312215648183, 10.823480578226622)

In [257]:
sep = np.hypot(xg, yg).value*xg.unit
totmag = -2.5*np.log10(np.sum(fakeimage))
fibermag2 = -2.5*np.log10(np.sum(fakeimage[sep < 2*u.arcsec]))
fibermag3 = -2.5*np.log10(np.sum(fakeimage[sep < 3*u.arcsec]))
totmag, fibermag2, fibermag3, totmag-fibermag2, totmag-fibermag3


Out[257]:
(11.954420014859119,
 18.064082188736595,
 17.192285883944148,
 -6.1096621738774761,
 -5.237865869085029)

"Production"-level based on above experiments


In [296]:
def simulate_dwarf(starcat, 
                   center,
                   realdistance,
                   simdistance,
                   catmsk = None,
                   mag='r',
                   pixel_scale = 0.396*u.arcsec/u.pixel, # SDSS imager
                   image_size = 1*u.arcmin, #on a side
                   seeing_fwhm = 1.43*u.arcsec, #median for DR7 imaging - http://classic.sdss.org/dr7/products/general/seeing.html
                   sky_brightness = 20.86 * u.mag * u.arcsec**-2, #SDSS r-band median -  - http://classic.sdss.org/dr7/products/general/seeing.html
                   inst_zeropoint = 28.2 *u.mag, #mag corresponding to 1 DN/sec. this is ~r-band for SDSS DR7 based on .005 NMGYpercount
                   exposure_time = 59.3*u.second, #SDSS
                   readnoise = 0*u.count,
                   maxstars=10000,  #maximum stars to simulate
                   verbose=True):
    galactocentric = Galactocentric(galcen_distance=realdistance, galcen_ra=center.ra, galcen_dec=center.dec,z_sun=0*u.kpc)
    gcoo = SkyCoord(starcat['ra']*u.hourangle, starcat['dec']*u.deg, distance=realdistance).transform_to(galactocentric)
    stars_at_simdist = SkyCoord(CartesianRepresentation(x=gcoo.x + simdistance, y=gcoo.y, z=gcoo.z))

    imsize = np.ceil((image_size/pixel_scale).to(u.pix).value)
    xg, yg = np.mgrid[-image_size/2:image_size/2:imsize*1j, -image_size/2:image_size/2:imsize*1j] * image_size.unit
    fakeimagenosky = np.zeros(xg.shape)

    rflux = 10**((starcat['r'] - starcat['ar'])/-2.5)
    if catmsk is None:
        catmsk = np.ones(len(starcat), dtype=bool)
    idxs = np.random.permutation(np.where(catmsk)[0])[:maxstars]

    star_dra = stars_at_simdist.ra.wrap_at(180*u.deg)
    star_ddec = stars_at_simdist.dec.wrap_at(180*u.deg)

    st = time.time()
    convolve(fakeimagenosky, xg, yg, rflux[idxs], star_dra.arcmin[idxs], star_ddec.arcmin[idxs], seeing_fwhm.to('arcmin').value)
    if verbose:
        print(time.time()-st, 'sec for', len(idxs), 'stars')

    # correct for distance
    distance_factor=((simdistance/realdistance)**-2).decompose().value

    # and pixel size
    dxdy = (np.mean(np.diff(xg[:,0])).value * np.mean(np.diff(yg[0])).value)*xg.unit*yg.unit
    fakeimagenosky *= dxdy.value*distance_factor*(np.sum(catmsk)/len(idxs))

    skyflux = u.arcsec**-2*10**(sky_brightness/(u.mag*u.arcsec**-2)/-2.5)
    skyfluxperpixel = (skyflux*dxdy).decompose()
    fakeimage = fakeimagenosky + skyfluxperpixel.value

    #poissonified
    pfakeimage = np.random.poisson(exposure_time/u.second*fakeimage*10**(inst_zeropoint/(2.5*u.mag)))
    pfakeimage += np.random.randn(*fakeimage.shape)*readnoise_cnts # read noise

    return pfakeimage, fakeimage, fakeimagenosky, (xg, yg)

def show_fakeimage(img, xg, yg, imunit=u.arcsec, circles=[2*u.arcsec, 3*u.arcsec], mag=False, **kwargs):
    extent = (xg.to(imunit).value.min(), xg.to(imunit).value.max(), 
              yg.to(imunit).value.min(), yg.to(imunit).value.max())
    
    kwargs.setdefault('extent', extent)
    kwargs.setdefault('cmap', 'gray')
    if mag:
        img = -2.5*np.log10(img)
    plt.imshow(img, **kwargs)
    
    if circles is None:
        circles = []
    for rad in circles:
        plt.gca().add_patch(plt.Circle((0, 0), radius=rad.to(imunit).value, edgecolor='r', facecolor='none'))
    
    plt.xlabel(str(imunit))
    plt.ylabel(str(imunit))
    
def aperture_mags(img, apertures=[2*u.arcsec, 3*u.arcsec]):
    sep = np.hypot(xg, yg).value*xg.unit
    
    totmag = -2.5*np.log10(np.sum(img))
    apmags = np.array([-2.5*np.log10(np.sum(img[sep < ap])) for ap in apertures])
    return totmag, apmags, apmags-totmag

Test w/ Fornax to reproduce above


In [303]:
pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(fnx, fnx_coo, fnx_dist, sagadists[-1], fnxmsk)


(3.9524190425872803, 'sec for', 10000, 'stars')

In [304]:
show_fakeimage(pfakeimage, xg, yg)
plt.tight_layout()



In [305]:
show_fakeimage(fakeimagenosky, xg, yg, mag=True,vmin=24,vmax=28)
plt.colorbar()
plt.tight_layout()


/opt/local/Library/Frameworks/Python.framework/Versions/2.7/lib/python2.7/site-packages/IPython/kernel/__main__.py:61: RuntimeWarning: divide by zero encountered in log10

In [306]:
aperture_mags(fakeimagenosky)


Out[306]:
(20.285793413994725,
 array([ 21.57214877,  20.93191031]),
 array([ 1.28635535,  0.6461169 ]))

Now simulate all


In [309]:
fnx_coo = SkyCoord.from_name('Fornax dSph')
scl_coo = SkyCoord.from_name('Sculptor dSph')
leoi_coo = SkyCoord.from_name('Leo I dSph')

fnx_dist = u.Quantity(ldat[ldat['name'] == 'Fornax']['distance'])[0]
scl_dist = u.Quantity(ldat[ldat['name'] == 'Sculptor']['distance'])[0]
leoi_dist = u.Quantity(ldat[ldat['name'] == 'Leo I']['distance'])[0]

In [325]:
maxs = 10000

for d in sagadists[-3:]:
    plt.figure()

    plt.subplot(1,3,1)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(fnx, fnx_coo, fnx_dist, d, fnxmsk, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Fornax @ {0}'.format(d))
    print('Fornax @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.subplot(1,3,2)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(scl, scl_coo, scl_dist, d, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Sculptor @ {0}'.format(d))
    print('Sculptor @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.subplot(1,3,3)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(leoi, leoi_coo, leoi_dist, d, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Leo I @ {0}'.format(d))
    print('Leo I @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.tight_layout()


(3.8257431983947754, 'sec for', 10000, 'stars')
Fornax @ 30.0 Mpc aperture phot:(19.561656862219444, array([ 21.45943813,  20.73543203]), array([ 1.89778127,  1.17377517]))
(3.8727328777313232, 'sec for', 10000, 'stars')
Sculptor @ 30.0 Mpc aperture phot:(20.88634585239766, array([ 22.18143815,  21.6340071 ]), array([ 1.2950923 ,  0.74766125]))
(3.8812248706817627, 'sec for', 10000, 'stars')
Leo I @ 30.0 Mpc aperture phot:(19.758481460908261, array([ 21.41017791,  21.05231731]), array([ 1.65169645,  1.29383585]))
(3.9598288536071777, 'sec for', 10000, 'stars')
Fornax @ 35.0 Mpc aperture phot:(19.953183080100303, array([ 21.46229353,  20.8324072 ]), array([ 1.50911045,  0.87922412]))
(3.9839558601379395, 'sec for', 10000, 'stars')
Sculptor @ 35.0 Mpc aperture phot:(21.094637731443832, array([ 22.42789451,  21.9975702 ]), array([ 1.33325678,  0.90293247]))
(4.132309198379517, 'sec for', 10000, 'stars')
Leo I @ 35.0 Mpc aperture phot:(20.167389478526211, array([ 21.53336993,  21.2650444 ]), array([ 1.36598045,  1.09765492]))
(4.16658878326416, 'sec for', 10000, 'stars')
Fornax @ 42.0 Mpc aperture phot:(20.36450036855539, array([ 21.64951258,  21.01798788]), array([ 1.28501221,  0.65348751]))
(4.049621105194092, 'sec for', 10000, 'stars')
Sculptor @ 42.0 Mpc aperture phot:(21.541970765224526, array([ 22.42744964,  21.9665611 ]), array([ 0.88547888,  0.42459033]))
(4.056612968444824, 'sec for', 10000, 'stars')
Leo I @ 42.0 Mpc aperture phot:(20.5569469729327, array([ 21.79114544,  21.54519612]), array([ 1.23419847,  0.98824915]))

In [333]:
maxs = 1000000

for d in sagadists[-3:]:
    plt.figure()

    plt.subplot(1,3,1)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(fnx, fnx_coo, fnx_dist, d, fnxmsk, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Fornax @ {0}'.format(d))
    print('Fornax @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.subplot(1,3,2)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(scl, scl_coo, scl_dist, d, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Sculptor @ {0}'.format(d))
    print('Sculptor @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.subplot(1,3,3)
    pfakeimage, fakeimage, fakeimagenosky, (xg, yg) = simulate_dwarf(leoi, leoi_coo, leoi_dist, d, maxstars=maxs)
    show_fakeimage(pfakeimage, xg, yg)
    plt.title('Leo I @ {0}'.format(d))
    print('Leo I @ {0} aperture phot:{1}'.format(d, aperture_mags(fakeimagenosky)))

    plt.tight_layout()


(205.45911288261414, 'sec for', 518831, 'stars')
Fornax @ 30.0 Mpc aperture phot:(19.581102699986232, array([ 21.43402263,  20.72129531]), array([ 1.85291993,  1.14019261]))
(102.17570114135742, 'sec for', 266799, 'stars')
Sculptor @ 30.0 Mpc aperture phot:(20.81145064616517, array([ 22.15829341,  21.66139898]), array([ 1.34684276,  0.84994833]))
(26.53728985786438, 'sec for', 70914, 'stars')
Leo I @ 30.0 Mpc aperture phot:(19.782656546567004, array([ 21.38039879,  21.02607426]), array([ 1.59774224,  1.24341771]))
(4508.040508985519, 'sec for', 518831, 'stars')
Fornax @ 35.0 Mpc aperture phot:(19.915836648139322, array([ 21.50074471,  20.82150314]), array([ 1.58490806,  0.90566649]))
(120.43996095657349, 'sec for', 266799, 'stars')
Sculptor @ 35.0 Mpc aperture phot:(21.146184594318242, array([ 22.31335318,  21.83310942]), array([ 1.16716859,  0.68692483]))
(31.287028789520264, 'sec for', 70914, 'stars')
Leo I @ 35.0 Mpc aperture phot:(20.117390494720073, array([ 21.58529474,  21.28034618]), array([ 1.46790425,  1.16295568]))
(234.5745449066162, 'sec for', 518831, 'stars')
Fornax @ 42.0 Mpc aperture phot:(20.311742878377462, array([ 21.59688525,  20.96471014]), array([ 1.28514237,  0.65296727]))
(120.95794701576233, 'sec for', 266799, 'stars')
Sculptor @ 42.0 Mpc aperture phot:(21.542090824556368, array([ 22.50590887,  22.05195197]), array([ 0.96381804,  0.50986114]))
(32.12344193458557, 'sec for', 70914, 'stars')
Leo I @ 42.0 Mpc aperture phot:(20.513296724958199, array([ 21.85188391,  21.5998318 ]), array([ 1.33858719,  1.08653507]))

In [ ]: