Figures Using Bar Sizes

Requirements

This notebook is meant to be run within the full s4g_barfractions repository, including the associated Python modules and data files.

In addition, this notebook requires, directly or indirectly, the following Python packages:

numpy
matplotlib
Michaele Cappellari's Python package cap_loess_1d

By default, output PDF figure files are not saved to disk; to enable this, set the savePlots variable in the Setup cell to True and change the plotDir variable (same cell) to point to where you want the figures saved.

Setup



In [19]:

    
import numpy as np
import cap_loess_1d

import datautils as du
import plotutils as pu
import s4gutils

# paths for locating data, saving plots, etc.
dataDir = "./data/"
simDir = dataDir
# change the following if you want to save the figures somewhere convenient
baseDir = "/Users/erwin/Documents/Working/Paper-s4gbars/"
plotDir = baseDir + "plots/"
savePlots = False

s4gdata = du.ReadCompositeTable(dataDir+"s4gbars_table.dat", columnRow=25, dataFrame=True)
nDisksTotal = len(s4gdata.name)

fwhm_s4g1 = 1.66   # 3.6-micron FWHM in arcsec
fwhm_s4g2 = 2.0   # approx. S4G FWHM in arcsec acc. to Salo+2015
fwhm_kpc_s4g1 = pc(16.8) * fwhm_s4g1 / 1e3
fwhm_kpc_s4g2 = pc(16.8) * fwhm_s4g2 / 1e3
fwhm_kpc_gz2 = 1.25  # z = 0.01--0.06, mean z = 0.045, FWHM = 1.4 arcsec


# axis labels, etc., for plots
xtmstar = r"$\log \: (M_{\star} / M_{\odot})$"
xtfgas = r"$\log \: (M_{\rm HI} / M_{\star})$"
xtgmr = r"$g - r$"
ytfbar = r"Bar Fraction $f_{\rm bar}$"
ytbarsize_kpc = r"Bar size $a_{\rm vis}$ [kpc]"
ytbarsize_kpc_obs = r"Observed bar size $a_{\rm vis}$ [kpc]"

s4g_fwhm_txt = r"S$^{4}$G $\langle$FWHM$\rangle$"



In [21]:

    
%pylab inline

matplotlib.rcParams['figure.figsize'] = (8,6)
matplotlib.rcParams['xtick.labelsize'] = 16
matplotlib.rcParams['ytick.labelsize'] = 16
matplotlib.rcParams['axes.labelsize'] = 20

# kludge to fix matplotlib's font_manager bug which mistakenly ID's "Times New Roman Bold.ttf" as
# indicating a "roman" (i.e., "normal") weight
#del matplotlib.font_manager.weight_dict['roman']
matplotlib.font_manager._rebuild()









    



Populating the interactive namespace from numpy and matplotlib

Defining different subsamples via index vectors

Lists of integers defining indices of galaxies in Parent Disc Sample which meet various criteria that define specific subsamples.



In [22]:

    
# general subsamples: all barred, all unbarred, all spirals
ii_barred = [i for i in range(nDisksTotal) if s4gdata.sma[i] > 0]
ii_unbarred = [i for i in range(nDisksTotal) if s4gdata.sma[i] <= 0]
ii_spirals = [i for i in range(nDisksTotal) if s4gdata.t_s4g[i] > -0.5]


# Sample 1: spirals with D < 25 Mpc -- 663 spirals: 373 barred, 290 unbarred
ii_all_limited1 = [i for i in ii_spirals if s4gdata.dist[i] <= 25]
ii_barred_limited1 = [i for i in ii_all_limited1 if i in ii_barred]
ii_unbarred_limited1 = [i for i in ii_all_limited1 if i not in ii_barred]

ii_barred_m9 = [i for i in ii_barred if s4gdata.logmstar[i] >= 9]


# Sample 1m: spirals with D < 25 Mpc and log Mstar >= 8.5 -- 576 spirals: 356 barred, 220 unbarred
ii_all_limited1_m8_5 = [i for i in ii_all_limited1 if s4gdata.logmstar[i] >= 8.5]
ii_barred_limited1_m8_5 = [i for i in ii_all_limited1_m8_5 if i in ii_barred]
ii_unbarred_limited1_m8_5 = [i for i in ii_all_limited1_m8_5 if i not in ii_barred]

# limited subsample 2: D < 30 Mpc -- 856 galaxies: 483 barred, 373 unbarred
ii_all_limited2 = [i for i in ii_spirals if s4gdata.dist[i] <= 30]
ii_barred_limited2 = [i for i in ii_all_limited2 if i in ii_barred]
ii_unbarred_limited2 = [i for i in ii_all_limited2 if i not in ii_barred]

# limited subsample 2m: D < 30 Mpc and log Mstar >= 9 -- 639 galaxies: 398 barred, 241 unbarred
ii_all_limited2_m9 = [i for i in ii_all_limited2 if s4gdata.logmstar[i] >= 9]
ii_barred_limited2_m9 = [i for i in ii_all_limited2_m9 if i in ii_barred]
ii_unbarred_limited2_m9 = [i for i in ii_all_limited2_m9 if i not in ii_barred]
ii_barred_limited2_m9to11 = [i for i in ii_all_limited2_m9 if i in ii_barred and s4gdata.logmstar[i] <= 11]

Useful functions



In [23]:

    
# broken-linear function: y as function of mstar: 
#    y = alpha_1 + beta_1*mstar for mstar < mstar_break, alpha_2 + beta_2*mstar
#        for mstar > mstar_break
def simplefunc_brokenlinear( params, logmstar ):
    alpha_1 = params[0]
    beta_1 = params[1]
    mstar_break = params[2]
    beta_2 = params[3]
    alpha_2 = alpha_1 + (beta_1 - beta_2)*mstar_break
    if (np.iterable(logmstar) == 0):
        logmstar = [logmstar]
    npts = len(logmstar)
    vals = []
    for i in range(npts):
        if logmstar[i] < mstar_break:
            value = alpha_1 + beta_1*logmstar[i]
        else:
            value = alpha_2 + beta_2*logmstar[i]
        vals.append(value)
    return vals


# code to make using Cappellari LOESS function more useful:
# returns tuple of (x_sorted, y_predicted), where
#    x_sorted = x sorted into monotonically ascending
#    y_predicted = LOESS predicted y-values corresponding to x_sorted
def GetSortedLoess1D( x, y, frac=0.5, degree=1 ):
    ii_sorted = np.argsort(x)
    x_sorted = x[ii_sorted]
    y_sorted = y[ii_sorted]
    x_sorted, y_predicted, w = cap_loess_1d.loess_1d(x_sorted, y_sorted, frac=frac, degree=degree)
    return x_sorted, y_predicted

Figure 3: S4G Bar Sizes vs Distance

Intrinsic (deprojected) bar size in kpc versus galaxy stellar mass, with broken-linear fit (to log bar size vs log stellar mass).



In [25]:

    
plt.plot(s4gdata.dist[ii_barred], s4gdata.sma_kpc[ii_barred], 'ko', mfc='None',ms=4)
plt.plot(s4gdata.dist[ii_barred_m9], s4gdata.sma_kpc[ii_barred_m9], 'cD', mec='k', ms=4)
plt.xlabel("Distance [Mpc]")
plt.ylabel(r"Observed bar $a_{\rm vis}$ [kpc]")
xx = np.arange(0,61,1)
plt.plot(xx, 2*fwhm_s4g2*pc(xx)/1e3, 'k--')
plt.plot(xx, 3*fwhm_s4g2*pc(xx)/1e3, 'k--')
plt.plot(xx, 4*fwhm_s4g2*pc(xx)/1e3, 'k--')
plt.plot(xx, 5*fwhm_s4g2*pc(xx)/1e3, 'k--')
text(45,0.7,r"$a = 2 \times$ FWHM", fontsize=11)
text(52,1.3,r"$3$", fontsize=11)
text(53.5,1.9,r"$4$", fontsize=11)
text(57,2.6,r"$5$", fontsize=11)
plt.xlim(0,60);plt.ylim(0,5)
if savePlots: plt.savefig(plotDir+"barsize-vs-distance.pdf")

Figure 6: S4G Bar Sizes vs Stellar Mass

Log version



In [26]:

    
params_sample2 = np.array([ -0.6567681 ,   0.09511946,  10.10799995,   0.48968006])
mm = np.arange(8,12,0.01)
semilogy(s4gdata.logmstar[ii_barred_limited2], s4gdata.sma_dp_kpc2[ii_barred_limited2], 'o', mfc='0.9',ms=5, alpha=0.7)
semilogy(s4gdata.logmstar[ii_barred_limited1], s4gdata.sma_dp_kpc2[ii_barred_limited1], 'o', mfc='0.2',ms=5)
xlim(8.5,11.5);ylim(0.1,15)
plot(mm, 10**np.array(simplefunc_brokenlinear(params_sample2, mm)), 'r--', lw=2.5)
xlabel(xtmstar);ylabel(ytbarsize_kpc)
pu.MakeNiceLogAxes(whichAxis="y")
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
if savePlots: plt.savefig(plotDir+"barsize-vs-mass-with-fit_samples12.pdf")

Linear version



In [27]:

    
plot(s4gdata.logmstar[ii_barred_limited2], s4gdata.sma_dp_kpc2[ii_barred_limited2], 'o', mfc='0.9',ms=5, alpha=0.7)
plot(s4gdata.logmstar[ii_barred_limited1], s4gdata.sma_dp_kpc2[ii_barred_limited1], 'o', mfc='0.2',ms=5)
xlim(8.5,11.5);ylim(0,14)
plot(mm, 10**np.array(simplefunc_brokenlinear(params_sample2, mm)), 'r--', lw=2.5)
xlabel(xtmstar);ylabel(ytbarsize_kpc)
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
plt.savefig(plotDir+"barsize-vs-mass-with-fit_samples12_linear.pdf")

S4G Observed Bar Sizes vs Stellar Mass, Color, Gas Mass Fraction with FWHM

Note: In the paper, these three figures are stacked vertically to create a single composite figure (via an Adobe Illustrator file not included here).



In [34]:

    
savePlots = True

Figure 7 (top): Observed Bar Sizes vs Stellar Mass, with FWHM



In [35]:

    
semilogy(s4gdata.logmstar[ii_barred_limited2], s4gdata.sma_kpc[ii_barred_limited2], 'o', mec='k', color='1',ms=4, alpha=0.7)
semilogy(s4gdata.logmstar[ii_barred_limited1], s4gdata.sma_kpc[ii_barred_limited1], 'o', mec='k', color='0.5',ms=4, alpha=0.7)
xlim(8,11.5);ylim(0.1,15)
ax = gca()
ax.add_patch(Rectangle((8,0.1), 3.5, fwhm_kpc_gz2 - 0.1, facecolor='b', alpha=0.1))
ax.add_patch(Rectangle((8,fwhm_kpc_gz2), 3.5, fwhm_kpc_gz2, facecolor='b', alpha=0.05))
pu.MakeNiceLogAxes(whichAxis="y")

axhline(fwhm_kpc_s4g2, ls='--', lw=1.5, color='0.2')
axhline(2*fwhm_kpc_s4g2, ls='--', lw=0.75, color='0.2')
axhline(fwhm_kpc_gz2, ls='--', lw=1.5, color='b')
axhline(2*fwhm_kpc_gz2, ls='--', lw=0.75, color='b')

text(10.7,1.15*fwhm_kpc_s4g2, s4g_fwhm_txt, fontsize=10)
text(10.55,1.11*2*fwhm_kpc_s4g2, r"$2 \times$" + s4g_fwhm_txt, fontsize=10)
text(10.7,1.1*fwhm_kpc_gz2, r"GZ2 $\langle$FWHM$\rangle$", color='b',fontsize=10)
text(11.1,1.1*2*fwhm_kpc_gz2, r"$2 \times$GZ2", color='b',fontsize=10)
xlabel(xtmstar,fontsize=15);ylabel(ytbarsize_kpc_obs,fontsize=15)
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
if savePlots: plt.savefig(plotDir+"barsize-vs-mass-with-fwhm.pdf")

Figure 7 (middle): Observed Bar Sizes vs Galaxy Color, with FWHM



In [36]:

    
semilogy(s4gdata.gmr_tc[ii_barred_limited1_m8_5], s4gdata.sma_kpc[ii_barred_limited1_m8_5], 'o', mec='k', color='1',ms=4, alpha=0.7)
semilogy(s4gdata.gmr_tc[ii_barred_limited2_m9], s4gdata.sma_kpc[ii_barred_limited2_m9], 'o', mec='k', color='0.3',ms=4, alpha=0.7)
xlim(0,1);ylim(0.1,15)
ax = gca()
ax.add_patch(Rectangle((0,0.1), 1, fwhm_kpc_gz2 - 0.1, facecolor='b', alpha=0.1))
ax.add_patch(Rectangle((0,fwhm_kpc_gz2), 1, fwhm_kpc_gz2, facecolor='b', alpha=0.05))
pu.MakeNiceLogAxes(whichAxis="y")
plt.xlabel(xtgmr,fontsize=15)
ylabel(ytbarsize_kpc_obs,fontsize=15)

axhline(fwhm_kpc_s4g2, ls='--', lw=1.5, color='0.2')
axhline(2*fwhm_kpc_s4g2, ls='--', lw=0.75, color='0.2')
axhline(fwhm_kpc_gz2, ls='--', lw=1.5, color='b')
axhline(2*fwhm_kpc_gz2, ls='--', lw=0.75, color='b')

text(0.77,1.1*fwhm_kpc_s4g2, s4g_fwhm_txt, fontsize=10)
text(0.77,1.1*2*fwhm_kpc_s4g2, r"$2 \times$" + s4g_fwhm_txt, fontsize=10)
text(0.83,1.1*fwhm_kpc_gz2, r"GZ2 $\langle$FWHM$\rangle$", color='b',fontsize=10)
text(0.88,1.1*2*fwhm_kpc_gz2, r"$2 \times$GZ2", color='b',fontsize=10)
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
if savePlots: plt.savefig(plotDir+"barsize-vs-gmr-with-fwhm.pdf")

Figure 7 (bottom): Observed Bar Sizes vs Gas Mass Ratio, with FWHM



In [37]:

    
semilogy(s4gdata.logfgas[ii_barred_limited1_m8_5], s4gdata.sma_kpc[ii_barred_limited1_m8_5], 'o', mec='k', color='1',ms=4, alpha=0.7)
semilogy(s4gdata.logfgas[ii_barred_limited2_m9], s4gdata.sma_kpc[ii_barred_limited2_m9], 'o', mec='k', color='0.3',ms=4, alpha=0.7)
xlim(-3,1.5);ylim(0.1,15)
ax = gca()
ax.add_patch(Rectangle((-3,0.1), 4.5, fwhm_kpc_gz2 - 0.1, facecolor='b', alpha=0.1))
ax.add_patch(Rectangle((-3,fwhm_kpc_gz2), 4.5, fwhm_kpc_gz2, facecolor='b', alpha=0.05))
pu.MakeNiceLogAxes(whichAxis="y")
plt.xlabel(r"$\log (M_{\rm HI} / M_{\star})$", fontsize=15)
ylabel(ytbarsize_kpc_obs,fontsize=15)

axhline(fwhm_kpc_s4g2, ls='--', lw=1.5, color='0.2')
axhline(2*fwhm_kpc_s4g2, ls='--', lw=0.75, color='0.2')
axhline(fwhm_kpc_gz2, ls='--', lw=1.5, color='b')
axhline(2*fwhm_kpc_gz2, ls='--', lw=0.75, color='b')
text(0.45,1.1*fwhm_kpc_s4g2, s4g_fwhm_txt, fontsize=10)
text(0.45,1.1*2*fwhm_kpc_s4g2, r"$2 \times$" + s4g_fwhm_txt, fontsize=10)
text(0.7,1.1*fwhm_kpc_gz2, r"GZ2 $\langle$FWHM$\rangle$", color='b',fontsize=10)
text(0.9,1.1*2*fwhm_kpc_gz2, r"$2 \times$GZ2", color='b',fontsize=10)
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
if savePlots: plt.savefig(plotDir+"barsize-vs-fgas-with-fwhm.pdf")

Figure 8: Observed Bar Sizes: GZ2 (Hoyle+2011) vs S4G



In [ ]:

    
# get Hoyle+2011 Galaxy Zoo 2 data
ff = "./data/external/GalaxyZoo2_barlengths_alldata.txt"
h11table = du.ReadCompositeTable(ff, columnRow=0, dataFrame=True)

# get LOESS fits
h11xx, h11yy = GetSortedLoess1D(h11table.logMstar, np.log10(h11table.sma_kpc))
h11yy = 10**h11yy
s4gxx, s4gyy = GetSortedLoess1D(s4gdata.logmstar[ii_barred], np.log10(s4gdata.sma_kpc[ii_barred]))
s4gyy = 10**s4gyy

# get precomputed 10% and 90% limits for Hoyle+2011 and S4G bar sizes as fn. of log stellar mass
# (see the R notebook s4gbars_R_quantile-loess.ipynb for how these are calculated)
h11x10,h11y10 = s4gutils.Read2ColumnProfile('./data/hoyle+11_gz2_barsizes_10percentile.txt')
h11x90,h11y90 = s4gutils.Read2ColumnProfile('./data/hoyle+11_gz2_barsizes_90percentile.txt')
s4gx10,s4gy10 = s4gutils.Read2ColumnProfile('./data/s4g_barsizes_10percentile.txt')
s4gx90,s4gy90 = s4gutils.Read2ColumnProfile('./data/s4g_barsizes_90percentile.txt')


f,(ax1,ax2) = subplots(1,2, figsize=(15,5), sharey=True)

ax1.semilogy(h11table.logMstar, h11table.sma_kpc, 'o', ms=2, color='b', alpha=0.2, label="Hoyle+11")
ax1.set_xlim(8.5,11.5);ax1.set_ylim(0.1,20)
ax1.set_xlabel(xtmstar, fontsize=15)
ax1.set_ylabel(r"Observed bar sma [kpc]", fontsize=15)
ax1.plot(h11xx, h11yy, 'b', lw=2,label='Hoyle+11 LOESS')
ax1.plot(h11x10, 10**h11y10, 'b--', label="Hoyle+11 10,90%")
ax1.plot(h11x90, 10**h11y90, 'b--')
ax1.legend(loc='lower right', ncol=2, fontsize=10)
pu.MakeNiceLogAxes(whichAxis="y", axisObj=ax1)

ax2.semilogy(s4gdata.logmstar[ii_barred], s4gdata.sma_kpc[ii_barred], 'ro', ms=3, alpha=0.25, label='S4G')
ax2.set_xlim(8.5,11.5);ax2.set_ylim(0.1,20)
ax2.set_xlabel(xtmstar, fontsize=15)
ax2.plot(s4gxx, s4gyy, 'r', lw=2.5, label='S4G LOESS')
ax2.plot(h11xx, h11yy, 'b', lw=2, label='Hoyle+11 LOESS')
ax2.plot(h11x10, 10**h11y10, 'b--', label="GZ2 10,90%")
ax2.plot(h11x90, 10**h11y90, 'b--')
ax2.plot(s4gx10, 10**s4gy10, 'r--', lw=1.5, label="S4G 10,90%")
ax2.plot(s4gx90, 10**s4gy90, 'r--', lw=1.5)
ax2.legend(loc='lower right', ncol=3, fontsize=10)
pu.MakeNiceLogAxes(whichAxis="y", axisObj=ax1)

subplots_adjust(wspace=0.1)
if savePlots: savefig(plotDir+"barsizes_H11-vs-S4G.pdf")

Figure 9: S4G Relative Bar Sizes

Intrinsic (deprojected) bar semi-major axis divided by optical radius $R_{25}$, as a function of stellar mass, with LOESS fit.



In [ ]:

    
barsize_r25 = s4gdata.sma_dp_kpc2 / s4gdata.R25_kpc

s4gxx, s4gyy = GetSortedLoess1D(s4gdata.logmstar[ii_barred_limited2_m9to11], np.log10(barsize_r25[ii_barred_limited2_m9to11]), frac=0.3)
s4gyy = 10**s4gyy


semilogy(s4gdata.logmstar[ii_barred_limited2], barsize_r25[ii_barred_limited2], 'o', color='1',mew=0.6, ms=4, alpha=0.7)
plot(s4gxx, s4gyy, 'r-', lw=2)
xlim(8.5,11.5)
ylim(0.03,1.5)
xlabel(xtmstar)
ylabel(r"Relative bar size: $a_{\rm vis} / R_{25}$")
pu.MakeNiceLogAxes(whichAxis="y")
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)

if savePlots: savefig(plotDir+"barsize-R25_vs_logmstar-with-loess.pdf")

Figure 11: S4G Observed Bar Sizes vs Stellar Mass with High-Redshift FWHM



In [32]:

    
fwhm_kpc_hst1 = 0.54
fwhm_kpc_hst2 = 0.81

semilogy(s4gdata.logmstar[ii_barred_limited2], s4gdata.sma_kpc[ii_barred_limited2], 'o', color='1',ms=4, alpha=0.7)
semilogy(s4gdata.logmstar[ii_barred_limited1], s4gdata.sma_kpc[ii_barred_limited1], 'o', color='0.5',ms=4, alpha=0.7)
xlim(8,11.5);ylim(0.1,15)
pu.MakeNiceLogAxes(whichAxis="y")
axhline(fwhm_kpc_s4g2, ls='--', lw=1.2, color='0.2')
axhline(2*fwhm_kpc_s4g2, ls='--', lw=0.7, color='0.2')
axhline(fwhm_kpc_hst1, ls='--', lw=1.2, color='g')
axhline(2*fwhm_kpc_hst1, ls='--', lw=0.7, color='g')
axhline(fwhm_kpc_hst2, ls='--', lw=1.2, color='r')
axhline(2*fwhm_kpc_hst2, ls='--', lw=0.7, color='r')
text(10.7,1.1*fwhm_kpc_s4g2, r"S4G $\langle$FWHM$\rangle$", fontsize=11)
text(10.55,1.1*2*fwhm_kpc_s4g2, r"$2 \times$S4G $\langle$FWHM$\rangle$", fontsize=11)
text(10.75,1.06*fwhm_kpc_hst1, r"$z = 0.4 \: \langle$FWHM$\rangle$", color='g',fontsize=11)
text(10.75,1.06*fwhm_kpc_hst2, r"$z = 1 \: \langle$FWHM$\rangle$", color='r',fontsize=11)
xlabel(xtmstar);ylabel(ytbarsize_kpc_obs)
# push bottom of plot upwards so that x-axis label isn't clipped in PDF output
plt.subplots_adjust(bottom=0.14)
if savePlots: plt.savefig(plotDir+"barsize-vs-mass-with-high-z-fwhm.pdf")



In [ ]: