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ENH: example for galaxy demographics #520
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""" | ||||||||||||||||||||||||||
Galaxy Demographics | ||||||||||||||||||||||||||
=================== | ||||||||||||||||||||||||||
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In this example we reproduce the results from de la Bella et al. 2021 [1]_. | ||||||||||||||||||||||||||
In that paper the authors distinguished between active galaxies | ||||||||||||||||||||||||||
(centrals and satellites) and quiescent galaxies (mass-quenched and satellite-quenched), | ||||||||||||||||||||||||||
describing the galaxy demographics with a set of continuity equations that are solved analytically. | ||||||||||||||||||||||||||
Such equations invoke two quenching mechanisms that transform star-forming galaxies into quiescent | ||||||||||||||||||||||||||
objects: mass quenching and satellite quenching. | ||||||||||||||||||||||||||
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They showed that the combination of the two quenching mechanisms produces | ||||||||||||||||||||||||||
a double Schechter function for the quiescent population. | ||||||||||||||||||||||||||
They demonstrated that the satellite-quenched galaxies are indeed a subset | ||||||||||||||||||||||||||
of the active galaxies and that the mass-quenched galaxies have a different | ||||||||||||||||||||||||||
faint-end slope parameter by one unit. The connection between quenching and | ||||||||||||||||||||||||||
galaxy populations reduced significantly the parameter space of the simulations. | ||||||||||||||||||||||||||
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This example uses de la Bella et al. model implemented in `skypy.galaxies.stellar_mass` | ||||||||||||||||||||||||||
and shows how to sample any type of galaxy population | ||||||||||||||||||||||||||
from a general Schechter mass function. | ||||||||||||||||||||||||||
""" | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
# Schechter Parameters | ||||||||||||||||||||||||||
# -------------------- | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# We generate their Figure 4 and use the best-fit values of the blue parameters | ||||||||||||||||||||||||||
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# in Wiegel et al. 2016 [2]_. We follow de la Bella et al.'s procedure | ||||||||||||||||||||||||||
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# to compute the fraction of satellite galaxies from [2] | ||||||||||||||||||||||||||
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# and use their fixed value for the fraction of satellite-quenched galaxies | ||||||||||||||||||||||||||
# :math:`f_{\rho} = 0.5`. | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# Finally we generate the different galaxy samples by feeding the Schechter parameters | ||||||||||||||||||||||||||
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# as inputs for the Schechter mass function. | ||||||||||||||||||||||||||
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import numpy as np | ||||||||||||||||||||||||||
import matplotlib.pyplot as plt | ||||||||||||||||||||||||||
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from astropy.cosmology import FlatLambdaCDM | ||||||||||||||||||||||||||
from astropy.table import Table | ||||||||||||||||||||||||||
from astropy.units import Quantity | ||||||||||||||||||||||||||
from skypy.galaxies import schechter_smf | ||||||||||||||||||||||||||
# from skypy.galaxies.stellar_mass import (schechter_smf_amplitude_centrals, | ||||||||||||||||||||||||||
# schechter_smf_amplitude_satellites, | ||||||||||||||||||||||||||
# schechter_smf_amplitude_mass_quenched, | ||||||||||||||||||||||||||
# schechter_smf_amplitude_satellite_quenched | ||||||||||||||||||||||||||
# ) | ||||||||||||||||||||||||||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I understand this can only be included after #516 is merged. Please adapt the indentation when when this PR is ready to be merged. |
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# %% | ||||||||||||||||||||||||||
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# Weigel et al. 2016 parameters for the active population | ||||||||||||||||||||||||||
phiblue = 10**-2.423 | ||||||||||||||||||||||||||
mstarb = 10**10.60 | ||||||||||||||||||||||||||
alphab = -1.21 | ||||||||||||||||||||||||||
blue = (phiblue, alphab, mstarb) | ||||||||||||||||||||||||||
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# Fraction of satellite-quenched galaxies and satellites | ||||||||||||||||||||||||||
frho = 0.5 | ||||||||||||||||||||||||||
fsat = 0.4 | ||||||||||||||||||||||||||
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# Weigel+16 redshift and cosmology | ||||||||||||||||||||||||||
z_min, z_max = 0.02, 0.06 | ||||||||||||||||||||||||||
z_range = np.linspace(z_min, z_max, 100) | ||||||||||||||||||||||||||
cosmology = FlatLambdaCDM(H0=70, Om0=0.3) | ||||||||||||||||||||||||||
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# Sky area (SDSS DR7 8423 deg2) | ||||||||||||||||||||||||||
sky_area = Quantity(2000, "deg2") | ||||||||||||||||||||||||||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. I guess the number in the comment should match the defined number. |
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# %% | ||||||||||||||||||||||||||
# First we use the model implemented in `skypy.galaxies.stellar_mass`. | ||||||||||||||||||||||||||
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# To be replaced by the SkyPy function once it's merged | ||||||||||||||||||||||||||
def schechter_smf_phi_centrals(phi_blue_total, fsatellite): | ||||||||||||||||||||||||||
if np.ndim(phi_blue_total) == 1 and np.ndim(fsatellite) == 1: | ||||||||||||||||||||||||||
phi_blue_total = phi_blue_total[:, np.newaxis] | ||||||||||||||||||||||||||
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sum_phics = (1 - fsatellite) * (1 - np.log(1 - fsatellite)) | ||||||||||||||||||||||||||
return (1 - fsatellite) * phi_blue_total / sum_phics | ||||||||||||||||||||||||||
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def schechter_smf_phi_satellites(phi_centrals, fsatellite): | ||||||||||||||||||||||||||
return phi_centrals * np.log(1 / (1 - fsatellite)) | ||||||||||||||||||||||||||
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def schechter_smf_phi_mass_quenched(phi_centrals, phi_satellites): | ||||||||||||||||||||||||||
return phi_centrals + phi_satellites | ||||||||||||||||||||||||||
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def schechter_smf_phi_satellite_quenched(phi_satellites, fenvironment): | ||||||||||||||||||||||||||
return - np.log(1 - fenvironment) * phi_satellites | ||||||||||||||||||||||||||
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# SkyPy amplitudes | ||||||||||||||||||||||||||
phic = schechter_smf_phi_centrals(phiblue, fsat) | ||||||||||||||||||||||||||
phis = schechter_smf_phi_satellites(phic, fsat) | ||||||||||||||||||||||||||
phimq = schechter_smf_phi_mass_quenched(phic, phis) | ||||||||||||||||||||||||||
phisq = schechter_smf_phi_satellite_quenched(phis, frho) | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
# Finally we simulate the galaxy populations. | ||||||||||||||||||||||||||
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# Schechter mass functions | ||||||||||||||||||||||||||
z_centrals, m_centrals = schechter_smf(z_range, mstarb, phic, alphab, 1e9, 1e12, sky_area, cosmology) | ||||||||||||||||||||||||||
z_satellites, m_satellites = schechter_smf(z_range, mstarb, phis, alphab, 1e9, 1e12, sky_area, cosmology) | ||||||||||||||||||||||||||
z_massq, m_mass_quenched = schechter_smf(z_range, mstarb, phimq, alphab + 1, 1e9, 1e12, sky_area, cosmology) | ||||||||||||||||||||||||||
z_satq, m_satellite_quenched = schechter_smf(z_range, mstarb, phisq, alphab, 1e9, 1e12, sky_area, cosmology) | ||||||||||||||||||||||||||
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Adding line breaks prevents the user from scrolling horizontally in the docs. |
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logm_centrals = np.log10(m_centrals) | ||||||||||||||||||||||||||
logm_satellites = np.log10(m_satellites) | ||||||||||||||||||||||||||
logm_massq = np.log10(m_mass_quenched) | ||||||||||||||||||||||||||
logm_satq = np.log10(m_satellite_quenched) | ||||||||||||||||||||||||||
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# log Mass bins | ||||||||||||||||||||||||||
bins = np.linspace(9, 12, 35) | ||||||||||||||||||||||||||
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# Sky volume | ||||||||||||||||||||||||||
dV_dz = (cosmology.differential_comoving_volume(z_range) * sky_area).to_value('Mpc3') | ||||||||||||||||||||||||||
dV = np.trapz(dV_dz, z_range) | ||||||||||||||||||||||||||
dlm = (np.max(bins)-np.min(bins)) / (np.size(bins)-1) | ||||||||||||||||||||||||||
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# log distribution of masses | ||||||||||||||||||||||||||
logphi_centrals = np.histogram(logm_centrals, bins=bins)[0] / dV / dlm | ||||||||||||||||||||||||||
logphi_satellites = np.histogram(logm_satellites, bins=bins)[0] / dV / dlm | ||||||||||||||||||||||||||
logphi_massq = np.histogram(logm_massq, bins=bins)[0] / dV / dlm | ||||||||||||||||||||||||||
logphi_satq = np.histogram(logm_satq, bins=bins)[0] / dV / dlm | ||||||||||||||||||||||||||
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logphi_active = logphi_centrals + logphi_satellites | ||||||||||||||||||||||||||
logphi_passive = logphi_massq + logphi_satq | ||||||||||||||||||||||||||
logphi_total = logphi_active + logphi_passive | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
# Validation against SSD DR7 data | ||||||||||||||||||||||||||
# ------------------------------- | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# Here we compare our sampled galaxies and | ||||||||||||||||||||||||||
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# we validate the model using the results from the best fit to | ||||||||||||||||||||||||||
# SDSS DR7 data in Weigel et al. (2016) [2]. | ||||||||||||||||||||||||||
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# The authors presented a comprehensive method to determine | ||||||||||||||||||||||||||
# stellar mass functions and apply it to samples in the local universe, | ||||||||||||||||||||||||||
# in particular to SDSS DR7 data in the redshift range from 0.02 to 0.06. | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# Their data is presented as logarithmic distribution, therefore, | ||||||||||||||||||||||||||
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# to perform the comparison we need to apply a conversion factor. | ||||||||||||||||||||||||||
# This factor allows us to go from :math:`\phi` to a :math:`\log \phi` plot | ||||||||||||||||||||||||||
# and compare with Weigel et al 2016 best-fit model. | ||||||||||||||||||||||||||
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# Load the data | ||||||||||||||||||||||||||
wtotal = Table.read('weigel16_total.csv', format='csv') | ||||||||||||||||||||||||||
wred = Table.read('weigel16_quiescent.csv', format='csv') | ||||||||||||||||||||||||||
wblue = Table.read('weigel16_active.csv', format='csv') | ||||||||||||||||||||||||||
wcentral = Table.read('weigel16_central.csv', format='csv') | ||||||||||||||||||||||||||
wsatellite = Table.read('weigel16_satellite.csv', format='csv') | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
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# Plot | ||||||||||||||||||||||||||
fig, (ax1, ax2, ax3) = plt.subplots(nrows=1, ncols=3, figsize=(16, 6), sharex=True, sharey=True) | ||||||||||||||||||||||||||
fig.suptitle('Galaxy Demographics Simulation', fontsize=26) | ||||||||||||||||||||||||||
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ax1.plot(wblue['logm'], 10**wblue['logphi'], color='k', label='Weigel+16 active', lw=1) | ||||||||||||||||||||||||||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. The Weigel+ lines for the passive and the total sample include errors. Does the blue sample not have errors? |
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ax1.step(bins[:-1], logphi_active, where='post', label='SkyPy active', color='blue', zorder=3, lw=1) | ||||||||||||||||||||||||||
ax1.step(bins[:-1], logphi_centrals, where='post', label='SkyPy centrals', color='royalblue', zorder=3, lw=1) | ||||||||||||||||||||||||||
ax1.step(bins[:-1], logphi_satellites, where='post', label='SkyPy satellites', color='cyan', zorder=3, lw=1) | ||||||||||||||||||||||||||
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ax2.plot(wred['logm'], 10**wred['logphi'], color='k', label='Weigel+16 passive', lw=1) | ||||||||||||||||||||||||||
ax2.fill_between(wred['logm'], 10**wred['upper_error'], 10**wred['lower_error'], color='salmon', alpha=0.1) | ||||||||||||||||||||||||||
ax2.step(bins[:-1], logphi_passive, where='post', label='SkyPy passive', color='red', zorder=3, lw=1) | ||||||||||||||||||||||||||
ax2.step(bins[:-1], logphi_massq, where='post', label='SkyPy mass-quenched', color='coral', zorder=3, lw=1) | ||||||||||||||||||||||||||
ax2.step(bins[:-1], logphi_satq, where='post', label='SkyPy sat-quenched', color='maroon', zorder=3, lw=1) | ||||||||||||||||||||||||||
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ax3.plot(wtotal['logm'], 10**wtotal['logphi'], color='k', label='Weigel+16 total', lw=1) | ||||||||||||||||||||||||||
ax3.plot(wcentral['logm'], 10**wcentral['logphi'], '--', color='grey', label='Weigel+16 centrals', lw=1) | ||||||||||||||||||||||||||
ax3.plot(wsatellite['logm'], 10**wsatellite['logphi'], '--', color='grey', label='Weigel+16 satellites', lw=1) | ||||||||||||||||||||||||||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Does it make sense to plot these two lines with the same line style? There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. What are these lines supposed to demonstrate in the first place? Does it make sense to remove them or also show the SkyPy fits of these two components? |
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ax3.fill_between(wtotal['logm'], 10**wtotal['upper_error'], 10**wtotal['lower_error'], color='plum', alpha=0.1) | ||||||||||||||||||||||||||
ax3.step(bins[:-1], logphi_total, where='post', label='SkyPy total', color='purple', zorder=3, lw=1) | ||||||||||||||||||||||||||
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There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Could you add line breaks here such that the user does not need to scroll horizontally? |
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for ax in [ax1, ax2, ax3]: | ||||||||||||||||||||||||||
ax.legend(loc='lower left', fontsize='small', frameon=False) | ||||||||||||||||||||||||||
ax.set_xlabel(r'Stellar mass, $log (M/M_{\odot})$', fontsize=18) | ||||||||||||||||||||||||||
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This is to prevent There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Maybe increase the fontsize for both labels |
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ax.set_xlim((9, 11.9)) | ||||||||||||||||||||||||||
ax.set_ylim((2e-6,5e-2)) | ||||||||||||||||||||||||||
ax.set_yscale('log') | ||||||||||||||||||||||||||
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ax1.set_ylabel(r'$\phi /h^3 Mpc^{-3}$', fontsize=18) | ||||||||||||||||||||||||||
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I prefer and learned to not put the units into math mode. This makes it easier to distinguish between parameters/variables and units. |
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# plt.savefig('galaxy_simulation.pdf') | ||||||||||||||||||||||||||
There was a problem hiding this comment. Choose a reason for hiding this commentThe reason will be displayed to describe this comment to others. Learn more. Remove this comment |
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plt.tight_layout() | ||||||||||||||||||||||||||
plt.show() | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
# Sonification | ||||||||||||||||||||||||||
# ------------ | ||||||||||||||||||||||||||
# The sonification, or transformation of physical data via sound, | ||||||||||||||||||||||||||
# is becoming increasingly important to make astronomy accessible | ||||||||||||||||||||||||||
# for those who are visually impaired, and to enhance visualisations | ||||||||||||||||||||||||||
# and convey information that visualisation alone cannot. | ||||||||||||||||||||||||||
# In this work [1] the authors also made their main plot available | ||||||||||||||||||||||||||
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# in sound format using the `STRAUSS`_ software (Trayford 2021) [3]_. | ||||||||||||||||||||||||||
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import IPython | ||||||||||||||||||||||||||
# Active population | ||||||||||||||||||||||||||
IPython.display.Audio("skypy_sim_active.wav") | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
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# Mass-quenched galaxies | ||||||||||||||||||||||||||
IPython.display.Audio("skypy_sim_massq.wav") | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
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# Satellite-quenched galaxies | ||||||||||||||||||||||||||
IPython.display.Audio("skypy_sim_satq.wav") | ||||||||||||||||||||||||||
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# %% | ||||||||||||||||||||||||||
# References | ||||||||||||||||||||||||||
# ---------- | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# .. [1] de la Bella et al. 2021, Quenching and Galaxy Demographics, arXiv 2112.11110. | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# .. [2] Weigel A. K., Schawinski K., Bruderer C., 2016, Monthly Notices of the | ||||||||||||||||||||||||||
# Royal Astronomical Society, 459, 2150 | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# .. [3] Trayford J., 2021, james-trayford/strauss: v0.1.0 Pre-release, `doi:10.5281/zenodo.5776280`_. | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# .. _doi:10.5281/zenodo.5776280: https://doi.org/10.5281/zenodo.5776280 | ||||||||||||||||||||||||||
# | ||||||||||||||||||||||||||
# .. _STRAUSS: https://strauss.readthedocs.io/en/latest/ |
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