Using the catalogues I: Stellar mass - halo mass relation
Showing running means, medians and "fancy medians"
Using the catalogues II: Galaxy stellar mass function
Loading particles within a spherical aperture around a galaxy
Calculating a quantity using particles for all haloes in a sample
Making histograms of particle properties
Making pretty pictures with py-sphviewer
The galaxy stellar mass function is of the most important descriptors of a galaxy population, defining how many galaxies of a given stellar mass occupy a given volume of space. It encodes information about the efficiency of galaxy formation and the hierarchical nature of the universe. It's also one of the key diagnostics on which the EAGLE model was calibrated, since, in simple terms, it tells you how many galaxies of a certain mass your model needs to produce to be realistic.
Let's have a go at reproducing Fig. 4 of Schaye et al. (2015), which shows the z=0.1 GSMFs of three of the key EAGLE runs. This is a good example of how you can work with multiple simulations in one script:
import numpy as np
import matplotlib.pyplot as plt
from catalogue_reading import *
# Establish the bin edges for our mass function
# 24 equal size bins in log space
bin_edges = np.linspace(7,12,25)
# Get the bin sizes - we'll need these for our normalisation
bin_sizes = bin_edges[1:]-bin_edges[:-1]
# Get the bin centres for plotting
bin_centres = (bin_edges[:-1]+bin_edges[1:])/2.
# Load the stellar masses in 30kpc apertures, convert to solar masses and take the log_10
Ref_100_mstar = np.log10(catalogue_read('Subhalo','ApertureMeasurements/Mass/030kpc',sim='L0100N1504',model='REFERENCE',tag='027_z000p101')[:,4] * 1e10)
# Make a histogram in our pre-defined bins.
# The second output is the bin edges, which we already have, so I use a dummy variable
Ref_100_histogram, _ = np.histogram(Ref_100_mstar,bins=bin_edges)
# Normalise the mass function. We take the number in each bin and divide by the comoving simulation volume times the logarithmic bin size
# This tells us how many galaxies of each mass are in each comoving Mpc^3 of simulation volume
Ref_100_gsmf = np.log10(Ref_100_histogram/(100.**3 * bin_sizes))
# Repeat the process for the two other models in the Schaye+15 plot
Recal_25_mstar = np.log10(catalogue_read('Subhalo','ApertureMeasurements/Mass/030kpc',sim='L0025N0752',model='RECALIBRATED',tag='027_z000p101')[:,4] * 1e10)
Recal_25_histogram, _ = np.histogram(Recal_25_mstar,bins=bin_edges)
Recal_25_gsmf = np.log10(Recal_25_histogram/(25.**3 * bin_sizes))
AGNdT9_50_mstar = np.log10(catalogue_read('Subhalo','ApertureMeasurements/Mass/030kpc',sim='L0050N0752',model='S15_AGNdT9',tag='027_z000p101')[:,4] * 1e10)
AGNdT9_50_histogram, _ = np.histogram(AGNdT9_50_mstar,bins=bin_edges)
AGNdT9_50_gsmf = np.log10(AGNdT9_50_histogram/(50.**3 * bin_sizes))
fig, ax = plt.subplots(figsize=(8,6))
ax.plot(bin_centres,AGNdT9_50_gsmf,lw=2,c='maroon',label='AGNdT9-L0050N0752')
ax.plot(bin_centres,Recal_25_gsmf,lw=2,c='turquoise',label='Recal-L0025N0752')
ax.plot(bin_centres,Ref_100_gsmf,lw=2,c='navy',label='Ref-L0100N1504')
ax.set_ylabel(r'$\log_{10}({\rm d}n/{\rm d}\log_{10} M_*)\,[{\rm cMpc}^{-3}]$',fontsize=16)
ax.set_xlabel(r'$\log_{10}(M_\star/M_\odot)$',fontsize=16)
ax.legend(loc='lower left',prop={'size':12})
plt.savefig('/path/to/your/directory/gsmf.png')
plt.show()This produces the following plot:
This produces a good match to the Schaye+15 plot, though not an exact one as the bin sizes differ slightly. As you can see, there are very many low-mass galaxies, very few high-mass galaxies, and a characteristic 'knee' at M_* = 10^10.5-10^11 solar masses. Galaxies in this mass range dominate the present-day mass density of the Universe.
The plot also gives you an idea of the sampling in each simulation volume; in a nutshell, it tells you what's 'available' in each box. As you can see, the bigger the boxes probe to higher masses and rarer objects. For example, the Ref-L0100N1504 volume is the only one to host any galaxies more massive than 10^11.5 solar masses, while the Recal-L0025N0752 volume contains no galaxies above 10^11 solar masses.