Optical Photometry

This example demonstrates how to model galaxy photometric magnitudes using the kcorrect spectral energy distribution templates as implemented in SkyPy.

kcorrect Spectral Templates

In SkyPy, the rest-frame spectral energy distributions (SEDs) of galaxies can be modelled as a linear combination of the five kcorrect basis templates [1]. One possible model for the coefficients is a redshift-dependent Dirichlet distribution [2] which can be sampled from using the dirichlet_coefficients function. The coefficients are then taken by the kcorrect.absolute_magnitudes and kcorrect.apparent_magnitudes methods to calculate the relevant photometric quantities using the speclite package. Note that since the kcorrect templates are defined per unit stellar mass, the total stellar mass of each galaxy must either be given or calculated from its absolute magnitude in another band using kcorrect.stellar_mass. An example simulation for the SDSS u- and r-band apparent magnitudes of “red” and “blue” galaxy populations is given by the following config file:

examples/galaxies/sdss_photometry.yml

cosmology: !astropy.cosmology.default_cosmology.get []
z_range: !numpy.linspace [0, 2, 21]
M_star: !astropy.modeling.models.Linear1D [-0.9408582, -20.40492365]
phi_star: !astropy.modeling.models.Exponential1D [0.00370253, -9.73858]
M_star_red: !astropy.modeling.models.Linear1D [-0.70798041, -20.37196157]
phi_star_red: !astropy.modeling.models.Exponential1D [0.0035097, -1.41649]
magnitude_limit: 23
sky_area: 10 deg2
tables:
  blue_galaxies:
    redshift, magnitude: !skypy.galaxies.schechter_lf
      redshift: $z_range
      M_star: $M_star
      phi_star: $phi_star
      alpha: -1.3
      m_lim: $magnitude_limit
      sky_area: $sky_area
    spectral_coefficients: !skypy.galaxies.spectrum.dirichlet_coefficients
      alpha0: [2.079, 3.524, 1.917, 1.992, 2.536]
      alpha1: [2.265, 3.862, 1.921, 1.685, 2.480]
      weight: [3.47e+09, 3.31e+06, 2.13e+09, 1.64e+10, 1.01e+09]
      redshift: $blue_galaxies.redshift
    stellar_mass: !skypy.galaxies.spectrum.kcorrect.stellar_mass
      coefficients: $blue_galaxies.spectral_coefficients
      magnitudes: $blue_galaxies.magnitude
      filter: bessell-B
    mag_u, mag_g, mag_r, mag_i, mag_z: !skypy.galaxies.spectrum.kcorrect.apparent_magnitudes
      coefficients: $blue_galaxies.spectral_coefficients
      redshift: $blue_galaxies.redshift
      filters: sdss2010-*
      stellar_mass: $blue_galaxies.stellar_mass
  red_galaxies:
    redshift, magnitude: !skypy.galaxies.schechter_lf
      redshift: $z_range
      M_star: $M_star_red
      phi_star: $phi_star_red
      alpha: -0.5
      m_lim: $magnitude_limit
      sky_area: $sky_area
    spectral_coefficients: !skypy.galaxies.spectrum.dirichlet_coefficients
      alpha0: [2.461, 2.358, 2.568, 2.268, 2.402]
      alpha1: [2.410, 2.340, 2.200, 2.540, 2.464]
      weight: [3.84e+09, 1.57e+06, 3.91e+08, 4.66e+10, 3.03e+07]
      redshift: $red_galaxies.redshift
    stellar_mass: !skypy.galaxies.spectrum.kcorrect.stellar_mass
      coefficients: $red_galaxies.spectral_coefficients
      magnitudes: $red_galaxies.magnitude
      filter: bessell-B
    mag_u, mag_g, mag_r, mag_i, mag_z: !skypy.galaxies.spectrum.kcorrect.apparent_magnitudes
      coefficients: $red_galaxies.spectral_coefficients
      redshift: $red_galaxies.redshift
      filters: sdss2010-*
      stellar_mass: $red_galaxies.stellar_mass

The config file can be downloaded here and the simulation can be run either from the command line and saved to FITS files:

$ skypy examples/galaxies/sdss_photometry.yml sdss_photometry.fits

or in a python script using the Pipeline class as demonstrated in the SDSS Photometry section below. For more details on writing config files see the Pipeline Documentation.

SDSS Photometry

Here we compare the apparent magnitude distributions of our simulated galaxies with data from a \(10 \, \mathrm{deg^2}\) region of the Sloan Digital Sky Survey [3]. The binned SDSS magnitude distributions were generated from a query of the DR7 data release and can be downloaded here.

from astropy.table import Table, vstack
from matplotlib import pyplot as plt
import numpy as np
from skypy.pipeline import Pipeline

# Execute SkyPy galaxy photometry simulation pipeline
pipeline = Pipeline.read("sdss_photometry.yml")
pipeline.execute()
skypy_galaxies = vstack([pipeline['blue_galaxies'], pipeline['red_galaxies']])

# SDSS magnitude distributions for a 10 degree^2 region
sdss_data = Table.read("sdss_dered_10deg2.ecsv", format='ascii.ecsv')

# Plot magnitude distributions for SkyPy simulation and SDSS data
bins = np.linspace(14.95, 25.05, 102)
plt.hist(skypy_galaxies['mag_r'], bins=bins, alpha=0.5, color='r', label='SkyPy-r')
plt.hist(skypy_galaxies['mag_u'], bins=bins, alpha=0.5, color='b', label='SkyPy-u')
plt.plot(sdss_data['magnitude'], sdss_data['dered_r'], color='r', label='SDSS-r')
plt.plot(sdss_data['magnitude'], sdss_data['dered_u'], color='b', label='SDSS-u')
plt.xlim(16, 24)
plt.yscale('log')
plt.xlabel(r'$\mathrm{Apparent\,Magnitude}$')
plt.ylabel(r'$\mathrm{N} \, [\mathrm{deg}^{-2} \, \mathrm{mag}^{-1}]$')
plt.legend()
plt.show()

References

[1]

13. 18. Blanton and S. Roweis, 2007, AJ, 125, 2348

[2]

J. Herbel, T. Kacprzak, A. Amara, A. Refregier, C.Bruderer and A. Nicola 2017, JCAP, 1708, 035

[3]

11. 14. Abazajian et al. 2009, ApJS, 182, 543