Target Data Models¶

The cosmos20_colors package includes approximate models for various summary statistics of COSMOS-20 galaxies, which we generically refer to as “target data models”. Such summary statistics are commonly used to calibrate the parameters of models of the galaxy–halo connection, and the purpose of the target data models is to simplify this calibration process, and to improve the reliability of extrapolations into various regimes of the data.

Completeness Models¶

Many of the target data models in the package are defined after first making some kind of completeness cut on the COSMOS-20 dataset, so that the measured summary statistics are not impacted by the depth limit of the survey.

Stellar Mass Completeness¶

One form of target summary statistics that is very convenient for galaxy–halo modeling is a probability distribution conditioned upon stellar mass and redshift, for example \(P(g-r\vert M_{\star},z)\), the distribution of \(g-r\) color for a sample of galaxies with the same stellar mass and redshift. Measuring such summary statistics at any given redshift requires a complete sample of galaxies of mass \(M_{\star}.\) The get_logsm_completeness function provides an approximate model for stellar mass completeness as a function of both redshift and the cut on apparent magnitude in the HSC i-band.

_images/logsm_completeness_model_check.png

For any choice of \(23 < m_i < 26\), \(90-95\%\) of galaxies in the COSMOS-20 dataset are more massive than the dashed black curve in the above plot.

Models for Cumulative Sky Density¶

A simple measurement that places tight constraints on galaxy abundance is the sky density of galaxies brighter than some apparent magnitude. This is a particularly robust measurement because it is insensitive to SED-fitting systematics and photo-z errors.

i-band apparent magnitude¶

The approximate_cuml_hsc_imag_sky_density function provides an approximate model for surface density of COSMOS-20 galaxies brighter than apparent magnitude in the HSC i-band.

_images/cuml_sky_density_app_imag_hsc.png

Models for Absolute Magnitude¶

One of the key quantities that impacts the luminosity function is \(\langle M_{x}\vert M_{\star}, z\rangle\), the average absolute magnitude (in some band \(x\)) as a function of stellar mass and redshift.

i-band Magnitude¶

The median_hsc_imag_model function provides an approximate model for median absolute magnitude in the HSC i-band as a function of redshift and stellar mass.