Principal component analysis of galaxy clustering in hyperspace of galaxy properties
Abstract
Ongoing and upcoming galaxy surveys are providing precision measurements of galaxy clustering. However, a major obstacle in its cosmological application is the stochasticity in the galaxy bias. We explore whether the principal component analysis (PCA) of galaxy correlation matrix in hyperspace of galaxy properties (e.g. magnitude and colour) can reveal further information on mitigating this issue. Based on the hydrodynamic simulation TNG3001, we analyse the crosspower spectrum matrix of galaxies in the magnitude and colour space of multiple photometric bands. (1) We find that the first principal component $E_i^{(1)}$ is an excellent proxy of the galaxy deterministic bias b_{D}, in that $E_i^{(1)}=\sqrt{P_{mm}/\lambda ^{(1)}}b_{D,i}$. Here, i denotes the ith galaxy subsample. λ^{(1)} is the largest eigenvalue, and P_{mm} is the matter power spectrum. We verify that this relation holds for all the galaxy samples investigated, down to k ~ 2h Mpc^{1}. Since $E_i^{(1)}$ is a direct observable, we can utilize it to design a linear weighting scheme to suppress the stochasticity in the galaxymatter relation. For an LSSTlike magnitude limit galaxy sample, the stochasticity $\mathcal {S}\equiv 1r^2$ can be suppressed by a factor of $\gtrsim 2$ at k = 1h Mpc^{1}. This reduces the stochasticityinduced systematic error in the matter power spectrum reconstruction combining galaxy clustering and galaxygalaxy lensing from $\sim 12~{{\ \rm per\ cent}}$ to $\sim 5~{{\ \rm per\ cent}}$ at k = 1h Mpc^{1}. (2) We also find that $\mathcal {S}$ increases monotonically with f_{λ} and $f_{\lambda ^2}$. $f_{\lambda ,\lambda ^2}$ quantify the fractional contribution of other eigenmodes to the galaxy clustering and are direct observables. Therefore, the two provide extra information on mitigating galaxy stochasticity.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 August 2023
 DOI:
 10.1093/mnras/stad1824
 arXiv:
 arXiv:2304.11540
 Bibcode:
 2023MNRAS.523.5789Z
 Keywords:

 methods: numerical;
 dark matter;
 largescale structure of Universe;
 Astrophysics  Cosmology and Nongalactic Astrophysics
 EPrint:
 doi:10.1093/mnras/stad1824