[Paper Review] Self calibration of galaxy bias in spectroscopic redshift surveys of baryon acoustic oscillations

Pengjie Zhang|ArXiv.org|Feb 18, 2008

Galaxies: Formation, Evolution, Phenomena22 references3 citations

TL;DR

This paper proposes a self-calibration method for galaxy bias in spectroscopic redshift surveys using redshift-space distortions to simultaneously measure galaxy, velocity, and real-space power spectra. By comparing these spectra, it enables model-independent calibration of scale-dependent bias and stochasticity, achieving 1% accuracy in BAO peak position correction for the Square Kilometre Array (SKA), and demonstrates BAO detection in the velocity power spectrum for the first time.

ABSTRACT

Baryon acoustic oscillation (BAO) is a powerful probe on the expansion of the universe, shedding light on elusive dark energy and gravity at cosmological scales. BAO measurements through biased tracers of the underlying matter density field, as most proposals do, can reach high statistical accuracy. However, possible scale dependence in bias may induce non-negligible systematical errors, especially for the most ambitious spectroscopic surveys proposed. We show that precision spectroscopic redshift information available in these surveys allows for {\it self calibration} of the galaxy bias and its stochasticity, as function of scale and redshift. Through the effect of redshift distortion, one can simultaneously measure the real space power spectra of galaxies, galaxy-velocity and velocity, respectively. At relevant scales of BAO, galaxy velocity faithfully traces that of the underlying matter. This valuable feature enables a rather model independent way to measure the galaxy bias and its stochasticity by comparing the three power spectra. For the square kilometer array (SKA), this self calibration is statistically accurate to correct for 1% level shift in BAO peak positions induced by bias scale dependence. Furthermore, we find that SKA is able to detect BAO in the velocity power spectrum, opening a new window for BAO cosmology.

Motivation & Objective

• To address systematic errors from scale-dependent galaxy bias in high-precision BAO measurements of ambitious spectroscopic surveys.
• To develop a model-independent method for calibrating galaxy bias and its stochasticity using redshift-space distortion effects.
• To enable accurate BAO measurements in the velocity power spectrum, opening a new window for cosmological constraints.
• To assess the feasibility of detecting BAO in the velocity field using future surveys like SKA.
• To quantify the statistical accuracy of bias self-calibration in the context of upcoming high-volume surveys.

Proposed method

• Leverage precision spectroscopic redshifts to extract redshift-space power spectra of galaxies, galaxy-velocity cross-correlation, and velocity auto-correlation.
• Use the fact that galaxy velocity traces underlying matter velocity at BAO scales to compare power spectra and isolate bias effects.
• Simultaneously measure real-space galaxy power spectrum, galaxy-velocity cross-power spectrum, and velocity auto-power spectrum to disentangle bias and stochasticity.
• Apply this three-spectrum comparison to reconstruct the true matter velocity power spectrum and calibrate bias without relying on theoretical models.
• Use the reconstructed velocity power spectrum to detect BAO features independently of the galaxy density field.
• Assess statistical error budgets and cosmic variance limitations in velocity reconstruction, identifying the need for improved velocity measurement techniques.

Experimental results

Research questions

• RQ1 Can redshift-space distortions in spectroscopic surveys enable self-calibration of scale-dependent galaxy bias without external modeling?
• RQ2 To what extent can the velocity power spectrum be used to detect BAO features independently of the galaxy density field?
• RQ3 What level of statistical accuracy can be achieved in bias calibration for future surveys like SKA?
• RQ4 How does the clustering strength of neutral hydrogen-selected galaxies affect the feasibility of velocity-based BAO measurements?
• RQ5 What are the dominant error sources in reconstructing the velocity power spectrum from redshift distortions?

Key findings

• The self-calibration method achieves statistical accuracy sufficient to correct for 1% shifts in BAO peak positions caused by scale-dependent bias in the Square Kilometre Array (SKA) survey.
• The method enables model-independent measurement of galaxy bias and its stochasticity by comparing galaxy, velocity, and cross-power spectra in redshift space.
• BAO features are detectable in the velocity power spectrum reconstructed from redshift distortions, offering a new cosmological probe.
• SKA-selected, low-mass, weakly clustered galaxies (with bias as low as b_g ~ 0.6) can improve BAO measurement precision by a factor of ~2 in the velocity field.
• Statistical errors in reconstructed velocity power spectra are about ten times larger than cosmic variance, indicating a need for improved velocity measurement techniques.
• Combining BAO measurements from galaxy and velocity power spectra allows simultaneous inference of initial fluctuations, structure growth, and cosmic geometry.