Outline
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(Image credit: Joerg Colberg, Ryan Scranton, Robert Lupton, SDSS) |
Introduction
Cosmic Magnification is due to the systematic lensing of the background distribution of galaxies or quasars by foreground galaxies (Ménard 2002). The lensing both distorts the background image and magnifies it, known in the weak limit as cosmic shear and cosmic magnification respectively. The magnification will have two effects: it will both increase the received flux of background objects, making the apparent magnitude limit of the survey fainter, and dilute the surface density of the source images by stretching the surface element. These two compteting effects will either result in a positive or negative correlation between the foreground and background effect (Scranton et al. 2005).
Detections of cosmic magnificiation have been controversial since claimed detections have either been in contradiction with each other or in disagreement with theoretical predictions. The first detection to be in agreement with theoretical predictions with respects to the amplitude, angular dependence and change in sign of the signal was reported by Scranton et al. 2005. They cross-correlated 200,000 background quasars wth 13 million foreground galaxies using 3,800 deg^2 from the third data release of the Sloan Digital Sky Survey.
Cosmic Magnification Signal
The expected cosmic magnification signal in configuration space is then described by (Scranton et al. 2005, Jain, Scranton & Sheth 2003):
,
where m is the magnitude of the sources, the lensing kernel is denoted by and
is the cross-correlation between the foreground galaxy population (g1) and the background population (g2). The term
denotes the power law number count slope of the background population, such that if
the resulting correlation will be positive and if
the correlation will be negative.
Observationally, the cosmic magnification is measured over a range of magnitudes so that the cosmic magnification signal can be written:
,
where:
.
Effect of Cosmic Magnification on Galaxy Correlations
A high redshift population of galaxies or Quasars (QSO) will inevitably be lensed by the foreground distribution of matter in the Universe. As discussed above, one of the effects of lensing is cosmic magnification, which will both change the number of observed galaxies ( or QSOs) at a given flux, and dilute the surface density at the source population's redshift. This will change the observed galaxy (or QSO) density, such that:
where is the observed overdensity at a position
,
is the instrinsic overdensity and
is the overdensity correction due to cosmic magnification.
This will propagate through to various correlations observables in the following way:
For the angular correlation function in configuration space:
,
For the spherical harmonic power spectrum:
,
For the real space correlation function:
.
Cosmic magnification can affect features in these correlation functions in three ways: by changing the position, amplitude and width of various peaks and features. Cosmic magnification is also expected to have a larger effect at high redshifts: this is due the to the cosmic magnification signal to increase with redshift, and the fact that the intrinsic galaxy correlation decreases with redshift.
- Effect on
:
Loverde et al. 2008 showed that cosmic magnification affected the BAO peak in the quantity by less than 1%, and the width was affected by less than 10%, while the effect on the location of the baryon peak was negligible. They showed that larger shifts and broadening occured galaxies (or QSOs) with broad selection functions and steep number counts
.
- Effect on
:
Loverde et al. 2008 showed that cosmic magnification affected the spherical harmonic power spectrum for . They showed that the matter/radiation peak in
could be shifted by 1-6% at redshifts z = 1.5, and up to 30% at redshift z = 3.5. The amplitude could be increase from 1-40% depending on the selection function and redshift.
- Effect on
:
Vallinotto et al. 2007 explored the effect on cosmic magnification on the real space correlation function. They found that while the BAO bump in for galaxies was mainly unchanged by cosmic magnification, that for QSOs (which have a different slope for the number count) could result in significant effects.
Effect of Cosmic Magnification on other correlations
Studying correlations between the galaxy field and the cosmic microwave background is useful to detect the presence of dark energy, by using the integrated Sachs-Wolfe (ISW) effect as a cosmological probe. However the ISW effect can be contaminated by cosmic magnification. The effect of cosmic magnification on the ISW signal is negligible at low redshifts (z<1.5) where the ISW signal dominates (Loverde et al. 2007).