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Register a new userLensing and time-delay contributions to galaxy correlations
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Added by
Daniele Bertacca DR.
Publication date
2013
fields
Physics
and research's language is
English
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Galaxy clustering on very large scales can be probed via the 2-point correlation function in the general case of wide and deep separations, including all the lightcone and relativistic effects. Using our recently developed formalism, we analyze the behavior of the local and integrated contributions and how these depend on redshift range, linear and angular separations and luminosity function. Relativistic corrections to the local part of the correlation can be non-negligible but they remain generally sub-dominant. On the other hand, the additional correlations arising from lensing convergence and time-delay effects can become very important and even dominate the observed total correlation function. We investigate different configurations formed by the observer and the pair of galaxies, and we find that the case of near-radial large-scale separations is where these effects will be the most important.
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We study the impact of lensing corrections on modeling cross correlations between CMB lensing and galaxies, cosmic shear and galaxies, and galaxies in different redshift bins. Estimating the importance of these corrections becomes necessary in the light of anticipated high-accuracy measurements of these observables. While higher order lensing corrections (sometimes also referred to as post Born corrections) have been shown to be negligibly small for lensing auto correlations, they have not been studied for cross correlations. We evaluate the contributing four-point functions without making use of the Limber approximation and compute line-of-sight integrals with the numerically stable and fast FFTlog formalism. We find that the relative size of lensing corrections depends on the respective redshift distributions of the lensing sources and galaxies, but that they are generally small for high signal-to-noise correlations. We point out that a full assessment and judgement of the importance of these corrections requires the inclusion of lensing Jacobian terms on the galaxy side. We identify these additional correction terms, but do not evaluate them due to their large number. We argue that they could be potentially important and suggest that their size should be measured in the future with ray-traced simulations. We make our code publicly available.
Correlations of galaxy ellipticities with large-scale structure, due to galactic tidal interactions, provide a potentially significant contaminant to measurements of cosmic shear. However, these intrinsic alignments are still poorly understood for galaxies at the redshifts typically used in cosmic shear analyses. For spiral galaxies, it is thought that tidal torquing is significant in determining alignments resulting in zero correlation between the intrinsic ellipticity and the gravitational potential in linear theory. Here, we calculate the leading-order correction to this result in the tidal-torque model from non-linear evolution, using second-order perturbation theory, and relate this to the contamination from intrinsic alignments to the recently-measured cross-correlation between galaxy ellipticities and the CMB lensing potential. On the scales relevant for CMB lensing observations, the squeezed limit of the gravitational bispectrum dominates the correlation. Physically, the large-scale mode that sources CMB lensing modulates the small-scale power and hence the intrinsic ellipticity, due to non-linear evolution. We find that the angular cross-correlation from tidal torquing has a very similar scale dependence as in the linear alignment model, believed to be appropriate for elliptical galaxies. The amplitude of the cross-correlation is predicted to depend strongly on the formation redshift, being smaller for galaxies that formed at higher redshift when the bispectrum of the gravitational potential was smaller. Finally, we make simple forecasts for constraints on intrinsic alignments from the correlation of forthcoming cosmic shear measurements with current CMB lensing measurements. We note that cosmic variance can be significantly reduced in measurements of the difference in the intrinsic alignments for elliptical and spiral galaxies if these can be separated (e.g., using colour).
Measurements of time delays between multiple quasar images produced by strong lensing are reaching a sensitivity that makes them a promising cosmological probe. Future surveys will provide significantly more measurements, reaching unprecedented depth in redshift, making strong lensing time delay (SLTD) observations competitive with other background probes. We forecast constraints on the nature of dark energy from upcoming SLTD surveys, simulating future catalogues with different numbers of lenses distributed up to redshift $zsim 1$ and focusing on cosmological parameters such as the Hubble constant $H_0$ and parametrisations of the dark energy equation of state. We also explore the impact of our ability to precisely model the lens mass profile and its environment, on the forecasted constraints. We find that in the most optimistic cases, SLTD will constrain $H_0$ at the level of $sim 0.1%$, while the CPL equation of state parameters, $w_0$ and $w_a$, can be determined with errors $sigma_{w_0}sim 0.05$ and $sigma_{w_a}sim 0.3$, respectively. Furthermore, we investigate the bias introduced when a wrong cosmological model is assumed for the analysis. We find that the value of $H_0$ could be biased up to $10 sigma$, assuming a perfect knowledge of the lens profile, when a $Lambda$CDM model is used to analyse data that really belong to a $w$CDM cosmology with $w=-0.9$. Based on these findings, we identify a consistency check of the assumed cosmological model in future SLTD surveys, by splitting the dataset in several redshift bins. Depending on the characteristics of the survey, this could provide a smoking gun for dark energy.
We present predictions for time delays between multiple images of the gravitationally lensed supernova, iPTF16geu, which was recently discovered from the intermediate Palomar Transient Factory (iPTF). As the supernova is of Type Ia where the intrinsic luminosity is usually well-known, accurately measured time delays of the multiple images could provide tight constraints on the Hubble constant. According to our lens mass models constrained by the {it Hubble Space Telescope} F814W image, we expect the maximum relative time delay to be less than a day, which is consistent with the maximum of 100 hours reported by Goobar et al. but places a stringent upper limit. Furthermore, the fluxes of most of the supernova images depart from expected values suggesting that they are affected by microlensing. The microlensing timescales are small enough that they may pose significant problems to measure the time delays reliably. Our lensing rate calculation indicates that the occurrence of a lensed SN in iPTF is likely. However, the observed total magnification of iPTF16geu is larger than expected, given its redshift. This may be a further indication of ongoing microlensing in this system.
We consider an alternative formula for time delay in gravitational lensing. Imposing a smoothness condition on the gravitationally deformed paths followed by the photons from the source to the observer, we show that our formula displays the same degrees of freedom as the standard one. In addition to this, it is shown that the standard expression for time delay is recovered when small angles are involved. These two features strongly support the claim that the formula for time delay studied in this paper is the generalization to the arbitrary angles of the standard one, which is valid at small angles. This could therefore result in a useful tool in Astrophysics and Cosmology which may be applied to investigate the discrepancy between the various estimates of the Hubble constant. As an aside, two interesting consequences of our proposal for time delay are discussed: the existence of a constraint on the gravitational potential generated by the lens and a formula for the mass of the lens in the case of central potential.
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