The Hubble Constant from Strongly Lensed Supernovae with Standardizable Magnifications

The dominant uncertainty in the current measurement of the Hubble constant (H 0) with strong gravitational lensing time delays is attributed to uncertainties in the mass profiles of the main deflector galaxies. Strongly lensed supernovae (glSNe) can provide, in addition to measurable time delays, lensing magnification constraints when knowledge about the unlensed apparent brightness of the explosion is imposed. We present a hierarchical Bayesian framework to combine a data set of SNe that are not strongly lensed and a data set of strongly lensed SNe with measured time delays. We jointly constrain (i) H 0 using the time delays as an absolute distance indicator, (ii) the lens model profiles using the magnification ratio of lensed and unlensed fluxes on the population level, and (iii) the unlensed apparent magnitude distribution of the SN population and the redshift–luminosity relation of the relative expansion history of the universe. We apply our joint inference framework on a future expected data set of glSNe and forecast that a sample of 144 glSNe of Type Ia with well-measured time series and imaging data will measure H 0 to 1.5%. We discuss strategies to mitigate systematics associated with using absolute flux measurements of glSNe to constrain the mass density profiles. Using the magnification of SN images is a promising and complementary alternative to using stellar kinematics. Future surveys, such as the Rubin and Roman observatories, will be able to discover the necessary number of glSNe, and with additional follow-up observations, this methodology will provide precise constraints on mass profiles and H 0.

Blending and obscuration in weak lensing magnification

We test the impact of some systematic errors in weak lensing magnification measurements with the COSMOS 30-band photo-z Survey flux limited to Iauto < 25.0 using correlations of both source galaxy counts and magnitudes. Systematic obscuration effects are measured by comparing counts and magnification correlations. We use the ACS-HST catalogs to identify potential blending objects (close pairs) and perform the magnification analyses with and without blended objects. We find that blending effects start to be important (∼ 0.04 mag obscuration) at angular scales smaller than 0.1 arcmin. Extinction and other systematic obscuration effects can be as large as 0.10 mag (U-band) but are typically smaller than 0.02 mag depending on the band. After applying these corrections, we measure a 3.9σ magnification signal that is consistent for both counts and magnitudes. The corresponding projected mass profiles of galaxies at redshift z ≃ 0.6 (MI ≃ −21) is Σ = 25 ± 6M⊙h3/pc2 at 0.1 Mpc/h, consistent with NFW type profile with M200 ≃ 2 × 1012M⊙h/pc2. Tangential shear and flux-size magnification over the same lenses show similar mass profiles. We conclude that magnification from counts and fluxes using photometric redshifts has the potential to provide complementary weak lensing information in future wide field surveys once we carefully take into account systematic effects, such as obscuration and blending.

Dynamical masses of brightest cluster galaxies – II. Constraints on the stellar IMF

ABSTRACT We use stellar and dynamical mass profiles, combined with a stellar population analysis, of 32 brightest cluster galaxies (BCGs) at redshifts of 0.05 ≤$z$ ≤ 0.30, to place constraints on their stellar initial mass function (IMF). We measure the spatially resolved stellar population properties of the BCGs, and use it to derive their stellar mass-to-light ratios ($\Upsilon _{\star \rm POP}$). We find young stellar populations (<200 Myr) in the centres of 22 per cent of the sample, and constant $\Upsilon _{\star \rm POP}$ within 15 kpc for 60 per cent of the sample. We further use the stellar mass-to-light ratio from the dynamical mass profiles of the BCGs ($\Upsilon _{\star \rm DYN}$), modelled using a multi-Gaussian expansion and Jeans Anisotropic Method, with the dark matter contribution explicitly constrained from weak gravitational lensing measurements. We directly compare the stellar mass-to-light ratios derived from the two independent methods, $\Upsilon _{\star \rm POP}$ (assuming some IMF) to $\Upsilon _{\star \rm DYN}$ for the subsample of BCGs with no young stellar populations and constant $\Upsilon _{\star \rm POP}$. We find that for the majority of these BCGs, a Salpeter (or even more bottom-heavy) IMF is needed to reconcile the stellar population and dynamical modelling results although for a small number of BCGs, a Kroupa (or even lighter) IMF is preferred. For those BCGs better fit with a Salpeter IMF, we find that the mass-excess factor against velocity dispersion falls on an extrapolation (towards higher masses) of known literature correlations. We conclude that there is substantial scatter in the IMF amongst the highest mass galaxies.

To β or not to β: can higher order Jeans analysis break the mass–anisotropy degeneracy in simulated dwarfs?

ABSTRACT We test a non-parametric higher order Jeans analysis method, GravSphere, on 32 simulated dwarf galaxies comparable to classical Local Group dwarfs like Fornax. The galaxies are selected from A Project Of Simulating The Local Environment (APOSTLE) suite of cosmological hydrodynamics simulations with cold dark matter (CDM) and self-interacting dark matter (SIDM) models, allowing us to investigate cusps and cores in density distributions. We find that, for CDM dwarfs, the recovered enclosed mass profiles have a bias of no more than 10 per cent, with a 50 per cent scatter in the inner regions and a 20 per cent scatter near the half-light radius, consistent with standard mass estimators. The density profiles are also recovered with a bias of no more than 10 per cent and a scatter of 30 per cent in the inner regions. For SIDM dwarfs, the mass and density profiles are recovered within our 95 per cent confidence intervals but are biased towards cuspy dark matter distributions. This is mainly due to a lack of sufficient constraints from the data. We explore the sources of scatter in the accuracy of the recovered profiles and suggest a χ2 statistic to separate successful models from biased ones. Finally, we show that the uncertainties on the mass profiles obtained with GravSphere are smaller than those for comparable Jeans methods and that they can be further improved if stronger priors, motivated by cosmological simulations, are placed on the velocity anisotropy. We conclude that GravSphere is a promising Jeans-based approach for modelling dark matter distributions in dwarf galaxies.

TDCOSMO

Time-delay cosmography of lensed quasars has achieved 2.4% precision on the measurement of the Hubble constant, H0. As part of an ongoing effort to uncover and control systematic uncertainties, we investigate three potential sources: 1- stellar kinematics, 2- line-of-sight effects, and 3- the deflector mass model. To meet this goal in a quantitative way, we reproduced the H0LiCOW/SHARP/STRIDES (hereafter TDCOSMO) procedures on a set of real and simulated data, and we find the following. First, stellar kinematics cannot be a dominant source of error or bias since we find that a systematic change of 10% of measured velocity dispersion leads to only a 0.7% shift on H0 from the seven lenses analyzed by TDCOSMO. Second, we find no bias to arise from incorrect estimation of the line-of-sight effects. Third, we show that elliptical composite (stars + dark matter halo), power-law, and cored power-law mass profiles have the flexibility to yield a broad range in H0 values. However, the TDCOSMO procedures that model the data with both composite and power-law mass profiles are informative. If the models agree, as we observe in real systems owing to the “bulge-halo” conspiracy, H0 is recovered precisely and accurately by both models. If the two models disagree, as in the case of some pathological models illustrated here, the TDCOSMO procedure either discriminates between them through the goodness of fit, or it accounts for the discrepancy in the final error bars provided by the analysis. This conclusion is consistent with a reanalysis of six of the TDCOSMO (real) lenses: the composite model yields H0 = 74.0−1.8+1.7 km s−1 Mpc−1, while the power-law model yields 74.2−1.6+1.6 km s−1 Mpc−1. In conclusion, we find no evidence of bias or errors larger than the current statistical uncertainties reported by TDCOSMO.

Systematic versus statistical uncertainties in masses and magnifications of the Hubble Frontier Fields

ABSTRACT The Hubble Frontier Fields data, along with multiple data sets obtained by other telescopes, have provided some of the most extensive constraints on cluster lenses to date. Multiple lens modelling teams analyzed the fields and made public a number of deliverables. By comparing these results, we can then undertake a unique and vital test of the state of cluster lens modelling. Specifically, we see how well the different teams can reproduce similar magnifications and mass profiles. We find that the circularly averaged mass profiles of the fields are remarkably constrained (scatter $\lt 5{{\ \rm per\ cent}}$) at distances of 1 arcmin from the cluster core, yet magnifications can vary significantly. Averaged across the six fields, we find a bias of −6 per cent (−17 per cent) and a scatter of ∼40 per cent (∼65 per cent) at a modest magnification of 3 (10). Statistical errors reported by individual teams are often significantly smaller than the differences among all the teams, indicating the importance of continued systematics studies in cluster lensing.

A precise analytical approximation for the deprojection of the Sérsic profile

The Sérsic model shows a close fit to the surface brightness (or surface density) profiles of elliptical galaxies and galaxy bulges, and possibly also those of dwarf spheroidal galaxies and globular clusters. The deprojected density and mass profiles are important for many astrophysical applications, in particular for mass-orbit modeling of these systems. However, the exact deprojection formula for the Sérsic model employs special functions that are not available in most computer languages. We show that all previous analytical approximations to the 3D density profile are imprecise at low Sérsic index (n ≲ 1.5). We derived a more precise analytical approximation to the deprojected Sérsic density and mass profiles by fitting two-dimensional tenth-order polynomials to the residuals of the analytical approximations by Lima Neto et al. (1999, MNRAS, 309, 481; LGM) for these profiles, relative to the numerical estimates. Our LGM-based polynomial fits have typical relative precision better than 0.2% for both density and mass profiles, for Sérsic indices 0.5 ≤ n ≤ 10 and radii 0.001 < r/Re < 1000. Our approximation is much more precise than previously published approximations (except, in some models, for a few discrete values of the index). An appendix compares the deprojected Sérsic profiles with those of other popular simple models.