Michele Cappellari

Abstract:

We reanalyzed spectra that were taken as part of the SL2S lens galaxy survey with the goal to obtain the stellar velocity dispersion with a precision and accuracy sufficient for time-delay cosmography. In order to achieve this goal, we imposed stringent cuts on the signal-to-noise ratio (S/N), and employed recently developed methods to mitigate and quantify residual systematic errors that are transferred from template libraries and fitting process. We also quantified the covariance across the sample. For galaxy spectra with S/N $>20/$Å, our new measurements have an average random uncertainty of 3-4%, an average systematic uncertainty of 2%, and a covariance across the sample of 1%. We find a negligible covariance between spectra taken with different instruments. The systematic uncertainty and covariance need to be included when the sample is used as an external dataset in time-delay cosmography. We revisited empirical scaling relations of lens galaxies based on the improved kinematics. We show that the SL2S sample, the TDCOSMO time-delay lens sample, and the lower-redshift SLACS sample follow the same correlation of the effective radius, stellar velocity dispersion, and lensing mass, known as the lensing-mass fundamental plane, as the previously derived correlation that assumed isothermal mass profiles for the deflectors. We also derived for the first time the lensing-mass fundamental plane assuming free power-law mass density profiles, and we show that the three samples also follow the same correlation. This is consistent with a scenario in which massive galaxies evolve by growing their radii and mass, but stay within the plane.

Abstract:

The stellar velocity dispersion ( σ ) of massive elliptical galaxies is a key ingredient in breaking the mass-sheet degeneracy and obtaining precise and accurate cosmography from gravitational time delays. The relative uncertainty on the Hubble constant H 0 is double the relative error on σ . Therefore, time-delay cosmography imposes much more demanding requirements on the precision and accuracy of σ than galaxy studies. While precision can be achieved with an adequate signal-to-noise ratio (S/N), the accuracy critically depends on key factors such as the elemental abundance and temperature of stellar templates, flux calibration, and wavelength ranges. We carried out a detailed study of the problem using multiple sets of galaxy spectra of massive elliptical galaxies with S/N ∼ 30–160 Å −1 , along with state-of-the-art empirical and semi-empirical stellar libraries and stellar population synthesis templates. We show that the choice of stellar library is generally the dominant source of residual systematic errors. We propose a general recipe for mitigating and accounting for residual uncertainties. We show that a sub-percent level of accuracy can be achieved on individual spectra with our data quality, which we subsequently validated with simulated mock datasets. The covariance between velocity dispersions measured for a sample of spectra can also be reduced to sub-percent levels. We recommend this recipe for all applications that require high precision and accurate stellar kinematics. Thus, we have made all the software publicly available to facilitate its implementation. This recipe will also be used in future TDCOSMO collaboration papers.

Abstract:

Adaptive binning is a crucial step in the analysis of large astronomical data sets, such as those from integral-field spectroscopy, to ensure a sufficient signal-to-noise ratio () for reliable model fitting. However, the widely used Voronoi-binning method and its variants suffer from two key limitations: they scale poorly with data size, often as , creating a computational bottleneck for modern surveys, and they can produce undesirable non-convex or disconnected bins. I introduce PowerBin, a new algorithm that overcomes these issues. I frame the binning problem within the theory of optimal transport, for which the solution is a Centroidal Power Diagram (CPD), guaranteeing convex bins. Instead of formal CPD solvers, which are unstable with real data, I develop a fast and robust heuristic based on a physical analogy of packed soap bubbles. This method reliably enforces capacity constraints even for non-additive measures like with correlated noise. I also present a new bin-accretion algorithm with complexity, removing the previous bottleneck. The combined PowerBin algorithm scales as , making it about two orders of magnitude faster than previous methods on million-pixel data sets. I demonstrate its performance on a range of simulated and real data, showing it produces high-quality, convex tessellations with excellent uniformity. The public python implementation provides a fast, robust, and scalable tool for the analysis of modern astronomical data.