Statistics of mass substructure from strong gravitational lensing: quantifying the mass fraction and mass function

A Bayesian statistical formalism is developed to quantify the level at which the mass function slope (alpha) and the projected cumulative mass fraction (f) of (CDM) substructure in strong gravitational-lens galaxies, with arcs or Einstein rings, can be recovered as function of the lens-survey parameters and the detection threshold of the substructure mass. The method is applied to different sets of mock data to explore a range of observational limits: (i) the number of lens galaxies in the survey, (ii) the mass threshold, Mlow, for the detection of substructures and (iii) the uncertainty of the measured substructure masses. We explore two different priors on the mass function slope: a uniform prior and a Gaussian prior with alpha = 1.90+-0.1. With a substructure detection threshold Mlow=3x10^8 Msun, the number of lenses available now (n_l=30), a true dark-matter mass fraction in (CDM) substructure <=1.0% and a prior of alpha = 1.90+-0.1, we find that the upper limit of f can be constrained down to a level <=1.0% (95% CL). In the case of a Gaussian prior on alpha, it is always possible to set stringent constraints on both parameters. We also find that lowering the detection threshold has the largest impact on the ability to recover alpha, because of the (expected) steep mass-function slope. In the future, thanks to new surveys with telescopes, such as SKA, LSST and JDEM and follow-up telescopes with high-fidelity data, a significant increase in the number of known lenses will allow us to recover the satellite population in its completeness. For example, a sample of 200 lenses, equivalent in data-quality to the Sloan Lens ACS Survey and a detection threshold of 10^8 Msun, allows one to determine f=0.5+-0.1% (68% CL) and alpha=1.90+-0.2 (68% CL).Comment: MNRAS (in press

The Kinematics of High Proper Motion Halo White Dwarfs

We analyse the kinematics of the entire spectroscopic sample of 99 recently discovered high proper-motion white dwarfs by Oppenheimer et al. using a maximum-likelihood analysis, and discuss the claim that the high-velocity white dwarfs are members of a halo population with a local density at least ten times greater than traditionally assumed. We argue that the observations, as reported, are consistent with the presence of an almost undetected thin disc plus a thick disc, with densities as conventionally assumed. In addition, there is a kinematically distinct, flattened, halo population at the more than 99% confidence level. Surprisingly, the thick disc and halo populations are indistinguishable in terms of luminosity, color and apparent age (1-10 Gyr). Adopting a bimodal, Schwarzschild model for the local velocity ellipsoid, with the ratios sigma_U:sigma_V:sigma_W=1:2/3:1/2, we infer radial velocity dispersions of sigma_U=62(+8/-10) km/s and 150(+80/-40) km/s (90% C.L.) for the local thick disc and halo populations, respectively. The thick disc result agrees with the empirical relation between asymmetric drift and radial velocity dispersion, inferred from local stellar populations. The local thick-disc plus halo density of white dwarfs is n^{td+h}=(1.9+-0.5)x10^-3 pc^-3 (90% C.L.), of which n^{h}=1.1(+2.1/-0.7)x10^-4 pc^-3 (90% C.L.) belongs to the halo, a density about five times higher than previously thought. (Abridged)Comment: 19 pages, 11 figures; submitted to MNRA

White Dwarfs: Contributors and Tracers of the Galactic Dark-Matter Halo

We examine the claim by Oppenheimer et al. (2001) that the local halo density of white dwarfs is an order of magnitude higher than previously thought. As it stands, the observational data support the presence of a kinematically distinct population of halo white dwarfs at the >99% confidence level. A maximum-likelihood analysis gives a radial velocity dispersion of sigma^h_U=150(+80/-40) km/s and an asymmetric drift of v_a^h=176(+102/-80) km/s, for a Schwarzschild velocity distribution function with sigma_U:sigma_V:sigma_W=1:2/3:1/2. Halo white dwarfs have a local number density of 1.1(+2.1/-0.7)x10^-4 pc-3, which amounts to 0.8(+1.6/-0.5) per cent of the nominal local dark-matter halo density and is 5.0(+9.5/-3.2) times higher and thus only marginally in agreement with previous estimates (all errors indicate the 90% C.L.). We discuss several direct consequences of this white-dwarf population (e.g. microlensing) and postulate a potential mechanism to eject young white dwarfs from the disc to the halo, through the orbital instabilities in triple or multiple stellar systems.Comment: 5 pages, to appear in the proceedings of the Yale Cosmology Workshop "The Shapes of Galaxies and their Halos" (ed. Priya Natarajan); revised numerical results, using a corrected likelihood function (thanks to David Graff and Andy Gould); general conclusions remain simila

Quantifying Suppression of the Cosmological 21-cm Signal due to Direction Dependent Gain Calibration in Radio Interferometers

The 21-cm signal of neutral hydrogen - emitted during the Epoch of Reionization - promises to be an important source of information for the study of the infant universe. However, its detection is impossible without sufficient mitigation of other strong signals in the data, which requires an accurate knowledge of the instrument. Using the result of instrument calibration, a large part of the contaminating signals are removed and the resulting residual data is further analyzed in order to detect the 21-cm signal. Direction dependent calibration (DDC) can strongly affect the 21-cm signal, however, its effect has not been precisely quantified. In the analysis presented here we show how to exactly calculate what part of the 21-cm signal is removed as a result of the DDC. We also show how a-priori information about the frequency behavior of the instrument can be used to reduce signal suppression. The theoretical results are tested using a realistic simulation based on the LOFAR setup. Our results show that low-order smooth gain functions (e.g. polynomials) over a bandwidth of ~10\,MHz - over which the signal is expected to be stationary - is sufficient to allow for calibration with limited, quantifiable, signal suppression in its power spectrum. We also show mathematically and in simulations that more incomplete sky models lead to larger 21-cm signal suppression, even if the gain models are enforced to be fully smooth. This result has immediate consequences for current and future radio telescopes with non-identical station beams, where DDC might be necessary (e.g. SKA-low).Comment: Submitted to MNRAS on 10-Aug-201

Micro & strong lensing with the Square Kilometer Array: The mass--function of compact objects in high--redshift galaxies

We present the results from recent VLA 8.5-GHz and WSRT 1.4 and 4.9-GHz monitoring campaigns of the CLASS gravitational lens B1600+434 and show how the observed variations argue strongly in favor of microlensing by MACHOs in the halo of a dark-matter dominated edge-on disk galaxy at z=0.4. The population of flat-spectrum radio sources with micro-Jy flux-densities detected with the Square-Kilometer-Array is expected to have dimensions of micro-arcsec. They will therefore vary rapidly as a result of Galactic scintillation (diffractive and refractive). However, when positioned behind distant galaxies they will also show variations due to microlensing, even more strongly than in the case of B1600+434. Relativistic or superluminal motion in these background sources typically leads to temporal variations on time scales of days to weeks. Scintillation and microlensing can be distinguished, and separated, by their different characteristic time scales and the frequency dependence of their modulations. Monitoring studies with Square-Kilometer-Array at GHz frequencies will thus probe both microscopic and macroscopic properties of dark matter and its mass-function as a function of redshift, information very hard to obtain by any other method.Comment: 8 pages, 5 figures, to appear in Perspectives in Radio Astronomy: Scientific Imperatives at cm and m Wavelengths (Dwingeloo: NFRA), Edited by: M.P. van Haarlem & J.M. van der Huls

Robust Foregrounds Removal for 21-cm Experiments

Direct detection of the Epoch of Reionization via the redshifted 21-cm line will have unprecedented implications on the study of structure formation in the early Universe. To fulfill this promise current and future 21-cm experiments will need to detect the weak 21-cm signal over foregrounds several order of magnitude greater. This requires accurate modeling of the galactic and extragalactic emission and of its contaminants due to instrument chromaticity, ionosphere and imperfect calibration. To solve for this complex modeling, we propose a new method based on Gaussian Process Regression (GPR) which is able to cleanly separate the cosmological signal from most of the foregrounds contaminants. We also propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere. Using this method, chromatic effects causing the so-called "wedge" are effectively eliminated (i.e. deconvolved) in the cylindrical ($k_{\perp}, k_{\parallel}$) power spectrum.Comment: Subbmited to the Proceedings of the IAUS333, Peering Towards Cosmic Dawn, 4 pages, 2 figure