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Register a new userOver-constrained Gravitational Lens Models and the Hubble Constant
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Added by
Christopher S. Kochanek
Publication date
2019
fields
Physics
and research's language is
English
Authors
C. S. Kochanek
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It is well known that measurements of H0 from gravitational lens time delays scale as H0~1-k_E where k_E is the mean convergence at the Einstein radius R_E but that all available lens data other than the delays provide no direct constraints on k_E. The properties of the radial mass distribution constrained by lens data are R_E and the dimensionless quantity x=R_E a(R_E)/(1-k_E)$ where a(R_E) is the second derivative of the deflection profile at R_E. Lens models with too few degrees of freedom, like power law models with densities ~r^(-n), have a one-to-one correspondence between x and k_E (for a power law model, x=2(n-2) and k_E=(3-n)/2=(2-x)/4). This means that highly constrained lens models with few parameters quickly lead to very precise but inaccurate estimates of k_E and hence H0. Based on experiments with a broad range of plausible dark matter halo models, it is unlikely that any current estimates of H0 from gravitational lens time delays are more accurate than ~10%, regardless of the reported precision.
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There are now 10 firm time delay measurements in gravitational lenses. The physics of time delays is well understood, and the only important variable for interpreting the time delays to determine H_0 is the mean surface mass density <k> (in units of the critical density for gravitational lensing) of the lens galaxy at the radius of the lensed images. More centrally concentrated mass distributions with lower <k> predict higher Hubble constants, with H_0~1-<k> to lowest order. While we cannot determine <k> directly given the available data on the current time delay lenses, we find H_0=48+/-3 km/s/Mpc for the isothermal (flat rotation curve) models, which are our best present estimate for the mass distributions of the lens galaxies. Only if we eliminate the dark matter halo of the lenses and use a constant mass-to-light ratio (M/L) model to find H_0=71+/-3 km/s/Mpc is the result consistent with local estimates. Measurements of time delays in better-constrained systems or observations to obtain new constraints on the current systems provide a clear path to eliminating the <k> degeneracy and making estimates of H_0 with smaller uncertainties than are possible locally. Independent of the value of H_0, the time delay lenses provide a new and unique probe of the dark matter distributions of galaxies and clusters because they measure the total (light + dark) matter surface density.
Present day estimates of the Hubble constant based on Cepheids and on the cosmic microwave background radiation are uncertain by roughly 10% (on the conservative assumption that the universe may not be PERFECTLY flat). Gravitational lens time delay measurements can produce estimates that are less uncertain, but only if a variety of major difficulties are overcome. These include a paucity of constraints on the lensing potential, the degeneracies associated with mass sheets and the central concentration of the lensing galaxy, multiple lenses, microlensing by stars, and the small variability amplitude typical of most quasars. To date only one lens meets all of these challenges. Several suffer only from the central concentration degeneracy, which may be lifted if one is willing to assume that systems with time delays are either like better constrained systems with non-variable sources, or alternatively, like nearby galaxies.
We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (i) the three independent time-delays and flux-ratios from VLA observations, (ii) the radio-image positions from VLBA observations, (iii) the shape of the deconvolved Einstein Ring from optical and infrared HST images, (iv) the extinction-corrected lens-galaxy centroids and structural parameters, and (v) a stellar velocity dispersion, sigma_ap=247+-35 km/s, of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck--II telescope. The lens mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes which are the key parameters to determine the value of H_0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum-chi^2 model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein Ring. A combined gravitational-lens and stellar dynamical analysis leads to a value of the Hubble Constant of H_0=75(+7/-6) km/s/Mpc (68 percent CL; Omega_m=0.3, Omega_Lambda=0.7. The non-linear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H_0. The lens galaxy G1 is ~5 times more massive than the secondary lens galaxy (G2), and has a mass density slope of gamma_G1=2.03(+0.14/-0.14) +- 0.03 (68 percent CL) for rho~r^-gamma, very close to isothermal (gamma=2). (Abridged)
The detection of GW170817 in both gravitational waves and electromagnetic waves heralds the age of gravitational-wave multi-messenger astronomy. On 17 August 2017 the Advanced LIGO and Virgo detectors observed GW170817, a strong signal from the merger of a binary neutron-star system. Less than 2 seconds after the merger, a gamma-ray burst (GRB 170817A) was detected within a region of the sky consistent with the LIGO-Virgo-derived location of the gravitational-wave source. This sky region was subsequently observed by optical astronomy facilities, resulting in the identification of an optical transient signal within $sim 10$ arcsec of the galaxy NGC 4993. These multi-messenger observations allow us to use GW170817 as a standard siren, the gravitational-wave analog of an astronomical standard candle, to measure the Hubble constant. This quantity, which represents the local expansion rate of the Universe, sets the overall scale of the Universe and is of fundamental importance to cosmology. Our measurement combines the distance to the source inferred purely from the gravitational-wave signal with the recession velocity inferred from measurements of the redshift using electromagnetic data. This approach does not require any form of cosmic distance ladder; the gravitational wave analysis can be used to estimate the luminosity distance out to cosmological scales directly, without the use of intermediate astronomical distance measurements. We determine the Hubble constant to be $70.0^{+12.0}_{-8.0} , mathrm{km} , mathrm{s}^{-1} , mathrm{Mpc}^{-1}$ (maximum a posteriori and 68% credible interval). This is consistent with existing measurements, while being completely independent of them. Additional standard-siren measurements from future gravitational-wave sources will provide precision constraints of this important cosmological parameter.
We present strong-lensing models, as well as mass and magnification maps, for the cores of the six HST Frontier Fields galaxy clusters. Our parametric lens models are constrained by the locations and redshifts of multiple image systems of lensed background galaxies. We use a combination of photometric redshifts and spectroscopic redshifts of the lensed background sources obtained by us (for Abell 2744 and Abell S1063), collected from the literature, or kindly provided by the lensing community. Using our results, we (1) compare the derived mass distribution of each cluster to its light distribution, (2) quantify the cumulative magnification power of the HFF clusters, (3) describe how our models can be used to estimate the magnification and image multiplicity of lensed background sources at all redshifts and at any position within the cluster cores, and (4) discuss systematic effects and caveats resulting from our modeling methods. We specifically investigate the effect of the use of spectroscopic and photometric redshift constraints on the uncertainties of the resulting models. We find that the photometric redshift estimates of lensed galaxies are generally in excellent agreement with spectroscopic redshifts, where available. However, the flexibility associated with relaxed redshift priors may cause the complexity of large-scale structure that is needed to account for the lensing signal to be underestimated. Our findings thus underline the importance of spectroscopic arc redshifts, or tight photometric redshift constraints, for high precision lens models. All products from our best-fit lens models (magnification, convergence, shear, deflection field) and model simulations for estimating errors are made available via the Mikulski Archive for Space Telescopes.
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