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Register a new userSHARP - III: First Use Of Adaptive Optics Imaging To Constrain Cosmology With Gravitational Lens Time Delays
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Accurate and precise measurements of the Hubble constant are critical for testing our current standard cosmological model and revealing possibly new physics. With Hubble Space Telescope (HST) imaging, each strong gravitational lens system with measured time delays can allow one to determine the Hubble constant with an uncertainty of $sim 7%$. Since HST will not last forever, we explore adaptive-optics (AO) imaging as an alternative that can provide higher angular resolution than HST imaging but has a less stable point spread function (PSF) due to atmospheric distortion. To make AO imaging useful for time-delay-lens cosmography, we develop a method to extract the unknown PSF directly from the imaging of strongly lensed quasars. In a blind test with two mock data sets created with different PSFs, we are able to recover the important cosmological parameters (time-delay distance, external shear, lens mass profile slope, and total Einstein radius). Our analysis of the Keck AO image of the strong lens system RXJ1131-1231 shows that the important parameters for cosmography agree with those based on HST imaging and modeling within 1-$sigma$ uncertainties. Most importantly, the constraint on the model time-delay distance by using AO imaging with $0.045$resolution is tighter by $sim 50%$ than the constraint of time-delay distance by using HST imaging with $0.09$when a power-law mass distribution for the lens system is adopted. Our PSF reconstruction technique is generic and applicable to data sets that have multiple nearby point sources, enabling scientific studies that require high-precision models of the PSF.
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We present the measurement of the Hubble Constant, $H_0$, with three strong gravitational lens systems. We describe a blind analysis of both PG1115+080 and HE0435-1223 as well as an extension of our previous analysis of RXJ1131-1231. For each lens, we combine new adaptive optics (AO) imaging from the Keck Telescope, obtained as part of the SHARP AO effort, with Hubble Space Telescope (HST) imaging, velocity dispersion measurements, and a description of the line-of-sight mass distribution to build an accurate and precise lens mass model. This mass model is then combined with the COSMOGRAIL measured time delays in these systems to determine $H_{0}$. We do both an AO-only and an AO+HST analysis of the systems and find that AO and HST results are consistent. After unblinding, the AO-only analysis gives $H_{0}=82.8^{+9.4}_{-8.3}~rm km,s^{-1},Mpc^{-1}$ for PG1115+080, $H_{0}=70.1^{+5.3}_{-4.5}~rm km,s^{-1},Mpc^{-1}$ for HE0435-1223, and $H_{0}=77.0^{+4.0}_{-4.6}~rm km,s^{-1},Mpc^{-1}$ for RXJ1131-1231. The joint AO-only result for the three lenses is $H_{0}=75.6^{+3.2}_{-3.3}~rm km,s^{-1},Mpc^{-1}$. The joint result of the AO+HST analysis for the three lenses is $H_{0}=76.8^{+2.6}_{-2.6}~rm km,s^{-1},Mpc^{-1}$. All of the above results assume a flat $Lambda$ cold dark matter cosmology with a uniform prior on $Omega_{textrm{m}}$ in [0.05, 0.5] and $H_{0}$ in [0, 150] $rm km,s^{-1},Mpc^{-1}$. This work is a collaboration of the SHARP and H0LiCOW teams, and shows that AO data can be used as the high-resolution imaging component in lens-based measurements of $H_0$. The full time-delay cosmography results from a total of six strongly lensed systems are presented in a companion paper.
Strongly lensed quasars can provide measurements of the Hubble constant ($H_{0}$) independent of any other methods. One of the key ingredients is exquisite high-resolution imaging data, such as Hubble Space Telescope (HST) imaging and adaptive-optics (AO) imaging from ground-based telescopes, which provide strong constraints on the mass distribution of the lensing galaxy. In this work, we expand on the previous analysis of three time-delay lenses with AO imaging (RXJ1131-1231, HE0435-1223, and PG1115+080), and perform a joint analysis of J0924+0219 by using AO imaging from the Keck Telescope, obtained as part of the SHARP (Strong lensing at High Angular Resolution Program) AO effort, with HST imaging to constrain the mass distribution of the lensing galaxy. Under the assumption of a flat $Lambda$CDM model with fixed $Omega_{rm m}=0.3$, we show that by marginalizing over two different kinds of mass models (power-law and composite models) and their transformed mass profiles via a mass-sheet transformation, we obtain $Delta t_{rm BA}hhat{sigma}_{v}^{-2}=6.89substack{+0.8-0.7}$ days, $Delta t_{rm CA}hhat{sigma}_{v}^{-2}=10.7substack{+1.6-1.2}$ days, and $Delta t_{rm DA}hhat{sigma}_{v}^{-2}=7.70substack{+1.0-0.9}$ days, where $h=H_{0}/100~rm km,s^{-1},Mpc^{-1}$ is the dimensionless Hubble constant and $hat{sigma}_{v}=sigma^{rm ob}_{v}/(280~rm km,s^{-1})$ is the scaled dimensionless velocity dispersion. Future measurements of time delays with 10% uncertainty and velocity dispersion with 5% uncertainty would yield a $H_0$ constraint of $sim15$% precision.
Strong lensing gravitational time delays are a powerful and cost effective probe of dark energy. Recent studies have shown that a single lens can provide a distance measurement with 6-7 % accuracy (including random and systematic uncertainties), provided sufficient data are available to determine the time delay and reconstruct the gravitational potential of the deflector. Gravitational-time delays are a low redshift (z~0-2) probe and thus allow one to break degeneracies in the interpretation of data from higher-redshift probes like the cosmic microwave background in terms of the dark energy equation of state. Current studies are limited by the size of the sample of known lensed quasars, but this situation is about to change. Even in this decade, wide field imaging surveys are likely to discover thousands of lensed quasars, enabling the targeted study of ~100 of these systems and resulting in substantial gains in the dark energy figure of merit. In the next decade, a further order of magnitude improvement will be possible with the 10000 systems expected to be detected and measured with LSST and Euclid. To fully exploit these gains, we identify three priorities. First, support for the development of software required for the analysis of the data. Second, in this decade, small robotic telescopes (1-4m in diameter) dedicated to monitoring of lensed quasars will transform the field by delivering accurate time delays for ~100 systems. Third, in the 2020s, LSST will deliver 1000s of time delays; the bottleneck will instead be the aquisition and analysis of high resolution imaging follow-up. Thus, the top priority for the next decade is to support fast high resolution imaging capabilities, such as those enabled by the James Webb Space Telescope and next generation adaptive optics systems on large ground based telescopes.
We consider several aspects of the generalized multi-plane gravitational lens theory, in which light rays from a distant source are affected by several main deflectors, and in addition by the tidal gravitational field of the large-scale matter distribution in the Universe when propagating between the main deflectors. Specifically, we derive a simple expression for the time-delay function in this case, making use of the general formalism for treating light propagation in inhomogeneous spacetimes which leads to the characterization of distance matrices between main lens planes. Applying Fermats principle, an alternative form of the corresponding lens equation is derived, which connects the impact vectors in three consecutive main lens planes, and we show that this form of the lens equation is equivalent to the more standard one. For this, some general relations for cosmological distance matrices are derived. The generalized multi-plane lens situation admits a generalized mass-sheet transformation, which corresponds to uniform isotropic scaling in each lens plane, a corresponding scaling of the deflection angle, and the addition of a tidal matrix (mass sheet plus external shear) to each main lens. We show that the time delay for sources in all lens planes scale with the same factor under this generalized mass-sheet transformation, thus precluding the use of time-delay ratios to break the mass-sheet transformation.
We present high-spatial resolution imaging obtained with the Submillimeter Array (SMA) at 880um and the Keck Adaptive Optics (AO) system at Ks-band of a gravitationally lensed sub-millimeter galaxy (SMG) at z=4.243 discovered in the Herschel-Astrophysical Terahertz Large Area Survey. The SMA data (angular resolution ~0.6) resolve the dust emission into multiple lensed images, while the Keck AO Ks-band data (angular resolution ~0.1) resolve the lens into a pair of galaxies separated by 0.3. We present an optical spectrum of the foreground lens obtained with the Gemini-South telescope that provides a lens redshift of z_lens = 0.595 +/- 0.005. We develop and apply a new lens modeling technique in the visibility plane that shows that the SMG is magnified by a factor of mu = 4.1 +/- 0.2 and has an intrinsic infrared (IR) luminosity of L_IR = (2.1 +/- 0.2) x 10^13 Lsun. We measure a half-light radius of the background source of r_s = 4.4 +/- 0.5 kpc which implies an IR luminosity surface density of Sigma_IR = (3.4 +/- 0.9) x 10^11 Lsun kpc^-2, a value that is typical of z > 2 SMGs but significantly lower than IR luminous galaxies at z~0. The two lens galaxies are compact (r_lens ~ 0.9 kpc) early-types with Einstein radii of theta_E1 = 0.57 +/- 0.01 and theta_E2 = 0.40 +/- 0.01 that imply masses of M_lens1 = (7.4 +/- 0.5) x 10^10 Msun and M_lens2 = (3.7 +/- 0.3) x 10^10 Msun. The two lensing galaxies are likely about to undergo a dissipationless merger, and the mass and size of the resultant system should be similar to other early-type galaxies at z~0.6. This work highlights the importance of high spatial resolution imaging in developing models of strongly lensed galaxies discovered by Herschel.
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