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Register a new userImpact of Microlensing on Observational Strategies for Gravitational Time Delay Measurements
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Kai Liao
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Microlensing not only brings extra magnification lightcurves on top of the intrinsic ones but also shifts them in time domain, making the actual time-delays between images of strongly lensed active galactic nucleus change on the $sim$ day(s) light-crossing time scale of the emission region. The microlensing-induced time-delays would bias strong lens time-delay cosmography if uncounted. However, due to the uncertainties of the disk size and the disk model, the impact is hard to accurately estimate. In this work, we study how to reduce the bias with designed observation strategy based on a standard disk model. We find long time monitoring of the images could alleviate the impact since it averages the microlensing time-lag maps due to the peculia motion of the source relative to the lens galaxy. In addition, images in bluer bands correspond to smaller disk sizes and therefore benefit time-delay measurements as well. We conduct a simulation based on a PG 1115+080-like lensed quasar. The results show the time-delay dispersions caused by microlensing can be reduced by $sim40%$ with 20-year lightcurves while u band relative to r band reduces $sim75%$ of the dispersions. Nevertheless, such an effect can not be totally eliminated in any cases. Further studies are still needed to appropriately incorporate it in inferring an accurate Hubble constant.
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Time-delay strong lensing provides a unique way to directly measure the Hubble constant ($H_{0}$). The precision of the $H_{0}$ measurement depends on the uncertainties in the time-delay measurements, the mass distribution of the main deflector(s), and the mass distribution along the line of sight. Tie and Kochanek (2018) have proposed a new microlensing effect on time delays based on differential magnification of the coherent accretion disc variability of the lensed quasar. If real, this effect could significantly broaden the uncertainty on the time delay measurements by up to $30%$ for lens systems such as PG1115+080, which have relatively short time delays and monitoring over several different epochs. In this paper we develop a new technique that uses the time-delay ratios and simulated microlensing maps within a Bayesian framework in order to limit the allowed combinations of microlensing delays and thus to lessen the uncertainties due to the proposed effect. We show that, under the assumption of Tie and Kochanek (2018), the uncertainty on the time-delay distance ($D_{Delta t}$, which is proportional to 1/$H_{0}$) of short time-delay ($sim18$ days) lens, PG1115+080, increases from $sim7%$ to $sim10%$ by simultaneously fitting the three time-delay measurements from the three different datasets across twenty years, while in the case of long time-delay ($sim90$ days) lens, the microlensing effect on time delays is negligible as the uncertainty on $D_{Delta t}$ of RXJ1131-1231 only increases from $sim2.5%$ to $sim2.6%$.
It has recently been proposed that gravitationally lensed type-Ia supernovae can provide microlensing-free time-delay measurements provided that the measurement is taken during the achromatic expansion phase of the explosion and that color light curves are used rather than single-band light curves. If verified, this would provide both precise and accurate time-delay measurements, making lensed type-Ia supernovae a new golden standard for time-delay cosmography. However, the 3D geometry of the expanding shell can introduce an additional bias that has not yet been fully explored. In this work, we present and discuss the impact of this effect on time-delay cosmography with lensed supernovae and find that on average it leads to a bias of a few tenths of a day for individual lensed systems. This is negligible in view of the cosmological time delays predicted for typical lensed type-Ia supernovae but not for the specific case of the recently discovered type-Ia supernova iPTF16geu, whose time delays are expected to be smaller than a day.
Microlenses with typical stellar masses (a few ${rm M}_{odot}$) have traditionally been disregarded as potential sources of gravitational lensing effects at LIGO/Virgo frequencies, since the time delays are often much smaller than the inverse of the frequencies probed by LIGO/Virgo, resulting in negligible interference effects at LIGO/Virgo frequencies. While this is true for isolated microlenses in this mass regime, we show how, under certain circumstances and for realistic scenarios, a population of microlenses (for instance stars and remnants from a galaxy halo or from the intracluster medium) embedded in a macromodel potential (galaxy or cluster) can conspire together to produce time delays of order one millisecond which would produce significant interference distortions in the observed strains. At sufficiently large magnification factors (of several hundred), microlensing effects should be common in gravitationally lensed gravitational waves. We explore the regime where the predicted signal falls in the frequency range probed by LIGO/Virgo. We find that stellar mass microlenses, permeating the lens plane, and near critical curves, can introduce interference distortions in strongly lensed gravitational waves. For those lensed events with negative parity, (or saddle points, never studied before in the context of gravitational waves), and that take place near caustics of macromodels, they are more likely to produce measurable interference effects at LIGO/Virgo frequencies. This is the first study that explores the effect of a realistic population of microlenses, plus a macromodel, on strongly lensed gravitational waves.
We present the first year of Hubble Space Telescope imaging of the unique supernova (SN) Refsdal, a gravitationally lensed SN at z=1.488$pm$0.001 with multiple images behind the galaxy cluster MACS J1149.6+2223. The first four observed images of SN Refsdal (images S1-S4) exhibited a slow rise (over ~150 days) to reach a broad peak brightness around 20 April, 2015. Using a set of light curve templates constructed from SN 1987A-like peculiar Type II SNe, we measure time delays for the four images relative to S1 of 4$pm$4 (for S2), 2$pm$5 (S3), and 24$pm$7 days (S4). The measured magnification ratios relative to S1 are 1.15$pm$0.05 (S2), 1.01$pm$0.04 (S3), and 0.34$pm$0.02 (S4). None of the template light curves fully captures the photometric behavior of SN Refsdal, so we also derive complementary measurements for these parameters using polynomials to represent the intrinsic light curve shape. These more flexible fits deliver fully consistent time delays of 7$pm$2 (S2), 0.6$pm$3 (S3), and 27$pm$8 days (S4). The lensing magnification ratios are similarly consistent, measured as 1.17$pm$0.02 (S2), 1.00$pm$0.01 (S3), and 0.38$pm$0.02 (S4). We compare these measurements against published predictions from lens models, and find that the majority of model predictions are in very good agreement with our measurements. Finally, we discuss avenues for future improvement of time delay measurements -- both for SN Refsdal and for other strongly lensed SNe yet to come.
Time-delay cosmography with gravitationally lensed quasars plays an important role in anchoring the absolute distance scale and hence measuring the Hubble constant, $H_{0}$, independent of traditional distance ladder methodology. A current potential limitation of time delay distance measurements is the mass-sheet transformation (MST) which leaves the lensed imaging unchanged but changes the distance measurements and the derived value of $H_0$. In this work we show that the standard method of addressing the MST in time delay cosmography, through a combination of high-resolution imaging and the measurement of the stellar velocity dispersion of the lensing galaxy, depends on the assumption that the ratio, $D_{rm s}/D_{rm ds}$, of angular diameter distances to the background quasar and between the lensing galaxy and the quasar can be constrained. This is typically achieved through the assumption of a particular cosmological model. Previous work (TDCOSMO IV) addressed the mass-sheet degeneracy and derived $H_{0}$ under the assumption of $Lambda$CDM model. In this paper we show that the mass sheet degeneracy can be broken without relying on a specific cosmological model by combining lensing with relative distance indicators such as supernovae type Ia and baryon acoustic oscillations, which constrain the shape of the expansion history and hence $D_{rm s}/D_{rm ds}$. With this approach, we demonstrate that the mass-sheet degeneracy can be constrained in a cosmological-model-independent way, and hence model-independent distance measurements in time-delay cosmography under mass-sheet transformations can be obtained.
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