Caustic Crossing Stars Probe Dark Matter Subhalos

The phenomenon of gravitational lensing is a spectacular demonstration of how space and time can deform under the influence of mass. Owing to the tremendous amount of matter (visible and invisible!!) they possess, galaxy clusters are such powerful “lenses” that they create the mirage of multiple appearances for the background sources and dramatically distort their apparent shapes near lensing caustics. In fact, when approaching a lensing caustic, stars in a distant galaxy can be magnified by so much that they become individually detectable to telescopes [see a recent HST detection in galaxy cluster MACSJ1149].

Those highly magnified stars flicker due to micro-lensing (Venumadhav, LD & Miralda-Escudé 2017; Diego et al 2018; Oguri et al 2018). The micro-lensing rate is enhanced by orders of magnitude due to the interaction between clustering lensing and micro-lensing. This feature makes caustic crossing stars observationally much more accessible — the stars’ images intermittently brighten for a few to a hundred times a year — this process can last for thousands of years!

Remarkably, the phenomenon of caustic crossing stars is sensitive to the lumpiness of dark matter in the cluster halo on sub-kiloparsec scales. In a recent study I led (LD, Venumadhav, Kaurov & Miralda-Escudé 1804.03149), we envisage an astrometric method to detect dark matter substructure on mass scales of 106–108 solar masses. The method aims to look for image position distortions that break the symmetric pattern across the lensing critical curve which would be generically expected if dark matter is smoothly distributed. Figure 1 shows an example of how low-mass subhalos in the Cold Dark Matter (CDM) theory disrupt the otherwise smooth critical curve.

Figure 1: Simulated effect of substructure on the cluster’s critical curve. From left to right increasingly smaller dark matter subhalos are included. The smooth critical curve is strongly disrupted. Each individual bright star shows a pair of images (blue and red), whose positions are subject to perturbation by subhalos.

Compared to the Hubble Space Telescope (HST), the forthcoming James Webb Space Telescope (JWST) will be a more powerful instrument to discover caustic crossing stars and measure their image positions. Giant optical/IR telescopes on the ground may also have great scientific potential for this application if atmospheric seeing can be put under control with the technique of adaptive optics.

Lensing of Gravitational Waves

Detection of astrophysical gravitational waves (GWs) by aLIGO/Virgo has marked the beginning of gravitational wave astronomy. Forthcoming runs with an upgraded network of ground-based detectors will uncover more compact binary coalescences from further away.

Traversing a huge distance before reaching the Earth, GWs are prone to gravitational lensing by intervening mass clumps. Unlike distant optical sources such as quasars or supernovae, GWs detectable to ground-based observatories have very long wavelengths λ ~ 105–107 m, which can be comparable to the Schwarzschild length scale of the intervening mass clump. This feature gives rise to wave diffraction effects when gravitational waves are lensed!

Our recent study (LD, Li, Zackay, Mao & Lu 1810.00003) proposes to use GWs to probe small dark matter clumps in the Universe by detecting amplitude and phase modulations induced by diffraction. We have developed a novel search method based on dynamic programming which does not require exact diffraction-distorted waveform templates (which is not known in practice!). Figure 2 demonstrates how dynamic programming can recover the diffraction signature.

Figure 2: Agnostic reconstruction of amplitude and phase modulations using dynamic programming.

Third-generation GW detectors (e.g. the Einstein Telescope) are under concept study. They will routinely detect binary blackhole mergers from high redshifts, which would be ideal sources to probe dark matter clumps across the Universe along the line of sight. Through wave diffraction effects, we may detect the compact central cusps of low-mass (~ 104–106 solar masses) dark matter halos as predicted by the Cold Dark Matter theory! It is surprising that faint spacetime ripples may turn out to be wonderful probes to reveal Nature’s dark secrets.

GWs can also be lensed by a whole intervening galaxy. Similar to optical lensing, the waves can be amplified or de-amplified. This can produce seemingly very massive (LD, Venumadhav & Sigurdson 2017; Broadhurst et al 1802.05273) or very high-redshift (Oguri 2018) black hole sources.

When galaxy lensing produces multiple lensed images of GWs, some images are “flipped” due to over-focusing. We found that the waveform of a flipped image is distorted by an additional phase shift even in the regime of geometrical lensing (LD & Venumadhav 1702.04724). This phase shift is a topological one due to wave self-intersection. Difficult to measure in electromagnetic waves, this interesting effect however can be measured in GWs, which would vividly demonstrate that space-time ripples also obey the universal behavior of wave propagation and interference.

Fast Parameter Estimation for Gravitational Waves

Parameter estimation is crucial for the extraction of physical information about the source from the strain data. Evaluating the matched filter likelihood function can be computationally expensive if the data is analyzed at a high sampling rate and if the GW signal lasts for a longer duration in band. This challenge will become particularly prominent for upgraded ground-based detectors and for the forthcoming space-based detector LISA.

Do you know that even a non-expert in GW analysis can overcome such computational difficulty if one is clever? In a recent work (Zackay, LD & Venumadhav 1806.08792) we developed a technique called relative binning, which speeds up likelihood evaluation by approximating the likelihood function in the vicinity of the maximum likelihood solution. Our method is conceptually simple and easy to implement.

We have successfully applied relative binning to GW170817, the first binary neutron star merger event detected in GWs and confirmed in electromagnetic counterparts. We performed Bayesian parameter estimation for GW170817 by coupling our likelihood code to popular Monte Carlo samplers (LD, Zackay & Venumadhav 1806.08793), and obtained results consistent with those published by aLIGO/Virgo (1805.11579).

We provide a tutorial Python code (download from here) that demonstrates how the likelihood function can be evaluated using relative binning. Our method should benefit (astro-)physicists who are non-experts in GW data analysis but are eager to learn something about GW sources using publicly available strain data.

Timing Lensed Fast Radio Bursts

Fast radio bursts (FRBs) are extragalactic, highly-dispersed, and extremely swift radio outbursts detected by radio astronomers. Their sources and the underlying physical mechanism for radiation are heated topics in astrophysics. The most impressive example so far is FRB 121102, which, thanks to very-long-baseline interferometric technique, has been found to be associated with an underlying source that resides in a distant galaxy at z=0.2 and sporadical repeats. It has been thought that many FRB sources, if not all of them, may repeatedly give off radio bursts.

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Figure 4: The geometry of an FRB source lensed by an intervening galaxy.

Like other extragalactic sources, we may in the future find a repeating FRB source lensed by an intervening galaxy and hence split into multiple images (Figure 4). In that case, we would be able to perform a fantastic timing test (LD & Lu 2017). The idea is that one can measure with milli-second precision the arrival times of each individual burst as it shows up at different lensed images. The delays in the arrival times between different images can show subtle variations over time, which will be sensitive to the source’s physical motion (e.g. if the source orbits around a companion). Therefore, we can turn the gravitational lens into a powerful “microscope” that is capable of resolving the source’s motion on the scale of astronomical units! This would allow astronomers to better understand the physics of the underlying FRB engine.