Microlensing of Extremely Magnified Stars near Caustics of Galaxy Clusters

Abstract

Recent observations of lensed galaxies at cosmological distances have detected individual stars that are extremely magnified when crossing the caustics of lensing clusters. In idealized cluster lenses with smooth mass distributions, two images of a star of radius R approaching a caustic brighten as t −1/2 and reach a peak magnification ∼ 10 6 (10 R /R) 1/2 before merging on the critical curve. We show that a mass fraction (κ 10 −4.5 ) in microlenses inevitably disrupts the smooth caustic into a network of corrugated microcaustics, and produces light curves with numerous peaks. Using analytical calculations and numerical simulations, we derive the characteristic width of the network, caustic-crossing frequencies, and peak magnifications. For the lens parameters of a recent detection and a population of intracluster stars with κ ∼ 0.01, we find a source-plane width of ∼ 20 pc for the caustic network, which spans 0.2 arcsec on the image plane. A source star takes ∼ 2 × 10 4 years to cross this width, with a total of ∼ 6 × 10 4 crossings, each one lasting for ∼ 5 hr (R/10 R ) with typical peak magnifications of ∼ 10 4 (R/10 R ) −1/2 . The exquisite sensitivity of caustic-crossing events to the granularity of the lens-mass distribution makes them ideal probes of dark matter components, such as compact halo objects and ultralight axion dark matter.

Gravitational-Wave Fringes at LIGO: Detecting Compact Dark Matter by Gravitational Lensing

“…Here, the O(1) evolution of the frequency in the LIGO band produces O(1) cycles of fringe patterns, which is easiest to detect. Resulting optimistic sensitivity f DM 10 −2 is comparable to or stronger than existing constraints from mircolensing [21], millilensing [23], star's caustic-crossing [36][37][38], and star-cluster survival [39] as well as various proposed searches [40,41]. The GW fringe sensitivity will further improve with longer observation time.…”

Probing Dark Matter Subhalos in Galaxy Clusters Using Highly Magnified Stars

“…Deep images at high resolution are likely to reveal star clusters and compact star-forming associates in the source galaxy. Near a caustic, their physical size l limits the maximum magnification factor µ [2 (l/D S ) |d sin α|] −1/2 /[2(1 − κ 0 )] (Venumadhav et al 2017), or µ 600 (l/pc) −1/2 in the case of Abell 370, at which the elongated image has a length ∼ 50 mas (l/pc) 1/2 . Depending on the compactness, these structures may be under-resolved or marginally resolved.…”

“…First, each macroimage is broken into a series of aligned microimages along the degenerate direction, with a typical angular spread r f θ 1/2 κ 1/4 /|d sin α| 1/2 1 mas, where θ is the Einstein radius of a microlens (Venumadhav et al 2017). This spread is not resolvable by present telescopes, so each track of microimages appears as a single macroimage.…”

Gravitational Lensing Signatures of Axion Dark Matter Minihalos in Highly Magnified Stars

“…However, intracluster stars introduce intermittent microlensing flux variations and micro-caustic crossings at which a pair of micro-images dominate the flux. This makes the highly magnified stars more easily identifiable from their variability, even though the maximum magnifications reached are reduced to ∼ 10 4 (Venumadhav et al 2017;Diego et al 2018;Oguri et al 2018). Flux variations of up to a factor of ten have been observed from microlensing events in the fields of MACS J1149 ) and of MACS J0416 (Chen et al 2019).…”

“…This fold approximation is accurate when the highly magnified images are much closer to the micro-critical curve than the typical angular scale of variation of the vectord. The presence of microlenses generates a region around the macro-critical curve of the cluster lens where the micro-critical curves interact and join together, forming a network of width ∼ κ |d| −1 (Venumadhav et al 2017). Within this network, the scale of variation ofd is about the mean separation between microlenses, ∼ θ /κ 1/2 , where θ is the Einstein angular radius of each individual microlens of mass M , θ = (4 G M /D eff c 2 ) 1/2 , with D eff = D L D S /D LS .…”