Imaging dark matter at the smallest scales with z  ≈ 1 lensed stars

¹ Instituto de Física de Cantabria (CSIC-UC), Avda. Los Castros s/n, 39005 Santander, Spain
² Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong
³ Physics Department, Ben-Gurion University of the Negev, PO Box 653, Be’er-Sheva 84105, Israel
⁴ Department of Physics, University of the Basque Country UPV/EHU, 48080 Bilbao, Spain
⁵ DIPC, Basque Country UPV/EHU, 48080 San Sebastian, Spain
⁶ Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain
⁷ Minnesota Institute for Astrophysics, University of Minnesota, 116 Church Street SE, Minneapolis, MN 55455, USA
⁸ School of Physics and Astronomy, University of Minnesota, 116 Church Street, Minneapolis, MN 55455, USA
⁹ Department of Astronomy, University of California, Berkeley, CA 94720-3411, USA
¹⁰ Department of Physics & Astronomy, McMaster University, 1280 Main Street West, Hamilton L8S 4M1, Canada
¹¹ Canadian Institute for Theoretical Astrophysics (CITA), University of Toronto, 60 St. George St., Toronto M5S 3H8, Canada
¹² INAF – Astrophysics and Space Science Observatory of Bologna, Via Piero Gobetti 93/3, 40129 Bologna, Italy
¹³ INFN–Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy
¹⁴ Department of Physics, University of California, 366 Physics North MC 7300, Berkeley, CA 94720, USA
¹⁵ Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, PA 19104, USA
¹⁶ Physics & Astronomy Department, University of California, Los Angeles, CA 90095, USA
¹⁷ Center for Frontier Science, Chiba University, 1-33 Yayoi-cho, Inage-ku, Chiba 263-8522, Japan
¹⁸ Department of Astronomy & Astrophysics, University of Chicago, Chicago, IL 60637, USA
¹⁹ Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
²⁰ Steward Observatory, University of Arizona, 933 N. Cherry Ave., Tucson, AZ 85721, USA
²¹ School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287-1404, USA

Received: 22 April 2024
Accepted: 7 June 2024

Abstract

Recent observations of caustic-crossing galaxies at redshift 0.7 ≲ z ≲ 1 show a wealth of transient events. Most of them are believed to be microlensing events of highly magnified stars. Earlier work predicts such events should be common near the critical curves (CCs) of galaxy clusters (“near region”), but some are found relatively far away from these CCs (“far region”). We consider the possibility that substructure on milliarcsecond scales (few parsecs in the lens plane) is boosting the microlensing signal in the far region. We study the combined magnification from the macrolens, millilenses, and microlenses (“3M lensing”), when the macromodel magnification is relatively low (common in the far region). After considering realistic populations of millilenses and microlenses, we conclude that the enhanced microlensing rate around millilenses is not sufficient to explain the high fraction of observed events in the far region. Instead, we find that the shape of the luminosity function (LF) of the lensed stars combined with the amount of substructure in the lens plane determines the number of microlensing events found near and far from the CC. By measuring β (the exponent of the adopted power law LF, dN/dL = ϕ(L)∝(1/L)^β), and the number density of microlensing events at each location, one can create a pseudoimage of the underlying distribution of mass on small scales. We identify two regimes: (i) positive-imaging regime where β > 2 and the number density of events is greater around substructures, and (ii) negative-imaging regime where β < 2 and the number density of microlensing events is reduced around substructures. This technique opens a new window to map the distribution of dark-matter substructure down to ∼10³ M_⊙. We study the particular case of seven microlensing events found in the Flashlights program in the Dragon arc (z = 0.725). A population of supergiant stars having a steep LF with β = 2.55_−0.56^+0.72 fits the distribution of these events in the far and near regions. We also find that the new microlensing events from JWST observations in this arc imply a surface mass density substructure of Σ_∗ = 54 M_⊙ pc⁻², consistent with the expected population of stars from the intracluster medium. We identify a small region of high density of microlensing events, and interpret it as evidence of a possible invisible substructure, for which we derive a mass of ∼1.3 × 10⁸ M_⊙ (within its Einstein radius) in the galaxy cluster.