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    Forecasted detection limits on the dark matter density in supermassive black hole binaries for LISA

    Matthias Daniel1,*, Kris Pardo2,†, and Laura Sagunski1,‡

    • 1Institute for Theoretical Physics, Goethe University, 60438 Frankfurt am Main, Germany
    • 2Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089, USA

    • *Contact author: daniel@itp.uni-frankfurt.de
    • †Contact author: kmpardo@usc.edu
    • ‡Contact author: sagunski@itp.uni-frankfurt.de

    Phys. Rev. D 113, 023004 – Published 6 January, 2026

    DOI: https://doi.org/10.1103/pbrj-vqwq

    Abstract

    Supermassive black hole binaries (SMBHBs) are among the most powerful known sources of gravitational waves (GWs). Accordingly, these systems could dominate GW emission in the micro- and millihertz frequency range. Within this domain, SMBHs evolve rapidly and merge with each other. Dynamical friction from stars and gas at the centers of galaxies typically helps to bring together two SMBHs when they are at relatively far separations (≈kpc−100  pc), but becomes less efficient at smaller separations. However, dark matter (DM) spikes around SMBHs could enhance dynamical friction at close separations and, thus, shorten the evolution times. In this paper, we simulate the effects of DM spikes on GW signals in the micro- to millihertz frequency range and confirm that the GW signals from SMBHBs with DM spikes can be clearly distinguished from those without any additional matter. Making use of the projected sensitivity curve of the Laser Interferometer Space Antenna, we forecast upper limits for the (dark) matter density for given future SMBHB observations. We then compare these thresholds with the theoretical density profiles expected for self-interacting dark matter spikes.

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