Detecting ultralight dark matter in the Galactic Center with pulsars around Sgr A*

TL;DR

This work investigates ultralight dark matter (ULDM) near Sgr A* by modeling nonrelativistic bound structures—the gravitational atom (GA) and a self-gravitating spherical soliton—through the Schrödinger-Poisson framework and examining their gravitational influence on a pulsar in a close orbit. A post-Newtonian timing framework is developed to propagate the ULDM-induced acceleration into pulsar timing observables, with projected sensitivities computed using a Fisher-mmatrix formalism under SKA-like precision (σ_TOA ≈ 1 ms) over a 5-year span. The results show that long-term pulsar timing could detect or constrain ULDM clouds with total mass ~M⊙ for boson mass m ~ 10^-18 eV, achieving β ≈ M_c/M down to ~10^-7–10^-6 for favorable orbital configurations, surpassing current S2-based limits and probing regimes beyond the halo–soliton relation. The study also analyzes the role of BH spin, orbital geometry, and multi-state ULDM configurations, highlighting potential oscillating gravitational signatures and the necessity of accounting for environmental effects, ultimately underscoring pulsar timing as a powerful probe of GC ULDM physics.

Abstract

Ultralight dark matter (ULDM) model is a leading dark matter candidate that arises naturally in extensions of the Standard Model. In the Galactic Center, ULDM manifests as dense hydrogen-like boson clouds or self-gravitating soliton cores. We present the first study of the gravitational effects of these ULDM structures on pulsar orbits around Sgr A*, using pulsar timing as a precision dynamical probe, based on a comprehensive and practical framework that includes various kinds of black hole and orbital parameters. Our analysis shows that long-term pulsar monitoring -- one of the key objectives of future SKA science -- could detect a boson cloud with a total mass as low as $O(M_\odot)$ for boson mass $m \sim 10^{-18}\,\mathrm{eV}$, and probe a wide range of soliton core masses in the lower-mass regime, assuming a conservative timing precision of $σ_{\mathrm{TOA}}=1\,\mathrm{ms}$.

Figures (12)

• Figure 1: Enclosed mass of the spherical soliton in the GC for various boson masses and soliton masses. The inner profiles are well approximated by $m^6\,D(\beta)\,(Mr)^3/6$, shown as dashed lines. The semi-major axes of the considered pulsar orbits with given periods are indicated by the gray vertical lines. The mass of Sgr A* is $M=4.3\times 10^6M_\odot$.
• Figure 2: Projected sensitivities to the mass ratio $\beta$ versus $\alpha$ for scalar GA in the $|211\rangle$ state (top) and spherical soliton (bottom). The result for the soliton also applies to the vector or spin-2 GA in its superradiant ground state for $\beta<\alpha$. Red region is excluded by Schwarzschild precession of S2 star and the green region is excluded by stellar dynamics of the clockwise rotating disk Beloborodov:2006is. The blue dashed line denotes the sensitivities in case of timing precision $\sigma_{\text{TOA}}=10\, \mu\text{s}$. The gray dashed line marks the boundary $\beta = \alpha$, corresponding to the threshold of superradiance. Below the black dashed line, the soliton satisfies $r_{0.5}>M+M_\text{c}$. The brown dashed line shows the soliton mass given by the soliton-halo relation for our galaxy Schive:2014draSchive:2014hza.
• Figure S1: $g(\beta)$.
• Figure S2: The function $F_1(y,\alpha)$ characterizing the radial profile of the ground state, and the function $A(y,\alpha)$ characterizing the gravitational acceleration.
• Figure S3: The function $D(\beta)$ characterizing the central mass density of the ground state.