Boson Cloud Atlas: Direct mass measurements of superradiance clouds near black holes

TL;DR

This work proposes a direct test for ultralight boson clouds around spinning black holes by comparing two independent spin measurements: continuum fitting (requiring a dynamical mass) and Fe Kα line spectroscopy (not needing a dynamical mass). A mismatch between the inferred spins signals an extended dark mass, interpreted as a boson cloud formed via BH superradiance, with the cloud mass fraction ζ = M_c/M recoverable from the Kerr ISCO relation. The authors model the cloud evolution through the first few superradiant states |211⟩, |322⟩, and |433⟩, deriving ζ from χ measurements and propagating uncertainties to assess detectability. They find that achieving ~1% spin-precision (σ_χ ~ 10^−2) could enable a 2σ detection of a cloud with M_c ≳ a few percent of M, particularly for higher-mass BHs where the SR cloud effects are more pronounced; the method provides a direct probe of extended DM around BHs but hinges on reducing both statistical and systematic errors in spin measurements and on robust modeling of disk physics.

Abstract

Ultralight scalars emerge naturally in several motivated particle physics scenarios and are viable candidates for dark matter. While laboratory detection of such bosons is challenging, their existence in nature can be imprinted on measurable properties of astrophysical black holes (BHs). The phenomenon of superradiance can convert the BH spin kinetic energy into a bound cloud of scalars. In this letter, we propose a new technique for directly measuring the mass of a dark cloud around a spinning BH. We compare the measurement of the BH spin obtained with two independent electromagnetic techniques: continuum fitting and iron K$α$ spectroscopy. Since the former technique depends on a dynamical observation of the BH mass while the latter does not, a mismatch between the two measurements can be used to infer the presence of additional extended mass around the BH. We find that a precision of $\sim 1\%$ on the two spin measurements is required to exclude the null hypothesis of no dark mass around the BH at a 2$σ$ confidence level for dark masses about a few percent of the BH mass, as motivated in some superradiance scenarios.

Figures (3)

• Figure 1: Discovery/exclusion potential of our method for stellar mass BHs ( left panels) and massive BHs ( right panels), shown as curves of $\zeta(t_{\rm age})/\Delta\zeta>1,\ 2,\ 5$ in bottom panels. These curves can be understood as the spin measurement precision $\sigma_\chi$ necessary to achieve 1$\sigma$, 2$\sigma$, and $5\sigma$ detections of a boson cloud with a mass fraction $\zeta$ (shown in middle panels) produced by an ULS with mass $\mu$ ( top panels). As the cloud mass evolves over time, we show old systems (1 Gyr, in blue) and young ones (1 Myr, red). The peaks correspond to clouds in $\left| n\ell m \right\rangle = \{\left| 211 \right\rangle, \left| 322 \right\rangle, \left| 433 \right\rangle\}$ states, respectively from left to right. The data points represent known XRBs with two independent spin measurements. CF and K$\alpha$ measurements are distinguished by empty and filled markers, respectively. The symbols correspond to 4U 1543-475 (circles), XTE J1550-56 (up triangles), GRO J1655-40 (down triangles), LMC X-1 (diamonds), and GRS1915+105 (stars).
• Figure 2: Statistical analysis of mock measurements, inspired by the 4U 1543-475 system. The spin distributions ( panels (a) and (e)) are modelled as skewed Gaussians designed to reproduce the 90% CL bounds (gray). We superimpose results (green) for distributions with errors reduced by one order of magnitude and the $\chi_1$ maximum probability value shifted to a value closer to the maximum probability of $\chi_2$. If the black line $\chi_1=\chi_2$ in the probability density contour plot ( panel (d)) does not cross the contours, a detection can be claimed. We infer the likelihood of $\zeta$ ( panels (c) and (b), for the large and small error cases, respectively).
• Figure 3: Left panels: The evolution of the cloud+BH variables $\{\zeta,\ \alpha/\alpha_0,\chi\}$, from top to bottom respectively), comparing the numerical result from the system of Eqs. \ref{['eq:ode_eps']}- \ref{['eq:ode_chi']} (solid lines) and the analytical expressions Eqs. \ref{['eq:cloud_mass_evol']}- \ref{['eq:chi_evol']} (thick dashed lines). We choose an initial BH mass of 10 $M_\odot$ and different values of $\alpha_0=\{0.05,0.1,0.2,0.5\}$. The initial spin has been chosen to be $\chi_0=0.998$. Right panel: The cloud mass as a function of different initial $\alpha_0$ for the same benchmark initial BH. We consider two different ages of the system: 1 Gyr (blue) and 5 Myr (red). We see here how a younger system achieves higher masses. The grey dashed lines show the saturation mass for the different states, solid lines show the numerical result and thick dashed lines are our analytical estimate, used in the reach/exclusion plot and in the main text for the values that satisfy the cloud saturation condition.