Constraints on Ultralight Scalar Bosons within Black Hole Spin Measurements from the LIGO-Virgo GWTC-2

Clouds of ultralight bosons—such as axions—can form around a rapidly spinning black hole, if the black hole radius is comparable to the bosons’ wavelength. The cloud rapidly extracts angular momentum from the black hole, and reduces it to a characteristic value that depends on the boson’s mass as well as on the black hole mass and spin. Therefore, a measurement of a black hole mass and spin can be used to reveal or exclude the existence of such bosons. Using the black holes released by LIGO and Virgo in their GWTC-2, we perform a simultaneous measurement of the black hole spin distribution at formation and the mass of the scalar boson. We find that the data strongly disfavor the existence of scalar bosons in the mass range between $1.3\times {10}^{-13}$ and $2.7\times {10}^{-13}\mathrm{eV}$. Our mass constraint is valid for bosons with negligible self-interaction, that is, with a decay constant $f_a\gtrsim 10^{14}\mathrm{GeV}$. The statistical evidence is mostly driven by the two binary black holes systems GW190412 and GW190517, which host rapidly spinning black holes. The region where bosons are excluded narrows down if these two systems merged shortly ($\sim {10}^5\mathrm{yr}$) after the black holes formed.

Figure 1

Marginalized posteriors (solid lines) of the scalar boson mass ${\mu }_s$ inferred from the dataset $\mathbf{d}$ consists of the full BBH catalog (blue line), the dataset excluding GW190517 only (purple line), as well as both GW190412 and GW190517 (orange line). When the rapidly spinning BBHs GW190412 and GW190517 are included, there is only 0.01% posterior support between $1.3\times {10}^{-13}\le {\mu }_s\le 2.7\times {10}^{-13}\mathrm{eV}$ (gray region). The prior (black dashed line) of ${\mu }_s$ is log uniform between $3\times {10}^{-14}$ and ${10}^{-11}\mathrm{eV}$.

Figure 2

Exclusion regions (gray shaded region) enclosed by the critical spin curves of ${\mu }_s=2\times {10}^{-13}\mathrm{eV}$ (black solid line) and ${\mu }_s={10}^{-12}\mathrm{eV}$ (black dash-dotted line) in the black hole mass-spin $(M_1,{\chi }_1)$ plane. The joint posteriors of the primary black holes of GW190412 (green contours) and GW190517 (red contours) are shown at 68% and 95% credible contours using the GWTC-2 default prior [87].