Hidden Universality in the Merger Rate Distribution in the Primordial Black Hole Scenario

作者：Kocsis Bence; Suyama Teruaki; Tanaka Takahiro; Yokoyama Shuichiro

来源：Astrophysical Journal, 2018, 854(1): 41.

DOI：10.3847/1538-4357/aaa7f4

<jats:title>Abstract</jats:title>
<jats:p>It has been proposed that primordial black holes (PBHs) form binaries in the radiation dominated era. Once formed, some fraction of them may merge within the age of the universe by gravitational radiation reaction. We investigate the merger rate of the PBH binaries when the PBHs have a distribution of masses around <jats:inline-formula>
<jats:tex-math>
<?CDATA ${ \mathcal O }(10){M}_{\odot }$?>
</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaa7f4ieqn1.gif" xlink:type="simple" />
</jats:inline-formula>, which is a generalization of the previous studies where the PBHs are assumed to have the same mass. After deriving a formula for the merger time probability distribution in the PBH mass plane, we evaluate it under two different approximations. We identify a quantity constructed from the mass distribution of the merger rate density per unit cosmic time and comoving volume <jats:inline-formula>
<jats:tex-math>
<?CDATA ${ \mathcal R }({m}_{1},{m}_{2})$?>
</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaa7f4ieqn2.gif" xlink:type="simple" />
</jats:inline-formula>, <jats:inline-formula>
<jats:tex-math>
<?CDATA $\alpha =-{({m}_{1}+{m}_{2})}^{2}{\partial }^{2}\mathrm{ln}{ \mathcal R }/\partial {m}_{1}\partial {m}_{2}$?>
</jats:tex-math>
<jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="apjaaa7f4ieqn3.gif" xlink:type="simple" />
</jats:inline-formula>, which universally satisfies 0.97 ≲ <jats:italic>α</jats:italic> ≲ 1.05 for all binary masses independently of the PBH mass function. This result suggests that the measurement of this quantity is useful for testing the PBH scenario.</jats:p>

• 出版日期2018-2-10