Merging stellar and intermediate-mass black holes in dense clusters: implications for LIGO, LISA and the next generation of gravitational wave detectors

Kavli Affiliate: Xian Chen

| First 5 Authors: Manuel Arca-Sedda, Pau Amaro-Seoane, Xian Chen, ,

| Summary:

We study the formation of intermediate-mass ratio inspirals (IMRIs) triggered
by the interactions between two stellar black holes (BHs) and an
intermediate-mass BH (IMBH) inhabiting the centre of a dense star cluster. We
exploit $N$-body models varying the IMBH mass, the stellar BH mass spectrum,
and the star cluster properties. These simulations are coupled with a
semi-analytic procedure to characterise the evolution of the remnant IMBH. The
IMRIs formation probability attains values $sim 5-50%$, with larger values
corresponding to larger IMBH masses. IMRIs map out the stellar BH mass
spectrum, thus they might be used to unravel BH populations in star clusters
harboring an IMBH. After the IMRI phase, an IMBH initially nearly
maximal(almost non-rotating) tends to decrease(increase) its spin. If IMBHs
grow mostly via repeated IMRIs, we show that only IMBH seeds sufficiently
massive ($M_{rm seed} > 300$ M$_odot$) can grow up to $M_{rm imbh} >10^3$
M$_odot$ in dense globular clusters. Assuming that these seeds form at a
redshift $zsim 2-6$, we find that around $1-5%$ of them would reach masses
$sim 500-1500$ M$_odot$ at redshift $z=0$ and would exhibit low-spins,
$S_{rm imbh} < 0.2$. Measuring the mass and spin of IMBHs involved in IMRIs
could help unravelling their formation mechanisms. We show that LISA can detect
IMBHs in Milky Way globular clusters with a signal-to-noise ratio SNR$=10-100$,
or in the Large Magellanic Cloud with an SNR$=8-40$. We provide the IMRIs
merger rate for LIGO ($Gamma_{rm LIG} = 0.003-1.6$ yr$^{-1}$), LISA
($Gamma_{rm LIS} = 0.02-60$ yr$^{-1}$), ET ($Gamma_{rm ET} = 1-600$
yr$^{-1}$), and DECIGO ($Gamma_{rm DEC} = 6-3000$ yr$^{-1}$). Our simulations
show that IMRIs’ mass and spin encode crucial insights on the mechanisms that
regulate IMBH formation and that the synergy among different detectors would
enable us to fully unveil them. (Abridged)

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