Estimating the detectable rate of capture of stellar mass black holes by massive central black holes in normal galaxies

Abstract

The capture and subsequent inspiral of stellar mass black holes on eccentric orbits by central massive black holes, is one of the more interesting likely sources of gravitational radiation detectable by LISA. We estimate the rate of observable events and the associated uncertainties. A moderately favourable mass function could provide many detectable bursts each year, and a detection of at least one burst per year is very likely given our current understanding of the populations in cores of normal spiral galaxies. I.The proposed LISA observatory ( [1-3] and this volume) has optimal sensitivity to gravitational radiation in the 10 −3 -10 −2 Hz range. As such it is well matched to the expected frequency of gravitational radiation emitted by compact objects in the last stages of spiral-in to massive black holes with total masses of M BH ∼ 10 6 M ⊙ (see eg. [4]). Previous papers [5,6] considered the "likely" signal from degenerate compact objects in the cusps of normal galaxies, captured by central black holes such as are inferred to be present in the Milky Way [7] and the nearby dwarf elliptical, M32 [8-10].Here we consider the rate for capture of stellar mass black holes expected to be present in the cusps of normal galaxies, and estimate the detectable rate of events by LISA, under both very conservative assumptions and with more optimistic estimates of the black hole population (see also [11,12]).There are several large, systematic uncertainties in estimating the rate of black hole capture. The proportion of galaxies harbouring a central black hole is poorly constrained, although theoretical prejudices suggest central black holes may be ubiquitous [13][14][15]. The mass function of any central black holes is highly uncertain; there are strong observational biases on detection of central black holes, and few galaxies for which there are strong observational constraints as yet [16]. The mass function and total number of stellar mass black holes is also highly uncertain [17]. Stellar mass black holes may form with masses as low as 2 M ⊙ and go up to masses of 50-100 M ⊙ . The range of masses of main sequence stars that form a black hole remnant and the resultant mass of the remnant is also uncertain, and binarity and metallicity may both affect the remnant mass. There are observational biases against detecting the higher mass range of stellar mass black holes as they may sustain higher accretion rates while in binaries, and be detectable in our galaxy for correspondingly shorter time.We assume, conservatively, that masses of central black holes in galaxies are proportional to the mass of the luminous spheroid of the host galaxy [13], with a space density of ∼ 3 × 10 −3 Mpc −3 for the range of black hole masses of interest; and that stellar mass black holes are formed from main sequence stars with zero-age masses greater than 15 M ⊙ , drawn from a Salpeter mass function extending to 30 M ⊙ , with a total number fraction of ∼ 10 −4 black holes per formed star. It is possible, if not likely, that this underestimates su...

Gravitational-wave signature of an inspiral into a supermassive horizonless object

“…In this paper, we have investigated the possibility that the inspiral of a several solar-mass CO into a boson star may produce a distinctive spectrum of GWs. LISA is conservatively expected to observe several such inspirals each year with appreciable signal-to-noise ratios [9,10].…”

“…Conservatively, event rates of order 10 ÿ8 per galaxy per year are anticipated, implying 0.1 captures per year out to 1 Gpc [9]. This result could be enhanced by an order of magnitude by a top-heavy IMF, either due to low metallicity in the early universe or starbursts in the high-density environment of the galactic cusp itself [10]. EMRIs about a 10 6 M central object would produce GWs in the frequency band 10 ÿ4 to 10 ÿ2 Hz probed by LISA, making them an interesting subject for theoretical investigation.…”

The Newtonian and Relativistic Theory of Orbits and the Emission of Gravitational Waves

“…One expects that small compact objects (1 ÷ 20M ⊙ ) from the surrounding stellar population will be captured by these black holes following many-body scattering interactions at a relatively high rate [112,113]. It is well known that the capture of stellar-mass compact objects by massive MBHs could constitute, potentially, a very important target for LISA [114,115].…”

The Newtonian and Relativistic Theory of Orbits and the Emission of Gravitational Waves

“…One expects that small compact objects ( 1÷ 20 M ) from the surrounding stellar population will be captured by these black holes following many-body scattering interactions at a relatively high rate [109]. It is well known that the capture of stellar-mass compact objects by massive MBHs could constitute, potentially, a very important target for LISA [110,111].…”