Intermediate and Extreme Mass-Ratio Inspirals -- Astrophysics, Science Applications and Detection using LISA

TL;DR

The review analyzes how intermediate and extreme mass-ratio inspirals (IMRIs/EMRIs) will enable high-fidelity measurements of massive black holes and rigorous tests of general relativity in the strong-field regime with LISA. It synthesizes astrophysical formation channels, numerical dynamics, and data-analysis/waveform modelling approaches—including PN, numerical relativity, self-force, adiabatic, and kludge templates—and discusses detection strategies amid a crowded LISA data stream. It highlights key unsolved questions in event rates, dynamical processes near MBHs (e.g., resonant relaxation, mass segregation), and the development of efficient, accurate waveforms for parameter extraction and GR tests. The work emphasizes the potential for precise MBH mass/spin measurements, insights into galaxy evolution and cosmology, and robust tests of Kerr black-hole spacetimes, underlining the need for continued progress in numerical simulations and waveform sophistication to realize LISA's scientific payoff.

Abstract

Black hole binaries with extreme ($\gtrsim 10^4:1$) or intermediate ($\sim 10^2-10^4:1$) mass ratios are among the most interesting gravitational wave sources that are expected to be detected by the proposed Laser Interferometer Space Antenna. These sources have the potential to tell us much about astrophysics, but are also of unique importance for testing aspects of the general theory of relativity in the strong field regime. Here we discuss these sources from the perspectives of astrophysics, data analysis, and applications to testing general relativity, providing both a description of the current state of knowledge and an outline of some of the outstanding questions that still need to be addressed. This review grew out of discussions at a workshop in September 2006 hosted by the Albert Einstein Institute in Golm, Germany.

Figures (8)

• Figure 1: Inspiral trajectories in the semi-major axis, eccentricity plane. The thick diagonal line represents the last stable orbit using effective Keplerian values ($R_{\rm p}\simeq 4R_{\mathrm{S}}$ for $e\ll 0.1$, see CKP94 for the general relation). The thin diagonal lines (in green in the on-line colour version) show inspiral trajectories due to emission of gravitational waves (GWs) and thin dotted (blue) lines are contours of constant time left until plunge, $\tau_\mathrm{GW}$, as labelled in years on the right Peters64. We assume a $10\,M_\odot$ stellar black hole orbiting a $10^6\,M_\odot$ MBH on a slowly evolving Keplerian ellipse. The thick (red) dash-dotted line shows $\tilde{e}(a)$, defined by $t_e=\tau_\mathrm{GW}$ (Eq. \ref{['eq.EMRIcond']} with $C_{\rm EMRI}=1$) assuming a constant value $t_\mathrm{rlx}=1$ Gyr. Below this line, the effects of relaxation on the orbit are negligible in comparison to emission of GWs. We schematically show typical orbital trajectories for EMRIs. Stars captured by tidal binary splitting initially have $a$ of order 100-1000 AU [$5\times(10^{-4}-10^{-3})\,$pc] and $e=0.9-0.99$MFHL05. On a time scale of order $t_\mathrm{rlx}\ln(1-\tilde{e})^{-1}$, the eccentricity random-walks into the GW-dominated region, leading to a nearly-circular EMRI. If the star has not been deposited by binary splitting but has diffused from large radii or has been captured by GW emission, it will initially have a much larger value of $a$, therefore producing a higher eccentricity EMRI. One sees that stars with $a\mathrel{\hbox{$\sim$$>$}} 5\times 10^{-2}$ pc can not enter the inspiral domain unless $a$ is first reduced significantly, which takes of order $t_{\rm rlx}$. The grey region is the domain for sources whose orbital frequency is in the LISA band $P_{\rm orb}<10^4\,$s.
• Figure 2: Methods appropriate to the various realms of stellar dynamics.
• Figure 3: The various methods used to study collisional stellar dynamics.
• Figure 4: Power spectral density of one of the unequal arm Michelson TDI channel. It contains 1 MBH inspirals at luminosity distances of 3.3 Gpc and 1 EMRI at luminosity distances of 2.3 Gpc. The duration of the EMRI was taken to be one and a half years. The galactic binary realisation used here was drawn from the distribution described in nelemans01
• Figure 5: Spectrogram of the signal from an EMRI on an inclined and eccentric orbit. One can see several harmonics modulated by orbital precession and LISA's orbital motion.