Revised event rates for extreme and extremely large mass-ratio inspirals

Author:

Vázquez-Aceves Verónica1ORCID,Zwick Lorenz2,Bortolas Elisa34ORCID,Capelo Pedro R2ORCID,Amaro Seoane Pau1567,Mayer Lucio2,Chen Xian78ORCID

Affiliation:

1. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, China

2. Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland

3. Dipartimento di Fisica ‘G. Occhialini’, Universitá degli Studi di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy

4. INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy

5. Institute of Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain

6. DESY Zeuthen, 15738 Zeuthen, Germany

7. Kavli Institute for Astronomy and Astrophysics at Peking University, 100871 Beijing, China

8. Department of Astronomy, School of Physics, Peking University, 100871 Beijing, China

Abstract

ABSTRACT One of the main targets of the Laser Interferometer Space Antenna (LISA) is the detection of extreme mass-ratio inspirals (EMRIs) and extremely large mass-ratio inspirals (X-MRIs). Their orbits are expected to be highly eccentric and relativistic when entering the LISA band. Under these circumstances, the inspiral time-scale given by Peters’ formula loses precision and the shift of the last-stable orbit (LSO) caused by the massive black hole spin could influence the event rates estimate. We re-derive EMRIs and X-MRIs event rates by implementing two different versions of a Kerr loss-cone angle that includes the shift in the LSO, and a corrected version of Peters’ time-scale that accounts for eccentricity evolution, 1.5 post-Newtonian hereditary fluxes, and spin-orbit coupling. The main findings of our study are summarized as follows: (1) implementing a Kerr loss-cone changes the event rates by a factor ranging between 0.9 and 1.1; (2) the high-eccentricity limit of Peters’ formula offers a reliable inspiral time-scale for EMRIs and X-MRIs, resulting in an event-rate estimate that deviates by a factor of about 0.9–3 when compared to event rates computed with the corrected version of Peters’ time-scale and the usual loss-cone definition. (3) Event-rate estimates for systems with a wide range of eccentricities should be revised. Peters’ formula overestimates the inspiral rates of highly eccentric systems by a factor of about 8–30 compared to the corrected values. Besides, for e0 ≲ 0.8, implementing the corrected version of Peters’ formula is necessary to obtain accurate estimates.

Funder

National Science Foundation of China

Swiss National Science Foundation

European Research Council

Publisher

Oxford University Press (OUP)

Subject

Space and Planetary Science,Astronomy and Astrophysics

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