Mono- and oligochromatic extreme-mass-ratio inspirals

The gravitational capture of a stellar-mass object by a supermassive black hole represents a unique probe of warped spacetime. The small object, typically a stellar-mass black hole, describes a very large number of cycles before crossing the event horizon. Because of the mass difference, we call these captures extreme-mass-ratio inspirals (EMRIs). Their merger event rate at the Galactic Center is negligible, but the amount of time spent in the early inspiral is not. Early EMRIs (E-EMRIs) spend hundreds of thousands of years in band during this phase. At very early stages, the peak of the frequency will not change during an observational time. At later stages in the evolution, it will change a bit and finally the EMRI explores a wide range of them when it is close to merger. We distinguish between “monocromatic” E-EMRIs, which do not change their (peak) frequency, oligochromatic E-EMRIs, which explore a short range and polychromatic ones, and the EMRIs which have been discussed so far in the literature. We derive the number of E-EMRIs at the Galactic Center, and we also calculate their signal-to-noise ratios (SNR) and perform a study of parameter extraction. We show that parameters such as the spin and the mass can be extracted with an error which can be as small as <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>11</a:mn></a:mrow></a:msup></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:msup><c:mrow><c:mn>10</c:mn></c:mrow><c:mrow><c:mo>−</c:mo><c:mn>5</c:mn></c:mrow></c:msup><c:msub><c:mrow><c:mi>M</c:mi></c:mrow><c:mrow><c:mo stretchy="false">⊙</c:mo></c:mrow></c:msub></c:mrow></c:math>. There are between hundreds and thousands of E-EMRIs in their monochromatic stage at the Galactic Centre (GC), and tens in their oligochromatic phase. The SNR ranges from a minimum of 10 (larger likelihood) to a maximum of <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:msup><f:mn>10</f:mn><f:mn>6</f:mn></f:msup></f:math> (smaller likelihood). Moreover, we derive the contribution signal corresponding to the incoherent sum of continuous sources of oligochromatic E-EMRIs with two representatives masses, <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mn>10</h:mn><h:msub><h:mi>M</h:mi><h:mo stretchy="false">⊙</h:mo></h:msub></h:math> and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>40</k:mn><k:msub><k:mi>M</k:mi><k:mo stretchy="false">⊙</k:mo></k:msub></k:math>, and show that their curves will cover a significant part of Laser Interferometer Space Antennas (LISAs) sensitivity curve. Depending on their level of circularization, they might be detected as individual sources or form a foreground population. Published by the American Physical Society 2024