An "inside-out" approach to modeling supermassive black hole binary inspiral
Abstract
The inspiral and merger of two supermassive black holes (SMBHs) releases immense energy in low-frequency gravitational waves (GWs). Recent pulsar timing array (PTA) observations of the stochastic nHz GW background (GWB) are consistent with a SMBH binary origin. GW data from PTAs and from the upcoming Laser Interferometer Space Antenna (LISA) can probe late-stage binary evolution where electromagnetic constraints are scarce. However, the complexity of the relevant astrophysics necessitates a well optimized approach. I argue that a key physical quantity to constrain with PTAs is the orbital semi-major axis at which binary inspiral transitions from the astrophysical to the GW-dominated regime (aGW). This quantity should be treated as a free parameter in analysis of the GWB. Using this premise, I present a simple analytic framework for modeling SMBH binary inspiral in an "inside-out" fashion. At orbital separations slightly larger than aGW, a power-law scaling for the astrophysical inspiral timescale is assumed, while the outermost phase (prior to the PTA regime) is simply modeled via a delay time. I show that the GWB spectral shape and amplitude are most sensitive to aGW (normalized to 109 M⊙, equal-mass binaries and expressed in gravitational units), with weaker dependence on the inner power-law index and the outer delay time. The GWB is largely insensitive to the mass and mass-ratio scaling of aGW and to the boundary between the inner and outer astrophysical inspiral regimes. I compare with models for gas- and stellar-driven binary inspiral and discuss implications for LISA and for GW source parameter inference.
Related
- From Inspiral to Expansion: The Wake-Driven Torque on Binary Black Holes in Gaseous Medium
- Distinguishing lensing and precessional modulation in binary black-hole inspiral waveforms
- Exploring the faint limit of the ESA Plato space mission. A case study of extragalactic research with the self-lensing supermassive black hole binary candidate, Spikey
- The Loud Tail of the Supermassive Black Hole Binary Population: Multimessenger Candidates and Prospects for SKAO
- Bridging the Population Synthesis of Supermassive Binary Black Holes and the Gravitational Wave Background
BibTeX
@misc{blecha2026insideout,
title = {{An "inside-out" approach to modeling supermassive black hole binary inspiral}},
author = {Laura Blecha},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.06269},
eprint = {2608.06269},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06269},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An "inside-out" approach to modeling supermassive black hole binary inspiral
AU - Laura Blecha
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.06269
UR - https://arxiv.org/abs/2608.06269
AB - The inspiral and merger of two supermassive black holes (SMBHs) releases immense energy in low-frequency gravitational waves (GWs). Recent pulsar timing array (PTA) observations of the stochastic nHz GW background (GWB) are consistent with a SMBH binary origin. GW data from PTAs and from the upcoming Laser Interferometer Space Antenna (LISA) can probe late-stage binary evolution where electromagnetic constraints are scarce. However, the complexity of the relevant astrophysics necessitates a well optimized approach. I argue that a key physical quantity to constrain with PTAs is the orbital semi-major axis at which binary inspiral transitions from the astrophysical to the GW-dominated regime (a_GW). This quantity should be treated as a free parameter in analysis of the GWB. Using this premise, I present a simple analytic framework for modeling SMBH binary inspiral in an "inside-out" fashion. At orbital separations slightly larger than a_GW, a power-law scaling for the astrophysical inspiral timescale is assumed, while the outermost phase (prior to the PTA regime) is simply modeled via a delay time. I show that the GWB spectral shape and amplitude are most sensitive to a_GW (normalized to 10^9 M_⊙, equal-mass binaries and expressed in gravitational units), with weaker dependence on the inner power-law index and the outer delay time. The GWB is largely insensitive to the mass and mass-ratio scaling of a_GW and to the boundary between the inner and outer astrophysical inspiral regimes. I compare with models for gas- and stellar-driven binary inspiral and discuss implications for LISA and for GW source parameter inference.
ER -