{
  "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 ($a_{\\rm GW}$). 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 $a_{\\rm GW}$, 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 $a_{\\rm GW}$ (normalized to $10^9 M_{\\odot}$, 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 $a_{\\rm GW}$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.06269",
  "author_total": 1,
  "authors": [
    {
      "name": "Laura Blecha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cj45bchp5bg2p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.06269",
  "fulltext_url": null,
  "id": "cj45bchp5bg2p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.06269",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "astro-ph.HE"
    ],
    [
      "openalex",
      "3103|Pulsars and Gravitational Waves Research"
    ]
  ],
  "openalex": "W7201887878",
  "pdf_url": "https://arxiv.org/pdf/2608.06269",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cj45bchp5bg2p.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:32Z",
      "native_id": "2608.06269",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.06269"
    }
  ],
  "subjects": [
    {
      "field": "astronomy",
      "origin": "arxiv:astro-ph.HE",
      "subfield": "high-energy-astrophysics"
    }
  ],
  "title": "An \"inside-out\" approach to modeling supermassive black hole binary inspiral",
  "title_text": "An \"inside-out\" approach to modeling supermassive black hole binary inspiral",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:28Z",
  "url": "https://research.draconitic.com/paper/cj45bchp5bg2p",
  "venue": "arXiv",
  "versions": []
}