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Accretion onto black holes inside neutron stars with piecewise-polytropic equations of state: analytic and numerical treatments
High Energy Astrophysical Phenomena · Submitted 15 Oct 2021
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.
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The abstract, sentence by sentence
We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). | background 0.52 | 0.47 | 0.04 | asserted 0.48 |
| s1 | We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. | method 0.54 | 0.95 | 0.09 | asserted 1.00 |
| s2 | We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. | result 0.84 | 0.95 | 0.10 | asserted 1.00 |
| s3 | We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star. | result 0.96 | 0.96 | 0.80 | asserted 1.00 |
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The paper
Original abstract
We consider spherically symmetric accretion onto a small, possibly primordial, black hole residing at the center of a neutron star governed by a cold nuclear equation of state (EOS). We generalize the relativistic Bondi solution for such EOSs, approximated by piecewise polytropes, and thereby obtain analytical expressions for the steady-state matter profiles and accretion rates. We compare these rates with those found by time-dependent, general relativistic hydrodynamical simulations upon relaxation and find excellent agreement. We consider several different candidate EOSs, neutron star masses and central densities and find that the accretion rates vary only little, resulting in an accretion rate that depends primarily on the black hole mass, and only weakly on the properties of the neutron star.
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How the literature uses it
9 arXiv papers cite this in 12 sentences
Papers citing it · 9 sentences without a confident label
Uses its data or values 1 paper
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The nascent BH, with a very small mass $M_BH =m_χ N^BH_χ$, consumes the NS host over a timescale of $τ_swallow= 10^12 s (10^-16 M_⊙M_BH)$ [ref] , significantly smaller than stellar lifetimes.
Can LIGO Detect Non-Annihilating Dark Matter? · Introduction · 0.81
Cites it as background 2 papers
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At the most compact end of the spectrum, PBH capture by neutron stars and white dwarfs has been studied extensively, as rapid PBH growth in these dense systems can lead to the destruction of the host star and thus potentially place constraints on the PBH abundance [ref] .
The Life and Death of Stars That Capture Primordial Black Holes · Introduction · 0.92
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Inspired by the early works [ref] , there are recent studies on the spike or cusp profiles around a BH by quite different approaches for various DM models [ref] .
Self-interacting Dark Scalar Spikes around Black Holes via Relativistic Bondi Accretion · Introduction · 0.93
What it cites · 35 sentences without a confident label
Builds on 1 paper
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In this paper we generalize the results of RBS and [ref] to allow for realistic, nuclear EOSs, approximated by piecewise polytropes (PWPs).
Accretion onto a small black hole at the center of a neutron star · Introduction · 1.00
Uses the method or tool of 12 papers
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As discussed in Section III.C.2 of [ref] , we may compute the former from the latter using [equation] where $α_*$ is the lapse function in the local asymptotic region.
Accretion onto a small black hole at the center of a neutron star · Numerical treatment · 0.88
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The specific internal energy $ϵ$ then takes the form [equation] (see eq. 5 in [ref] ) where the $b_i$ are constants of integration that are chosen to make $ϵ$ continuous across the boundaries between different regions.
Constraints on a phenomenologically parameterized neutron-star equation of state · Nuclear EOSs: approximation by piecewise polytropes · 0.89
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We then evolve these data using the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formalism ( [ref] ; see also [ref] for a textbook discussion), implemented in spherical polar coordinates [ref] with the help of a reference-metric formalism [ref] .
On the Numerical Integration of Einstein's Field Equations · Numerical treatment · 1.00
Uses data or values from 1 paper
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A list of the $Γ_i$ for a large number of EOSs is given in Table III of [ref] .
Constraints on a phenomenologically parameterized neutron-star equation of state · Nuclear EOSs: approximation by piecewise polytropes · 0.83
Compares with 2 papers
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Using $M_⊙= 4.9 ×10^-6 = 1.6 ×10^-13$ we may write ([ref]) as [equation] which is just slightly larger than the minimum accretion rate reported in [ref] (where it was computed under the assumption of single Gamma-law EOSs).[Note that [ref] provided estimates for the rate of gravitational mass-energy accretion, which, during the quasi-stationary Bondi accretion phase, is slightly larger than that for the accretion of rest mass (see Table III in [ref] ).]
Neutron Stars Harboring a Primordial Black Hole: Maximum Survival Time · Results · 0.90
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Using $M_⊙= 4.9 ×10^-6 = 1.6 ×10^-13$ we may write ([ref]) as [equation] which is just slightly larger than the minimum accretion rate reported in [ref] (where it was computed under the assumption of single Gamma-law EOSs).[Note that [ref] provided estimates for the rate of gravitational mass-energy accretion, which, during the quasi-stationary Bondi accretion phase, is slightly larger than that for the accretion of rest mass (see Table III in [ref] ).]
Accretion onto a small black hole at the center of a neutron star · Results · 0.90
Cites as background 7 papers
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East and Lehner [ref] considered black holes with masses $M_BH ≥10^-2 M_NS$ and adopted nuclear EOSs (modeled with the “piecewise-polytrope" approximation described below).
Fate of a neutron star with an endoparasitic black hole and implications for dark matter · Introduction · 0.83
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Multiple authors have suggested that neutron stars may act as dark-matter detectors (e.g. [ref] ).
Constraints on primordial black holes as dark matter candidates from capture by neutron stars · Introduction · 0.91
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Multiple authors have suggested that neutron stars may act as dark-matter detectors (e.g. [ref] ).
Detecting Dark Matter with Imploding Pulsars in the Galactic Center · Introduction · 0.91
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