Inferring the neutron star equation of state with nuclear-physics informed semiparametric models
Bibliographic record
Abstract
Abstract Over the past decade, an abundance of information from neutron-star observations, nuclear experiments and theory has transformed our efforts to elucidate the properties of dense matter. However, at high densities relevant to the cores of neutron stars (NSs), substantial uncertainty about the dense matter equation of state (EoS) remains. In this work, we present a semiparametric EoS framework aimed at better integrating knowledge across these domains in astrophysical inference. We use a meta-model and realistic crust at low densities, and Gaussian process (GP) extensions at high densities. Comparisons between our semiparametric framework to fully nonparametric EoS representations show that imposing nuclear theoretical and experimental constraints through the meta-model up to nuclear saturation density results in constraints on the pressure up to twice nuclear saturation density. We also show that our GP trained on EoS models with nucleonic, hyperonic, and quark compositions extends the range of EoS explored at high density compared to a piecewise polytropic extension schema, under the requirements of causality of matter and of supporting the existence of heavy pulsars (PSRs). We find that maximum Tolman–Oppenheimer–Volkoff masses above <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>3.2</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> can be supported by causal EoS compatible with nuclear constraints at low densities. We then combine information from existing observations of heavy PSR masses, gravitational waves emitted from binary NS mergers, and x-ray pulse profile modeling of millisecond PSRs within a Bayesian inference scheme using our semiparametric EoS prior. With information from all public NS Interior Composition ExploRer PSRs (including PSR J0030+0451, PSR J0740+6620, PSR J0437–4715, and PSR J0614–3329), we find an astrophysically favored pressure at two times nuclear saturation density of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>P</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mi>ρ</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>nuc</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo stretchy="false">)</mml:mo> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>1.98</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>1.08</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>2.13</mml:mn> </mml:mrow> </mml:msubsup> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>34</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> dyn cm −2 , a radius of a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.4</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> NS value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>R</mml:mi> <mml:mrow> <mml:mn>1.4</mml:mn> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>11.4</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.60</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.98</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:math> km, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>M</mml:mi> <mml:mrow> <mml:mrow> <mml:mi>max</mml:mi> </mml:mrow> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msubsup> <mml:mn>2.31</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.23</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>+</mml:mo> <mml:mn>0.35</mml:mn> </mml:mrow> </mml:msubsup> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">M</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>⊙</mml:mo> </mml:mrow> </mml:msub> </mml:mrow> </mml:math> at the 90% credible level (C.L).
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".