Perturbative QCD and the Neutron Star Equation of State

Somasundaram, Rahul; Tews, Ingo; Margueron, J.

doi:10.48550/arxiv.2204.14039

“…In contrast the standard pQCD asymptotic constraint leads to a softening of the EoS at high densities as was already concluded in the Bayesian analyses of Refs. [52,136]. The similarity in the speed of sound translates into the credible bands for P (ε), M (R) and Λ(M ).…”

Section: Conformal Limit Reached From Abovementioning

confidence: 98%

Inference of the sound speed and related properties of neutron stars

Brandes¹,

Weise²,

Kaiser³

2022

Preprint

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Information on the phase structure of strongly interacting matter at high baryon densities can be gained from observations of neutron stars and their detailed analysis. In the present work Bayesian inference methods are used to set constraints on the speed of sound in the interior of neutron stars, based on recent multi-messenger data in combination with limiting conditions from nuclear physics at low densities. Two general parametric representations are introduced for the sound speed cs in order to examine the independence with respect to choices for the parametrisation of Priors. Credible regions for neutron star properties are analysed, in particular with reference to the quest for possible phase transitions in cold dense matter. The evaluation of Bayes factors implies extreme evidence for a violation of the conformal bound, c 2 s ≤ 1/3, inside neutron stars. Given the presently existing data base, it can be concluded that the occurrence of a first-order phase transition in the core of even a two-solar-mass neutron star is unlikely, while a continuous crossover cannot be ruled out. At the same time it is pointed out that the discovery of a superheavy neutron star with a mass M ∼ 2.3 − 2.4 M would strengthen evidence for a phase change in the deep interior of the star.

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“…While effective field-theory calculations are arguably the most important tool to obtain theoretical predictions for the behavior of dense matter, the associated uncertainties become large at densities several times n s , such as those present in neutron-star cores. In addition, firstprinciple perturbative quantum chromodynamics (QCD) calculations are only reliable at densities much larger than those realized in the neutron-star interior but provide important consistency conditions for the modeling of matter at lower densities (Fraga et al 2014;Annala et al 2020Annala et al , 2022Gorda et al 2022;Somasundaram et al 2022). Our theoretical control of even basic quantities, such as the equation of state (EOS) of dense nuclear and quark matter that, in the simplest case, is a relation between pressure and the energy density p(e), is therefore still very limited, often forcing the use of agnostic approaches to build the EOS of nuclear matter at neutron-star densities.…”

Section: Introductionmentioning

confidence: 99%

A General, Scale-independent Description of the Sound Speed in Neutron Stars

Ecker

¹

,

Rezzolla

²

2022

ApJL

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Using more than a million randomly generated equations of state that satisfy theoretical and observational constraints, we construct a novel, scale-independent description of the sound speed in neutron stars, where the latter is expressed in a unit cube spanning the normalized radius, r/R, and the mass normalized to the maximum one, M/M TOV. From this generic representation, a number of interesting and surprising results can be deduced. In particular, we find that light (heavy) stars have stiff (soft) cores and soft (stiff) outer layers, or that the maximum of the sound speed is located at the center of light stars but moves to the outer layers for stars with M/M TOV ≳ 0.7, reaching a constant value of c s 2 = 1 / 2 as M → M TOV. We also show that the sound speed decreases below the conformal limit c s 2 = 1 / 3 at the center of stars with M = M TOV. Finally, we construct an analytic expression that accurately describes the radial dependence of the sound speed as a function of the neutron-star mass, thus providing an estimate of the maximum sound speed expected in a neutron star.

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“…Next, we consider how perturbative QCD boundary conditions imposed in model-agnostic approaches can have a relevant impact on the EOSs at densities realised in neutron stars close to their maximum mass (Somasundaram et al 2022;Gorda et al 2022). We study the impact of these boundary conditions by comparing results where they are imposed to those where they are not imposed.…”

Section: Data Availabilitymentioning

confidence: 99%

“…Between these limits, at densities a few times larger than 𝑛 𝑠 , such as those realised in neutron-star cores, these methods are not applicable, hence our knowledge about even the most basic neutron-star properties like their mass-radius relation and in particular their maximum mass is incomplete. In this regime the currently available theoretical options are specific-model building (see, e.g., Bastian 2021;Demircik et al 2021a;Ivanytskyi & Blaschke 2022, for some recent works), and model agnostic EOS-samplings (see, e.g., Greif et al 2019; An-★ E-mail: ecker@itp.uni-frankfurt.de (CE) nala et al 2020;Dietrich et al 2020;Altiparmak et al 2022, for some recent attempts), for which CET and QCD provide important constraints Gorda et al 2022;Somasundaram et al 2022).…”

Section: Introductionmentioning

confidence: 99%

Impact of large-mass constraints on the properties of neutron stars

Ecker¹,

Rezzolla²

2022

Preprint

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The maximum mass of a nonrotating neutron star, 𝑀 TOV , plays a very important role in deciphering the structure and composition of neutron stars and in revealing the equation of state (EOS) of nuclear matter. Although with a large-error bar, the recent mass estimate for the black-widow binary pulsar PSR J0952-0607, i.e., 𝑀 = 2.35 ± 0.17 𝑀 , provides the strongest lower bound on 𝑀 TOV and suggests that neutron stars with very large masses can in principle be observed. Adopting an agnostic modelling of the EOS, we study the impact that large masses have on the neutron-star properties. In particular, we show that assuming 𝑀 TOV 2.35 𝑀 constrains tightly the behaviour of the pressure as a function of the energy density and moves the lower bounds for the stellar radii to values that are significantly larger than those constrained by the NICER measurements, rendering the latter ineffective in constraining the EOS. We also provide updated analytic expressions for the lower bound on the binary tidal deformability in terms of the chirp mass and show how larger bounds on 𝑀 TOV lead to tighter constraints for this quantity. In addition, we point out a novel quasi-universal relation for the pressure profile inside neutron stars that is only weakly dependent from the EOS and the maximum-mass constraint. Finally, we study how the sound speed and the conformal anomaly are distributed inside neutron stars and show how these quantities depend on the imposed maximum-mass constraints.

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Perturbative QCD and the Neutron Star Equation of State

Cited by 9 publications

References 53 publications

Inference of the sound speed and related properties of neutron stars

Inference of the sound speed and related properties of neutron stars

A General, Scale-independent Description of the Sound Speed in Neutron Stars

Impact of large-mass constraints on the properties of neutron stars

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