Inference of the sound speed and related properties of neutron stars

Abstract

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.

Repulsive vector interaction as a trigger for the non-conformal peak in $V_s^2$

“…Basically, it interpolates between a regime where repulsion is high (the EoS is stiff) and a regime where repulsion low (the EoS is soft). Thanks to this property the model is able to predict a non-monotonic behavior for V 2 s which is in line with recent estimates [18,34,35]. Regarding the conformal measure the results indicate that a non-conformal peak in V 2 s is not in tension with the trace anomaly being positive for all densities, a result which agrees with a scenario proposed in Ref.…”

“…In this case, recent simulations [18] indicate that the most probable scenario is the one in which V 2 s is a non-monotonic function of n B , which in turn suggests the existence of at least one local maximum where V 2 s > 1/3. This possibility is supported by a large number of applications employing frameworks such as quarkyonic matter [19][20][21][22], models for dense QCD [23][24][25][26][27][28][29][30], as well as models based on the gauge/gravity duality [31][32][33], hadron percolation threshold [34], and Bayesian inference methods [35] among others. To emphasize the importance of V 2 s it is worth mentioning that changes in its slope can also provide important information related to the phase transitions and cross-overs that can take place within dense baryonic matter.…”

“…Also, remark that δ was chosen so as to give a smooth transition within a narrow 10 MeV width since taking δ → 0 could lead to discontinuities in V 2 s which do not seem to be observed in Refs. [18,34,35]. With this conservative choice one can anticipate that the transition from the repulsive/stiff phase to the non-repulsive/soft phase will be driven by a cross-over.…”

“…Finally, it should be emphasized that the shape of the curve generated with G V (µ) resembles some of those recently predicted in Refs. [18,34,35].…”

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

“…Because the sound speed provides a direct measure of the stiffness of matter within the star, it represents a very accurate tool to probe the stellar interior and is obviously directly related the maximum mass that any EOS can support. The properties of the sound speed at finite densities have been studied extensively with various approaches in the recent past (see, e.g., Ecker et al 2017;McLerran & Reddy 2019;Leonhardt et al 2020;Margueron et al 2021;Duarte et al 2021;Pal et al 2022;Altiparmak et al 2022;Brandes et al 2022;Braun & Schallmo 2022;, and references therein). There is now widespread consensus that the sound speed is much smaller than the speed of light (𝑐 2 𝑠 1) in low-density matter (𝑛 𝑛 𝑠 ) and approaches the conformal limit 𝑐 2 𝑠 = 1/3 from below at large densities (𝑛 40 𝑛 𝑠 ).…”