skip to main content


Title: Deducing neutron star equation of state parameters directly from telescope spectra with uncertainty-aware machine learning
Abstract Neutron stars provide a unique laboratory for studying matter at extreme pressures and densities. While there is no direct way to explore their interior structure, X-rays emitted from these stars can indirectly provide clues to the equation of state (EOS) of the superdense nuclear matter through the inference of the star's mass and radius. However, inference of EOS directly from a star's X-ray spectra is extremely challenging and is complicated by systematic uncertainties. The current state of the art is to use simulation-based likelihoods in a piece-wise method which relies on certain theoretical assumptions and simplifications about the uncertainties. It first infers the star's mass and radius to reduce the dimensionality of the problem, and from those quantities infer the EOS. We demonstrate a series of enhancements to the state of the art, in terms of realistic uncertainty quantification and a path towards circumventing the need for theoretical assumptions to infer physical properties with machine learning. We also demonstrate novel inference of the EOS directly from the high-dimensional spectra of observed stars, avoiding the intermediate mass-radius step. Our network is conditioned on the sources of uncertainty of each star, allowing for natural and complete propagation of uncertainties to the EOS.  more » « less
Award ID(s):
2012152 2116686 1909490
NSF-PAR ID:
10420973
Author(s) / Creator(s):
; ; ; ; ; ; ; ;
Date Published:
Journal Name:
Journal of Cosmology and Astroparticle Physics
Volume:
2023
Issue:
02
ISSN:
1475-7516
Page Range / eLocation ID:
016
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. The interiors of neutron stars reach densities and temperatures beyond the limits of terrestrial experiments, providing vital laboratories for probing nuclear physics. While the star's interior is not directly observable, its pressure and density determine the star's macroscopic structure which affects the spectra observed in telescopes. The relationship between the observations and the internal state is complex and partially intractable, presenting difficulties for inference. Previous work has focused on the regression from stellar spectra of parameters describing the internal state. We demonstrate a calculation of the full likelihood of the internal state parameters given observations, accomplished by replacing intractable elements with machine learning models trained on samples of simulated stars. Our machine-learning-derived likelihood allows us to performmaximum a posterioriestimation of the parameters of interest, as well as full scans. We demonstrate the technique by inferring stellar mass and radius from an individual stellar spectrum, as well as equation of state parameters from a set of spectra. Our results are more precise than pure regression models, reducing the width of the parameter residuals by 11.8% in the most realistic scenario. The neural networks will be released as a tool for fast simulation of neutron star properties and observed spectra. 
    more » « less
  2. Neutron stars provide a window into the properties of dense nuclear matter. Several recent observational and theoretical developments provide powerful constraints on their structure and internal composition. Among these are the first observed binary neutron star merger, GW170817, whose gravitational radiation was accompanied by electromagnetic radiation from a short γ-ray burst and an optical afterglow believed to be due to the radioactive decay of newly minted heavy r-process nuclei. These observations give important constraints on the radii of typical neutron stars and on the upper limit to the neutron star maximum mass and complement recent pulsar observations that established a lower limit. Pulse-profile observations by the Neutron Star Interior Composition Explorer (NICER) X-ray telescope provide an independent, consistent measure of the neutron star radius. Theoretical many-body studies of neutron matter reinforce these estimates of neutron star radii. Studies using parameterized dense matter equations of state (EOSs) reveal several EOS-independent relations connecting global neutron star properties. 
    more » « less
  3. CTCV J2056–3014 is a nearby cataclysmic variable with an orbital period of approximately 1.76 h at a distance of about 853 light-years from the Earth. Its recently reported X-ray properties suggest that J2056–3014 is an unusual accretion-powered intermediate polar that harbors a fast-spinning white dwarf (WD) with a spin period of 29.6 s. The low X-ray luminosity and the relatively modest accretion rate per unit area suggest that the shock is not occurring near the WD surface. It has been argued that, under these conditions, the maximum temperature of the shock cannot be directly used to determine the mass of the WD (which, under the abovementioned assumptions, would be around 0.46 M ⊙ ). Here, we explore the stability of this rapidly rotating WD using a modern equation of state (EoS) that accounts for electron–ion, electron–electron, and ion–ion interactions. For this EoS, we determine the mass density thresholds for the onset of pycnonuclear fusion reactions and study the impact of microscopic stability and rapid rotation on the structure and stability of WDs, considering them with helium, carbon, oxygen, and neon. From this analysis, we obtain a minimum mass for CTCV J2056–3014 of 0.56 M ⊙ and a maximum mass of around 1.38 M ⊙ . If the mass of CTCV J2056–3014 is close to the lower mass limit, its equatorial radius would be on the order of 10 4 km due to rapid rotation. Such a radius is significantly larger than that of a nonrotating WD of average mass (0.6  M ⊙ ), which is on the order of 7 × 10 3 km. The effects on the minimum mass of J2056–3014 due to changes in the temperature and composition of the stellar matter were found to be negligibly small. 
    more » « less
  4. null (Ed.)
    The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H 0 = 73.3 −1.8 +1.7 km s −1 Mpc −1 , describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H 0 . We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H 0 . Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H 0 = 74.5 −6.1 +5.6 km s −1 Mpc −1 . Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H 0 = 67.4 −3.2 +4.1 km s −1 Mpc −1 . This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H 0 . While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H 0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H 0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data. 
    more » « less
  5. ABSTRACT

    The merging of a binary system involving two neutron stars (NSs), or a black hole (BH) and an NS, often results in the emission of an electromagnetic (EM) transient. One component of this EM transient is the epic explosion known as a kilonova (KN). The characteristics of the KN emission can be used to probe the equation of state (EoS) of NS matter responsible for its formation. We predict KN light curves from computationally simulated BH–NS mergers, by using the 3D radiative transfer code possis. We investigate two EoSs spanning most of the allowed range of the mass–radius diagram. We also consider a soft EoS compatible with the observational data within the so-called 2-families scenario in which hadronic stars co-exist with strange stars. Computed results show that the 2-families scenario, characterized by a soft EoS, should not produce a KN unless the mass of the binary components are small (MBH ≤ 6 M⊙ and MNS ≤ 1.4 M⊙) and the BH is rapidly spinning (χBH ≥ 0.3). In contrast, a strong KN signal potentially observable from future surveys (e.g. the Vera Rubin Observatory) is produced in the 1-family scenario for a wider region of the parameter space, and even for non-rotating BHs (χBH = 0) when MBH = 4 M⊙ and MNS = 1.2 M⊙. We also provide a fit that allows for the calculation of the unbound mass from the observed KN magnitude, without running timely and costly radiative transfer simulations. Findings presented in this paper will be used to interpret light curves anticipated during the fourth observing run (O4), of the advanced LIGO, advanced Virgo, and KAGRA interferometers and thus to constrain the EoS of NS matter.

     
    more » « less