Theoretical nuclear astrophysics at the University of Tennessee, Knoxville and Oak Ridge National Laboratory

- PI: Asst. Prof. Andrew W. Steiner
- Postdoc: Dr. Sophia Han (2015-)
- Graduate students: Spencer Beloin (2015-), Xingfu Du (2016-), and Mohammad Al-Mamun (2018-)
- Previous group members

I study how neutron star observations can be used to understand how neutrons and protons interact and how nuclear physics plays a role in astrophysical objects and processes. Recently, I have

- determined how the equation of state and superfluid nature of dense matter is determined by neutron star observations,
- helped determine how nuclear masses are constrained by observed abundances of r-process nuclei,
- and combined modern theoretical results on neutron matter and neutron star observations to make predictions for neutron star tidal deformabilities for LIGO.

Our large collaborative effort (led by Rita Lau and Hendrik Schatz) on nuclear reactions in neutron star crusts was recently submitted to the arXiv. This work follows the full sequence of nuclear reactions that X-ray burst ashes undergo while they are pushed deeper into the neutron star by accretion. This work finds that the impurity parameter in the inner crust is likely small.

Aarran Shaw and Craig Heinke led a new analysis of X-ray data from the neutron star in M13 which I helped with, giving a likely radius for the neutron star between 10.6 and 14.2 km (including distance uncertainties). Our work in on posted on the arXiv and published in MNRAS.

UTK graduate student Xingfu Du led the construction of a new equation of state (EOS) for homogeneous matter now available at arxiv.org. In collaboration with Jeremy Holt at Texas A&M and myself, Xingfu created a new EOS which includes an estimate of the uncertainty for every point in density, temperature, and electron fraction space. The EOS properly reproduces the virial expansion in the non-degenerate limit, has an equation of state of nuclear matter which matches that expected from nuclear structure experiments, and has a high-density equation of state which matches neutron star radius observations.

In a new article now on arxiv.org, I construct a new formalism for curve-fitting when a model generates a curve embedded in a higher-dimensional space occupied by the data. I construct a conditional probability distribution (for use, e.g. in Bayesian inference) for the general case, and I show how it depends on the metric which determines the embedding. I show that the conditional probability reproduces the traditional \( \chi^2 \) likelihood in the proper limit and then apply it to a general fitting problem not amenable to other methods.

In collaboration with Craig Heinke, Slavko Bogdanov, Chengkui Li, Wynn Ho, Arash Bahramian, and Sophia Han, we performed an analysis of the potential effect that systematic uncertainties have when determining the neutron star mass-radius curve from observations of eight quiescent low-mass X-ray binaries. We consider both hydrogen and helium atmosphere models and and models of dense matter which prefer or disfavor phase transitions. We find most likely radii below 12 km, but potentially as large as 14.5 km in the case of an uneven temperature distribution resulting in a hot spot on the surface. Our paper is available at arxiv.org.

UTK graduate student Spencer Beloin, postdoc Sophia Han,
Dany
Page and I just finished our paper which determines
neutron superfluid and proton superconducting gaps from
observations of neutron stars. Most importantly, our work
is the first to *quantify* the fitting problem,
matching models to data using a likelihood function rather
than doing "chi by eye". This method enables us to
determine how the superfluid gaps depend on density and
also what the most probable compositions of the individual
neutron star envelopes. Our paper is published
in Phys.
Rev. C and is also available on
the arXiv.

In this paper led by Joonas Nättilä and in collaboration with Cole Miller, Jari Kajava, Valery Suleimanov, and Juri Poutanen, we fit neutron star atmosphere models to hard-state X-ray bursts in 4U 1702-429 determining the mass and radius of this neutron star. Our paper is published in Astronomy and Astrophysics and available at arxiv.org.

UTK postdoc Sophia Han and I varied equations of state, superfluid properties, envelope compositions, neutron star masses, and direct Urca thresholds in order to attempt to explain the luminosities and time-averaged accretion rates of SAX J1808 and Aql X-1. neutron star envelopes. We found that, presuming neutron stars contain no exotic matter, there is a very small region in the large parameter space which is able to reproduce the observations for these two stars. Our paper is published in Phys. Rev. C.

As part of the long-range planning progress for the DOE Nuclear Science Advisory committee, several members of the science community reviewed the fundamental science questions at the intersections of nuclear physics and astrophysics. Our paper is published in Prog. in Nucl. Part. Phys.

Will Newton, Kent Yagi, and I just submitted a paper showing that either a measurement of the moment of inertia of one of the neutron stars in the double pulsar J0737-3039, or the tidal deformability in a neutron star merger in LIGO will potentially disentangle electron capture supernovae and ultra-stripped core-collapse supernovae. Our paper is now on the arXiv.

In a collaboration with Or Hen, Eli Piasetzky, and Larry Weinstein, we show that using a correlated Fermi gas (CFG) model for the symmetry energy results is as compatible with neutron star mass and radius observations as the naive Fermi gas (FFG) model. The demarcation of kinetic and potential energy parts of the symmetry energy is drastically different the CFG and FFG models, but when compared at the same values of S and L, the density dependence of the sum is very similar. Our paper is posted on the arXiv.

In a new paper published in J. Phys. G., Matt Mumpower, Gail McLaughlin, and Rebecca Surman, and I show that the abundances in the rare earth peak require a specific pattern of nuclear masses in order to reproduce observed abundances depending on the astrophysical site that one assumes for the r-process. Many of the relevant nuclear masses are too far from stability to measure, but a few of them are within reach of FRIB. A combination of nuclear mass measurements, and models like ours which directly connect these measurements to r-process abundances, may determine the astrophysical site of the rare earth peak in the near future. Our paper is also posted on the arxiv.

The rare earth peak is a peak in the observed abundances of r-process nuclei in the A=165 mass region. In a collaboration with Matt Mumpower, Gail McLaughlin, and Rebecca Surman, we determine the nuclear masses of neutron-rich nuclei which are required to produce the rare earth peak. For example, for a very neutron-rich cold r-process, a strong kink in the nuclear masses near Z=60 and N=100 is required to reproduce observations. Matt's method is particularly important because it treats the beta-decay and neutron-capture rates self-consistently, instead of treating the reaction rates as completely separate from the nuclear structure input. Our paper is now published at the Astrophysical Journal and is also on the arXiv.

In work led by Joonas Nättilä at the University of Turku in Finland, we determine the radii of neutron stars using PRE X-ray bursts in the hard state. The cooling tail of the burst is matched to a quantitative model of the neutron star atmosphere to obtain a faithful description of the neutron star structure. We find that the radius of a 1.4 \( \mathrm{M}_{\odot} \) neutron star is, to within 95% confidence, between 10.5 and 12.8 km. Our paper is published in Astron. & Astrophys. and posted at the arXiv.

In a Rev. Mod. Phys. colloquium paper written by a team led by Anna Watts, we review the potential of hard X-ray timing instruments to determine neutron star masses and radii. In particular, instruments which have an effective area of 10 \( \mathrm{m}^2 \) in the 2-30 keV band (as would be provided by the Large Observatory for X-ray Timing) can potentially lead to neutron star mass and radius constraints on the few percent level. Our article is also available on the arXiv.

Jim Lattimer, Ed Brown, and I show how prior distributions affect our the relationship between, for example, the radius of a 1.4 \( \mathrm{M}_{\odot} \) neutron star, the maximum mass, and the pressure of the EOS at various densities. We find that neutron star radii are unlikely to be smaller than 10 km, independent of the choice of prior distribution. We also examine new universal relations between moment of inertia, binding energy, compactness, and tidal deformability. Our paper is published in EPJA.

In a collaboration led by Chris Fryer at LANL, we determine how the fate of a neutron star merger is connected with the maximum mass of the cold non-rotating neutron star. In our article in ApJ, we show that if the non-rotating maximum mass is smaller than 2.3-2.4 \( \mathrm{M}_{\odot} \), then the remnant will likely be a black hole. Our paper was highlighted in the AAS publication Nova. The arXiv version is here.

In an article published in Phys. Rev. C, Paulo Bedaque and I use a phenomenological model of hyperons in nuclear matter and quantify the location at which the interaction between Lambda hyperons and dense matter must become repulsive (e.g. through \( n n \Lambda \) or \( n \Lambda \Lambda \) interactions) in order to ensure the creation of a two solar mass neutron star. This paper is also available on the arXiv.