arXiv subjects

Madappa Prakash

Publications and source records attributed to Madappa Prakash.

At least 19 recordsLinked to original sources

arXiv2025

Framework for phase transitions between the Maxwell and Gibbs constructions at finite temperature

The characteristics of the hadron-to-quark first-order phase transition differ depending on whether charge neutrality is locally or globally fulfilled. In $\beta$-equilibrated matter, these two possibilities correspond to the Maxwell and Gibbs constructions. Recently, we presented a new framework in which a continuously-varying parameter allows one to describe a first-order phase transition in intermediate scenarios to the two extremes of fully local and fully global charge neutrality. In this work, we extend the previous framework to finite temperatures and out-of-$\beta$ equilibrium conditions, making it available for simulations of core-collapse supernovae and binary neutron star mergers. We investigate its impact on key thermodynamic quantities across a range of baryon densities, temperatures, and electron fractions. We find that when matter is not in $\beta$-equilibrium, the pressure in the mixed phase is not constant even for the case of fully-local charge neutrality. Moreover, we compute the thermal index using three different approaches, demonstrating that the finite-temperature extension of an equation of state using a constant thermal index can be ill-defined when applied to the mixed phase.

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arXiv2024

Characterizing the nuclear models informed by PREX and CREX: a view from Bayesian inference

New measurements of the weak charge density distributions of $^{48}$Ca and $^{208}$Pb challenge existing nuclear models. In the post-PREX-CREX era, it is unclear if current models can simultaneously describe weak charge distributions along with accurate measurements of binding energy and charge radii. In this letter, we explore the parameter space of relativistic and non-relativistic models to study the differences between the electric and weak form factors, $\Delta F=F_{ch}-F_{W}$, in $^{48}$Ca and $^{208}$Pb. We show, for the first time, which aspects of mean-field models are the most important in determining the relative magnitude of the neutron skin in lead and calcium nuclei. We carefully disentangle the tension between the PREX-2/CREX constraints and the ability of the RMF and Skyrme models to accurately describe binding energies and charge radii. We find that the nuclear symmetry energy coefficient $S_V$ and the isovector spin-orbit coefficient $b'_4$ play different roles in determining $\Delta F$ of $^{48}$Ca and $^{208}$Pb. Consequently, adjusting $S_V$ or $b'_4$ shifts predicted $\Delta F$ values toward or away from PREX-2/CREX measurements. Additionally, $S_V$ and the slope L are marginally correlated given the prior constraints of our Bayesian inference, allowing us to infer them separately from PREX-2/CREX data.

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arXiv2024

Dense Nuclear Matter Equation of State from Heavy-Ion Collisions

The nuclear equation of state (EOS) is at the center of numerous theoretical and experimental efforts in nuclear physics. With advances in microscopic theories for nuclear interactions, the availability of experiments probing nuclear matter under conditions not reached before, endeavors to develop sophisticated and reliable transport simulations to interpret these experiments, and the advent of multi-messenger astronomy, the next decade will bring new opportunities for determining the nuclear matter EOS, elucidating its dependence on density, temperature, and isospin asymmetry. Among controlled terrestrial experiments, collisions of heavy nuclei at intermediate beam energies (from a few tens of MeV/nucleon to about 25 GeV/nucleon in the fixed-target frame) probe the widest ranges of baryon density and temperature, enabling studies of nuclear matter from a few tenths to about 5 times the nuclear saturation density and for temperatures from a few to well above a hundred MeV, respectively. Collisions of neutron-rich isotopes further bring the opportunity to probe effects due to the isospin asymmetry. However, capitalizing on the enormous scientific effort aimed at uncovering the dense nuclear matter EOS, both at RHIC and at FRIB as well as at other international facilities, depends on the continued development of state-of-the-art hadronic transport simulations. This white paper highlights the essential role that heavy-ion collision experiments and hadronic transport simulations play in understanding strong interactions in dense nuclear matter, with an emphasis on how these efforts can be used together with microscopic approaches and neutron star studies to uncover the nuclear EOS.

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arXiv2023

Framework for phase transitions between the Maxwell and Gibbs constructions

By taking the nucleon-to-quark phase transition within a neutron star as an example, we present a thermodynamically consistent method to calculate the equation of state of ambient matter so that transitions that are intermediate to those of the familiar Maxwell and Gibbs constructions can be described. This method does not address the poorly known surface tension between the two phases microscopically (as, for example, in the calculation of the core pasta phases via the Wigner-Seitz approximation) but instead combines the local and global charge neutrality conditions characteristic of the Maxwell and Gibbs constructions, respectively. Overall charge neutrality is achieved by dividing the leptons to those that obey local charge neutrality (Maxwell) and those that maintain global charge neutrality (Gibbs). The equation of state is obtained by using equilibrium constraints derived from minimizing the total energy density. The results of this minimization are then used to calculate neutron star mass-radius curves, tidal deformabilities, equilibrium and adiabatic sound speeds, and nonradial $g$-mode oscillation frequencies for several intermediate constructions. Various quantities of interest transform smoothly from their Gibbs structures to those of Maxwell as the local-to-total electron ratio $η$, introduced to mimic the hadron-to-quark interface tension from $0$ (Gibbs) to $\infty$ (Maxwell), is raised from $0$ to $1$. A notable exception is the $g$-mode frequency for the specific case of $η=1$ for which a gap appears between the quark and hadronic branches.

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arXiv2022

Long Range Plan: Dense matter theory for heavy-ion collisions and neutron stars

Since the release of the 2015 Long Range Plan in Nuclear Physics, major events have occurred that reshaped our understanding of quantum chromodynamics (QCD) and nuclear matter at large densities, in and out of equilibrium. The US nuclear community has an opportunity to capitalize on advances in astrophysical observations and nuclear experiments and engage in an interdisciplinary effort in the theory of dense baryonic matter that connects low- and high-energy nuclear physics, astrophysics, gravitational waves physics, and data science

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arXiv2022

Impact of the equation of state on $f$- and $p$- mode oscillations of neutron stars

We investigate the impact of the neutron-star matter equation of state on the $f$- and $p_1$-mode oscillations of neutron stars obtained within the Cowling approximation and linearized general relativity. The $f$- and $p_1$-mode oscillation frequencies, and their damping times are calculated using representative sets of Skyrme Hartree-Fock and relativistic mean-field models, all of which reproduce nuclear systematics and support $2M_\odot$ neutron stars. Our study shows strong correlations between the frequencies of $f$- and $p_1$-modes and their damping times with the pressure of $β$-equilibrated matter at densities equal to or slightly higher than the nuclear saturation density $ρ_0$. Such correlations are found to be almost independent of the composition of the stars. The frequency of the $p_1$-mode of $1.4M_\odot$ star is strongly correlated with the slope of the symmetry energy $L_0$ and $β$-equilibrated pressure at density $ρ_0$. Compared to GR calculations, the error in the Cowling approximation for the $f$-mode is about 30\% for neutron stars of low mass, whereas it decreases with increasing mass. The accuracy of the $p_1$-mode is better than 15\% for neutron stars of maximum mass, and improves for lower masses and higher number of radial nodes.

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arXiv2022

Quasi-normal g-modes of neutron stars with quarks

Quasi-normal oscillation modes of neutron stars provide a means to probe their interior composition using gravitational wave astronomy. We compute the frequencies and damping times of composition-dependent core g-modes of neutron stars containing quark matter employing linearized perturbative equations of general relativity. We find that ignoring background metric perturbations due to the oscillating fluid, as in the Cowling approximation, underestimates the g-mode frequency by up to 10% for higher mass stars, depending on the parameters of the nuclear equation of state and how the mixed phase is constructed. The g-mode frequencies are well-described by a linear scaling with the central lepton (or combined lepton and quark) fraction for nucleonic (hybrid) stars. Our findings suggest that neutron stars with and without quarks are manifestly different with regards to their quasi-normal g-mode spectrum, and may thus be distinguished from one another in future observations of gravitational waves from merging neutron stars.

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arXiv2021

$g$-modes of neutron stars with hadron-to-quark crossover transitions

We perform the first study of the principal core $g$-mode oscillation in hybrid stars containing quark matter, utilizing a crossover model for the hadron-to-quark transition inspired by lattice QCD. The ensuing results are compared with our recent findings of $g$-mode frequencies in hybrid stars with a first-order phase transition using Gibbs constructions. We find that models using Gibbs construction yield $g$-mode amplitudes and the associated gravitational energy radiated that dominate over those of the chosen crossover model owing to the distinct behaviors of the equilibrium and adiabatic sound speeds in the various models. Based on our results, we conclude that were $g$-modes to be detected in upgraded LIGO and Virgo detectors it would indicate a first-order phase transition akin to a Gibbs construction.

astro-ph.HE↗

arXiv2021

g-mode Oscillations in Hybrid Stars: A Tale of Two Sounds

We study the principal core g-mode oscillation in hybrid stars containing quark matter and find that they have an unusually large frequency range ($\approx$ 200 - 600 Hz) compared to ordinary neutron stars or self-bound quark stars of the same mass. Theoretical arguments and numerical calculations that trace this effect to the difference in the behaviour of the equilibrium and adiabatic sound speeds in the mixed phase of quarks and nucleons are provided. We propose that the sensitivity of core g-mode oscillations to non-nucleonic matter in neutron stars could be due to the presence of a mixed quark-nucleon phase. Based on our analysis, we conclude that for binary mergers where one or both components may be a hybrid star, the fraction of tidal energy pumped into resonant g-modes in hybrid stars can exceed that of a normal neutron star by a factor of 2-3, although resonance occurs during the last stages of inspiral. A self-bound star, on the other hand, has a much weaker tidal overlap with the g-mode. The cumulative tidal phase error in hybrid stars, $Δϕ\cong$ 0.5 rad, is comparable to that from tides in ordinary neutron stars, presenting a challenge in distinguishing between the two cases. However, should the principal g-mode be excited to sufficient amplitude for detection in a post-merger remnant with quark matter in its interior, its frequency would be a possible indication for the existence of non-nucleonic matter in neutron stars.

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arXiv2021

Limiting masses and radii of neutron stars and their implications

We combine equation of state of dense matter up to twice nuclear saturation density ($n_{\rm sat}=0.16\, \text{fm}^{-3}$) obtained using chiral effective field theory ($χ$EFT), and recent observations of neutron stars to gain insights about the high-density matter encountered in their cores. A key element in our study is the recent Bayesian analysis of correlated EFT truncation errors based on order-by-order calculations up to next-to-next-to-next-to-leading order in the $χ$EFT expansion. We refine the bounds on the maximum mass imposed by causality at high densities, and provide stringent limits on the maximum and minimum radii of $\sim1.4\,{\rm M}_{\odot}$ and $\sim2.0\,{\rm M}_{\odot}$ stars. Including $χ$EFT predictions from $n_{\rm sat}$ to $2\,n_{\rm sat}$ reduces the permitted ranges of the radius of a $1.4\,{\rm M}_{\odot}$ star, $R_{1.4}$, by $\sim3.5\, \text{km}$. If observations indicate $R_{1.4}<11.2\, \text{km}$, our study implies that either the squared speed of sound $c^2_{s}>1/2$ for densities above $2\,n_{\rm sat}$, or that $χ$EFT breaks down below $2\,n_{\rm sat}$. We also comment on the nature of the secondary compact object in GW190814 with mass $\simeq 2.6\,{\rm M}_{\odot}$, and discuss the implications of massive neutron stars $>2.1 \,{\rm M}_{\odot}\,(2.6\,{\rm M}_{\odot})$ in future radio and gravitational-wave searches. Some form of strongly interacting matter with $c^2_{s}>0.35\, (0.55)$ must be realized in the cores of such massive neutron stars. In the absence of phase transitions below $2\,n_{\rm sat}$, the small tidal deformability inferred from GW170817 lends support for the relatively small pressure predicted by $χ$EFT for the baryon density $n_{\rm B}$ in the range $1-2\,n_{\rm sat}$. Together they imply that the rapid stiffening required to support a high maximum mass should occur only when $n_{\rm B} \gtrsim 1.5-1.8\,n_{\rm sat}$.

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arXiv2020

On the minimum radius of very massive neutron stars

Prospects of establishing the radii of massive neutron stars in PSR J1614-2230 and PSR J0740+6620 from NICER and Chandra observatories hold the potential to constrain the equation of state (EoS) of matter to densities well beyond those encountered in canonical stars of mass $\sim 1.4\,{\rm M}_{\odot}$. In this work, we investigate the relation between the radii of very massive neutron stars up to the maximum mass, $M_{\rm max}$, supported by dense matter EoSs. Results from models with hadronic matter are contrasted with those that include a first-order hadron-to-quark phase transition. We find that a lower bound on $M_{\rm max}$ with an upper bound on the radius of massive pulsars serves to rule out too soft quark matter, and an upper bound on $M_{\rm max}$ with a lower bound on the radius of massive pulsars strongly disfavors a transition into too-stiff quark matter appearing at low densities. The complementary role played by radius inferences from future gravitational wave events of inspiraling binary neutron stars is also briefly discussed.

astro-ph.HE↗

arXiv2020

NS 1987A in SN 1987A

The possible detection of a compact object in the remnant of SN 1987A presents an unprecedented opportunity to follow its early evolution. The suspected detection stems from an excess of infrared emission from a dust blob near the compact object's predicted position. The infrared excess could be due to the decay of isotopes like 44Ti, accretion luminosity from a neutron star or black hole, magnetospheric emission or a wind originating from the spindown of a pulsar, or thermal emission from an embedded, cooling neutron star (NS 1987A). It is shown that the last possibility is the most plausible as the other explanations are disfavored by other observations and/or require fine-tuning of parameters. Not only are there indications the dust blob overlaps the predicted location of a kicked compact remnant, but its excess luminosity also matches the expected thermal power of a 30 year old neutron star. Furthermore, models of cooling neutron stars within the Minimal Cooling paradigm readily fit both NS 1987A and Cas A, the next-youngest known neutron star. If correct, a long heat transport timescale in the crust and a large effective stellar temperature are favored, implying relatively limited crustal n-1S0 superfluidity and an envelope with a thick layer of light elements, respectively. If the locations don't overlap, then pulsar spindown or accretion might be more likely, but the pulsar's period and magnetic field or the accretion rate must be rather finely tuned. In this case, NS 1987A may have enhanced cooling and/or a heavy-element envelope.

astro-ph.HE↗

arXiv2017

Enforcing causality in nonrelativistic equations of state at finite temperature

We present a thermodynamically consistent method by which equations of state based on nonrelativistic potential models can be modified so that they respect causality at high densities, both at zero and finite temperature (entropy). We illustrate the application of the method using the high density phase parametrization of the well known APR model in its pure neutron matter configuration as an example. We also show that, for models with only contact interactions, the adiabatic speed of sound is independent of the temperature in the limit of very large temperature. This feature is approximately valid for models with finite-range interactions as well, insofar as the temperature dependence they introduce to the Landau effective mass is weak. In addition, our study reveals that in first principle nonrelativistic models of hot and dense matter, contributions from higher than two-body interactions must be screened at high density to preserve causality.

astro-ph.HE↗

arXiv2016

Thermal Effects in Dense Matter Beyond Mean Field Theory

The formalism of next-to-leading order Fermi Liquid Theory is employed to calculate the thermal properties of symmetric nuclear and pure neutron matter in a relativistic many-body theory beyond the mean field level which includes two-loop effects. For all thermal variables, the semi-analytical next-to-leading order corrections reproduce results of the exact numerical calculations for entropies per baryon up to 2. This corresponds to excellent agreement down to sub-nuclear densities for temperatures up to $20$ MeV. In addition to providing physical insights, a rapid evaluation of the equation of state in the homogeneous phase of hot and dense matter is achieved through the use of the zero-temperature Landau effective mass function and its derivatives.

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arXiv2016

White Paper on Nuclear Astrophysics

This white paper informs the nuclear astrophysics community and funding agencies about the scientific directions and priorities of the field and provides input from this community for the 2015 Nuclear Science Long Range Plan. It summarizes the outcome of the nuclear astrophysics town meeting that was held on August 21-23, 2014 in College Station at the campus of Texas A&M University in preparation of the NSAC Nuclear Science Long Range Plan. It also reflects the outcome of an earlier town meeting of the nuclear astrophysics community organized by the Joint Institute for Nuclear Astrophysics (JINA) on October 9- 10, 2012 Detroit, Michigan, with the purpose of developing a vision for nuclear astrophysics in light of the recent NRC decadal surveys in nuclear physics (NP2010) and astronomy (ASTRO2010). The white paper is furthermore informed by the town meeting of the Association of Research at University Nuclear Accelerators (ARUNA) that took place at the University of Notre Dame on June 12-13, 2014. In summary we find that nuclear astrophysics is a modern and vibrant field addressing fundamental science questions at the intersection of nuclear physics and astrophysics. These questions relate to the origin of the elements, the nuclear engines that drive life and death of stars, and the properties of dense matter. A broad range of nuclear accelerator facilities, astronomical observatories, theory efforts, and computational capabilities are needed. With the developments outlined in this white paper, answers to long standing key questions are well within reach in the coming decade.

astro-ph.SR↗

arXiv2016

Hot and dense matter beyond relativistic mean field theory

Properties of hot and dense matter are calculated in the framework of quantum hadro-dynamics by including contributions from two-loop (TL) diagrams arising from the exchange of iso-scalar and iso-vector mesons between nucleons. Our extension of mean-field theory (MFT) employs the same five density-independent coupling strengths which are calibrated using the empirical properties at the equilibrium density of iso-spin symmetric matter. Results of calculations from the MFT and TL approximations are compared for conditions of density, temperature, and proton fraction encountered in astrophysics applications involving compact objects. The TL results for the equation of state (EOS) of cold pure neutron matter at sub- and near-nuclear densities agree well with those of modern quantum Monte Carlo and effective field-theoretical approaches. Although the high-density EOS in the TL approximation for neutron-star matter is substantially softer than its MFT counterpart, it is able to support a $2M_\odot$ neutron star required by recent precise determinations. In addition, radii of $1.4M_\odot$ stars are smaller by $\sim 1$ km than obtained in MFT. In contrast to MFT, the TL results also give a better account of the single-particle or optical potentials extracted from analyses of medium-energy proton-nucleus and heavy-ion experiments. In degenerate conditions, the thermal variables are well reproduced by results of Landau's Fermi-Liquid theory in which density-dependent effective masses feature prominently. The ratio of the thermal components of pressure and energy density expressed as $Γ_{th}=1+(P_{th}/ε_{th})$, often used in astrophysical simulations, exhibits a stronger dependence on density than on proton fraction and temperature in both MFT and TL calculations. The prominent peak of $Γ_{th}$ at supra-nuclear density found in MFT is, however, suppressed in TL calculations.

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arXiv2015

Degenerate limit thermodynamics beyond leading order for models of dense matter

Analytical formulas for next-to-leading order temperature corrections to the thermal state variables of interacting nucleons in bulk matter are derived in the degenerate limit. The formalism developed is applicable to a wide class of non-relativistic and relativistic models of hot and dense matter currently used in nuclear physics and astrophysics (supernovae, proto-neutron stars and neutron star mergers) as well as in condensed matter physics. We consider the general case of arbitrary dimensionality of momentum space and an arbitrary degree of relativity (for relativistic mean-field theoretical models). For non-relativistic zero-range interactions, knowledge of the Landau effective mass suffices to compute next-to-leading order effects, but in the case of finite-range interactions, momentum derivatives of the Landau effective mass function up to second order are required. Numerical computations are performed to compare results from our analytical formulas with the exact results for zero- and finite-range potential and relativistic mean-field theoretical models. In all cases, inclusion of next-to-leading order temperature effects substantially extends the ranges of partial degeneracy for which the analytical treatment remains valid.

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arXiv2015

Thermal properties of hot and dense matter with finite range interactions

We explore the thermal properties of hot and dense matter using a model that reproduces the empirical properties of isospin symmetric and asymmetric bulk nuclear matter, optical model fits to nucleon-nucleus scattering data, heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest well-measured neutron star mass of 2 $\rm{M}_\odot$. Results of this model which incorporates finite range interactions through Yukawa type forces are contrasted with those of a zero-range Skyrme model that yields nearly identical zero-temperature properties at all densities for symmetric and asymmetric nucleonic matter and the maximum neutron star mass, but fails to account for heavy-ion flow data due to the lack of an appropriate momentum dependence in its mean field. Similarities and differences in the thermal state variables and the specific heats between the two models are highlighted. Checks of our exact numerical calculations are performed from formulas derived in the strongly degenerate and non-degenerate limits. Our studies of the thermal and adiabatic indices, and the speed of sound in hot and dense matter for conditions of relevance to core-collapse supernovae, the thermal evolution of neutron stars from their birth and mergers of compact binary stars reveal that substantial variations begin to occur at sub-saturation densities before asymptotic values are reached at supra-nuclear densities.

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