HotandDenseMatterEquationofState

𝐹" 𝑇, 𝜌, 𝛿 = 𝐹") 𝑇, 𝜌, 𝛿 + 𝜆𝐹", 𝑇, 𝜌, 𝛿 + 𝜆-𝐹"- 𝑇, 𝜌, 𝛿 + 𝜆.𝐹". 𝑇, 𝜌, 𝛿 + 𝒪(𝜆1)

Realistictwo- andthree-bodychiralnuclearforcesareusedtocalculatethefreeenergyofnuclearmatteratvaryingtemperature,density,andcomposition.Thefreeenergypernucleonininfinitehomogeneousnuclearmattercanbeexpandedinperturbationtheoryasfollows:

Figure2:First-,second-,andthird- orderdiagrammaticcontributionstothegroundstateenergydensityofnuclearmatterbyHoltet.al.1 Thewavylinesindicatethe(antisymmetrized)density-dependentNNinteractionderivedfromchiraltwo- andthree-bodyforces.

Figure3:Pressureinisospinsymmetricnuclearmatterfortemperaturesintherange𝑇 = 0 − 25𝑀𝑒𝑉 byWellenhoferet.al.2

Figure4:PressureinpureneutronmatterbyWellenhofer et.al.2

𝟏 𝜌𝐸(,) = 12=𝑛,𝑛-

�

,-

12 (𝑉"@@ + 𝑉"@@ABC/3) 12 , 𝟐 𝜌𝐸(-) = −14= 12 𝑉"BHH 34

-�

,-.1

𝑛,𝑛-𝑛".𝑛"1𝑒. + 𝑒1 − 𝑒, − 𝑒-

𝟑 𝜌𝐸JJ. =

18 = 12 𝑉"BHH 34

�

,-.1LM

34 𝑉"BHH 56 56 𝑉"BHH 12 ×𝑛,𝑛-𝑛".𝑛"1𝑛"L𝑛"M

(𝑒. + 𝑒1 − 𝑒, − 𝑒-)(𝑒L + 𝑒M − 𝑒, − 𝑒-)

𝟒 𝜌𝐸QQ. =

18 = 12 𝑉"BHH 34

�

,-.1LM

34 𝑉"BHH 56 56 𝑉"BHH 12 ×𝑛",𝑛"-𝑛.𝑛1𝑛L𝑛M

(𝑒, + 𝑒- − 𝑒. − 𝑒1)(𝑒, + 𝑒- − 𝑒L − 𝑒M)

𝟓 𝜌𝐸JQ. = − = 12 𝑉"BHH 34

�

,-.1LM

54 𝑉"BHH 16 36 𝑉"BHH 52 ×𝑛,𝑛-𝑛".𝑛"1𝑛L𝑛"M

(𝑒. + 𝑒1 − 𝑒, − 𝑒-)(𝑒. + 𝑒M − 𝑒- − 𝑒L)

First-,second-,andthird-ordercontributionstotheenergydensity𝝆𝑬:

Abstract

TowardMicroscopicEquationsofStateforCore-CollapseSupernovaefromChiralEffectiveFieldTheory

B.Aboona1,2,J.W.Holt21.DepartmentofPhysicsandAstronomy,MiddleTennesseeStateUniversity,Murfreesboro,TN37132

2.CyclotronInstitute,TexasA&MUniversity,CollegeStation,TX77843

NumericalOptimizationonGPUsWeexplorethepossibilitytocalculatethenuclearequationofstateusingmassiveparallelcomputingonGPUaccelerators.TheGPUarchitectureallowsforthousandsofindependentthreadstoexecutesimultaneously,whichmayleadtosignificantlyimprovedcomputationalefficiencyofcurrentcodes.

Figure5:CUDAMemoryModel

Figure6:TheplottotheleftcomparesGPUandCPUruntimeasafunctionofdesirednumericalprecision(encodedinthenumberofintegrationmeshpoints).TheGPUcodeexhibitsamuchmorefavorablescalingcomparedtotheoptimizedCPUversion.

Core-CollapseSupernovae

Figure1

1. J. W. Holt, PRC 95 034326 (2017)2. C. Wellenhofer, PRC 92 015801 (2015))Figures:1. Figure 1:2. Figure 5:

References

https://heasarc.gsfc.nasa.gov/docs/nicer/nicer_about.htmhttps://sites.google.com/site/cudapros/website-builder

• IwouldliketothankDr.JeremyHoltforhismentorshipthroughoutthisproject.

• The Cyclotron Institute at Texas A&M• NSF grant: PHY – 1659847• DOE grant: DE-FG02-93ER40773

Acknowledgements

Chiral effective field theory provides a modernframework for understanding the structure anddynamics of nuclear many-body systems. Our aim is toextend the application of chiral effective field theory todescribe the nuclear equation of state required forsupercomputer simulations of core-collapsesupernovae. Given the large range of densities,temperatures, and proton fractions probed duringstellar core collapse, microscopic calculations of theequation of state require large computational resourceson the order of one million CPU hours. We investigatethe use of graphics processing units (GPUs) tosignificantly reduce the computational cost of thesecalculations, which will enable a more accurate andprecise description of this important input to numericalastrophysical simulations.

Stars between 10 − 30𝑀⨀ reach sufficiently hightemperatures to fuse nuclei up to iron. Once the ironcore reaches the Chandrasekhar mass of 1.4𝑀⊙, it canno longer be supported through electron degeneracypressure and undergoes gravitational collapse.

Short-range nuclear forces acting over femtoscaledistances eventually halt the collapse, which results in ashockwave that rebounds against the inward-fallingmatter above. Electron capture in the core releasesabundant neutrinos that deposit additional energybehind the shockwave, potentially leading to asuccessful supernova explosion.

The nuclear equation of state plays a critical role insimulating stellar core collapse and the hydrodynamicevolution of the resulting supernova explosion.

ConclusionsandFutureWorkThe Current GPU implementation offers a more efficientalgorithm than the original CPU program, especially thehighest numerical precisions achieved. This provides afirst step toward faster calculations needed forconstructing equation of state tables for astrophysicalsimulations.