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Omana Kuttan M, Steinheimer J, Zhou K, Stoecker H. QCD Equation of State of Dense Nuclear Matter from a Bayesian Analysis of Heavy-Ion Collision Data. PHYSICAL REVIEW LETTERS 2023; 131:202303. [PMID: 38039475 DOI: 10.1103/physrevlett.131.202303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2022] [Revised: 04/24/2023] [Accepted: 10/18/2023] [Indexed: 12/03/2023]
Abstract
Bayesian methods are used to constrain the density dependence of the QCD equation of state (EOS) for dense nuclear matter using the data of mean transverse kinetic energy and elliptic flow of protons from heavy ion collisions (HICs), in the beam energy range sqrt[s_{NN}]=2-10 GeV. The analysis yields tight constraints on the density dependent EOS up to 4 times the nuclear saturation density. The extracted EOS yields good agreement with other observables measured in HIC experiments and constraints from astrophysical observations both of which were not used in the inference. The sensitivity of inference to the choice of observables is also discussed.
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Affiliation(s)
- Manjunath Omana Kuttan
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany
- Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany
- Xidian-FIAS International Joint Research Center, Giersch Science Center, D-60438 Frankfurt am Main, Germany
| | - Jan Steinheimer
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany
| | - Kai Zhou
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany
| | - Horst Stoecker
- Frankfurt Institute for Advanced Studies, Ruth-Moufang-Strasse 1, D-60438 Frankfurt am Main, Germany
- Institut für Theoretische Physik, Goethe Universität Frankfurt, Max-von-Laue-Strasse 1, D-60438 Frankfurt am Main, Germany
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstrasse 1, D-64291 Darmstadt, Germany
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Huth S, Pang PTH, Tews I, Dietrich T, Le Fèvre A, Schwenk A, Trautmann W, Agarwal K, Bulla M, Coughlin MW, Van Den Broeck C. Constraining neutron-star matter with microscopic and macroscopic collisions. Nature 2022; 606:276-280. [PMID: 35676430 PMCID: PMC9177417 DOI: 10.1038/s41586-022-04750-w] [Citation(s) in RCA: 11] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2021] [Accepted: 04/11/2022] [Indexed: 11/16/2022]
Abstract
Interpreting high-energy, astrophysical phenomena, such as supernova explosions or neutron-star collisions, requires a robust understanding of matter at supranuclear densities. However, our knowledge about dense matter explored in the cores of neutron stars remains limited. Fortunately, dense matter is not probed only in astrophysical observations, but also in terrestrial heavy-ion collision experiments. Here we use Bayesian inference to combine data from astrophysical multi-messenger observations of neutron stars1-9 and from heavy-ion collisions of gold nuclei at relativistic energies10,11 with microscopic nuclear theory calculations12-17 to improve our understanding of dense matter. We find that the inclusion of heavy-ion collision data indicates an increase in the pressure in dense matter relative to previous analyses, shifting neutron-star radii towards larger values, consistent with recent observations by the Neutron Star Interior Composition Explorer mission5-8,18. Our findings show that constraints from heavy-ion collision experiments show a remarkable consistency with multi-messenger observations and provide complementary information on nuclear matter at intermediate densities. This work combines nuclear theory, nuclear experiment and astrophysical observations, and shows how joint analyses can shed light on the properties of neutron-rich supranuclear matter over the density range probed in neutron stars.
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Affiliation(s)
- Sabrina Huth
- Department of Physics, Technische Universität Darmstadt, Darmstadt, Germany.
- ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany.
| | - Peter T H Pang
- Nikhef, Amsterdam, The Netherlands.
- Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, Utrecht, The Netherlands.
| | - Ingo Tews
- Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA
| | - Tim Dietrich
- Institut für Physik und Astronomie, Universität Potsdam, Potsdam, Germany
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Potsdam, Germany
| | - Arnaud Le Fèvre
- GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
| | - Achim Schwenk
- Department of Physics, Technische Universität Darmstadt, Darmstadt, Germany
- ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany
- Max-Planck-Institut für Kernphysik, Heidelberg, Germany
| | | | - Kshitij Agarwal
- Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen, Germany
| | - Mattia Bulla
- The Oskar Klein Centre, Department of Astronomy, Stockholm University, AlbaNova, Stockholm, Sweden
| | - Michael W Coughlin
- School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA
| | - Chris Van Den Broeck
- Nikhef, Amsterdam, The Netherlands
- Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University, Utrecht, The Netherlands
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Drischler C, Furnstahl RJ, Melendez JA, Phillips DR. How Well Do We Know the Neutron-Matter Equation of State at the Densities Inside Neutron Stars? A Bayesian Approach with Correlated Uncertainties. PHYSICAL REVIEW LETTERS 2020; 125:202702. [PMID: 33258658 DOI: 10.1103/physrevlett.125.202702] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2020] [Revised: 07/28/2020] [Accepted: 09/25/2020] [Indexed: 06/12/2023]
Abstract
We introduce a new framework for quantifying correlated uncertainties of the infinite-matter equation of state derived from chiral effective field theory (χEFT). Bayesian machine learning via Gaussian processes with physics-based hyperparameters allows us to efficiently quantify and propagate theoretical uncertainties of the equation of state, such as χEFT truncation errors, to derived quantities. We apply this framework to state-of-the-art many-body perturbation theory calculations with nucleon-nucleon and three-nucleon interactions up to fourth order in the χEFT expansion. This produces the first statistically robust uncertainty estimates for key quantities of neutron stars. We give results up to twice nuclear saturation density for the energy per particle, pressure, and speed of sound of neutron matter, as well as for the nuclear symmetry energy and its derivative. At nuclear saturation density, the predicted symmetry energy and its slope are consistent with experimental constraints.
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Affiliation(s)
- C Drischler
- Department of Physics, University of California, Berkeley, California 94720, USA
- Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - R J Furnstahl
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - J A Melendez
- Department of Physics, The Ohio State University, Columbus, Ohio 43210, USA
| | - D R Phillips
- Department of Physics and Astronomy and Institute of Nuclear and Particle Physics, Ohio University, Athens, Ohio 45701, USA
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