Reduced-order surrogate models for scalar-tensor gravity in the strong field and applications to binary pulsars and GW170817

Junjie Zhao, Lijing Shao, Zhoujian Cao, Bo-Qiang Ma

Abstract

We investigate the scalar-tensor gravity of Damour and Esposito-Farèse (DEF), which predicts non-trivial phenomena in the nonperturbative strong-field regime for neutron stars (NSs). Instead of solving the modified Tolman-Oppenheimer-Volkoff equations, we construct reduced-order surrogate models, coded in the pySTGROM package, to predict the relations of a NS radius, mass, and effective scalar coupling to its central density. Our models are accurate at ~1% level and speed up large-scale calculations by two orders of magnitude. As an application, we use pySTGROM and Markov-chain Monte Carlo techniques to constrain parameters in the DEF theory, with five well-timed binary pulsars, the binary NS (BNS) inspiral GW170817, and a hypothetical BNS inspiral in the Advanced LIGO and next-generation GW detectors. In the future, as more binary pulsars and BNS mergers are detected, our surrogate models will be helpful in constraining strong-field gravity with essential speed and accuracy.

pySTGROM (for the DEF theory)

Packages required

numpy

scipy

h5py

Usage

The ROMs in the those range:

log10Alpha0 in [-5.3, -2.5]

beta0 in [-4.8, -4.0]

For now, we have built those ROMs for 16 EOSs.

EOSs AP3, AP4, BL_EOS, BSk20, BSk21, BSk22, BSk25, ENG, H4, MPA1, PAL1, SLy4, SLy9, SLy230a, WFF1, and WFF2.

The simply usage:

from stgrom import LoadModel

EOS_name = 'AP4' # EOSs AP3, AP4, BL_EOS, BSk20, BSk21, BSk22, BSk25, ENG, H4, MPA1, PAL1, SLy4, SLy9, SLy230a, WFF1, and WFF2.

log10Alpha0 = -5.0
beta0 = -4.5

mod4EOS = LoadModel(EOS_name)
mass, radius, alphaA = mod4EOS(log10Alpha0, beta0, mod4EOS.e_cs)

More, refer to Example.

Introduction

This notebook is a companion to the paper posted at arxiv:1907.00780. It contains three ROMs for each EOS.

We encourage use of these data in derivative works. If you use the material provided here, please cite the paper using the reference:

@article{Zhao:2019suc,
      author         = "Zhao, Junjie and Shao, Lijing and Cao, Zhoujian and Ma,
                        Bo-Qiang",
      title          = "{Reduced-order surrogate models for scalar-tensor gravity
                        in the strong field and applications to binary pulsars and
                        GW170817}",
      journal        = "Phys. Rev.",
      volume         = "D100",
      year           = "2019",
      pages          = "064034",
      doi            = "10.1103/PhysRevD.100.064034",
      eprint         = "1907.00780",
      archivePrefix  = "arXiv",
      primaryClass   = "gr-qc",
      SLACcitation   = "%%CITATION = ARXIV:1907.00780;%%"
}

Our paper are based on those papers:

In order to solve the modified Tolman-Oppenheimer-Volkoff (TOV) eqautions for neutron star, we use the solver for the DEF theory from Shao:2017gwu and make it more efficient with parallel computing.

@article{Shao:2017gwu,
      author         = "Shao, Lijing and Sennett, Noah and Buonanno, Alessandra
                        and Kramer, Michael and Wex, Norbert",
      title          = "{Constraining nonperturbative strong-field effects in
                        scalar-tensor gravity by combining pulsar timing and
                        laser-interferometer gravitational-wave detectors}",
      journal        = "Phys. Rev.",
      volume         = "X7",
      year           = "2017",
      number         = "4",
      pages          = "041025",
      doi            = "10.1103/PhysRevX.7.041025",
      eprint         = "1704.07561",
      archivePrefix  = "arXiv",
      primaryClass   = "gr-qc",
      reportNumber   = "LIGO-P1700073",
      SLACcitation   = "%%CITATION = ARXIV:1704.07561;%%"
}

The ROMs are based on the paper Field:2013cfa.

@article{Field:2013cfa,
      author         = "Field, Scott E. and Galley, Chad R. and Hesthaven, Jan S.
                        and Kaye, Jason and Tiglio, Manuel",
      title          = "{Fast prediction and evaluation of gravitational
                        waveforms using surrogate models}",
      journal        = "Phys. Rev.",
      volume         = "X4",
      year           = "2014",
      number         = "3",
      pages          = "031006",
      doi            = "10.1103/PhysRevX.4.031006",
      eprint         = "1308.3565",
      archivePrefix  = "arXiv",
      primaryClass   = "gr-qc",
      SLACcitation   = "%%CITATION = ARXIV:1308.3565;%%"
}

Acknowledgements

We are grateful to Bin Hu, Michael Kramer, and Masaru Shibata for comments. We thank Norbert Wex for stimulating discussions and carefully reading the manuscript.

Funding

This work was supported by the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology (2018QNRC001), and was partially supported by the National Natural Science Foundation of China (11721303, 11475006, 11690023, 11622546), the Strategic Priority Research Program of the Chinese Academy of Sciences through the grant No. XDB23010200, the European Research Council (ERC) for the ERC Synergy Grant BlackHoleCam under Contract No. 610058, and the High-performance Computing Platform of Peking University. Z.C. was supported by the "Fundamental Research Funds for the Central Universities".