Degeneracy in Studying the Supranuclear Equation of State and Modified Gravity with Neutron Stars

It is generally acknowledged that an extrapolation in physics from a well-known scale to an unknown scale is perilous. This prevents us from using laboratory experience to gain precise information for the supranuclear matter inside neutron stars (NSs). With operating and upcoming astronomical facilities, NSs' equation of state (EOS) is expected to be determined at a new level in the near future, under the assumption that general relativity (GR) is the correct theory for gravitation. While GR is a reasonable working assumption yet still an extrapolation, there could be a large uncertainty due to the not-so-well-tested strong gravitational field inside NSs. Here we review some recent theoretical efforts towards a better understanding of the degeneracy between the supranuclear EOS and alternative gravity theories.Comment: 11 pages, 6 figure

An independent test on the local position invariance of gravity with the triple pulsar PSR J0337+1715

We design a direct test of the local position invariance (LPI) in the post-Newtonian gravity, using the timing observation of the triple pulsar, PSR J0337+1715. The test takes advantage of the large gravitational acceleration exerted by the outer white dwarf to the inner neutron star -- white dwarf binary. Using machine-precision three-body simulations and dedicated Markov-chain Monte Carlo (MCMC) techniques with various sampling strategies and noise realizations, we estimate that the Whitehead's parameter could have already been limited to $|\xi| \lesssim 0.4$ (95\% CL), with the published timing data spanning from January 2012 to May 2013. The constraint is still orders of magnitude looser than the best limit, yet it is able to independently falsify Whitehead's gravity theory where $\xi=1$. In addition, the new test is immune to extra assumptions and involves full dynamics of a three-body system with a strongly self-gravitating neutron star.Comment: 14 pages, 4 figures; Classical and Quantum Gravity, in pres

A Bayesian Framework to Constrain the Photon Mass with a Catalog of Fast Radio Bursts

A hypothetical photon mass, $m_\gamma$, gives an energy-dependent light speed in a Lorentz-invariant theory. Such a modification causes an additional time delay between photons of different energies when they travel through a fixed distance. Fast radio bursts (FRBs), with their short time duration and cosmological propagation distance, are excellent astrophysical objects to constrain $m_\gamma$. Here for the first time we develop a Bayesian framework to study this problem with a catalog of FRBs. Those FRBs with and without redshift measurement are both useful in this framework, and can be combined in a Bayesian way. A catalog of 21 FRBs (including 20 FRBs without redshift measurement, and one, FRB 121102, with a measured redshift $z=0.19273 \pm 0.00008$) give a combined limit $m_\gamma \leq 8.7 \times 10^{-51}\, {\rm kg}$, or equivalently $m_\gamma \leq 4.9 \times 10^{-15}\, {\rm eV}/c^2$ ($m_\gamma \leq 1.5\times10^{-50} \, {\rm kg}$, or equivalently $m_\gamma \leq 8.4 \times 10^{-15} \,{\rm eV}/c^2$) at 68% (95%) confidence level, which represents the best limit that comes purely from kinematics. The framework proposed here will be valuable when FRBs are observed daily in the future. Increment in the number of FRBs, and refinement in the knowledge about the electron distributions in the Milky Way, the host galaxies of FRBs, and the intergalactic median, will further tighten the constraint.Comment: 10 pages, 6 figures; Physical Review D, in pres

New tests of local Lorentz invariance of gravity with small-eccentricity binary pulsars

In the post-Newtonian parametrization of semi-conservative gravity theories, local Lorentz invariance (LLI) violation is characterized by two parameters, alpha_1 and alpha_2. In binary pulsars the isotropic violation of LLI in the gravitational sector leads to characteristic preferred frame effects (PFEs) in the orbital dynamics, if the barycenter of the binary is moving relative to the preferred frame with a velocity w. For small-eccentricity binaries, the effects induced by alpha_1 and alpha_2 decouple, and can therefore be tested independently. We use recent timing results of two compact pulsar-white dwarf binaries with known 3D velocity, PSRs J1012+5307 and J1738+0333, to constrain PFEs for strongly self-gravitating bodies. We derive a limit |alpha_2| < 1.8e-4 (95% CL), which is the most constraining limit for strongly self-gravitating systems up to now. Concerning alpha_1, we propose a new, robust method to constrain this parameter. Our most conservative result, alpha_1 = -0.4^{+3.7}_{-3.1} e-5 (95% CL) from PSR J1738+0333, constitutes a significant improvement compared to current most stringent limits obtained both in Solar system and binary pulsar tests. We also derive corresponding limits for alpha_1 and alpha_2 for a preferred frame that is at rest with respect to our Galaxy, and preferred frames that locally co-move with the rotation of our Galaxy. (Abridged)Comment: 34 pages, 8 figures, 2 tables; accepted by Classical and Quantum Gravit

New limits on the violation of local position invariance of gravity

Within the parameterized post-Newtonian (PPN) formalism, there could be an anisotropy of local gravity induced by an external matter distribution, even for a fully conservative metric theory of gravity. It reflects the breakdown of the local position invariance of gravity and, within the PPN formalism, is characterized by the Whitehead parameter $\xi$. We present three different kinds of observation, from the Solar system and radio pulsars, to constrain it. The most stringent limit comes from recent results on the extremely stable pulse profiles of solitary millisecond pulsars, that gives $|\hat \xi| < 3.9 \times 10^{-9}$ (95% CL), where the hat denotes the strong-field generalization of $\xi$. This limit is six orders of magnitude more constraining than the current best limit from superconducting gravimeter experiments. It can be converted into an upper limit of $\sim 4 \times 10^{-16}$ on the spatial anisotropy of the gravitational constant.Comment: 13 pages, 4 figures; accepted by Classical and Quantum Gravit

Empirical Mantissa Distributions of Pulsars

The occurrence of digits one through nine as the leftmost nonzero digit of numbers from real world sources is often not uniformly distributed, but instead, is distributed according to a logarithmic law, known as Benford's law. Here, we investigate systematically the mantissa distributions of some pulsar quantities, and find that for most quantities their first digits conform to this law. However, the barycentric period shows significant deviation from the usual distribution, but satisfies a generalized Benford's law roughly. Therefore pulsars can serve as an ideal assemblage to study the first digit distributions of real world data, and the observations can be used to constrain theoretical models of pulsar behavior.Comment: 15 pages, 7 figures, final version in journal publicatio

Lorentz violation induced vacuum birefringence and its astrophysical consequences

In the electromagnetism of loop quantum gravity, two helicities of a photon have different phase velocities and group velocities, termed as "vacuum birefringence". Two novel phenomenons, "peak doubling" and "de-polarization", are expected to appear for a linearly polarized light from astrophysical sources. We show that the criteria to observe these two phenomenons are the same. Further, from recently observed $\gamma$-ray polarization from Cygnus X-1, we obtain an upper limit $\sim 8.7\times10^{-12}$ for Lorentz-violating parameter $\chi$, which is the most firm constraint from well-known systems. We also suggest to analyze possible existence of "peak doubling" through Fermi LAT GRBs.Comment: 4 latex pages, 2 figures, short version for publication in PRD. For a detailed long version, please look at the first version of this arXiv paperarXiv:1104.4438v