# Prospects of Constraining the Dense Matter Equation of State from Timing Analysis of Pulsars in Double Neutron Star Binaries: The Cases of PSR J0737 ‒ 3039A and PSR J1757 ‒ 1854

## Abstract

**:**

## 1. Introduction

## 2. Precession in Double Neutron Star Binaries

#### Periastron Advance

## 3. Results

## 4. Summary and Conclusions

## Acknowledgments

## Conflicts of Interest

## References

- Van Straten, W.; Bailes, M.; Britton, M.; Kulkarni, S.R.; Anderson, S.B.; Manchester, R.N.; Sarkissian, J. A test of general relativity from the three-dimensional orbital geometry of a binary pulsar. Nature
**2001**, 412, 158–160. [Google Scholar] [CrossRef] [PubMed] - Deller, A.T.; Boyles, J.; Lorimer, D.R.; Kaspi, V.M.; McLaughlin, M.A.; Ransom, S.; Stairs, I.H.; Stovall, K. VLBI Astrometry of PSR J2222 − 0137: A Pulsar Distance Measured to 0.4% Accuracy. Astrophys. J.
**2013**, 770, 145. [Google Scholar] [CrossRef] - Deller, A.T.; Vigeland, S.J.; Kaplan, D.L.; Goss, W.M.; Brisken, W.F.; Chatterjee, S.; Cordes, J.M.; Janssen, G.H.; Lazio, T.J.W.; Petrov, L.; et al. Microarcsecond VLBI Pulsar Astrometry with PSRπ. I. Two Binary Millisecond Pulsars with White Dwarf Companions. Astrophys. J.
**2017**, 828, 8. [Google Scholar] [CrossRef] - Lorimer, D.; Kramer, M. Handbook of Pulsar Astronomy; Cambridge Observing Handbooks for Research Astronomers; Cambridge University Press: Cambridge, UK, 2005; pp. 32–58. [Google Scholar]
- Freire, P.C.C.; Wex, N. The orthometric parametrization of the Shapiro delay and an improved test of general relativity with binary pulsars. Mon. Not. R. Astron. Soc.
**2010**, 409, 199–212. [Google Scholar] [CrossRef] - Kramer, M.; Stairs, I.H.; Manchester, R.N. Strong-field tests of gravity with the double pulsar. Annalen der Physik
**2006**, 15, 34–42. [Google Scholar] [CrossRef] - Stairs, I. Testing General Relativity with Pulsar Timing. Living Rev. Relat.
**2003**, 6, 5. [Google Scholar] [CrossRef] [PubMed] - Kramer, M. Pulsars as probes of gravity and fundamental physics. Int. J. Mod. Phys.
**2016**, 25, 1630029–1630061. [Google Scholar] [CrossRef] - Kramer, M.; Stairs, I.H.; Manchester, R.N. Tests of General Relativity from Timing the Double Pulsar. Science
**2006**, 314, 97–102. [Google Scholar] [CrossRef] [PubMed] - Demorest, P.B.; Pennucci, T.; Ransom, S.M.; Roberts, M.S.E.; Hessels, J.W.T. A two-solar-mass neutron star measured using Shapiro delay. Nature
**2010**, 467, 1081–1083. [Google Scholar] [CrossRef] [PubMed] - Antoniadis, J.; Freire, P.C.C.; Wex, N.; Tauris, T.M.; Lynch, R.S. A Massive Pulsar in a Compact Relativistic Binary. Science
**2013**, 340, 1233232. [Google Scholar] [CrossRef] [PubMed] - Abbott, B.P. GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral. Phys. Rev. Lett.
**2017**, 119, 161101. [Google Scholar] [CrossRef] [PubMed] - Annala, E.; Gorda, T.; Kurkela, A.; Vuorinen, A. Gravitational-wave constraints on the neutron-star-matter Equation of State. arXiv
**2017**, arXiv:1711.02644. [Google Scholar] - Ayriyan, A.; Bastian, N.U.; Blaschke, D.; Grigorian, H.; Maslov, K.; Voskresensky, D.N. How robust is a third family of compact stars against pasta phase effects? arXiv
**2017**, arXiv:1711.03926. [Google Scholar] - Kurkela, A.; Romatschke, P.; Vuorinen, A. Cold quark matter. Phys. Rev. D
**2010**, 81, 105021. [Google Scholar] [CrossRef] - Perera, B.B.P.; McLaughlin, M.A.; Kramer, M.; Stairs, I.H.; Ferdman, R.D.; Freire, P.C.C.; Possenti, A.; Breton, R.P.; Manchester, R.N.; Burgay, M.; et al. The Evolution of PSR J0737 − 3039B and a Model for Relativistic Spin Precession. Astrophys. J.
**2010**, 721, 1193–1205. [Google Scholar] [CrossRef] - Cameron, A.D.; Champion, D.J.; Kramer, M.; Bailes, M.; Barr, E.D. The High Time Resolution Universe Pulsar Survey—XIII. PSR J1757 − 1854, the most accelerated binary pulsar.
**2018**, 475, L57–L61. [Google Scholar] [CrossRef] - Stovall, K.; Freire, P.C.C.; Chatterjee, S.; Demorest, P.B.; Lorimer, D.R. PALFA Discovery of a Highly Relativistic Double Neutron Star Binary. Astrophys. J.
**2018**, 231, 453. [Google Scholar] - Barker, B.M.; O’Connell, R.F. The gravitational interaction: Spin, rotation, and quantum effects—A review. Gen. Relat. Gravit.
**1979**, 11, 149–175. [Google Scholar] [CrossRef] - Perera, B.B.P.; Kim, C.; McLaughlin, M.A.; Ferdman, R.D.; Kramer, M.; Stairs, I.H.; Freire, P.C.C.; Possenti, A. Realistic Modeling of the Pulse Profile of PSR J0737 − 3039A. Astrophys J.
**2014**, 787, 51. [Google Scholar] [CrossRef] - Pol, N.; McLaughlin, M.; Kramer, M.; Stairs, I.; Perera, B.B.P.; Possenti, A. A direct measurement of sense of rotation of PSR J0737 − 3039A. Astrophys. J.
**2018**, 853, 73. [Google Scholar] [CrossRef] - Breton, R.P.; Kaspi, V.M.; Kramer, M. Relativistic Spin Precession in the Double Pulsar. Science
**2008**, 321, 104–107. [Google Scholar] [CrossRef] [PubMed] - Damour, T.; Schafer, G. Higher-order relativistic periastron advances and binary pulsars. Nuovo Cim. B
**1988**, 101, 127–176. [Google Scholar] [CrossRef] - Kopeikin, S.M. Proper Motion of Binary Pulsars as a Source of Secular Variations of Orbital Parameters. Astrophys. J.
**1996**, 467, L93. [Google Scholar] [CrossRef] - Bagchi, M. Rotational parameters of strange stars in comparison with neutron stars. New Astron.
**2010**, 15, 126–134. [Google Scholar] [CrossRef] - Ferdman, R.D.; Stairs, I.H.; Kramer, M.; Breton, R.P.; McLaughlin, M.A.; Freire, P.C.C.; Possenti, A.; Stappers, B.W.; Kaspi, V.M.; Manchester, R.N.; et al. The Double Pulsar: Evidence for Neutron Star Formation without an Iron Core-collapse Supernova. Astrophys. J.
**2013**, 767, 85. [Google Scholar] [CrossRef] - Akmal, A.; Pandharipande, V.R.; Ravenhall, D.G. Equation of state of nucleon matter and neutron star structure. Phys. Rev. C
**1998**, 58, 1804–1828. [Google Scholar] [CrossRef] - Nozawa, T.; Stergioulas, N.; Gourgoulhon, E.; Eriguchi, Y. Construction of highly accurate models of rotating neutron stars—Comparison of three different numerical schemes. Astron. Astrophys. Suppl. Ser.
**1998**, 132, 431–454. [Google Scholar] [CrossRef] - Deller, A.T.; Bailes, M.; Tingay, S.J. Implications of a VLBI Distance to the Double Pulsar J0737-3039A/B. Science
**2009**, 323, 1327–1329. [Google Scholar] [CrossRef] [PubMed] - Pathak, D.; Bagchi, M. GalDynPsr: A package to estimate dynamical contributions in the rate of change of the period of radio pulsars. arXiv
**2017**, arXiv:1712.06590. [Google Scholar] - Kramer, M.; Wex, N. TOPICAL REVIEW: The double pulsar system: A unique laboratory for gravity. Class. Quantum Gravity
**2009**, 26, 073001. [Google Scholar] [CrossRef] - Kehl, M.S.; Wex, N.; Kramer, M.; Liu, K. Future measurements of the Lense-Thirring effect in the Double Pulsar. In Proceedings of the Fourteenth Marcel Grossmann Meeting, Rome, Italy, 12–18 July 2015. [Google Scholar]
- Cordes, J.M.; Lazio, T.J.W. NE2001.I. A New Model for the Galactic Distribution of Free Electrons and its Fluctuations. arXiv
**2001**, arXiv:astro-ph/0207156. [Google Scholar] - Cordes, J.M.; Lazio, T.J.W. NE2001. II. Using Radio Propagation Data to Construct a Model for the Galactic Distribution of Free Electrons. arXiv
**2003**, arXiv:astro-ph/0301598. [Google Scholar] - Yao, J.M.; Manchester, R.N.; Wang, N. A New Electron-density Model for Estimation of Pulsar and FRB Distances. Astrophys. J.
**2017**, 835, 29. [Google Scholar] [CrossRef] - Weisberg, J.M.; Huang, Y. Relativistic measurements from timing the binary pulsar PSR B1913 + 16. Astrophys. J.
**2016**, 829, 55. [Google Scholar] [CrossRef] - Martinez, J.G.; Stovall, K.; Freire, P.C.C.; Deneva, J.S.; Jenet, F.A.; McLaughlin, M.A.; Bagchi, M.; Bates, S.D.; Ridolfi, A. Pulsar J0453+1559: A Double Neutron Star System with a Large Mass Asymmetry. Astrophys. J.
**2015**, 812, 143. [Google Scholar] [CrossRef] - Martinez, J.G.; Stovall, K.; Freire, P.C.C.; Deneva, J.S.; Tauris, T.M.; Ridolfi, A.; Wex, N.; Jenet, F.A.; McLaughlin, M.A.; Bagchi, M. Pulsar J1411+2551: A Low-mass Double Neutron Star System. Astrophys. J.
**2017**, 851, L29. [Google Scholar] [CrossRef] - Janssen, G.H.; Stappers, B.W.; Kramer, M.; Nice, D.J.; Jessner, A.; Cognard, I.M.B.; Purver, M.B. Multi-telescope timing of PSR J1518 + 4904. Astron. Astrophys.
**2008**, 490, 753–761. [Google Scholar] - Fonseca, E.; Stairs, I.H.; Thorsett, S.E. A Comprehensive Study of Relativistic Gravity Using PSR B1534 + 12. Astrophys. J.
**2014**, 787, 82. [Google Scholar] [CrossRef] - Keith, M.J.; Kramer, M.; Lyne, A.G.; Eatough, R.P.; Stairs, I.H.; Possenti, A.; Camilo, F.; Manchester, R.N. PSR J1753 − 2240: A mildly recycled pulsar in an eccentric binary system. Mon. Not. R. Astron. Soc.
**2009**, 393, 623–627. [Google Scholar] [CrossRef] - Ferdman, R.D.; Stairs, I.H.; Kramer, M.; Janssen, G.H.; Bassa, C.G.; Stappers, B.W.; Demorest, P.B.; Cognard, I.; Desvignes, G.; Theureau, G.; et al. PSR J1756 − 2251: A pulsar with a low-mass neutron star companion. Mon. Not. R. Astron. Soc.
**2014**, 443, 2183–2196. [Google Scholar] [CrossRef] [Green Version] - Lynch, R.S.; Freire, P.C.C.; Ransom, S.M.; Jacoby, B.A. The Timing of Nine Globular Cluster Pulsars. Astrophys. J.
**2012**, 745, 109. [Google Scholar] [CrossRef] - Corongiu, A.; Kramer, M.; Stappers, B.W.; Lyne, A.G.; Jessner, A.; Possenti, A.; D’Amico, N.; Löhmer, O. The binary pulsar PSR J1811 − 1736: Evidence of a low amplitude supernova kick. Astron. Astrophys.
**2007**, 462, 703–709. [Google Scholar] [CrossRef] - Hobbs, G.; Lyne, A.G.; Kramer, M.; Martin, C.E.; Jordan, C. Long-term timing observations of 374 pulsars. Mon. Not. R. Astron. Soc.
**2004**, 353, 1311–1344. [Google Scholar] [CrossRef] - Champion, D.J.; Lorimer, D.R.; McLaughlin, M.A.; Cordes, J.M.; Arzoumanian, Z.; Weisberg, J.M.; Taylor, J.H. PSR J1829 + 2456: A relativistic binary pulsar. Mon. Not. R. Astron. Soc.
**2004**, 350, L61–L65. [Google Scholar] [CrossRef] - Van Leeuwen, J.; Kasian, L.; Stairs, I.H.; Lorimer, D.R.; Camilo, F. The Binary Companion of Young, Relativistic Pulsar J1906+0746. Astrophys. J.
**2015**, 798, 118. [Google Scholar] [CrossRef] - Weisberg, J.M.; Nice, D.J.; Taylor, J.H. Timing Measurements of the Relativistic Binary Pulsar PSR B1913 + 16. Astrophys. J.
**2010**, 722, 1030–1034. [Google Scholar] [CrossRef] - Swiggum, J.K.; Rosen, R.; McLaughlin, M.A.; Lorimer, D.R.; Heatherly, S. PSR J1930 − 1852: A Pulsar in the Widest Known Orbit around Another Neutron Star. Astrophys. J.
**2015**, 805, 156. [Google Scholar] [CrossRef] - Jacoby, B.A.; Cameron, P.B.; Jenet, F.A.; Anderson, S.B.; Murty, R.N.; Kulkarni, S.R. Measurement of Orbital Decay in the Double Neutron Star Binary PSR B2127 + 11C. Astrophys. J.
**2006**, 644, L113–L116. [Google Scholar] [CrossRef] - Iorio, L. Prospects for measuring the moment of inertia of pulsar J0737-3039A. New Astron.
**2009**, 1, 40–43. [Google Scholar] [CrossRef] - O’Connell, R.F. Proposed New Test of Spin Effects in General Relativity. Phys. Rev. Lett.
**2004**, 93, 081103. [Google Scholar] [CrossRef] [PubMed] - Bejger, M.; Bulik, T.; Haensel, P. Constraints on the dense matter equation of state from the measurements of PSR J0737 − 3039A moment of inertia and PSR J0751 + 1807 mass. Mon. Not. R. Astron. Soc.
**2005**, 364, 635–639. [Google Scholar] [CrossRef] - Iorio, L. General relativistic spin-orbit and spin-spin effects on the motion of rotating particles in an external gravitational field. Gen. Relat. Gravit.
**2012**, 44, 719–736. [Google Scholar] [CrossRef] - Iorio, L. Post-Keplerian perturbations of the orbital time shift in binary pulsars: an analytical formulation with applications to the galactic center. Eur. Phys. J. C
**2017**, 77, 439. [Google Scholar] [CrossRef]

1. | |

2. | Although for the last few years, the slow pulsar of the system is not visible and is believed to be beaming away from the Earth due to its spin-precession [16]. |

3. | RNS stands for ‘Rapidly Rotating Neutron Star’, a package to calculate different properties of rotating neutron stars, freely available at http://www.gravity.phys.uwm.edu/rns/. |

**Figure 1.**Orientation of different vectors relevant for the estimation of ${\dot{\omega}}_{\mathrm{LT}a}$ where the subscript a refers to the object being observed, i.e., the pulsar (so the companion would be represented by the subscript $a+1$). The vectors are as follow: $\mathbf{k}$ is the unit vector along the orbital angular momentum, ${\mathbf{h}}_{a}$ is the unit vector along the line-of-sight and ${\mathbf{s}}_{a}$ is the unit spin vector. The angles in the figures are: i is the inclination angle between the orbit of the pulsar and the sky-plane, as well as the angle between $\mathbf{k}$ and ${\mathbf{h}}_{a}$, ${\chi}_{a}$ is the angle between $\mathbf{k}$ and ${\mathbf{s}}_{a}$ and ${\lambda}_{a}$ is the angle between ${\mathbf{h}}_{a}$ and ${\mathbf{s}}_{a}$. The left and right panels are for ${\chi}_{a}<i$ and ${\chi}_{a}>i$, respectively. In both panels, two positions of ${\mathbf{s}}_{a}$ are shown corresponding to maximum and minimum values of ${\lambda}_{a}$ (see the text). The pulsar, i.e., the object a, is located at the vertex of the fiducial cone (gray in color) made by the precessing ${\mathbf{s}}_{a}$ around $\mathbf{k}$.

**Figure 2.**Variation of ${\dot{\omega}}_{{\mathrm{LT}}_{p}}$ with ${\chi}_{p}$ (in degrees) along the horizontal axis and ${\lambda}_{p}$ (in degrees) along the vertical axis for PSR J1757 − 1854. The color code represents values of ${\dot{\omega}}_{{\mathrm{LT}}_{p}}$ in $\mathrm{deg}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{y}}^{-1}$.

**Table 1.**Relevant observed parameters for known pulsars in DNSs. See the references for these parameters with more significant digits and uncertainties. The timing model (e.g., DDGR) is mentioned when more than one timing solution is available in the original reference.

DNS | Masses | e | ${\mathit{P}}_{\mathbf{b}}$ | $sin\mathit{i}$ | ${\mathit{P}}_{\mathit{s}1}$ | $\dot{\mathit{\omega}}$ | ${\mathit{\chi}}_{\mathit{p}}$ | Refs. |
---|---|---|---|---|---|---|---|---|

${\mathbf{M}}_{\odot}$ | Days | ms | $\phantom{\rule{3.33333pt}{0ex}}\mathbf{deg}\phantom{\rule{3.33333pt}{0ex}}{\mathbf{y}}^{-1}$ | deg | ||||

J0453+1559 | 1.559 | 0.11251832 | 4.072468588 | 0.9671343 | 45.781816163093 | 0.0379412 | − | R1 |

(DDGR) | 1.174 | |||||||

J0737−3039A | $1.3381$ | 0.0877775 | 0.10225156248 | 0.99974 | 22.70 | 16.89947 | $<6.1\phantom{\rule{3.33333pt}{0ex}}\mathrm{or}\phantom{\rule{3.33333pt}{0ex}}<2.3$ | R2, R${\chi}_{1}$ |

J0737−3039B | $1.2489$ | 2773.46 | 138 | |||||

J1411+2551 | $\le 1.62$ | 0.1699308 | 2.61585677939 | − | 62.452895517590 | 0.0768 | − | R3 |

$\ge 0.92$ | ||||||||

J1518+4904 | $\le 1.17$ | 0.24948451 | 8.6340050964 | $\le 0.73$ | 40.934988908 | 0.0113725 | − | R4 |

$\ge 1.55$ | ||||||||

B1534+12 | $1.3455$ | 0.27367740 | 0.420737298881 | 0.97496 | 37.9044411783 | 1.755795 | $27.0\pm 3.0$ | R5 |

(DDGR) | $1.3330$ | $153.0\pm 3.0$ | ||||||

J1753−2240 ^{†} | − | 0.303582 | 13.6375668 | − | 95.1378086771 | − | − | R6 |

$\ge 0.4875$ | ||||||||

J1756−2251 | 1.341 | 0.1805694 | 0.31963390143 | 0.93 | 28.4615890259983 | 2.58240 | $<5.9$ | R7 |

1.230 | ($1\sigma $ value) | |||||||

J1757−1854 | 1.3384 | 0.6058142 | 0.18353783587 | 0.9945 | 21.497231890027 | 10.3651 | $\sim 25$ | R8 |

1.3946 | (theoretical) | |||||||

J1807−2500B ^{†} | 1.3655 | 0.747033198 | 9.9566681588 | 0.9956 | 4.18617720284089 | 0.0183389 | − | R9 |

$({g}_{1})$ | 1.2064 | |||||||

J1811−1736 | $\le 1.64$ | 0.828011 | 18.7791691 | − | 104.1819547968 | 0.0090 | − | R10 |

$\ge 0.93$ | ||||||||

B1820−11 ^{†} | − | 0.794608 | 357.76199 | − | 279.828696565349 | 0.00007 | − | R11 |

J1829+2456 | $\le 1.38$ | 0.13914 | 1.176028 | − | 41.00982358 | 0.28 | − | R12 |

$\ge 1.22$ | ||||||||

J1906+0746 | 1.291 | 0.0852996 | 0.16599304686 | 0.690882411 | 144.07315538 | 7.5844 | ${110}_{-55}^{+21}$ | R13 |

(DDGR) | 1.322 | |||||||

B1913+16 | $1.4398$ | 0.6171334 | 0.322997448911 | 0.68 ^{‡} | 59.03000322 | 4.226598 | 22 | R14, R_{χ1} |

$1.3886$ | ||||||||

J1930−1852 | $\le 1.32$ | 0.39886340 | 45.0600007 | − | 185.52016047926 | 0.00078 | − | R15 |

$\ge 1.30$ | ||||||||

J1946+2052 | − | 0.063848 | 0.07848804 | − | 16.9601753230 | 25.6 | − | R16 |

B2127+11C | 1.358 | 0.681395 | 0.33528204828 | − | 30.52929614864 | 4.4644 | − | R17 |

$({g}_{2})$ | 1.354 |

^{†}Candidate DNS;

^{‡}was never published, but here, I quote the value used byWeisberg & Huang [36]; pulsars denoted with g are in globular clusters; g

_{1}is in NGC 6544, and g

_{2}is in M15; References: R1: Martinez et al. [37], R2: Kramer et al. [9], R3: Martinez et al. [38], R4: Janssen et al. [39], R5: Fonseca, Stairs, Thorsett [40], R6: Keith et al. [41], R7: Ferdman et al. [42], R8: Cameron et al. [17], R9: Lynch et al. [43], R10 Corongiu et al. [44], R11: Hobbs et al. [45], R12: Champion et al. [46], R13: van Leeuwen et al. [47], R14: Weisberg, Nice, & Taylor [48], R15: Swiggum et al. [49], R16: Stovall et al. [18], R17: Jacoby et al. [50], R

_{χ1}(for χ

_{p}): Perera et al. [20].

**Table 2.**Values of ${\dot{\omega}}_{{\mathrm{PN}}_{p}}$, ${\dot{\omega}}_{{\mathrm{LT}}_{p},\phantom{\rule{3.33333pt}{0ex}}\parallel}$ and ${\dot{\omega}}_{{\mathrm{LT}}_{p},\phantom{\rule{3.33333pt}{0ex}}max}$ for known pulsars in DNSs using ${I}_{p}=1.26\times {10}^{45}\phantom{\rule{3.33333pt}{0ex}}\mathrm{gm}\phantom{\rule{3.33333pt}{0ex}}{\mathrm{cm}}^{2}$ and neglecting the Lense-Thirring effect of the companion. To show the difference between ${\dot{\omega}}_{{\mathrm{LT}}_{p},\parallel}$ and ${\dot{\omega}}_{{\mathrm{LT}}_{p},\phantom{\rule{3.33333pt}{0ex}}max}$, I keep values up to five decimal places even for the cases where $sini$ is known with less accuracy.

DNS | ${\dot{\mathit{\omega}}}_{{\mathbf{PN}}_{\mathit{p}}}$ | ${\dot{\mathit{\omega}}}_{{\mathbf{LT}}_{\mathit{p}},\phantom{\rule{3.33333pt}{0ex}}\parallel}$ | ${\dot{\mathit{\omega}}}_{{\mathbf{LT}}_{\mathit{p}},\phantom{\rule{3.33333pt}{0ex}}\mathit{max}}$ |
---|---|---|---|

$(\mathbf{deg}\phantom{\rule{3.33333pt}{0ex}}{\mathbf{y}}^{-1})$ | $(\mathbf{deg}\phantom{\rule{3.33333pt}{0ex}}{\mathbf{y}}^{-1})$ | $(\mathbf{deg}\phantom{\rule{3.33333pt}{0ex}}{\mathbf{y}}^{-1})$ | |

J0453+1559 | 0.03794 | $-1.30190\times {10}^{-7}$ | $-1.31310\times {10}^{-7}$ |

J0737−3039A | 16.90312 | $-4.74458\times {10}^{-4}$ | $-4.74489\times {10}^{-4}$ |

J1411+2551 | 0.07681 | $-2.32510\times {10}^{-7}$ | − |

J1518+4904 | 0.01138 | $-4.48005\times {10}^{-8}$ | − |

B1534+12 | 1.75533 | $-1.84880\times {10}^{-5}$ | $-1.86078\times {10}^{-5}$ |

J1753−2240 | − | − | − |

J1756−2251 | 2.58363 | $-4.01930\times {10}^{-5}$ | $-4.09703\times {10}^{-5}$ |

J1757−1854 | 10.36772 | $-3.02752\times {10}^{-4}$ | $-3.03170\times {10}^{-4}$ |

J1807−2500B | 0.01834 | $-8.98082\times {10}^{-7}$ | $-8.99076\times {10}^{-7}$ |

J1811−1736 | 0.00895 | $-1.45038\times {10}^{-8}$ | − |

B1820−11 | − | − | − |

J1829+2456 | 0.29284 | $-1.96704\times {10}^{-6}$ | − |

J1906+0746 | 7.58528 | $-2.91884\times {10}^{-5}$ | $-3.29423\times {10}^{-5}$ |

B1913+16 | 4.22760 | $-3.43984\times {10}^{-5}$ | $-3.90790\times {10}^{-5}$ |

J1930−1852 | 0.00079 | $-3.86975\times {10}^{-10}$ | − |

J1946+2052 | − | − | − |

B2127+11C | 4.46458 | $-8.11241\times {10}^{-5}$ | − |

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Bagchi, M.
Prospects of Constraining the Dense Matter Equation of State from Timing Analysis of Pulsars in Double Neutron Star Binaries: The Cases of PSR J0737 ‒ 3039A and PSR J1757 ‒ 1854. *Universe* **2018**, *4*, 36.
https://doi.org/10.3390/universe4020036

**AMA Style**

Bagchi M.
Prospects of Constraining the Dense Matter Equation of State from Timing Analysis of Pulsars in Double Neutron Star Binaries: The Cases of PSR J0737 ‒ 3039A and PSR J1757 ‒ 1854. *Universe*. 2018; 4(2):36.
https://doi.org/10.3390/universe4020036

**Chicago/Turabian Style**

Bagchi, Manjari.
2018. "Prospects of Constraining the Dense Matter Equation of State from Timing Analysis of Pulsars in Double Neutron Star Binaries: The Cases of PSR J0737 ‒ 3039A and PSR J1757 ‒ 1854" *Universe* 4, no. 2: 36.
https://doi.org/10.3390/universe4020036