Does the Mass-Gap Hint at the Existence of New Types Compact Objects?

Ramen Kumar Parui *

ARC, Room No-F101, Block-F, Mall Enclave, 13, K. B. Sarani, Kolkata-700080, India.

*Author to whom correspondence should be addressed.


The discovery of gravitational waves (GW) from the coalescence binary system reduces the mass-gap to (2.6 – 5) M . Hypothetical stars such as the super-Chandrasekhar mass white dwarf, quark star, boson star, electro weak star, grav-star, dark matter star , supermassive neutron star, etc may exist between neutron star (NS) and black hole (BH) within this range. Comparing the observed results with numerical calculations this author suggests the detected unseen companion compact object with mass 3.3 M in the binary J05215658 + 4359220 is a triaxially deformed quark star (or triaxial star). If this is correct, then the mass gap will again reduce from (2.6–5) M to (3.3 – 5) M. Application of the solutions of the Vaidya-Tikekar Ansatz in modeling Einstein’s general relativity hints that the maximum mass of a compact object ~ 4.178 M (i.e., four times the solar mass) in realistic case. This author proposes that compact objects with higher masses are possible in a triaxially deformed compact state. As the lighter dark matter is five times more massive than the baryonic matter it is also suggested that further higher mass is possible when the compact object is triaxially deformed, consisting of lighter dark matter or unknown matter whose nature or form is not yet known to us. As the detection of gravitational waves can be a convenient method to collect evidence of quark stars (e.g. strange quark stars) or dark matter admixed with normal matter neutron stars we encourage the GW community to search for their electromagnetic counterparts during their observation of compact objects through LIGO or VIRGO.

Keywords: Mass-gap, compact object, neutron star, gravitational wave

How to Cite

Parui , R. K. (2023). Does the Mass-Gap Hint at the Existence of New Types Compact Objects?. International Astronomy and Astrophysics Research Journal, 5(1), 102–114. Retrieved from


Download data is not yet available.


Einstein A. Sitzungsber. Preuss Acad Wiss. 1916;1:688.

Einstein A. Die Grundlage der allgemeinen Relativitätstheorie. Ann Phys. 1916;354(7):769-822.

Pandharipande VR, Pines D, Smith RA. Neutron star structure: Theory, observation, and speculation. Astrophys J. 1976;208:550.

Schwarzschild K, der Kniglich S. Preussischen Academie der Wissenschaften zu Berlin, Phys Math, Klasse. 1916;424:1.

Chandrasekhar S. The maximum mass of an ideal white dwarf. Astrophys J. 1931;74:81.

Farr WM, Sravan N, Cantrell A, Kreidberg L, Bailyn CD, Mandel I. et al. The mass distribution of stellar-mass blackholes. Astrophys J. 2011;741(2):103.

California institute of tech. Sci Daily; 2020.

Ӧzel F, Paltis D, Narayan R, McClintock JE. The Blackhole mass distribution in the Galaxy. Astrophys J. 2010;751:1918.

Abbott BP, Abbott R, Abbott TD, Abraham S, Acernese F, Ackley K, et al. Binary Black Hole population properties inferred from the first and second observing runs of advanced LIGO and advanced Virgo. Astrophys J. 2019;882(2):L24.

Kreidberg L, Bailyn CD, Farr WM, Kalogera V. Mass Measurements of Black Holes in x-ray transients: is there a mass gap? Astrophys J. 2012;757(1):36.

Abbott R, Abbott TD, Abraham S, Acernese F, Ackley K, Adams C et al. GW190814: gravitational waves from the coalescence of a 23 M⊙ Black Hole with a 2.6 M⊙ compact object. Astrophys J Lett. 2020;896:L44.

Thompson TA, Kochanek CS, Stanek KZ, Badenes C, Post RS, Jayasinghe T. et al. A noninteracting low-mass black hole-giant star binary system. Science. 2019;366(6465):637-40.

Zwicky F. On collapsed neutron stars. Astrophys J. 1938;88:522.

Zwicky F. On the theory and observation of highly collapsed stars. Phys Rev. 1939;55(8):726-43.

Srinivasan G. The maximum mass of neutron stars. Astron Astrophys Rev. 2002;11(1):67-96.

Oppenheimer JR, Volkoff GM. On massive neutron core Phys. Rev. 1939;55:374.

Cameron AGW. Neutron star models. Astrophys J. 1959;130:884.

Chamel N, Haensel P, Zdunik JL, Fantina AF. On the maximum mass of neutron stars. Int J Mod Phys E. 2013; 22(7):130018.

Antoniadis J, Freire PCC. et al. A massive pulsar in a compact relativistic binary science. 2013;340:448.

Cromartie HT, Fonseca E, Ransom SM, Demorest PB, Arzoumanian Z, Blumer H. et al. Relativistic Shapiro delay measurements of an extremely massive millisecond pulsar. Nat Astron. 2020;4(1):72-6.

Shao D-S, Tang S-P, Jiang J, Fan Y. Maximum mass cutoff in the neutron star mass distribution and the prospect of forming supramassive objects in the double neutron star mergers. Phys Rev D. 2020;102(6):063006.

Hughes SA. Trust but verify: the Case for astrophysical black holes. 2006;L006.

Kulkarni SR. Lecture Notes- ”How to find stellar Black-holes”; 2019.

Stairs IH. Pulsars in binary systems: probing binary stellar evolution and general relativity. Science. 2004;304(5670):547-52.

McClintock JE, Remilland RE. Compact stellar X-ray Sources. UK: Cambridge University Press; 2006.

Hu H, Bao S, Zhang Y. et al. PTEP. 2020;2020:043001.

Thorsett SE, Chakrabarty D. Neutron star mass measurements. I. Radio Pulsars. Astrophys J. 1999;512(1):288-99.

Kaper L, van der Meer A et al. Measuring the masses of Neutron Stars. Messenger. 2006;126:27.

Clark JS, Goodwin SP, Crowther PA, Kaper L, Fairbairn M, Langer N et al. Physical parameters of the high-mass X-ray binary 4U1700-37. Astron Astro Phys. 2002;392(3):909-20.

Doroshenko V, Suleimanov V, Pühlhofer G, Santangelo A. A strangely light neutron star within a supernova remnant. Nat Astron. October 24 2022;6(12):1444-51.

Suwa Y, Yoshida TY, Shibata M, Umeda H, Takahashi K. On the minimum mass of neutron stars. MNRAS. 2018;481(3): 3305-12.

Espino PL, Paschalidis V, Baumgarte TW, Stuart TW, Shapiro L. Dynamical stability of quasi-toroidal differentially rotating neutron stars. Phys Rev D. 2019;99: 083017.

Wei H, Yu Zh X. Inverse chameleon mechanism and mass limits for compact stars JCAP. 2021;2108:011.

Kalita S, Mukhopadhyay B, Govindarajan TR. Super-Chandrasekhar limiting mass white dwarfs as emergent phenomena of noncommutative squashed fuzzy spheres. Int J Mod Phys D. 2021;30(5):2150034.

Chavanis P-H, Harko T. Bose-Einstein Condensate general relativistic stars. Phys Rev D. 2012;86(6):064011.

Eslam-Panah B, Bordbar G. et al. Expansion of magnetic neutron stars in an energy (in)dependent spacetime. Astrophys J. 2017;848:24.

Giacosa F, Pagliara G. Neutron stars in the large-NC limit. Nucl Phys A. 2017;968:366-78.

Pandharipande VR, Pines D, Smith RA. Neutron star structure: theory, observation, and speculation. Astrophys J. 1976;208:550-66.

Shapiro SL, Teukolsky SA. Black holes, Whitedwarfs and Neutron stars: The Physics of Compact Objects. NY: John Wiley; 1983.

Elebert P, Reynolds MT, Callanan PJ, Hurley DJ, Ramsay G, Lewis F. et al. Optical spectroscopy and photometry of SAX J1808.4-3658 in outburst. MNRAS. 2009;395(2):884-94.

Abubekerov MK, Antokhina EA, Cherepashchuk AM, Shimanskii VV. The mass of the compact object in the X-ray binary her X-1/HZ her. Astron Rep. 2008;52(5):379-89.

Rawls MR, Orosz JA, McClintock JE, Torres MAP, Bailyn CD, Buxton MM. Refined neutron star mass determinations for six eclipsing X-ray pulsar binaries. Astrophys J. 2011;730:25.

Demorest PB, Pennucci T, Ransom SM, Roberts MS, Hessels JW. Shapiro delay measurement of a two solar mass neutron star. Nature. 2010;467(7319):1081-3.

Hansraj S, Govender M, Moodly L, Singh KN. Strange stars in the framework of higher curvature gravity. Phys Rev D. 2022;105(4):044030.

Thakore B, Goti R, Shah S, Pandya H, Pandya DM. Finch-Skea solutions of anisotropic stellar models in f(R) gravity. Astrophys Space Sci. 2021;366:95.

Horvath JE, Moraes PHRS. Modeling a 2.5M⊙ compact star with quark matter. Int J Mod Phys D. 2021;30(3):2150016.

Sharma R, Das S, Govender M, Pandya DM. Revisiting Vaidya-Tikekar stellar model in the linear regime. Ann Phys. 2020;414:168079.

Gondek-Rosińska D, Haensel P, Zdunik JL, Gourgoulhon E. Rapidly rotating strange stars. International Astronomical Union Colloquium. Proceedings of the IAU colloq. 2000;177: Pulsar Astronomy- and Beyond:661-2.

Szkudlarek M, Gondek-Rosińska D, Villain L, Ansorg M. Maximum mass of differentially rotating strange quark stars. Astrophys J. 2019;879(1):44.

Bodmer AR. Collapsed nuclei. Phys Rev D. 1971;4(6):1601-6. doi: 10.1103/PhysRevD.4.1601.

Witten E. Cosmic separation of phases. Phys Rev D. 1984;30(2):272-85.

Lai XY, Yu YW, Zhou EP, Li Y, Wu RX. Pulsar glitches in a strangeon star model. Res. J Astrophys Astron. 2018;18:24.

Dai ZG, Wang SQ, Wang JS, Wang LJ, Yu YW. The most luminous supernova ASASSN-15LH. Astrophys J. 2016;817:132.

Lai XY, Xu RX. Lennard-Jones quark matter and massive quark stars. MNRAS. 2009;398(1):L31-5.

Zhou E, Tsokaros A, Rezzolla L, Xu R, Uryū K. Uniformly rotating, axisymmetric, and triaxial quark stars in general relativity. Phys Rev D. 2018;97(2):23013.

Dai ZG, Wang SQ, Wang JS, Wang LJ, Yu YW. The most luminous supernova ASASSN-15LH. Astrophys J. 2016; 817:132:(4).

Parui RK. Evidence of a ”triaxial star”. In: Binary system, submitted to EPJ C; 2022.

Thompson TA, Kochanek CS, Stanek KZ, Badenes C, Post RS, Jayasinghe T et al. A noninteracting low-mass black hole-giant star binary system. Science. 2019;366(6465):637-40.. van den Heuvel EPJ, Tauris TM. Comment on “A noninteracting low-mass black hole-giant star binary system”. Science. 2020; 368(6491):id. eaba3282.

Vaidya PC, Tikekar R. Exact relativistic model for a superdense star. J Astrophys Astron. 1982;3(3):325-34.

Sasidharan AS, Sabu MC. General Solution to VAIDYA-Tikekar METRIC with Charged Distributions on Spheroidal Space time. Int J Maths Trends Tech. 2021;67:15.

Ozel F, Guver T, Psaltiz D. The Mass and radius of neutron star in the buldge low mass X-ray Binary KS 1731-260. Astrophys J. 2009;693:1775-9.

Murad MH, Fatema S. Some exact static charged perfect fluid spheres and relativistic compact Electrically charged stellar models in General Relativity. Eur Phys J C. 2015;75(11):533.

Dong SB, Shappee BJ, Prieto JL, Jha SW, Stanek KZ, Holoien TW. et al. Astronomy. ASASSN-15lh: A highly super-luminous supernova. Science. 2016;351(6270):257-60.

Jotania K, Tikekar R. On relativistic models of strange stars. Int J Mod Phys D. 2006;15(8):1175-82.

Ianni A, Mannarelli M, Rossi N. A new approach to dark matter from the mass–radius diagram of the Universe. Results Phys. 2022;38:105544.

Tulin S, Yu H-B. Dark matter self-interactions and small scale structure. Phys Rep. 2018;730:1-57.

Wang XD, Qi B, Yang GL, Zhang NB, Wang SY. Possible maximum mass of dark matter existing in compact stars based on the self-interacting fermionic model. Int J Mod Phys D. 2019;28(11):1950148.

Sagun V, Giangrandi E, Ivanytski O, Lopes I, Bugaev K-A, Bugaev K. Constraints on the fermionic dark matter from observations of neutron stars. In: Proceedings of the PANIC. 2021;313.

Mukhopadhyay S, Atta D, Basu DN. Gravitational waves from isolated neutron stars: Mass dependence of -mode instability. JPS Conference Proceedings. 2020;32:010073.

Zurek KM. Asymmetric dark matter: theories, signatures, and constraints. Phys Rep. 2013;537:91.

Leung K-L, Chu M-C, Lin L-M. Tidal deformability of dark matter admixed neutron stars. Phys Rev D. 2022;105(12):123010.

Kumar N, Sokolov VV. Mass distribution and ”Mass Gap” of compact stellar remnants in binary systems. Astrophys Bull. 2022;77(2):197-213.

Panotopoulos G, Rincón Á. Electrically charged strange quark stars with a non-linear equation of state. Eur Phys J C. 2019;79(6):524.

Pant N, Pradhan N, Murad MH. A family of exact solutions of Einstein-Maxwell field equations in isotropic coordiantes: An application to optimization of quark star mass. Astrophys Space Sci. 2014; 352(1):135-41.

Dong H, Kuo TTS, Lee H. K, Machleidt R, Rho M. Half Skyrmions and the equation of state for compact star matter. Phys Rev C. 2013;87:054332.

Godzieba DA, Radice D, Bernuzzi S. On the maximum mass of neutron stars and GW190814. Astrophys J. 2021;908(2):122. doi: 10.3847/1538-4357/abd4dd.

Khadkikar S, Mangat CS, Banik S. Quasi-stationary sequences of hypermassive neutron stars with exotic equation of state. J Astrophys Astron. 2022;43(2):57. doi: 10.1007/s12036-022-09849-0.

Rather IA, Rahaman U, Dexheimer V, Usmani AA, Patra SK. Heavy magnetic neutron stars. Astrophys J. 2021;77 : 917.

Alaverdyan GB, Vartanyan YL. Maximum mass of hybrid stars in the quark bag model. Astrophysics. 2017;60(4):563-71.

Mariani M, Orsaria M, Vucetich H. Constant Hybrid Stars: a first approximation of cooling evolution. Astron Astro Phys. 2017;601:A21.

Blaschke D, Cierniak M. Studying the onset of deconfinement with mul-messenger astronomy of neutron stars. Astron Nachr. 2021;342:13909.

Papakonstantinou P, Hyun CH. Energy density modeling of strongly interacting matter: atomic Nuclei and Dense star. Symmetry. 2023;15(3):683.

Chu PC, Zhou Y, Jiang Y-Y, Ma H-Y, Liu H, Zhang X-M et al. Quark star matter in heavy quark stars. Eur Phys J C. 2021;81(1):93.

Dondi NA, Drago A, Pagliara G. Conditions for the Co-existence of stable strange quark matter. EPJ Web Conference Series. XIIth Quark Confinement and the Hadron Spectrum. 2017;137:09004.

Van Kerkwijik BR, Kulkarni SR. Evidence for a Massive Neutron Star from a Radial-velocity study of the companion to the Black Widow Pulsar B1957+20. Astrophys J. 2011;728:95.

Parui RK. A remark on ”do triaxial supermassive compact star exist?” Int. Astron. Astrophys. Res J. 2023;5:33.

Parui RK. A new compact star—the ”triaxial star”—and the detection of a cosmic baby: A possibility. Int Astron Astrophys Res J. 2023;5:38.

Zevin M, Spera M, Berry CPL, Kalogera V. Exploring the lower mass-gap and unequal mass regime in compact Binary evolution. Astrophys J. 2020; 899(1):L1.

Abbott R, Abbott TD, Abbott S, Abraha F, Acernese K, Ackley A et al. Observation of gravitational waves from two neutron star–Black Hole coalescences. Astrophys J Lett. 2021;915:L5.

Mallick R, Singh S, Nandi R. Maximum mass of hybrid stars formed via shock induced phase transition in cold neutron stars. MNRAS. 2021;503(4): 4829-37.

Liu H, Yang Y-H, Han Y, Chu P-C. properties of quark matter and hybrid stars from a quasiparticle model. Arxiv: 2305.01246v.i [nucl-th]; 2023.

Sotani H, Harada T. Nonradial oscillations of quark stars. Phys Rev D. 2003; 68(2):024019.

Sotani H, Kohri K, Harada T. Restricting quark matter models by gravitational wave observation. Phys Rev D. 2004;69(8): 084008.