The detection of the gravitational-wave is a novel way to explore the universe. Along with increasing sensitivity of the detectors, it is possible that LIGO/VIRGO/KAGRA will observe more compact stars in the future. The compact stars include black holes, neutron stars, exotic stars etc. More and more gravitational-wave events can help people to figure out the properties of compact stars. In this thesis, we try to search the dark stars from the O1/O2 events, and performed the parameter estimation with tidal signature. When the properties of the one source is similar with the black hole, but it has the tidal deformability and match the dark matter EoSs. We can suppose this source that could be a dark star. However, we compare the tidal/non-tidal Bayes factor for the gravitational-wave events, only GW170817 has the tidal deformability. In addition, we propose three scenarios of the compact hybrid stars, and explore their M-R and M-Λ relations. We try to explain this GW190425 event through three scenarios of the hybrid stars. We find the free parameter region of the hybrid stars through the inference results of GW190425.

[1] Albert Einstein. Zur allgemeinen relativitätstheorie. Akademie der Wissenschaften, in Kommission bei W. de Gruyter, 1915.

[2] A Einstein. Näherungsweise integration der feldgleichungen der gravitation, 22 jun 1916. 1916.

[3] John Archibald Wheeler and Kenneth Ford. Geons, black holes and
quantum foam: a life in physics, 2000.

[4] Robert J Lambourne. Relativity, gravitation and cosmology. Cambridge University Press, 2010.

[5] Ta-Pei Cheng. Relativity, gravitation and cosmology: a basic introduction, volume 11. Oxford University Press, 2009.

[6] Bangalore Suryanarayana Sathyaprakash and Bernard F Schutz. Physics, astrophysics and cosmology with gravitational waves. Living reviews in relativity, 12(1):2, 2009.

[7] Michele Vallisneri, Jonah Kanner, Roy Williams, Alan Weinstein, and Branson Stephens. The LIGO open science center. Journal of Physics: Conference Series, 610:012021, may 2015.

[8] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett., 116:061102, Feb 2016.

[9] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Binary black hole mergers in the first advanced ligo observing run. Phys. Rev. X, 6:041015, Oct 2016.

[10] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Gw170817: Observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett., 119:161101, Oct 2017.

[11] A. von Kienlin, C. Meegan, and A. Goldstein. GRB 170817A: Fermi GBM detection. GRB Coordinates Network, 21520:1, Jan 2017.

[12] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Gwtc-1: A gravitational-wave transient catalog of compact binary mergers observed by ligo and virgo during the first and second observing runs. Phys. Rev. X, 9:031040, Sep 2019.

[13] Bruce Allen, Warren G. Anderson, Patrick R. Brady, Duncan A. Brown, and Jolien D. E. Creighton. Findchirp: An algorithm for detection of gravitational waves from inspiraling compact binaries. Phys. Rev. D, 85:122006, Jun 2012.

[14] Alexander H Nitz. Distinguishing short duration noise transients in ligo data to improve the pycbc search for gravitational waves from high mass binary black hole mergers. Classical and Quantum Gravity, 35(3):035016, 2018.

[15] C. M. Biwer et al. Pycbc inference: A python-based parameter estimation toolkit for compact binary coalescence signals. Publications of the Astronomical Society of the Pacific, 131(996):024503, 2019.

[16] Alessandra Buonanno, Bala R. Iyer, Evan Ochsner, Yi Pan, and B. S. Sathyaprakash. Comparison of post-newtonian templates for compact binary inspiral signals in gravitational-wave detectors. Phys. Rev. D, 80:084043, Oct 2009.

[17] Sascha Husa, Sebastian Khan, Mark Hannam, Michael Pürrer, Frank Ohme, Xisco Jiménez Forteza, and Alejandro Bohé. Frequency-domain gravitational waves from nonprecessing black-hole binaries. i. new numerical waveforms and anatomy of the signal. Phys. Rev. D, 93:044006, Feb 2016.

[18] Sebastian Khan, Sascha Husa, Mark Hannam, Frank Ohme, Michael Pürrer, Xisco Jiménez Forteza, and Alejandro Bohé. Frequency-domain gravitational waves from nonprecessing black-hole binaries. ii. a phenomenological model for the advanced detector era. Phys. Rev. D, 93:044007, Feb 2016.

[19] Alessandra Buonanno and Thibault Damour. Effective one-body approach to general relativistic two-body dynamics. Physical Review D, 59(8):084006, 1999.

[20] Yi Pan, Alessandra Buonanno, Michael Boyle, Luisa T Buchman, Lawrence E Kidder, Harald P Pfeiffer, and Mark A Scheel. Inspiral-merger-ringdown multipolar waveforms of nonspinning black-hole binaries using the effective-one-body formalism. Physical Review D, 84(12):124052, 2011.

[21] Alessandro Nagar, Sebastiano Bernuzzi, Walter Del Pozzo, Gunnar Riemenschneider, Sarp Akcay, Gregorio Carullo, Philipp Fleig, Stanislav Babak, Ka Wa Tsang, Marta Colleoni, et al. Time-domain effective-one-body gravitational waveforms for coalescing compact binaries with nonprecessing spins, tides, and self-spin effects. Physical Review D, 98(10):104052, 2018.

[22] BP Abbott, R Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, VB Adya, et al. Gw170817: Measurements of neutron star radii and equation of state. Physical review letters, 121(16):161101, 2018.

[23] Sergey Postnikov, Madappa Prakash, and James M Lattimer. Tidal love numbers of neutron and self-bound quark stars. Physical Review D, 82(2):024016, 2010.

[24] Monica Colpi, Stuart L. Shapiro, and Ira Wasserman. Boson stars: Gravitational equilibria of self-interacting scalar fields. Phys. Rev. Lett., 57:2485–2488, Nov 1986.

[25] Andrea Maselli, Pantelis Pnigouras, Niklas Grønlund Nielsen, Chris Kouvaris, and Kostas D Kokkotas. Dark stars: gravitational and electromagnetic observables. Physical Review D, 96(2):023005, 2017.

[26] J Mark Heinzle, Niklas Rohr, and Claes Uggla. Spherically symmetric relativistic stellar structures. arXiv preprint gr-qc/0304012, 2003.

[27] Tanja Hinderer. Tidal love numbers of neutron stars. The Astrophysical Journal, 677(2):1216, 2008.

[28] Kilar Zhang, Takayuki Hirayama, Ling-Wei Luo, and Feng-Li Lin. Compact star of holographic nuclear matter and gw170817. Physics Letters B, 801:135176, 2020.

[29] Tejaswi Venumadhav, Barak Zackay, Javier Roulet, Liang Dai, and Matias Zaldarriaga. New binary black hole mergers in the second observing run of advanced ligo and advanced virgo. Phys. Rev. D, 101:083030, Apr 2020.

[30] Benjamin P Abbott, R Abbott, TD Abbott, MR Abernathy, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, et al. Gw151226: observation of gravitational waves from a 22-solar-mass binary black hole coalescence. Physical review letters, 116(24):241103, 2016.

[31] LIGO Scientific, BP Abbott, R Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, RX Adhikari, et al. Gw170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Physical Review Letters, 118(22):221101, 2017.

[32] Benjamin P Abbott, Richard Abbott, TD Abbott, F Acernese, K Ackley, C Adams, T Adams, P Addesso, Rana X Adhikari, VB Adya, et al. Gw170814: a three-detector observation of gravitational waves from a binary black hole coalescence. Physical review letters, 119(14):141101, 2017.

[33] Vitor Cardoso and Paolo Pani. Testing the nature of dark compact objects: a status report. Living Reviews in Relativity, 22(1):1–104, 2019.

[34] Taylor Binnington and Eric Poisson. Relativistic theory of tidal love numbers. Physical Review D, 80(8):084018, 2009.

[35] Thibault Damour and Alessandro Nagar. Relativistic tidal properties of neutron stars. Physical Review D, 80(8):084035, 2009.

[36] Éanna É Flanagan and Tanja Hinderer. Constraining neutron-star tidal love numbers with gravitational-wave detectors. Physical Review D, 77(2):021502, 2008.

[37] B. P. Abbott et al. (LIGO Scientific Collaboration and Virgo Collaboration). Properties of the binary neutron star merger gw170817. Phys. Rev. X, 9:011001, Jan 2019.

[38] Nelson Christensen and Renate Meyer. Using markov chain monte carlo methods for estimating parameters with gravitational radiation data. Phys. Rev. D, 64:022001, May 2001.

[39] Walter R Gilks, Sylvia Richardson, and David Spiegelhalter. Markov chain Monte Carlo in practice. Chapman and Hall/CRC, 1995.

[40] Nelson Christensen, Renate Meyer, and Adam Libson. A metropolis–hastings routine for estimating parameters from compact binary inspiral events with laser interferometric gravitational radiation data. Classical and Quantum Gravity, 21(1):317, 2003.

[41] D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman. emcee: The mcmc hammer. PASP, 125:306–312, 2013.

[42] Tim Dietrich, Sebastiano Bernuzzi, and Wolfgang Tichy. Closed-form tidal approximants for binary neutron star gravitational waveforms constructed from high-resolution numerical relativity simulations. Physical Review D, 96(12):121501, 2017.

[43] Samantha A Usman, Alexander H Nitz, Ian W Harry, Christopher M Biwer, Duncan A Brown, Miriam Cabero, Collin D Capano, Tito Dal Canton, Thomas Dent, Stephen Fairhurst, et al. The pycbc search for gravitational waves from compact binary coalescence. Classical and Quantum Gravity, 33(21):215004, 2016.

[44] Surabhi Sachdev, Sarah Caudill, Heather Fong, Rico KL Lo, Cody Messick, Debnandini Mukherjee, Ryan Magee, Leo Tsukada, Kent Blackburn, Patrick Brady, et al. The gstlal search analysis methods for compact binary mergers in advanced ligo’s second and advanced virgo’s first observing runs. arXiv preprint arXiv:1901.08580, 2019.

[45] Cody Messick, Kent Blackburn, Patrick Brady, Patrick Brockill, Kipp Cannon, Romain Cariou, Sarah Caudill, Sydney J Chamberlin, Jolien DE Creighton, Ryan Everett, et al. Analysis framework for the prompt discovery of compact binary mergers in gravitational-wave data. Phys. Rev. D, 95:042001, Feb 2017.

[46] S. Klimenko, G. Vedovato, M. Drago, F. Salemi, V. Tiwari, G. A. Prodi, C. Lazzaro, K. Ackley, S. Tiwari, C. F. Da Silva, and G. Mitselmakher. Method for detection and reconstruction of gravitational wave transients with networks of advanced detectors. Phys. Rev. D, 93:042004, Feb 2016.

[47] Tejaswi Venumadhav, Barak Zackay, Javier Roulet, Liang Dai, and Matias Zaldarriaga. New search pipeline for compact binary mergers: Results for binary black holes in the first observing run of advanced ligo. Phys. Rev. D, 100:023011, Jul 2019.

[48] Kilar Zhang, Guo-Zhang Huang, and Feng-Li Lin. Gw170817 and gw190425 as hybrid stars of dark and nuclear matters. arXiv preprint arXiv:2002.10961, 2020.

[49] Michael Klasen, Martin Pohl, and Günter Sigl. Indirect and direct search for dark matter. Progress in Particle and Nuclear Physics, 85:1–32, 2015.

[50] DS Akerib, S Alsum, HM Araújo, X Bai, AJ Bailey, J Balajthy, P Beltrame, EP Bernard, A Bernstein, TP Biesiadzinski, et al. Results from a search for dark matter in the complete lux exposure. Phys. Rev. Lett., 118:021303, Jan 2017.

[51] Xiangyi Cui, Abdusalam Abdukerim, Wei Chen, Xun Chen, Yunhua Chen, Binbin Dong, Deqing Fang, Changbo Fu, Karl Giboni, Franco Giuliani, et al. Dark matter results from 54-ton-day exposure of pandax-ii experiment. Phys. Rev. Lett., 119:181302, Oct 2017.

[52] Elena Aprile, J Aalbers, F Agostini, M Alfonsi, FD Amaro, M Anthony, F Arneodo, P Barrow, L Baudis, Boris Bauermeister, et al. First dark matter search results from the xenon1t experiment. Phys. Rev. Lett., 119:181301, Oct 2017.

[53] Chris Kouvaris and Niklas Grønlund Nielsen. Asymmetric dark matter stars. Physical Review D, 92(6):063526, 2015.

[54] Noah Sennett, Tanja Hinderer, Jan Steinhoff, Alessandra Buonanno, and Serguei Ossokine. Distinguishing boson stars from black holes and neutron stars from tidal interactions in inspiraling binary systems. Physical Review D, 96(2):024002, 2017.

[55] BP Abbott, R Abbott, TD Abbott, S Abraham, F Acernese, K Ackley, C Adams, RX Adhikari, VB Adya, C Affeldt, et al. Gw190425: Observation of a compact binary coalescence with total mass 3.4 m?. The Astrophysical Journal Letters, 892(1):L3, 2020.

[56] Markus Kuster, Georg Raffelt, and Berta Beltrán. Axions: Theory, cosmology, and experimental searches, volume 741. Springer, 2007.

[57] Joshua Eby, Madelyn Leembruggen, Lauren Street, Peter Suranyi, and LCR Wijewardhana. Global view of qcd axion stars. Physical Review D, 100(6):063002, 2019.

[58] Otto A Hannuksela, Kaze WK Wong, Richard Brito, Emanuele Berti, and Tjonnie GF Li. Probing the existence of ultralight bosons with a single gravitational-wave measurement. Nature Astronomy, 3(5):447–451, 2019.

[59] David N Spergel and Paul J Steinhardt. Observational evidence for self-interacting cold dark matter. Physical Review Letters, 84(17):3760, 2000.

[60] Miguel Rocha, Annika HG Peter, James S Bullock, Manoj Kaplinghat, Shea Garrison-Kimmel, Jose Onorbe, and Leonidas A Moustakas. Cosmological simulations with self-interacting dark matter–i. constant-density cores and substructure. Monthly Notices of the Royal Astronomical Society, 430(1):81–104, 2013.
[61] Annika HG Peter, Miguel Rocha, James S Bullock, and Manoj Kaplinghat. Cosmological simulations with self-interacting dark matter–ii. halo shapes versus observations. Monthly Notices of the Royal Astronomical Society, 430(1):105–120, 2013.

[62] Manoj Kaplinghat, Sean Tulin, and Hai-Bo Yu. Dark matter halos as particle colliders: unified solution to small-scale structure puzzles from dwarfs to clusters. Physical Review Letters, 116(4):041302, 2016.

[63] F Douchin and P Haensel. A unified equation of state of dense matter and neutron star structure. Astronomy & Astrophysics, 380(1):151–167, 2001.

[64] https://compose.obspm.fr/eos/134.

[65] James M Lattimer. The nuclear equation of state and neutron star masses. Annual Review of Nuclear and Particle Science, 62:485–515, 2012.

[66] James M Lattimer and Andrew W Steiner. Neutron star masses and radii from quiescent low-mass x-ray binaries. The Astrophysical Journal, 784(2):123, 2014.

[67] Edward M Cackett, Jon M Miller, Sudip Bhattacharyya, Jonathan E Grindlay, Jeroen Homan, Michiel Van Der Klis, M Coleman Miller, Tod E Strohmayer, and Rudy Wijnands. Relativistic iron emission lines in neutron star low-mass x-ray binaries as probes of neutron star radii. The Astrophysical Journal, 674(1):415, 2008.

[68] Feryal Özel, Dimitrios Psaltis, Tolga Güver, Gordon Baym, Craig Heinke, and Sebastien Guillot. The dense matter equation of state from neutron star radius and mass measurements. The Astrophysical Journal, 820(1):28, 2016.

[69] James M Bardeen, Kip S Thorne, and David W Meltzer. A catalogue of methods for studying the normal modes of radial pulsation of general-relativistic stellar models. The Astrophysical Journal, 145:505, 1966.