1. THIN ACCRETION DISCS AROUND NEUTRON AND QUARK STARS T. Harko K. S. Cheng Z. Kovacs DEPARTMENT OF PHYSICS, THE UNIVERSITY OF HONG KONG, POK FU LAM ROAD, HONG KONG SAR, P.R. CHINA

2. CONTENT 1. What are strange stars? 2. Basic properties of strange stars 3. Thin accretion discs around neutron and strange stars 4. Equations of state of neutron and quark matter 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and quark stars 6. Summary

3. 1. WHAT ARE STRANGE STARS? Neutrons and protons are both composed of quarks The true ground state of the hadrons may be strange matter, not (Witten, PRD, 30, 272, 1984) Strange matter is a bulk quark matter phase consisting of: -a roughly equal numbers of up, down and strange quarks - a smaller number of electrons (to guarantee charge neutrality)

4. Formation of quark stars -conversion of a neutron star to a quark star due to the presence of a seed of strange matter at its core -conversion of a neutron star to a quark star due to the presence of a seed of strange matter at its core -there are two combustion modes: deflagration (slow combustion) and detonation (fast combustion) -there are two combustion modes: deflagration (slow combustion) and detonation (fast combustion) -conversion of proto-neutron stars formed during supernova explosion to strange stars -conversion of proto-neutron stars formed during supernova explosion to strange stars

5. 2. BASIC PROPERTIES OF STRANGE STARS The properties of the strange matter are determined by the thermodynamic potentials, The properties of the strange matter are determined by the thermodynamic potentials, which are functions of the chemical potentials. In the limit of the zero mass for the strange quark the equation of state becomes In the limit of the zero mass for the strange quark the equation of state becomes where is the vacuum energy associated with the quark phase where is the vacuum energy associated with the quark phase

6. HOW TO IDENTIFY A STRANGE STAR? It is very difficult to distinguish quark stars from neutron stars It is very difficult to distinguish quark stars from neutron stars There are differences in: There are differences in: -radial vibrations -radial vibrations -maximum rotation frequency -maximum rotation frequency -signals of quark deconfinement from the braking indexes of pulsars -signals of quark deconfinement from the braking indexes of pulsars -cooling curves -cooling curves

7. PHOTON EMISSIVITY OF STRANGE MATTER PHOTON EMISSIVITY OF STRANGE MATTER The plasma frequency of quark matter is The plasma frequency of quark matter is At low temperatures the equilibrium photon emissivity of quark matter is negligible small At low temperatures the equilibrium photon emissivity of quark matter is negligible small

8. 2. BREMSSTRAHLUNG RADIATION FROM THE ELECTROSPHERE The bremmstrahlung radiation from the electrosphere of the strange stars may be the main observational signature of a strange star (Jaikumar, Gale, Page & Prakash, PRD, 70, 2004, 023004) The bremmstrahlung radiation from the electrosphere of the strange stars may be the main observational signature of a strange star (Jaikumar, Gale, Page & Prakash, PRD, 70, 2004, 023004) The bremsstrahlung luminosity is well above the Eddington limit The bremsstrahlung luminosity is well above the Eddington limit

9. 2. Electron-positron emission of the electrosphere The extremely strong electric field at the surface of a strange star may be a powerful source of electron-positron pairs (Usov, PRL, 80, 230, 1998) The extremely strong electric field at the surface of a strange star may be a powerful source of electron-positron pairs (Usov, PRL, 80, 230, 1998) The electron-positron luminosity is The electron-positron luminosity is

10. Energy fluxes emitted via different radiation mechanisms -electron-electron bremsstrahlung (solid curve), electron-positron pair creation (dotted curve), quark-quark bremsstrahlung (dashed curve), pion emission (long dashed curve), thermal photon radiation (ultra-long dashed curve)

11. 2. BASIC PROPERTIES OF STRANGE STARS Bulk models of strange and neutron stars are relatively similar Bulk models of strange and neutron stars are relatively similar The most powerful method to directly observe strange stars may be via their electromagnetic emission The most powerful method to directly observe strange stars may be via their electromagnetic emission Surface bremsstrahlung radiation and electron- positron pair emission could lead to the observational detection of strange stars Surface bremsstrahlung radiation and electron- positron pair emission could lead to the observational detection of strange stars

12. 2. BASIC PROPERTIES OF STRANGE STARS -a possibility for indirectly detecting a quark star could be through the gravitational effect it produces on thin accretion discs (Kovacs et al., Astron. Astrophys., in press) -a possibility for indirectly detecting a quark star could be through the gravitational effect it produces on thin accretion discs (Kovacs et al., Astron. Astrophys., in press) -rapid rotation of compact general relativistic objects modifies the geometry of the space-time around them -rapid rotation of compact general relativistic objects modifies the geometry of the space-time around them -the external geometry depends on the multipole moments of the star, which in turn are determined by the equation of state of the dense matter -the external geometry depends on the multipole moments of the star, which in turn are determined by the equation of state of the dense matter

13. 3. Thin accretion discs around neutron and strange stars

15. - a thin accretion disc is a disc whose vertical size is negligible as compared to its horizontal extension - a thin accretion disc is a disc whose vertical size is negligible as compared to its horizontal extension - the matter moves in Keplerian orbits around the central object - the matter moves in Keplerian orbits around the central object -the matter is modeled by an anisotropic fluid source (Kovacs et al., Astron. Astrophys., in press) -the matter is modeled by an anisotropic fluid source (Kovacs et al., Astron. Astrophys., in press)

16. 3. Thin accretion discs around neutron and strange stars -the energy flux from the disc is given by -the energy flux from the disc is given by -angular velocity -energy per unit mass -angular momentum per unit mass -we consider an arbitrary stationary and axially symmetric geometry

17. 3. Thin accretion discs around neutron and strange stars -the geodesic equations take the form -the geodesic equations take the form -for stable circular orbits, the conditions must hold -the marginally stable orbits are determined by

18. 3. Thin accretion discs around neutron and strange stars -the accreted matter is considered in thermodynamic equilibrium -the accreted matter is considered in thermodynamic equilibrium -the radiation emitted by the disc is a black-body radiation -the radiation emitted by the disc is a black-body radiation

19. 4. Equations of state of neutron and quark matter  1. Akmal-Pandharipande-Ravenhall (APR) EOS (Akmal, A. et al., 1998, Phys. Rev. C, 58, 1804)  2. Douchin-Haensel (DH) EOS (Douchin, F., Haensel, P. 2001, Astron. Astrophys., 380, 151)  3. Shen-Toki-Oyamatsu-Sumiyoshi (STOS) EOS (Shen, H. et al., 1998, Nucl. Phys. A, 637, 435)  4. Relativistic Mean Field (RMF) equations of state with isovector scalar mean field (Kubis, S., Kutschera, M. 1997, Phys. Lett. B, 399, 191)  5. Baldo-Bombaci-Burgio (BBB) EOS (Baldo, M. et al., 1997, Astron. Astrophys., 328, 274)  6. Bag model equation of state (Q) EOS (Witten, E. 1984, Phys. Rev. D, 30, 272)  7. Color-Flavor-Locked (CFL) EOS (Lugones, G., Horvath, J. E. 2002, Phys. Rev. D, 66, 074017).

20. 4. Equations of state of neutron and quark matter

21.  -the space time geometry exterior to the star, as well as the physical parameters of the system, are computed by using the RNS code (Stergioulas, N. 2003, Living Rev. Rel., 6, 3)  -the RNS code is a fully relativistic, 3D computer code

22. 4. Equations of state of neutron and quark matter  1. Models with similar mass and angular velocity  2. Models rotating at Keplerian frequencies  3. Models with similar central densities and eccentricities

23. 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and quark stars a) models with same mass and angular velocity

26. 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and quark stars b) models rotating at Keplerian velocities

29. 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and quark stars c) models with same central density and eccentricity

32. 6. SUMMARY The observation of strange stars would open a unique possibility for the study of the superdense quark matter and of some fundamental physical processes The observation of strange stars would open a unique possibility for the study of the superdense quark matter and of some fundamental physical processes Some astronomical objects like powerful accreting X-ray sources, X-ray bursters, soft gamma ray repeaters etc. may be in fact strange stars Some astronomical objects like powerful accreting X-ray sources, X-ray bursters, soft gamma ray repeaters etc. may be in fact strange stars

33. 6. SUMMARY -the physical properties of thin accretion disc around rapidly rotating neutron and quark stars could discriminate between different types of compact objects -the physical properties of thin accretion disc around rapidly rotating neutron and quark stars could discriminate between different types of compact objects -due to differences in space-time structure, quark stars exhibit important differences in terms of the disc properties, as compared to neutron stars -due to differences in space-time structure, quark stars exhibit important differences in terms of the disc properties, as compared to neutron stars