thin accretion discs around neutron and quark stars

THIN ACCRETION DISCS THIN ACCRETION DISCS AROUND NEUTRON AND AROUND NEUTRON AND

QUARK STARSQUARK STARST. HarkoT. Harko

K. S. ChengK. S. ChengZ. KovacsZ. Kovacs

DEPARTMENT OF PHYSICS, THE UNIVERSITY OF HONG KONG, DEPARTMENT OF PHYSICS, THE UNIVERSITY OF HONG KONG, POK FU LAM ROAD, HONG KONG SAR, P.R. CHINAPOK FU LAM ROAD, HONG KONG SAR, P.R. CHINA

CONTENTCONTENT1. What are strange stars?1. What are strange stars?2. Basic properties of strange stars2. Basic properties of strange stars3. Thin accretion discs around neutron and 3. Thin accretion discs around neutron and strange starsstrange stars4. Equations of state of neutron and quark 4. Equations of state of neutron and quark mattermatter5. Electromagnetic signatures of accretion 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and discs around rapidly rotating neutron and quark starsquark stars6. Summary6. Summary

1. WHAT ARE STRANGE STARS?1. WHAT ARE STRANGE STARS?

Neutrons and protons are both composed of Neutrons and protons are both composed of quarksquarks

The true ground state of the hadrons may be The true ground state of the hadrons may be strange matter, notstrange matter, not (Witten, PRD, 30, 272, 1984)(Witten, PRD, 30, 272, 1984)

Strange matter is a bulk quark matter phase Strange matter is a bulk quark matter phase consisting of:consisting of:

-a roughly equal numbers of up, down and -a roughly equal numbers of up, down and strange quarksstrange quarks

- a smaller number of electrons (to - a smaller number of electrons (to guarantee charge neutrality)guarantee charge neutrality)

56Fe

Formation of quark starsFormation of quark stars

• -conversion of a neutron star to a -conversion of a neutron star to a quark star due to the presence of a quark star due to the presence of a seed of strange matter at its coreseed of strange matter at its core

• -there are two combustion modes: -there are two combustion modes: deflagration (slow combustion) and deflagration (slow combustion) and detonation (fast combustion)detonation (fast combustion)

• -conversion of proto-neutron stars -conversion of proto-neutron stars formed during supernova explosion formed during supernova explosion to strange starsto strange stars

2. BASIC PROPERTIES OF 2. BASIC PROPERTIES OF STRANGE STARSSTRANGE STARS

• The properties of the strange matter are The properties of the strange matter are determined by the thermodynamic potentials, determined by the thermodynamic potentials,

which are functions of the chemical potentials. which are functions of the chemical potentials.

• In the limit of the zero mass for the strange In the limit of the zero mass for the strange quark the equation of state becomesquark the equation of state becomes

• where is the vacuum energy associated with where is the vacuum energy associated with the quark phasethe quark phase

3/)4( BP B

HOW TO IDENTIFY A STRANGE HOW TO IDENTIFY A STRANGE STAR?STAR?

• It is very difficult to distinguish quark It is very difficult to distinguish quark stars from neutron starsstars 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 -signals of quark deconfinement from the braking indexes of pulsarsthe braking indexes of pulsars

• -cooling curves-cooling curves

PHOTON EMISSIVITY OF PHOTON EMISSIVITY OF STRANGE MATTERSTRANGE MATTER• The plasma frequency of quark matter isThe plasma frequency of quark matter is

• At low temperatures the equilibrium photon At low temperatures the equilibrium photon emissivity of quark matter is negligible smallemissivity of quark matter is negligible small

2/1)3/8( Bp nec3-fm 16.0

Bn MeV

MeV 23p

2. BREMSSTRAHLUNG 2. BREMSSTRAHLUNG RADIATION FROM THE RADIATION FROM THE ELECTROSPHEREELECTROSPHERE

•The bremmstrahlung radiation from The bremmstrahlung radiation from the electrosphere of the strange the electrosphere of the strange stars may be the main stars may be the main observational signature of a strange observational signature of a strange starstar (Jaikumar, Gale, Page & Prakash, PRD, 70, 2004, 023004)(Jaikumar, Gale, Page & Prakash, PRD, 70, 2004, 023004)

•The bremsstrahlung luminosity is The bremsstrahlung luminosity is well above the Eddington limitwell above the Eddington limit

-128 s erg 10

2. Electron-positron emission of 2. Electron-positron emission of the electrospherethe electrosphere• The extremely strong electric field at the The extremely strong electric field at the

surface of a strange star may be a surface of a strange star may be a powerful source of electron-positron pairs powerful source of electron-positron pairs (Usov, PRL, 80, 230, 1998)(Usov, PRL, 80, 230, 1998)

• The electron-positron luminosity is The electron-positron luminosity is 1-

51 s erg103L

Energy fluxes emitted via different Energy fluxes emitted via different radiation mechanismsradiation 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)


• Bulk models of strange and neutron stars Bulk models of strange and neutron stars are relatively similarare relatively similar

• The most powerful method to The most powerful method to directlydirectly observe strange stars may be via their observe strange stars may be via their electromagnetic emissionelectromagnetic emission

• Surface bremsstrahlung radiation and Surface bremsstrahlung radiation and electron-positron pair emission could lead electron-positron pair emission could lead to the observational detection of strange to the observational detection of strange starsstars


• -a possibility for -a possibility for indirectlyindirectly detecting a detecting a quark star could be through the quark star could be through the gravitational effect it produces on thin gravitational effect it produces on thin accretion discs (accretion discs (Kovacs et al., Astron. Kovacs et al., Astron. Astrophys., in pressAstrophys., in press))

• -rapid rotation of compact general -rapid rotation of compact general relativistic objects modifies the geometry of relativistic objects modifies the geometry of the space-time around themthe space-time around them

• -the external geometry depends on the -the external geometry depends on the multipole moments of the star, which in turn multipole moments of the star, which in turn are determined by the equation of state of are determined by the equation of state of the dense matter the dense matter

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


• - a thin accretion disc is a disc whose - a thin accretion disc is a disc whose vertical size is negligible as compared to vertical size is negligible as compared to its horizontal extensionits horizontal extension

• - the matter moves in Keplerian orbits - the matter moves in Keplerian orbits around the central objectaround the central object

• -the matter is modeled by an anisotropic -the matter is modeled by an anisotropic fluid source fluid source (Kovacs et al., Astron. Astrophys., in press)(Kovacs et al., Astron. Astrophys., in press)

tquuuT )(2


• -the energy flux from the disc is given by-the energy flux from the disc is given by

r

r

rr

ms

drLLELEg

MrF ,2

,0

4)(

E

L

-angular velocity

-energy per unit mass

-angular momentum per unit mass

-we consider an arbitrary stationary and axially symmetric geometry

22222 dgdgdrgdtdgdtgds rrttt

3. Thin accretion discs around 3. Thin accretion discs around neutron and strange starsneutron and strange stars• -the geodesic equations take the form-the geodesic equations take the form

ggg

gLgLEgErV

rVd

drg

ggg

gLgE

d

d

ggg

gLgE

d

dt

ttt

ttt

rrttt

ttt

ttt

ttt

2

22

2

22

21)(

),(,,

-for stable circular orbits, the conditions ,0)( rV 0)(, rV r must hold

-the marginally stable orbits msr are determined by 0, msrr rV

02,

2,

2,,

2 msrr

rrtttrrttrrtrr ggggLgLEgE

3. Thin accretion discs around 3. Thin accretion discs around neutron and strange starsneutron and strange stars• -the accreted matter is considered in -the accreted matter is considered in

thermodynamic equilibriumthermodynamic equilibrium

• -the radiation emitted by the disc is a -the radiation emitted by the disc is a black-body radiation black-body radiation

)()( 4 rTrF

ggg

rz

z

T

rdrdIdL

ttt

e

r

r e

ef

i

2

2

0

32

2

sinsin11

)1(

1/expcos

84

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

1. Akmal-Pandharipande-Ravenhall (APR) EOS (Akmal, A. 1. Akmal-Pandharipande-Ravenhall (APR) EOS (Akmal, A. et al., 1998, Phys. Rev. C, 58, 1804)et al., 1998, Phys. Rev. C, 58, 1804)

2. Douchin-Haensel (DH) EOS (Douchin, F., Haensel, P. 2. Douchin-Haensel (DH) EOS (Douchin, F., Haensel, P. 2001, Astron. Astrophys., 380, 151)2001, Astron. Astrophys., 380, 151)

3. Shen-Toki-Oyamatsu-Sumiyoshi (STOS) EOS (Shen, H. 3. Shen-Toki-Oyamatsu-Sumiyoshi (STOS) EOS (Shen, H. et al., 1998, Nucl. Phys. A, 637, 435)et al., 1998, Nucl. Phys. A, 637, 435)

4. Relativistic Mean Field (RMF) equations of state with 4. Relativistic Mean Field (RMF) equations of state with isovector scalar mean field (Kubis, S., Kutschera, M. 1997, isovector scalar mean field (Kubis, S., Kutschera, M. 1997, Phys. Lett. B, 399, 191)Phys. Lett. B, 399, 191)

5. Baldo-Bombaci-Burgio (BBB) EOS (Baldo, M. et al., 1997, 5. Baldo-Bombaci-Burgio (BBB) EOS (Baldo, M. et al., 1997, Astron. Astrophys., 328, 274)Astron. Astrophys., 328, 274)

6. Bag model equation of state (Q) EOS (Witten, E. 1984, 6. Bag model equation of state (Q) EOS (Witten, E. 1984, Phys. Rev. D, 30, 272)Phys. Rev. D, 30, 272)

7. Color-Flavor-Locked (CFL) EOS (Lugones, G., Horvath, J. 7. Color-Flavor-Locked (CFL) EOS (Lugones, G., Horvath, J. E. 2002, Phys. Rev. D, 66, 074017).E. 2002, Phys. Rev. D, 66, 074017).


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

-the RNS code is a fully relativistic, 3D -the RNS code is a fully relativistic, 3D computer codecomputer code


1. Models with similar mass and 1. Models with similar mass and angular velocityangular velocity

2. Models rotating at Keplerian 2. Models rotating at Keplerian frequenciesfrequencies

3. Models with similar central 3. Models with similar central densities and eccentricitiesdensities and eccentricities

5. Electromagnetic signatures of accretion discs around rapidly rotating 5. Electromagnetic signatures of accretion discs around rapidly rotating neutron and quark starsneutron and quark stars

a) models with same mass and angular velocitya) models with same mass and angular velocity


b) models rotating at Keplerian velocitiesb) models rotating at Keplerian velocities


c) models with same central density and eccentricityc) models with same central density and eccentricity

6. SUMMARY6. SUMMARY

• The observation of strange stars would The observation of strange stars would open a unique possibility for the study open a unique possibility for the study of the superdense quark matter and of of the superdense quark matter and of some fundamental physical processessome fundamental physical processes

• Some astronomical objects like Some astronomical objects like powerful accreting X-ray sources, X-ray powerful accreting X-ray sources, X-ray bursters, soft gamma ray repeaters etc. bursters, soft gamma ray repeaters etc. may be in fact strange stars may be in fact strange stars

6. SUMMARY6. SUMMARY

• -the physical properties of thin accretion -the physical properties of thin accretion disc around rapidly rotating neutron and disc around rapidly rotating neutron and quark stars could discriminate between quark stars could discriminate between different types of compact objectsdifferent types of compact objects

• -due to differences in space-time -due to differences in space-time structure, quark stars exhibit important structure, quark stars exhibit important differences in terms of the disc differences in terms of the disc properties, as compared to neutron starsproperties, as compared to neutron stars

thin accretion discs around neutron and quark stars

Documents