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Paczyński M odulation : D iagnostics of the Neutron Star EOS?

Paczyński M odulation : D iagnostics of the Neutron Star EOS?. Gabriel Török , Martin Urbanec, Karel Adámek, Pavel Bakala , Eva Šrámková, Zdeněk Stuchlík. Institute of Physics, Silesian University in Opava.

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Paczyński M odulation : D iagnostics of the Neutron Star EOS?

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  1. PaczyńskiModulation: Diagnostics of the Neutron Star EOS? Gabriel Török, Martin Urbanec, Karel Adámek, Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík Institute ofPhysics, Silesian University in Opava CZ.1.07/2.3.00/20.0071Synergy , GAČR 209/12/P740, 202/09/0772,SGS-01-2010, www.physics.cz

  2. 1. Outline Introduction: QPOs NS Compactness C (anotherintroduction) Epicyclic Resonance Model – Falsification using condition for Paczynski Modulation, C < 1 General Implications of Paczynski Modulation Mechanism (disc oscillation models): report on a work in progress

  3. 2. Introduction: QPOs • MOTIVATION Compact object: - black hole or neutron star(>10^10gcm^3) • LMXB Accretion disc LMXBs • T ~ 10^6K • >90% of radiation • in X-ray • Companion: • density comparable to the Sun • mass in units of solar masses • temperature ~ roughly as the T Sun • more or less optical wavelengths Observations: The X-ray radiation is absorbed by the Earth atmosphere and must be studied using detectors on orbiting satellites representing rather expensive research tool. On the other hand, it provides a unique chance to probe effects in the strong-gravity-field region (GM/r~c^2) and test extremal implications of General relativity (or other theories). Figs:space-art,nasa.gov

  4. 2. Introduction: QPOs • MOTIVATION Individual peaks can be related to a set of oscillators, as well as to time evolution of a singleoscillator. LMXBsshort-term X-ray variability: peaked noise (Quasi-PeriodicOscillations) Sco X-1 power • LowfrequencyQPOs (up to 100Hz) • hecto-hertz QPOs (100-200Hz),... • HF QPOs (~200-1500Hz): • Lower and upper QPO feature • forming twin peak QPOs frequency The HF QPO origin remains questionable, it is most often expected that it is associated to orbital motion in the inner part of the accretion disc. Fig:nasa.gov

  5. height h width w at ½ h Power Frequency 2. Introduction: QPOs Quality factor Q indicates sharpness of the peak, Q ~ h/w Amplitude r indicates strength of peak variability (its energy) in terms of “rms amplitude” = percentual fraction (root mean square fraction)of the peak energy with the respect to the total countrate (r ~ area under peak) BH QPOs (Galactic microquasars): frequencies up to 500Hz low amplitude and Q : typically up to r~5% and Q~5 NS QPOs: frequencies up to 1500Hz often amplitudes up to r~20% and quality factors up to Q~200

  6. 3. NS Compactness Kluzniak et al., ApJ (1990) KERR Torok et al.(2010),ApJ OBLATENESS The influence of NS oblateness on orbital frequenies has been extensively studied in last decade, e.g., Morsink, Stella, 1999, ApJ; Gondek-Rosińska, Stergioulas, Bulik, Kluźniak, Gourgoulhon, A&A (2001); Amsterdamski, Bulik, Gondek-Rosińska, Kluźniak, A&A (2002),…

  7. 3. NS Compactness OBLATENESS KERR

  8. 3. NS Compactness C = RNS/Rms OBLATENESS KERR

  9. 3. NS Compactness C = RNS/Rms OBLATENESS KERR 1

  10. 3. NS Compactness C = RNS/Rms OBLATENESS 1 KERR 1

  11. 3. NS Compactness 1 C = RNS/Rms OBLATENESS 1 KERR 1

  12. 3. NS Compactness high mass 1 C = RNS/Rms MASS OBLATENESS 1 KERR low mass 1

  13. 3. NS Compactness C = RNS/Rms

  14. 3. EpicyclicResonanceModelfor NS QPOsand NS Mass Within the group of non-linear models suggested by Abramowicz and Kluzniak there is one specific (often quted and discussed) model which relates QPOs to the axisymmetric vertical and radial accretion disc oscillations (Abramowicz& Kluzniak 2001). These oscillations have frequencies equal to the vertical and radial frequency of the perturbed geodesic motion. Two distinct simplifications can be than assumed(seeUrbanec etal. 2010, for refs): a) Observed frequencies are roughly equal to resonant eigenfrequencies. This for NSs FAILS. b) Alternatively, there are large corrections to the resonant eigenfrequencies. Abramowicz et al., 2005 Fig: J. Horák

  15. 3. EpicyclicResonanceModelfor NS QPOsand NS Mass For a non-rotating approximation it gives NS mass about (Bursa 2004, unp.). j The solution related to the high mass (i.e. Kerr) approximation thus cannot betrusted.

  16. 3. EpicyclicResonanceModelfor NS QPOsand NS Mass For a non-rotating approximation it gives NS mass about (Bursa 2004, unp.). q/j2 OBLATENESS KERR j Urbanec et al., (2010) , A&A Mass-spin relations inferred assuming Hartle-Thorne metric and various NS oblateness. One can expect that the red/yellow region is allowed by NS equations of state (EOS).

  17. 3. EpicyclicResonanceModelfor NS QPOsand NS Mass For a non-rotating approximation it gives NS mass about (Bursa 2004, unp.). j Urbanec et al., (2010) , A&A Mass-spin relations calculated assuming several modern EOS (of both “Nuclear” and “Strange” type) and realistic scatter from 600/900 Hz eigenfrequencies.

  18. 4. PaczynskiModulationand NS Compactness Possible relation between the X-ray QPO phenomenon and general relativity BohdanPaczyński, 1987 ”….suggest that the unsteady flow would make the boundary-layer luminosity variable, possibly giving rise to the X-ray quasi-periodic oscillation (QPO) phenomenon.” REQUIRED CONDITION: C = RNS/Rms < 1 After Abr. et al., (2007), Horák (2005)

  19. 4. PaczynskiModulationand NS Compactness high mass 1 C = RNS/Rms MASS OBLATENESS 1 KERR low mass 1

  20. 4. PaczynskiModulationand ImpliedRestrictions (EpicyclicResonanceModel) Urbanec et al., (2010) , A&A The condition for modulation is fulfilled only for rapidly rotating strange stars, which most likely falsifies the postulation of the 3:2 resonant mode eigenfrequencies being equal to geodesic radial and vertical epicyclic frequency…. (Typical spin frequencies of discussed sources are about 200-700Hz; based on X-ray bursts)

  21. 5. PaczynskiModulation– GeneralImplications Almost any disc-oscillation model requires C<1 Initial Distribution of NS [C<>1] => Distribution of QPO Sources MASS [MSun] SPIN [Hz]

  22. 5. PaczynskiModulation– GeneralImplications Almost any disc-oscillation model requires C<1 Initial Distribution of NS (one concrete EoS) Mass [Msun] 0 1 1.5 2 MASS [MSun] SPIN [Hz]

  23. 5. PaczynskiModulation– GeneralImplications Almost any disc-oscillation model requires C<1 Initial Distribution of NS (one concrete EoS) Mass [Msun] 0 1 1.5 2 MASS [MSun] SPIN [Hz]

  24. 5. PaczynskiModulation– GeneralImplications Resulting Distribution of QPO sources (the same EoS) Mass [Msun] 0 1 1.5 2 MASS [MSun] 0 500 1000 1500 Spin [Hz] SPIN [Hz]

  25. 5. PaczynskiModulation– GeneralImplications Resulting Distribution of QPO sources (another example) Mass [Msun] 0 1 1.5 2 MASS [MSun] 0 500 1000 1500 Spin [Hz] SPIN [Hz]

  26. 5. PaczynskiModulation– GeneralImplications Mass [Msun] 0 1 1.5 2 Number of Sources SPIN [Hz]

  27. 6. Conclusions Mass [Msun] 0 1 1.5 2 Number of Sources SPIN [Hz]

  28. END Thankyouforyourattention…

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