Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Paczyński Modulation: Diagnostics of the Neutron Star EOS? Gabriel Török, Martin Urbanec, Karel Adámek, Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík Institute of Physics, Silesian University in Opava CZ.1.07/2.3.00/20.0071 Synergy , GAČR 209/12/P740, 202/09/0772, SGS-01-2010, www.physics.cz 1. Outline 1. Introduction: QPOs 2. NS Compactness C (another introduction) 3. Epicyclic Resonance Model – Falsification using condition for Paczynski Modulation, C < 1 4. General Implications of Paczynski Modulation Mechanism (disc oscillation models): report on a work in progress 2. Introduction: QPOs MOTIVATION LMXBs Compact object: - black hole or neutron star (>10^10gcm^3) LMXB Accretion disc 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 2. Introduction: QPOs MOTIVATION Sco X-1 power LMXBs short-term X-ray variability: peaked noise (Quasi-Periodic Oscillations) Individual peaks can be related to a set of oscillators, as well as to time evolution of a single oscillator. • Low frequency QPOs (up to 100Hz) frequency • hecto-hertz QPOs (100-200Hz),... • HF QPOs (~200-1500Hz): Lower and upper QPO feature forming twin peak QPOs Fig: nasa.gov 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. 2. Introduction: QPOs Quality factor Q indicates sharpness of the peak, Q ~ h/w Power height h width w at ½ h 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) Frequency 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 Torok et al. (2010),ApJ 3. NS Compactness 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),… 3. NS Compactness C = RNS/Rms 3. NS Compactness C = RNS/Rms 3. NS Compactness 1 C = RNS/Rms 3. NS Compactness 1 1 C = RNS/Rms 3. NS Compactness 1 1 1 1 high mass MASS C = RNS/Rms 3. NS Compactness 1 1 low mass C = RNS/Rms 3. NS Compactness 3. Epicyclic Resonance Model for NS QPOs and 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 (see Urbanec et al. 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 3. Epicyclic Resonance Model for NS QPOs and 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 be trusted. 3. Epicyclic Resonance Model for NS QPOs and NS Mass (Bursa 2004, unp.). q/j2 j Urbanec et al., (2010) , A&A For a non-rotating approximation it gives NS mass about 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). 3. Epicyclic Resonance Model for NS QPOs and NS Mass j (Bursa 2004, unp.). Urbanec et al., (2010) , A&A For a non-rotating approximation it gives NS mass about Mass-spin relations calculated assuming several modern EOS (of both “Nuclear” and “Strange” type) and realistic scatter from 600/900 Hz eigenfrequencies. 4. Paczynski Modulation and NS Compactness Possible relation between the X-ray QPO phenomenon and general relativity ”….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) Bohdan Paczyński, 1987 1 high mass MASS C = RNS/Rms 4. Paczynski Modulation and NS Compactness 1 1 low mass Urbanec et al., (2010) , A&A 4. Paczynski Modulation and Implied Restrictions (Epicyclic Resonance Model) 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) 5. Paczynski Modulation – General Implications MASS [MSun] Almost any disc-oscillation model requires C<1 Initial Distribution of NS [C<>1] => Distribution of QPO Sources SPIN [Hz] 5. Paczynski Modulation – General Implications 0 Almost any disc-oscillation model requires C<1 Initial Distribution of NS (one concrete EoS) MASS [MSun] 1.5 Mass [Msun] 1 2 SPIN [Hz] 5. Paczynski Modulation – General Implications 0 Almost any disc-oscillation model requires C<1 Initial Distribution of NS (one concrete EoS) MASS [MSun] 1.5 Mass [Msun] 1 2 SPIN [Hz] 5. Paczynski Modulation – General Implications 0 Resulting Distribution of QPO sources (the same EoS) MASS [MSun] 1.5 Mass [Msun] 1 2 0 500 1000 1500 Spin [Hz] SPIN [Hz] 5. Paczynski Modulation – General Implications 0 MASS [MSun] 1.5 Mass [Msun] 1 Resulting Distribution of QPO sources (another example) 2 0 500 1000 1500 Spin [Hz] SPIN [Hz] 5. Paczynski Modulation – General Implications 1.5 Mass [Msun] 1 Number of Sources 0 2 SPIN [Hz] 6. Conclusions 1.5 Mass [Msun] 1 Number of Sources 0 2 SPIN [Hz] END Thank you for your attention…