Institute of Physics, Silesian University in Opava Gabriel Török GAČR 209/12/P740, CZ.1.07/2.3.00/ Synergy, GAČR G, SGS , CO-AUTHORS: Eva Šrámková, Pavel Bakala, Kateřina Goluchová, Andrea Kotrlová, Vladimír Karas, Marek Abramowicz, Zdeněk Stuchlík, Wlodek Kluzniak, Martin Wildner, Dalibor Wzientek Predictions of HF-QPO models explored with LOFT

Exploring signal from tori and spots with LOFT : Outline 1.Introduction: neutron star rapid X-ray variability, quasiperiodic oscillations, twin peaks, SPOTs and TORI 2.QPO frequencies, BH spin & epicyclic resonance model predictions 2.1 QPO frequencies and BH spin from geodesic models (summary of some older results by Torok et al, 2011, A&A) 2.2 Consideration of a>1 (Kotrlová et al 2014, A&A) 2.3 Nongeodesic effects (Šrámková et al 2014, submitted) 3.Observable signal from ER-tori and spots (RXTE vs. LOFT) 3.1 Spots – harmonic content of the signal (Bakala et al 2014, MNRAS) 3.2 Spots vs. tori (Bakala et al 2014, MNRAS) 4.Summary Tento projekt je spolufinancován Evropským sociálním fondem a státním rozpočtem České republiky

LMXB Accretion disc 1. Introduction: LMXBs, quasiperiodic oscillations, HF QPOs Upper frequency [Hz] 3:2 HF QPOs

1. Introduction: LMXBs, quasiperiodic oscillations, HF QPOs

There is a large variety of ideas proposed to explain the QPO phenomenon [For instance, Alpar & Shaham (1985); Lamb et al. (1985); Stella et al. (1999); Morsink & Stella (1999); Stella & Vietri (2002); Abramowicz & Kluzniak (2001); Kluzniak & Abramowicz (2001); Abramowicz et al. (2003a,b); Wagoner et al. (2001); Titarchuk & Kent (2002); Titarchuk (2002); Kato (1998, 2001, 2007, 2008, 2009a,b); Meheut & Tagger (2009); Miller at al. (1998a); Psaltis et al. (1999); Lamb & Coleman (2001, 2003); Kluzniak et al. (2004); Abramowicz et al. (2005a,b), Petri (2005a,b,c); Miller (2006); Stuchlík et al. (2007); Kluzniak (2008); Stuchlík et al. (2008); Mukhopadhyay (2009); Aschenbach 2004, Zhang (2005); Zhang et al. (2007a,b); Rezzolla et al. (2003); Rezzolla (2004); Schnittman & Rezzolla (2006); Blaes et al. (2007); Horak (2008); Horak et al. (2009); Cadez et al. (2008); Kostic et al. (2009); Chakrabarti et al. (2009), Bachetti et al. (2010)…] For several models one can evaluate predicted QPO frequencies (frequency.mass spin functions) and compare these with observation… 2.1 QPO frequencies and BH spin from the geodesic QPO models

Comparing the frequency.mass functions to the observation. For instance in the case of GRS (which here well represents all 3:2 microquasars). Spin a 2.1 QPO frequencies and BH spin from the geodesic QPO models Torok et al., (2011) A&A Clearly, different models imply very different spins…

When the dimensionless spin reads a>1, the situation is more complicated. Nevertheless, some models still imply smooth frequency.mass functions of the spin. 2.2 Consideration of a>1 (naked sigularities or superspinars - NaS) BHNaS Kotrlová et al., (2014) A&A For several models, there is an alternative compatible with existence of a superspinning compact object. Only epicyclic resonance model then implies spin close to unity, while others imply values that are several times higher.

2.2 Consideration of a>1 (naked sigularities or superspinars - NaS) Kotrlová et al., (2014) A&A More pairs of different 3:2 commensurable frequencies can be expected within a single source when a = 1 + small . Further treatment of this issue is rather difficult considering the present lack and low-resolution of the BH HF QPO data. It should, however, be resolvable using LOFT. The case of epicyclic resonance model

2.3. Non-geodesic effects consideration within ER model Pressure supported fluid tori (ER tori), impact on the resonant frequency Šrámková et al., (2014), A&A submitted

2.3. Non-geodesic effects consideration within ER model For low spins the non-geodesic effects are small. For high spins, resonant frequencies are RAPIDLY decreasing instead of increasing as the torus thickness rises. Thus, sources with a moderate spin should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin. Impact of pressure on the resonant frequency (to be tested with LOFT) Šrámková et al., (2014), in prep.

Global Empirical Model of Variability and Spectra (GRS , SPL State) Response Matrices (Detector) “DATA” Time and Spectral Distribution of Detected Counts TIMING ANALYSIS RESULTS TOTAL SOURCE FLUX MODEL + Comparing different orbital QPO models, RXTE and L QPO MODEL (SPOTs or TORUS) 3. Observable signal from ER tori and spots (RXTE vs. LOFT)

Small spots moving along slightly eccentric orbits close to ISCO Left: RXTE Right: LOFT LOG POWER 3.1 Spots – harmonic content of the signal Bakala et al., 2014, MNRAS

3.1 Spots vs. tori (comparison between specific models) Drifting spotsDrifting ER tori (opt. thin) Toy models of double peak QPOs assuming preferred orbits Harmonic content… Bakala et al., 2014, MNRAS

4. Exploring signal from tori and spots with LOFT: Summary Epicyclic resonance model: predicts that individual sources with a moderate spin should exhibit a smaller spread of the measured 3:2 QPO frequencies than sources with a near-extreme spin (GRS ) or superspinars. Verification of this prediction requires large amount of high resolution data obtained with LOFT. [Kotrlová et. al 2014, A&A; Šrámková et al. 2014, A&A, submitted] Spots: The harmonic content of the circular spot signal should be clearly recognized using LOFT observations. [Bakala et. al 2014, MNRAS, see also poster of Karas et al. here] Spots vs. Tori: Specific model signatures such as harmonics unresolvable with RXTE can be crucial. Good examples of LOFT capabilities (although specific models): -e.g., circ. spot vs. opt. thin torus X elongated spot vs. opt. thick torus -see poster of Karas et al. (opt. thin torus) and talk of Pavel Bakala (opt. thick torus) here for more on this issues….

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