On Some Prospects of the LOFT Mission: QPO Models Institute of Physics, Silesian University in Opava Gabriel Török CZ.1.07/2.3.00/ Synergy, GAČR 209/12/P740, 202/09/0772, SGS ,

density comparable to the Sun mass in units of solar masses temperature ~ roughly as the T Sun more or less optical wavelengths MOTIVATION Companion: Compact object: - black hole or neutron star (>10^10gcm^3) >90% of radiation in X-ray LMXB Accretion disc Observations: The X-ray radiation is absorbed by the Earth atmosphere and must be studied using detectors on orbiting satellites representing a 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). T ~ 10^6K Figs: space-art, nasa.gov 1. Introduction LMXBs

Fig: nasa.gov LMXBs short-term X-ray variability: peaked noise (Quasi-Periodic Oscillations ) Low frequency QPOs (up to 100Hz) hecto-hertz QPOs ( Hz),... HF QPOs (~ Hz): Lower and upper QPO feature forming twin peak QPOs frequency power Sco X-1 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. Individual peaks can be related to a set of oscillators, as well as to time evolution of a single oscillator. 1. Introduction MOTIVATION

2. LOFT LOFT is specifically designed to exploit the diagnostics of very rapid X-ray flux and spectral variability (already known to exist) that directly probe the motion of matter down to distances very close to black holes and neutron stars. Its factor of ~20 larger effective area than RXTE’s PCA (the largest area X-ray instrument ever flown) is crucial in this respect. (from LOFT webpage)

2. LOFT LOFT/LAD’s much improved energy resolution (better than 260 eV) compared to that of RXTE/PCA will also allow the simultaneous exploitation of spectral diagnostics, in particular the relativistically broadened 6-7 keV Fe-K lines. The timescales that LOFT will investigate range from submillisecond quasi-periodic oscillations (QPOs) to years long transient outbursts. LOFT is required to answer two fundamental questions of ESA's Cosmic Vision Theme Matter under extreme conditions: Does matter orbiting close to the event horizon follow the predictions of general relativity? What is the equation of state of matter in neutron stars? (from LOFT webpage)

3. LOFT & QPO Models (SFG1 Group Goals) (Several of) Competing models variously identify observed QPOs with the relativistic radial and vertical epicyclic frequencies or relativistic nodal and periastron precession. Very high-signal-to-noise LOFT/LAD measurements of the QPOs will unambiguously discriminate between such interpretations and in the process tease out yet untested general relativistic effects such as frame dragging, strong-field periastron precession, and the presence of an innermost stable orbit. Crucially, LOFT will provide access for the first time to types of information in these signals that are qualitatively new due to the capability to measure dynamical timescale phenomena within their coherence time, where so far only statistical averages of signals were accessible. This will allow studies that directly witness QPO formation and propagation and tie in with what state-of- the-art numerical work is just beginning to address. (from LOFT webpage)

Very high-signal-to-noise LOFT measurements of the QPOs will unambiguously discriminate between QPO interpretations. “ Models predict frequencies but give very little insights on amplitude - It is however likely that we see the tip of the iceberg (the fundamental, which is actually close to the PCA sensitivity) and that the clue is in the harmonic content of the signal, and this is a problem, because we don't know at which amplitude levels they will show up.” (from SFG1 materials) 3. LOFT & QPO Models (SFG1 Group Goals)

Very high-signal-to-noise LOFT measurements of the QPOs will unambiguously discriminate between QPO interpretations. Lightcurves corresponding to different disc oscillation modes and lightcurves corresponding to hot-spot models should be modelled including both the current models and the process of observation in order to obtain relevant PDS. 3. LOFT & QPO Models (SFG1 Group Goals)

4. Lightcurve Modelling: Implementation Basis & “Reverse Engineering” COLLABORATION: Pavel Bakala, Vladimír Karas, Michal Dovčiak, Martin Wildner, Dalibor Wzientek, Marek Abramowicz, Eva Šrámková, Kateřina Goluchová, Frederic Vincent, Grzegorz Mazur  Institute of Physics, Silesian University in Opava, CZ  Astronomical Institute, Prague, CZ  Copernicus Astronomical Center, Warszawa, PL  Institute for Theoretical Physics, University of Warsaw,PL  Laboratoire AstroParticule et Cosmologie, CNRS, Universite Paris Diderot, FR

4. Lightcurve Modelling: Implementation Basis & “Reverse Engineering” Global Empirical Model of Variability and Spectra (GRS , SPL State) + QPO MODEL TOTAL SOURCE FLUX MODEL

4. Lightcurve Modelling: Implementation Basis & “Reverse Engineering” Global Empirical Model of Variability and Spectra (GRS , SPL State) + TOTAL SOURCE FLUX MODEL QPO MODEL

4. Lightcurve Modelling: Implementation Basis & “Reverse Engineering” 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 + QPO MODEL

5. Some Results: Signal Strength Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Signal Strength (relative hot-spot brigthness) Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). [ ~ 1Crab source countrate] Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Signal Strength Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). [ ~ 1Crab source countrate] Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). [ ~ 1Crab source countrate] Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). [ ~ 1Crab source countrate] Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Model: Single spot orbiting close to inner edge of the accretion disc (simulation using KY Spot code). [ ~ 1Crab source countrate] Expectation: Keplerian frequency + harmonics

5. Some Results: Signal Strength Current BH status: weak signal with sporadic RXTE QPO detections - The applied simple model clearly illustrates the LOFT capability in such situation.

5. Some Results: Comparison Between QPO Models Frequency Power RXTE simulationsLOFT simulations Torus (Epicyclic Modes) SPOTS (ISCO, nurmax) Multiple spost created around two preferred radii (using KY Spot code). The m=0 epicyclic oscillations of the optically thin torus drifting through the resonant radius. M = 11M ⊙, D = 65°, a = 0, R1= 6M, R2=8M, n=0.1. M = 5.6M ⊙, D = 65°, a = 0, R0= 10.8M, n=0.1. Power Torus (Epicyclic Modes) Frequency Power SPOTS (ISCO, nurmax)

Frequency Power RXTE simulationsLOFT simulations Torus (Epicyclic Modes) SPOTS (ISCO, nurmax) Multiple spost created around two preferred radii (using KY Spot code). The m=0 epicyclic oscillations of the optically thin torus drifting through the resonant radius. M = 11M ⊙, D = 65°, a = 0, R1= 6M, R2=8M, n=0.1. M = 5.6M ⊙, D = 65°, a = 0, R0= 10.8M, n=0.1. Frequency Power Torus (Epicyclic Modes) Power SPOTS (ISCO, nurmax) 5. Some Results: Comparison Between QPO Models

RXTE simulationsLOFT simulations Frequency Power Torus (Epicyclic Modes) SPOTS (ISCO, nurmax) Frequency Power Torus (Epicyclic Modes) Power SPOTS (ISCO, nurmax) 5. Some Results: Comparison Between QPO Models

RXTE simulationsLOFT simulations GR Power Frequency Torus (Epicyclic Modes) SPOTS (ISCO, nurmax) Frequency Power Torus (Epicyclic Modes) Power SPOTS (ISCO, nurmax) 5. Some Results: Comparison Between QPO Models

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