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

On NS Mass-Spin Relations Implied by Models of Twin Peak QPOs

Gabriel Török, Pavel Bakala, Eva Šrámková, Zdeněk Stuchlík, Martin Urbanec, Kateřina Goluchová

• 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 (100-200Hz),...• HF QPOs (~200-1500Hz): Lower and upper QPO feature forming twin peak QPOs

frequency

pow

er

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. Observed Twin Peak QPO Frequencies

Lower frequency [Hz]

Upp

er fr

eque

ncy

[Hz]

One can solve the RP model definition equations (Kerr approximation)

Obtaining the relation between the expected lower and upper QPO frequency

which can be compared to the observation in order to estimate mass M and “spin” j …

3. Relativistic Precession Model: Inferring NS Parameters

The two frequencies scale with 1/M and they are also sensitive to j.For matching of the data it is an important question whether there exist identical or similar curves for different combinations of M and j.

3. Relativistic Precession Model: Ambiguity in M and j

Orbital RadiusISCOInfinity

3. Relativistic Precession Model: Ambiguity in M and j

Toro

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0), A

pJ

M = 2.5….4 MSUN Ms = 2.5 MSUN M ~ Ms[1+0.75(j+j^2)]

Orbital RadiusISCOInfinity

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M = 2.5….4 MSUN Ms = 2.5 MSUN M ~ Ms[1+0.75(j+j^2)]

The best fits of data of a given source should be therefore reached for the combinations of M and j which can be predicted just from one parametric fit assuming j = 0.

For each pair of parameters M and j, the RP model gives a different curve, but one can find classes of curves that are nearly identical.

bounded by the relation M ~ Ms[1+0.7(j+j^2)].

3. Relativistic Precession Model: Ambiguity in M and j

Orbital RadiusISCOInfinity

Orbital RadiusISCOInfinity

4. Results of Data Matching (Circinus X-1)

M-j relation expected from Ms = 2.2M_sunBest χ2 numericaly Best χ2 exact Kerr solutionBest χ2 linearized Kerr frequencies

Color-coded map of χ2 [M,j,10^6 points] well agrees with rough estimate given by simple one-parameter fit.

Toro

k et

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(201

0), A

pJ

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pJ

5. Justification

High-mass (i.e. compact) neutron star can be well approximated via simple and elegant terms associated to Kerr geometry. The non-rotating NS mass predicted by the RP model is high. Thus, the Kerr geometry has the potential to provide rather precise spin-corrections.

5. Justification

In the Hartle-Thorne spacetime there is a degeneracy not only between the NS mass and angular momentum but also between these quantities and the NS quadrupole moment q [here j (0, 0.3) and ∈ q/j^2 (1, 8)].∈

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6. Conclusions

• The twin peak QPO data matching by the RP model implies rather preferred mass-angular-momentum relations rather than single combinations of M and j.• Several other points will be discussed in the presentation of Kateřina Goluchová (Friday morning).

ADVERTISING

7. Advertising

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al.

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• The twin peak QPO data matching by the RP model implies rather preferred mass-angular-momentum relations rather than single combinations of M and j.• More in the talk of Kateřina Goluchová (Friday Morning):

The same conclusion holds for both high- and low- frequency sources. (e.g. 4U~1636-53 and Circinus X-1)

7. Advertising

Toro

k et

al.

2012

, ApJ

, acc

epte

d

• The twin peak QPO data matching by the RP model implies rather preferred mass-angular-momentum relations rather than single combinations of M and j.• More in the talk of Kateřina Goluchová (Friday Morning):

The same conclusion holds for both high- and low- frequency sources. (e.g. 4U~1636-53 and Circinus X-1)

The same conclusion is valid for several other twin peak QPO models.

7. Advertising• The twin peak QPO data matching by the RP model implies rather preferred mass-angular-momentum relations rather than single combinations of M and j.• More in the talk of Kateřina Goluchová (Friday Morning):

The same conclusion holds for both high- and low- frequency sources. (e.g. 4U~1636-53 and Circinus X-1)

The same conclusion is valid for several other twin peak QPO models.The M − j degeneracies can in principle be eliminated using angular

momentum estimates based on the X-ray burst observations

Toro

k et

al.

2012

, ApJ

, acc

epte

d

END

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