Constraining Models of Twin Peak Quasi-periodic
Oscillations with Realistic Neutron Star Equation of State
Gabriel Török
Institute of Physics, Research Centre for Computational Physics and Data Analysis,
Silesian University in Opava, Czech Republic
& Kateřina Goluchová, Martin Urbanec, Eva Šrámková,
Karel Adámek, Gabriela Urbancová, Tomáš Pecháček,
Pavel Bakala, Zdeněk Stuchlík, Jakub Juryšek
1. Motivation fundamental theories vs. LMXBs spectra and timing
Artists view of LMXBs
“as seen from a hypothetical planet”
Compact object:
- Black hole or neutron star
T ~ 10^6K
>90% X-ray
Accretion disc
Strong gravity & Dense matter laboratory
Observation and theory: The X-ray radiation absorbed by Earth
atmosphere is studied using detectors on orbiting satellites. The
observations allows to test fundamental physical theories under extreme
conditions that are impossible to reach in terestrial laboratories.
1. Motivation fundamental theories vs. LMXBs spectra and timing
LMXBs provide a unique chance to probe effects in the strong-gravity-field
region. The way how electromagnetic radiation propagates in space, its time
variability and shape of lines in its energetic spectrum are invaluable probes to
physical behavior of the matter in strong gravitational field. Similarly, a
systematic study of the properties of neutron stars allows us to explore
supradense matter.
Testing
Supra-dense
matter
2. Orbital motion and high frequency QPOs in NS LMXBs
HF QPOs appears in X-ray fluxes of several LMXB sources. Commonly to BH and
NS they often behave in pairs. There is a large variety of ideas proposed to
explain this phenomenon. Most often, QPOs are related to orbital motion in
strong gravity. There is a belief that gravitational field and NS properties can be
studied using QPO observations, e.g., using their frequency correlations.
Frequency
nU[Hz]
U
Van der Klis et al.
Power
L
Török et al., 2012, ApJ
NS correlations
HF QPOS
nL[Hz]
Several models have been proposed.
[e.g., 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); 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); ….. ]
3. Orbital models of HF QPOs and NS parameters
Models: Most of the models relate QPOs to the
orbital motion. For instance, “blob”
models (Stella et al., Cadez et al.,…).
It is possible to compare the model and
data (here atoll source 4U 1636-53).
-> preferred mass-spin relations.
RP
Parameters
(Kerr approx.):
RP
TD
Fits
(4U 1636-53):
RP
TD
Török et al., 2012, ApJ
TD
3. Orbital models of HF QPOs and NS parameters
Models: Blob models (Stella et al., Cadez et al.,…).
In order to include effects of NS oblateness one has to consider
predictions of QPO models assuming Hartle-Thorne spacetime as well as
requirements following from concrete NS equation of state.
Parameters
(H-T approx.):
Fits
(4U 1636-53):
QPOs, H-T geometry
Sly 4 EOS
3. Orbital models of HF QPOs and NS parameters
Models: Blob models (Stella et al., Cadez et al.,…).
In order to include effects of NS oblateness one has to consider
predictions of QPO models assuming Hartle-Thorne spacetime as well as
requirements following from concrete NS equation of state.
-> preferred mass-spin relations
RP
Parameters
(H-T approx.):
Fits
(4U 1636-53):
RP
TD
TD
3. Orbital models of HF QPOs and NS parameters
Models: Blob models (Stella et al., Cadez et al.,…).
In order to include effects of NS oblateness one has to consider
predictions of QPO models assuming Hartle-Thorne spacetime as well as
requirements following from concrete NS equation of state.
Finally, the spin frequency measured from X-ray bursts can be considered.
RP
Parameters
(H-T approx.):
Fits
(4U 1636-53):
RP
TD
TD
4. Orbital models of HF QPOs and NS parameters – large set of models
As well as the Sly4 EoS we have investigated a wide set of 18 EoS that are
based on different theoretical models that meet requirements of proposed
observational tests. We have considered 5 QPO models investigated previously
by Lin et al (2012, ApJ) and Torok et al. (2010, 2012, ApJ) who assumed high
mass (Kerr) approximation of NS spacetimes.
4. Orbital models of HF QPOs and NS parameters – large set of models
As well as the Sly4 EoS we have investigated a wide set of 18 EoS that are
based on different theoretical models that meet requirements of proposed
observational tests. We have considered 7 QPO models.
4. Conclusions
• We confront several QPO models with various neutron star equations of
state and present results of detailed calculations considering the influence
of the star's oblateness in Hartle-Thorne spacetimes.
• The confrontation results rather to spin-mass relations than to preferred
combinations of mass and spin.
• Considering a particular spin frequency close to 580 Hz measured in the
atoll source 4U 1636-53, we show that 51 out of 90 considered
combinations of EoS and QPO models can be excluded. The selection
effect comes from the correlation between the estimated mass and angular
momentum and the limits on maximal mass allowed by the individual EoS.
• Prospects: improved QPO models.
New model: an oscillating torus with cusp
that changes location close to ISCO.
The model can provide fits of data
comparable to those reached by other
models, or even better. The model
consideration is compatible with the
consideration of models of rotating NS.
Torok et al., 2016, MNRAS: Letters, 457.
4U 1636-53