arXiv subjects

Shoji Kato

Publications and source records attributed to Shoji Kato.

At least 19 recordsLinked to original sources

arXiv2020

A Possible Origin of kHZ QPOs in Low-Mass X-ray Binaries

A possible origin of kHz QPOs in low-mass X-ray binaries is proposed. Recent numerical MHD simulations of accretion disks with turbulent magnetic fields of MRI definitely show the presence of two-armed spiral structure in quasi-steady state of accretion disks. In such deformed disks, two-armed ($m=2$) c-mode ($n=1$) oscillations are excited by wave-wave resonant instability. Among these excited oscillations, the fundamental in the radial direction ($n_r=0$) will be the higher kHz QPO of a twin QPOs, and the first overtone ($n_r=1$) in the radial direction will be the lower kHz QPO of the twin. A possible cause of the twin high-frequency QPOs (HFQPOs) in BH X-ray binaries is also discussed.

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arXiv2017

Self-Trapping of G-Mode Oscillations in Relativistic Thin Disks, Revisited II: Revision of Boundary Condition

In a previous paper (Kato 2017a) we have examined how the self-trapping of g-mode oscillations in geometrically thin relativistic disks is affected by the presence of uniform vertical magnetic fields. Disks considered are isothermal in the vertical direction and are truncated at a certain height by presence of hot corona. After a correction of simple analytical error, we showed (Kato 2017b) that the self-trapping of axisymmetric g-mode oscillations in non-magnetized disks is destroyed by weak magnetic fields as Fu and Lai (2009) showed. In this paper, however, we re-examine the same problem by imposing a different more relevant boundary condition on the disk-corona surface and find that the self-trapping of axisymmetric g-mode oscillations seems to still exist like the case of non-magnetized disks.

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arXiv2017

Self-Trapping of G-Mode Oscillations in Relativistic Thin Disks, Revisited

We examine by a perturbation method how the self-trapping of g-mode oscillations in geometrically thin relativistic disks is affected by uniform vertical magnetic fields. Disks which we consider are isothermal in the vertical direction, but are truncated at a certain height by presence of hot coronae. We find that the characteristics of self-trapping of axisymmetric g-mode oscillations in non-magnetized disks is kept unchanged in magnetized disks at least till a strength of the fields, depending on vertical thickness of disks. These magnetic fields become stronger as the disk becomes thinner. This result suggests that trapped g-mode oscillations still remain as one of possible candidates of quasi-periodic oscillations observed in black-hole and neutron-star X-ray binaries in the cases where vertical magnetic fields in disks are weak.

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arXiv2014

Simultaneous Resonant Excitation of Low-frequency Eccentric Wave and Tilt Wave on Tidally Deformed Disks

Simultaneous excitation of low-frequency eccentric precessing mode (one-armed p-mode) and tilt mode on tidally deformed disks is considered. If the orbit of the secondary star is eccentric and its orbital plane is misaligned with the disk plane of the primary, the above-mentioned two low-frequency oscillation modes are simultaneously excited on the primary disk, the former having prograte precession and the latter having retrograde precession. This excitation of disk oscillations is due to a wave-wave resonant excitation process considered by Kato (2013). If parameter values relevant to Be/X-ray binary systems are adopted, the periods of these excited oscillations are around ten times of the orbital period of the secondary, which may be comparable with the time scale of giant outbursts observed in Be/X-ray systems.

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arXiv2013

Resonant Excitation of Disk Oscillations in Deformed Disks VII: Stability Criterion in MHD Systems

In a disk with an oscillatory deformation from an axisymmetric state with frequency $ω_{\rm D}$ and azimuthal wavenumber $m_{\rm D}$, a set of two normal mode oscillations with frequency and azimuthal wavenumber being ($ω_1$, $m_1$) and ($ω_2$, $m_2$) resonantly couple through the disk deformation, when the resonant conditions ($ω_1+ω_2+ω_{\rm D}=0$ and $m_1+m_2+m_{\rm D}=0$) are satisfied. In the case of hydrodynamical disks, the resonance amplifies the set of the oscillations if $(E_1/ω_1)(E_2/ω_2)>0$ (Kato 2013b), where $E_1$ and $E_2$ are wave energies of the two oscillations with $ω_1$ and $ω_2$, respectively. In this paper we show that this instability criterion is still valid even when the oscillations are ideal MHD ones in magnetized disks, if the displacements associated with the oscillations vanish on the boundary of the system.

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arXiv2013

Resonant Excitation of Tilt Mode in Tidally Deformed Disks

In a previous paper (Kato 2013b), we have shown that in deformed disks a pair of trapped oscillation modes can be resonantly excited through couplings with disk deformation. In this paper we examine in what cases tilts are excited on tidally deformed disks by the above-mentioned wave-wave resonant process. The results show that tilts can be excited in various evolutional stages of tidally deformed disks, although the wave mode which becomes the pair to the tilt and the mode of tidal waves contributing to the resonance change by change of disk stages.

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arXiv2013

Resonant Excitation of Disk Oscillations in Deformed Disks VI: Stability Criterion Revisited

We re-examine excitation of a set of disk oscillations in a deformed disk by a resonant process. We assume that the disk is deformed from an axisymmetric steady state by an oscillatory deformation with frequency $ω_{\rm D}$ and azimuthal wavenumber $m_{\rm D}$. Then, we consider two normal mode oscillations with a set of frequencies and azimuthal wavenumber being ($ω_1$, $m_1$) and ($ω_2$, $m_2$) and satisfying the resonant conditions ($ω_1+ω_2+ω_{\rm D}=0$ and $m_1+m_2+m_{\rm D}=0$). These oscillations are resonantly excited if $(E_1/ω_1)(E_2/ω_2)>0$, where $E_1$ and $E_2$ are wave energies of the above two oscillations, when the deformation is maintained by external forces or has a large amplitude compared with the oscillations. This instability condition is rather general as long as unperturbed density and pressure vanish on the surface of the system. Possibility of application to superhump and negative superhump in superoutburst state of dwarf novae are briefly discussed.

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arXiv2013

Tidal Instability and Superhump by a Wave-Wave Resonant Model

On a disk deformed to a non-axisymmetric form, a set of oscillations can be excited by their resonant interaction through the disk deformation (Kato et al. 2011). This resonant instability process has been proposed to suggest a possible cause of the high-frequency quasi-periodic oscillations (HF QPOs) observed in black-hole low-mass X-ray binaries. In the present paper, we examine whether the above-mentioned wave-wave resonant process can describe the tidal instability and superhump in dwarf novae. The results show that the process seems to well describe the observations. If this process is really the cause of the tidal instability and superhump, a two-armed oscillation with high frequency roughly on the magnitude of three times the orbital frequency is present on disks, although its expected amplitude may be small.

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arXiv2012

A Resonantly-Excited Disk-Oscillation Model of High-Frequency QPOs of Microquasars

A possible model of twin high-frequency QPOs (HF QPOs) of microquasars is examined. The disk is assumed to have global magnetic fields and to be deformed with a two-armed pattern. In this deformed disk, set of a two-armed ($m=2$) vertical p-mode oscillation and an axisymmetric ($m=0$) g-mode oscillation are considered. They resonantly interact through the disk deformation when their frequencies are the same. This resonant interaction amplifies the set of the above oscillations in the case where these two oscillations have wave energies of opposite signs. These oscillations are assumed to be excited most efficiently in the case where the radial group velocities of these two waves vanish at the same place. The above set of oscillations is not unique, depending on the node number, $n$, of oscillations in the vertical direction. We consider that the basic two sets of oscillations correspond to the twin QPOs. The frequencies of these oscillations depend on disk parameters such as strength of magnetic fields. For observational mass ranges of GRS 1915+105, GRO J1655-40, XTE J1550-564, and H1743-322, spins of these sources are estimated. High spins of these sources can be described if the disks have weak poloidal magnetic fields as well as toroidal magnetic fields of moderate strength. In this model the 3 : 2 frequency ratio of high-frequency QPOs is not related to their excitation, but occurs by chance.

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arXiv2012

An Attempt to Describe Frequency Correlations among kHz QPOs and HBOs by Two-Armed Nearly Vertical Oscillations

We examine whether the two-armed ($m=2$) vertical p-mode oscillations trapped in the innermost region of magnetized accretion disks with finite disk thickness can describe kHz QPOs and HBOs in LMXBs. First, we derive the frequency-frequency correlation of the two basic oscillations (both are fundamental modes in the vertical direction, but one is the fundamental and the other the first overtone in the radial direction), and compare it with the observed frequency correlation of twin kHz QPOs. Results show that the calculated frequency correlation can well describe observed correlation with reasonable values of parameters. Second, we examine whether the observed frequency correlation between kHz QPOs and HBO can be described by regarding HBO as the first overtone oscillation in the vertical direction (and the fundamental in the radial direction). The results suggest that i) innermost parts of disks on the horizontal branch are strongly diminished in their vertical thickness (presumably by hot coronae) and ii) the branch is roughly a sequence of variations of magnetic fields or disk temperature.

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arXiv2012

Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields II: Effects of Finite Thickness

We examine radial trapping of two-armed ($m=2$) vertical p-mode oscillations in geometrically thin relativistic disks which are vertically isothermal but terminated at a certain height by the presence of hot and low-density corona. The disks are assumed to be subject to toroidal magnetic fields. The oscillations are classified by $n$, a number related to the node number of oscillations in the vertical direction and starting from $n=1$. In modes with $n=1$, the frequencies of trapped oscillations depend little on the height of termination, but in modes with $n=2,3,...$ the frequencies decrease and the radial extends of trapped region become wide, as the termination height decreases. This study is a preparation to examine whether these oscillations can describe kilo-hertz quasi-periodic oscillations (kHz QPOs), horizontal branch oscillation (HBOs), and their correlations.

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arXiv2011

Correlated Frequency-Changes of Trapped Vertical p-mode Oscillations and kHz QPOs

We have examined the frequencies of trapped two-armed ($m=2$) nearly vertical oscillations (vertical p-mode) in vertically isothermal disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfvén speed, $c_{\rm A}$, is constant in the vertical direction. We have particularly focused our attention on how frequencies of the fundamental mode ($n_{\rm r}=0$) and first overtone ($n_{\rm r}=1$) in the radial direction change with correlation, when the ratio $c_{\rm A}^2/c_{\rm s}^2$ changes, $c_{\rm s}$ being the isothermal acoustic speed. The results show that in the case where the oscillations are fundamental mode ($n=1$) in the vertical direction, the correlated frequency changes of the above-mentioned oscillations seem to well describe, with standard values of the mass and spin of the central sources, the frequency correlation of kHz QPOs observed in neutron-star X-ray binaries.

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arXiv2011

Resonant Excitation of Disk Oscillations in Deformed Disks V: Effects of Dissipative Process

It is suggested that a set of positive- and negative-energy oscillations can be resonantly excited in the inner region of deformed (warped or eccentric) relativistic disks. In this paper we examine how a dissipative process affects on this wave excitation process. The results show that when the resonant condition in frequency is roughly satisfied and thus the oscillations are excited, introduction of a dissipative process works so as to decrease the growth rate of the oscillations. When the frequency difference of the two oscillations deviates more than a certain amount from that required by resonant condition, however, the oscillations are excited by introduction of dissipative process. This excitation by dissipative process can be understood as a special example of the double-diffusive instability.

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arXiv2011

Resonant Excitation of Disk Oscillations in Deformed Disks IV: A New Formulation Studying Stability

The possibility has been suggested that high-frequency quasi-periodic oscillations observed in low-mass X-ray binaries are resonantly excited disk oscillations in deformed (warped or eccentric) relativistic disks (Kato 2004). In this paper we examine this wave excitation process from a viewpoint somewhat different from that of previous studies. We study how amplitudes of a set of normal mode oscillations change secularly with time by their mutual couplings through disk deformation. As a first step, we consider the case where the number of oscillation modes contributing to the resonance coupling is two. The results show that two prograde oscillations interacting through disk deformation can grow if their wave energies have opposite signs.

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arXiv2010

Trapped, Two-Armed, Nearly Vertical Oscillations in Disks with Toroidal Magnetic Fields

We have examined trapping of two-armed ($m=2$) nearly vertical oscillations (vertical p-mode) in vertically isothermal ($c_{\rm s}=$ const.) relativistic disks with toroidal magnetic fields. The magnetic fields are stratified so that the Alfv{é}n speed, $c_{\rm A}$, is constant in the vertical direction. The ratio of $c_{\rm A}^2/c_{\rm s}^2$ in the vertical direction is taken as a parameter examining the effects of magnetic fields on wave trapping. We find that the two-armed nearly vertical oscillations are trapped in the inner region of disks and their frequencies decrease with increase of $c_{\rm A}^2/c_{\rm s}^2$. The trapped regions of the fundamental ($n=1$) and the first-overtone ($n=2$) are narrow (less than the length of the Schwarzschild radius, $r_{\rm g}$) and their frequencies are relatively high (on the order of the angular frequency of disk rotation in the inner region). On contrast to this, the second-overtone ($n=3$) are trapped in a wide region (a few times $r_{\rm g}$), and their frequencies are low and tend to zero in the limit of $c_{\rm A}^2/c_{\rm s}^2=2.0$.

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arXiv2010

Excitation of Trapped g-Mode Oscillations in Warped Disks around Black Holes

In order to study the origin of high-frequency quasi-periodic oscillations observed in X-ray binaries, Kato (2004) suggested a resonant excitation mechanism of disk oscillations in deformed disks. In this paper, we study numerically, following his formulation, whether trapped g-mode oscillations in a warped disk, where the warp amplitude varies with radius, can be excited by this mechanism. For simplicity, we adopt Newtonian hydrodynamic equations with relativistic expressions for the characteristic frequencies of disks. We also assume that the accretion disk is isothermal. We find that the fundamental modes of trapped g-mode oscillations with eigenfrequencies close to the maximum of epycyclic frequency are excited. The intermediate oscillations found are isolated in a narrow region around the resonance radius. After varying some parameters, we find that the growth rate increases as the warp amplitude or the black hole spin parameter increases, while it decreases as the sound speed increases.

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arXiv2010

Trapped, Two-Armed, Nearly Vertical Oscillations in Polytropic Disks

We have examined trapping of two-armed nearly vertical oscillations in polytropic disks. Two-armed nearly vertical oscillations are interesting in the sense that they are trapped in an inner region of disks with proper frequencies, if the inner edge of disks is a boundary that reflects oscillations. The frequencies of the trapped oscillations cover the frequency range of kHz QPOs to low frequency QPOs in LMXBs, depending on the modes of oscillations. Low frequency trapped oscillations are particularly interesting since their trapped region is wide. These low frequency oscillations are, however, present only when $Γ(\equiv 1+1/N)$ is close to but smaller than 4/3 (when spin parameter $a_*$ is zero), where $N$ is the polytropic index. The above critical value 4/3 slightly increases as $a_*$ increases.

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arXiv2010

Leaving the ISCO: the inner edge of a black-hole accretion disk at various luminosities

The "radiation inner edge" of an accretion disk is defined as the inner boundary of the region from which most of the luminosity emerges. Similarly, the "reflection edge" is the smallest radius capable of producing a significant X-ray reflection of the fluorescent iron line. For black hole accretion disks with very sub-Eddington luminosities these and all other "inner edges" locate at ISCO. Thus, in this case, one may rightly consider ISCO as the unique inner edge of the black hole accretion disk. However, even for moderate luminosities, there is no such unique inner edge as differently defined edges locate at different places. Several of them are significantly closer to the black hole than ISCO. The differences grow with the increasing luminosity. For nearly Eddington luminosities, they are so huge that the notion of the inner edge losses all practical significance.

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