... 2J1

Present address.

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... low-frequency

Two different low-frequency (<100 Hz) QPOs were known in the Z sources, the 6-20 Hz so-called normal and flaring-branch oscillation (NBO; Middleditch & Priedhorsky 1986) and the 15-60 Hz so-called horizontal branch oscillation (HBO; van der Klis et al. 1985).

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... (ISCO)

In general relativity, no stable orbital motion is possible within the innermost stable circular orbit (ISCO), $r_{\rm ISCO} = 6GM/c^2 \approx 12.5 M_{1.4~M_\odot}~\hbox{km}~$. The frequency of orbital motion at the ISCO, the highest possible stable orbital frequency, is $\nu_{\rm ISCO} \approx (1580/M_{1.4~M_\odot})~ \hbox{Hz}$.

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... magnetosphere

Note that the enhanced density gradient region is defined as follows: when we move outward from the surface of the star, the plasma density in the magnetosphere is more or less is constant, say $\rho_0$. At the point where magnetosphere interacts with the accretion disk (more likely at the disk's inner edge), however, there is a sudden increase in the magnetospheric plasma density, say $\rho>\rho_0$, due to the motion of accretion material along field lines. After this thin region (compared to the entire magnetosphere), the magnetospheric plasma density drops to $\rho_0$ again. Therefore, the enhanced density gradient region is not a region with a gradient in the plasma density only. It is a region with a different (higher) plasma density compared into the rest of the magnetosphere.

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... i.e.

In order to estimate the poloidal component of the inflow velocity $v_{\rm p}$, one needs to integrate the momentum Eq. (1a):

 

$$(1/2)(v_{\rm p}^2 + \Omega^2\varpi^2)-\Omega_{\rm s}\Omega \varpi^2 -GM/r =\rm constant~along$$

$$\hspace{5cm}{\rm a~given~field~line},$$ (6)

where M is the mass of the neutron star (Ghosh et al. 1977; Mestel 1968a,b). In the above equation the pressure term is neglected. Equation (6) shows conservation of energy in a frame corotating with the star, while in a nonrotating frame the extra term  $\Omega_{\rm s}\Omega\varpi^2$ appears, that represents the work done by the magnetic field on the flowing plasma. However, as argued by Ghosh et al. (1977) the poloidal velocity in the inner magnetosphere where  $r\ll r_{\rm A}$ is nearly equal to the free-fall velocity, i.e.

$$v_{\rm p}\sim (2GM/r)^{1/2}.$$ (7)

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... modes

In the cold-plasma approximation, the fast compressional wave (fast magnetosonic wave) is also called the compressional Alfvén wave.

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... velocity

To obtain Eq. (22f) we assumed that at equilibrium $\vec{\nabla}P=\vec{\nabla}(p+B^2/(8\pi))=0$. This is valid for a non-rotating or very slowly rotating star.

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...=0)

In the case of zero ambient flow, v_||=0, the parallel displacement $\xi_{\vert\vert}$ vanishes in the cold plasma.

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... star

To properly calculate the Alfvén velocity at the surface of the star, one would need to use the relativistic Alfvén velocity as defined in Eq. (19), i.e.

$$v_{\rm A}(r)=\frac{\mu \dot{M}^{-1/2}(2GM)^{1/4}r^{-9/4}}{\sqrt{1+\mu^2 \dot{M}^{-1}(2GM)^{1/2}r^{-9/2}/c^2}}\cdot$$ (30)

Here we assumed p=0. Using the above relation the Alfvén velocity at the surface of the star will be $\sim$0.8 c, .997 c, and c for $\mu=10^{26},~10^{27}$, and 10²⁸ G cm³, respectively. At further distances from the star, however, the relativistic Alfvén velocity reduces to its classical version which we used instead. The values given here for the relativistic Alfvén velocity at the stellar surface are for a neutron star with $R_{\rm s}=10$ km, ${\dot M}=10^{17}$ g s^-1 and $M=M_\odot$.

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... LMXBs

In Sco X-1 the correlation line between two frequencies has a steeper slope than 2/3 (see Belloni et al. 2004).

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