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

TL;DR

This paper investigates the trapping of two-armed nearly vertical oscillations in polytropic disks, revealing conditions under which they are confined and their potential relation to observed QPOs in low-mass X-ray binaries.

Contribution

It demonstrates the trapping mechanism of two-armed vertical oscillations in polytropic disks and identifies the conditions related to the polytropic index and spin parameter for their confinement.

Findings

Trapped oscillations cover frequencies from kHz to low-frequency QPOs.

Low-frequency trapping occurs near a polytropic index parameter of 4/3.

Trapping regions are wider for low-frequency oscillations.

Abstract

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 $\Gamma(\equiv 1+1/N)$ 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.