As a sequel to our recent works challenging toward the systematic inclusion of the effect of radiation on the trajectory of a test particle orbiting around a luminous spinning relativistic star eventually aiming at its application to the accretion flow. We explore in the present work the fine structure of the trajectory of test particle just entering the ``suspension orbit" under the purpose of a detailed investigation of test particle's trajectory in the vicinity of the ``suspension orbit". We end up with a rather puzzling behavior that, contrary to our expectation, the specific angular momentum of the test particle instantly rises instead of decreasing monotonically just before the test particle enters the ``suspension orbit".
Astrophysical accretion flow onto massive or compact stars is one of the major concerns in Astronomy and Astrophysics. In the current treatment of the accretion process, the effect of radiation on the inflow has been poorly addressed. Therefore in our recent works( [1], [2]), we have been challenging toward the systematic inclusion of the effects of radiation in the accretion process. To this end, we explored the effect of the radiation from a central star on the motion of a single test particle when the central star has the angular momentum and a finite radius to realize that there exists the "suspension orbit" that corresponds to the "critical point" in [3]. There ( [1]), the "suspension orbit" has been discovered for the first time and it can be defined as an orbit in which the test particle hovers around the central star at uniform velocity (for more detail, see [1]).
In the present work, we would like to pursue this effort further and in this sense, the present work can be regarded as a sequel to our earlier works ([1], [2]). To be more specific, we explore the fine structure of the trajectory of test particle just entering the “suspension orbit” under the purpose of a detailed investigation of test particle’s trajectory in the vicinity of the “suspension orbit”. To summarize the main result of our present work, as we shall see shortly in the text, we encounter a rather puzzling behavior that, contrary to our expectation, the specific angular momentum of the test particle instantly rises instead of decreasing monotonically just before the test particle enters the “suspension orbit”. Indeed, we find it anomalous as it contradicts to the Kepler’s law which is obviously the first principle. In the text of this paper, we will attempt to address the relevant physical interpretation of it.
As we mentioned in the introduction above, in this section we now would like to report on the fine structure of the test particle’s trajectory near the “suspension orbit” which exhibits some interesting features. To summarize the motivation behind our current research, so far we have been exploring the dynamics of a test particle orbiting around a luminous relativistic stars ( [1] and [2]). And the purpose of such study is to have some insight into the behavior of the accretion flow onto the relativistic stars emitting radiation such as the AGN or the X-ray binaries. In other words, we would like to understand the effect of radiation on the accretion inflow toward stars with strong gravity which has not been addressed in a systematic manner in the literature. To be more specific, based upon our earlier discovery of the “suspension orbit” ( [1]) which can be thought of as the generalization of the critical point ( [3]) for the case of sufficiently luminous non-rotating relativistic stars and the detailed study of the advent and the effect of the counter drag forces in our recent works ([1] and [2]), in the present work, we studied the behavior of the trajectory of the test particle just entering the “suspension orbit” that we have discovered in our earlier study ( [1]). This exploration can be thought of as a detailed investigation of test particle’s trajectory in the vicinity of the “suspension orbit”. We hope such a study of the fine structure would help our understanding of the nature of “suspension orbit” ( [1]). As can be seen in a moment, we will consider the co-rotating since we are interested in the dynamics of a test particle approaching a sufficiently luminous spinning relativistic star. Now, the geodesic equation for the azimuthal component of test particle’s velocity is given below:
where
1/2 (see [3]) for the radius of the star R ≥ 3M, the Eddington luminosity L ∞ Edd ≡ 4πmM/σ is the luminosity of a spherically symmetric source such that at infinity the outward radiation force balances the inward gravity (see [4]), L ∞ is the luminosity of the star as measured by an observer at infinity, and J (r) is given by
where j ≡ cJ/(GM 2 ) is the dimensionless angular momentum of the star and the average azimuthal velocity v of the radiation source as measured by an observer in the LNRF (Locally Non-Rotating Frame; see [5]; [6]) is calculated to be
We now turn to the numerical solutions of the test particle’s specific angular momentum that can be represented by the plots (Fig. 1). Interestingly enough, it turns out that the numerical solutions reveal contrasting characteristic features between the case when the “suspension orbit” develops just above or below the surface of the star and the other case when the “suspension orbit” emerges at a distance from the star. Therefore, we now start with the first case when the “suspension orbit” develops just above or below the surface of the star.
It is rather puzzling that contrary to our expectation, the specific angular momentum U φ of the test particle instantly rises instead of decreasing monotonically just before the test particle enters the “suspension orbit”. This b
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