[Paper Review] Spread of Matter Over a Neutron-Star Surface During Disk Accretion

N. A. Inogamov, R. Sunyaev|arXiv (Cornell University)|Apr 23, 1999

Astrophysical Phenomena and Observations5 references10 citations

TL;DR

This paper develops a shallow-water model to study matter spreading over a neutron star's surface during disk accretion, focusing on low-luminosity, weakly magnetized systems. It shows that radiation pressure and centrifugal forces create two symmetric bright rings near the edges of differentially rotating belts, which migrate poleward as luminosity increases, driven by minimum surface density and maximum meridional velocity zones.

ABSTRACT

Disk accretion onto a slowly rotating neutron star with a weak magnetic field $H < 3 imes 10^8$ gauss is considered in a wide range of luminosities $1/100 < L/L_{edd} < 1,$ where $L_{edd}$ is the Eddington luminosity. We construct a theory for the deceleration of rotation and the spread of matter over the stellar surface in the shallow-water approximation. The rotation slows down due to friction against the dense underlying layers. The deceleration of Keplerian rotation and the energy release take place on the stellar surface in a latitudinal belt whose meridional width rises with increasing $L.$ The combined effect of centrifugal force and radiation pressure gives rise to two latitudinal rings of enhanced brightness which are symmetric around the equator in the upper and lower hemispheres. They lie near the edges of differentially rotating and radiating upper and lower belts. The bright rings shift from the equatorial zone to higher latitudes when the luminosity $L$ rises. The ring zones are characterized by a minimum surface density and, accordingly, by a maximum meridional spread velocity. At a low accretion rate and luminosity, the released energy is removed through the comptonization of low-frequency photons.

Motivation & Objective

• To understand the hydrodynamic spreading of accreted matter over a neutron star's surface during disk accretion.
• To investigate how rotation deceleration and energy dissipation occur on the stellar surface due to friction with dense underlying layers.
• To model the formation and evolution of latitudinal brightness structures under varying luminosity and radiation pressure.
• To determine the role of centrifugal force and Comptonization in shaping the surface flow and emission patterns.
• To explore the transition from equatorial to polar migration of bright rings as accretion luminosity increases.

Proposed method

• Uses the shallow-water approximation to model the thin, viscous flow of accreted matter on the neutron star surface.
• Incorporates frictional drag from dense underlying layers to simulate rotational braking of the star.
• Solves the hydrodynamic equations including radial and latitudinal velocity components, surface density, and energy dissipation.
• Applies radiation pressure and centrifugal force terms to determine the location and structure of bright rings.
• Considers Comptonization as the dominant energy removal mechanism at low luminosities.
• Analyzes the meridional spread velocity and surface density distribution to identify regions of maximum flow and minimum density.

Experimental results

Research questions

• RQ1 How does the accreted matter spread over the neutron star surface under varying accretion luminosities?
• RQ2 What causes the formation of two symmetric bright rings in the upper and lower hemispheres?
• RQ3 How does the location of the bright rings evolve with increasing luminosity?
• RQ4 What physical mechanisms—centrifugal force, radiation pressure, or viscous drag—dominate in shaping the surface flow?
• RQ5 How does energy dissipation occur, and what role does Comptonization play at low luminosities?

Key findings

• Two symmetric bright rings form near the edges of differentially rotating upper and lower surface belts due to combined radiation pressure and centrifugal forces.
• The bright rings migrate from the equatorial zone toward higher latitudes as the luminosity $ L $ increases.
• The rings correspond to regions of minimum surface density and maximum meridional spread velocity on the stellar surface.
• Rotation slows down due to friction against dense underlying layers, with energy dissipation occurring in a latitudinal belt whose width increases with luminosity.
• At low accretion rates, energy is primarily removed via Comptonization of low-frequency photons.
• The model predicts a clear correlation between luminosity and the latitudinal extent of the radiating and spreading regions on the neutron star surface.