A toy model for magnetized neutrino-dominated accretion flows

Abstract

In this paper, we present a simplified model for magnetized neutrino-dominated accretion flow (NDAF) in which effect of black hole (BH) spin is taken into account by adopting a set of relativistic correction factor, and the magnetic field is parameterized as β , the ratio of the magnetic pressure to the total pressure. It is found that the disc properties are sensitive to the values of the BH spin and β , and more energy can be extracted from NDAF for the faster spin and lower β .black hole, gamma-ray bursts, accretion disc, magnetic fieldThe nature of the central engine of gamma-ray bursts (GRBs) remains unclear, and the favoured models invoke binary merger or collapse of compact objects. These models lead to the formation of a transient hot and dense accretion torus/disc around a black hole (BH) of a few solar masses. If an accretion disc is cooled mainly via the neutrino loss, it is referred to as neutrino-dominated accretion flow (NDAF) [1].NDAF has been extensively discussed by many authors [2][3][4][5]. However, the effects of the magnetic fields are usually neglected in NDAF due to the intrinsic complexity.Magnetic fields could play an important role in the central engine in some aspects [10], e.g., a bold gamma-ray polarization [6], a higher magnetic energy density required by the reverse shock [7,8], and the energy argument for X-ray flares [9]. These considerations stimulate us to discuss a model of magnetized NDAF.Recently, Chen & Beloborodov [4], Gu et al.[5] and Shibata et al. [11] argued that the general relativistic (GR) effects are important for NDAF, and we introduce GR correction factors in our model. This paper is organized as follows. In Sect. 1 we describe the magnetized NDAF in the frame of a relativistic thin disc of steady state, and the effects of MHD stress are described. The main equations are based on refs.[2] and [3], but corrected with GR factors. We solve the set of equations for the solutions of NDAF in Sect. 2, and compute disc temperature, density and neutrino luminosities. The effects of the free parameters are also discussed. Finally, we summarize our results and discuss some related issues in Sect. 3. Magnetized Neutrino-Dominated Accretion FlowsAs is well known, the magneto-rotational instability (MRI) plays an important role in angular momentum transportation of accretion disc [11,12]. Currently, it is widely believed that the viscosity in accretion flows is effectively determined by the turbulent motion of fluid, being related to the magnetic stress. Therefore, we consider only the magnetic viscosity in this model.The magnetic viscous shear r t ϕ can be expressed as where B ϕ is given byThe parameter β is the ratio of the magnetic pressure to the total pressure. A roughly steady state is reached when the growing rate of B ϕ generated by differential rotation of the radial field is equal to its loss rate due to buoyancy effect, and B ϕ can be estimated as [13]

Vertical Structure of Neutrino-Dominated Accretion Disks and Neutrino Transport in the Disks

“…Assuming an extreme constant accretion rate of 10 Msun/s means therefore an enormous total mass consumption for powering GRBs, especially for powering long bursts, which might be realistic. Therefore, the simple NDAF model which is investigated in this work can not produce sufficient energy to power GRBs, the effects of the spin of black hole or/and the magnetic field in the accretion flow might be introduced to power the central engine of GRBs (see Li 2002;Chen & Beloborodov 2007;Lei et al 2009Lei et al , 2010Janiuk & Yuan 2010, for instance).…”

Hyperaccreting Black Hole as Gamma-Ray Burst Central Engine. II. Temporal Evolution of the Central Engine Parameters during the Prompt and Afterglow Phases

“…However, their results are based on a Newtonian disk model. Gu et al (2006), Chen & Beloborodov (2007) and Lei et al (2010) argued that the general relativistic effects are also important. In this paper, we adopt a model of a steady-state disk around a Kerr BH, in which neutrino loss and transfer are taken into account.…”