Astronomy Reports 46, 366-379 (2002) Russian version in Astronomichekii Zhurnal, 79, 407-421 (2002) Printed 10 October 2018 Non-Steady State Accretion Disks in X-Ray Novae: Outburst Models for Nova Monocerotis 1975 and Nova Muscae 1991 G. V. Lipunova1⋆, N.I.Shakura1,2 1Sternberg Astronomical Institute, Universitetskiy pr., 13, Moscow 119992, Russia 2Max Planck Institut for Astrophysics, Garching, Germany Received June 25, 2001; in final form September 13, 2001 ABSTRACT We fit outbursts of two X-ray novae (Nova Monocerotis 1975 = A 0620–00 and Nova Muscae 1991 = GS1124–683) using a time-dependent accretion disk model. The model is based on a new solution for a diffusion-type equation for the non-steady-state accretion and describes the evolution of a viscous α–disk in a binary system after the peak of an outburst, when matter in the disk is totally ionized. The accretion rate in the disk decreases according to a power law. We derive formulas for the accretion rate and effective temperature of the disk. The model has three free input parameters: the mass of the central object M, the turbulence parameter α, and the normalization parameter δt. Results of the modeling are compared with the observed X-ray and optical B and V light curves. The resulting estimates for the turbulence parameter α are similar: 0.2–0.4 for A 0620–00 and 0.45–0.65 for GS 1124–683, suggesting a similar nature for the viscosity in the accretion disks around the compact objects in these sources. We also derive the distances to these systems as functions of the masses of their compact objects. DOI: 10.1134/1.1479424 1 INTRODUCTION compact star in a close binary. An important property of the disk in a binary system is that its outer radius Accretion provides an efficient mechanism for energy re- is limited. Angular momentum is carried away from the lease in stellar systems, making many astrophysical ob- outer boundary of the disk due to tidal forces, so that the jects observable. If the matter captured by the gravitation rotation of outer parts of the disk is synchronized with of the central body possesses nonzero angular momentum the rotation of the secondary. It is assumed that the size relative to this body, accretion occurs in a disk. This is of the accretion disk specified by the tidal interactions is true, for example, in binaries, where the angular momen- constant over the time interval considered. Another as- arXiv:0905.2515v1 [astro-ph.HE] 15 May 2009 tum is associated with the orbital rotation of the compo- sumption is that the rate of mass transfer from the sec- nents. In the course of accretion onto a compact object ondary to the disk is small compared to the accretion rate whose radius is comparable to the gravitational radius, within the disk. a substantial fraction of the total energy of the accreted matter mc2 is released. The last condition is satisfied, for example, in an Outbursts reflect one of the most fundamental prop- X-ray nova outburst. The accretion rate in the disk erties of accretion: its non-steady-state character. Cur- during the outburst reaches tenths of the Eddington −9 rently, a number of different models are proposed to ex- rate 10 (ϑ M/M⊙) M⊙/yr or more, where θ is the plain non-steady-state processes in accretion disks and to accretion efficiency and M is the mass of the cen- describe the observed source variability. One problem is tral object), while the observed rate of mass trans- to find an adequate description for the viscosity in the fer from the companion in quiescent periods is 10−11– −12 accretion disk: viscosity is essential for the accretion, and 10 M⊙/yr (Tanaka & Shibazaki 1996; Cherepashchuk the viscosity characteristics specify the features of time- 2000). X-ray novae are low-mass binaries contain- dependent disk behavior. ing a black hole or a neutron star (see, for exam- In Lipunova & Shakura (2000), a new solution for the ple, Cherepashchuk (2000)). The other component, a low- basic equation of time-dependent disk accretion is found mass dwarf, fills its Roche lobe, so matter continuously and applied to a model of an accretion α–disk around a flows into the disk (Cherepashchuk 2000). 2 G. V. Lipunova and N.I. Shakura Currently, more than 30 X-ray novae are for example, Cannizzo et al. (1988)); 10−2 for disks in ∼ known (Cherepashchuk 2000). Most of them have galactic nuclei (Siemiginowska & Czerny 1989); 1 for ∗ ∼ light curves with similar exponentially decreasing pro- Sgr A in an advection-dominated model (Narayan et al. files (Chen et al. 1997). During the burst rise, the 1995); and 0.1 0.3 in the inner, hot advective 2 6 ∼ − intensity increases by a factor of 10 –10 over several part of the disk for the X-ray novae GS 1124–683, days, whereas the exponential decrease of the light curve A 0620–00, and V404 Cyg, basing on spectra in the low lasts for several months, with a characteristic time of state (Narayan et al. 1996). about 30–40 days. Two mechanisms for X-ray nova outbursts are de- veloped: disk instability and unstable mass transfer from the secondary. A final choice between them has not been 2 MODEL FOR ACCRETION DISKS IN made, and each model faces some problems (see, for ex- X-RAY NOVAE ample, Cherepashchuk (2000)). In disk-instability models, The evolution of a viscous accretion disk is described by during the outburst, the central object accretes matter ac- the diffusion-type nonlinear differential equation (Filipov cumulated by the disk over decades of the quiescent state. 1984): This idea is supported by the fact that the mass-transfer ∂F F m ∂2F rate in quiescent periods is comparable to an accretion = D , (1) rate corresponding to the outburst energy divided by the ∂t hn ∂h2 time between outbursts (Tanaka & Shibazaki 1996). 2 where F = Wrϕ r is the total moment of the viscous In any case, an important point here is that we as- forces acting between adjacent rings of the disk divided sume the presence of a standard disk at the time of maxi- by 2π, Wrϕ is the component wrϕ of the viscous stress ten- mum brightness of the source, as confirmed by spectral sor integrated over the thickness of the disk, h = √GMr observations (Tanaka & Shibazaki 1996). By ”standard is the specific angular momentum, and M is the mass of disk” we mean a multi-color α–disk whose inner radius the central object. The dimensionless constants m and n coincides with the last stable orbit around the black hole, depend on the type of opacity in the disk. If the opacity is with the velocity of radial motion of gas being small com- determined largely by absorption (free–free and bound– pared to other characteristic velocities in the disk. Then, free transitions), then m = 3/10 and n = 4/5. The “dif- the solution of Lipunova & Shakura (2000) can be applied fusion coefficient” D specified by the vertical structure of to the decay of an X-ray nova outburst. The light curve the disk relates the surface density Σ, F , and h (Filipov calculated using the solution describes observations when 1984; Lyubarskij & Shakura 1987): the contribution of the accretion disk dominates in the soft X-ray radiation of the system. This phase is char- (GM)2 F 1−m Σ= . (2) acterized by a definite spectral state and can be distin- 2 (1 m) D h3−n guished in the evolution of an X-ray nova. − Relation (2) is derived from an analysis of the vertical Modeling the light curves of an X-ray nova in several structure of the disk. X-ray and optical bands enables one to derive the basic A class of solutions for Eq. (1) is derived parameter of the disk, the turbulence parameter α (this in Lyubarskij & Shakura (1987) during studies of the evo- is a new, independent method for determining α in as- lution of a torus of matter around the gravitating center trophysical disks), as well as the relationship between the under the action of viscous forces, which are parameter- distance and mass of the compact component. ized by the turbulent viscosity parameter α introduced Here, we apply our model to Nova Monocerotis in Shakura (1972). In particular, a solution was obtained A 0620–00, which is the brightest nova in X-rays observed for the stage when the torus has evolved to an accretion- to the present time, and Nova Muscae GS 1124–683. 1 disk configuration, from which matter flows onto the cen- Currently, the most likely mechanism for turbu- tral object. When the accretion rate through the inner lence and angular-momentum transfer in accretion disks edge decreases, the outer radius of the disk simultane- is thought to be Velikhov–Chandrasekhar magnetic– ously increases—the matter carries angular momentum rotational instability (Velikhov 1959; Chandrasekhar away from the center. In this model, the accretion rate 1961), which is investigated in application to accretion decreases with time as a power law. The power-law index disks by Balbus & Hawley (1991). Calculations suggest − depends on the type of opacity in the disk. that this type of instability corresponds to α 10 2. ∼ An important property of a disk in a binary sys- The parameter α, which was introduced by Shakura tem is the cutoff of the disk at the outer radius, (1972), describes large-scale turbulent motions. The large- in the region where the angular momentum is car- scale development of MHD turbulence has been sim- ried away due to the orbital motion (see, for ex- ulated, for example, by Armitage (1998) and Hawley − ample, Ichikawa & Osaki (1994)).