NASA Technical Reports Server (NTRS) 19940026624: Can a variable alpha induce limit cycle behavior and exponential luminosity decay in transient soft x ray sources?

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by  NASA Technical Reports Server (NTRS)

LPITechnical Report94-03, Part I 3
mation about the structure, stability, and dynamics of the disk. observational data on transient soft X-ray novae, which are low-
Using the basic thermal Keplerian disk paradigm, we consider in mass X-ray binaries. It is widely believed that nonsteady mass
particular generalizations of the standard optically thindisk models i transfer from the secondary onto the compact primary, through an
needed to accommodate the extremely rich variety of dynamical i accretion disk, is the reason for the observed spectacular events in
phenomena exhibited by black hole candidates, ranging from flares i the form of often repetitive outbursts, with recurrence times ranging
of electron-positron annihilations and quasiperiodic oscillations in ! from Ito60 yrandduration time onthe scale of months. Though not
the X-ray intensity to X-ray novae activity. These in turn provide having reached yet a consensus about the nature oftbe mechanism
probes of the disk structure and global geometry. The goal is to that regulates the mass transfer, the disk thermal instability model
construct a single unified framework to interpret a large variety of [I-4] seems tohe favored by the fact that the rise inthe hard X-ray
black hole phenomena. This paper will concentrate on the interface luminosity is priorto the rise in the soft X-ray luminosity, while the
between basic theory and observational data modeling. -- mass transfer instability model [5-7] seems to behindered by the
N94-31127 fact that the luminosity during quiescence is unable to trigger the
+ thermal instability. However, itshould be stressed that, remarkably,
NONLINEAR CALCULA;I'IONS OF THE TIME _the X-ray light curves of these X-ray novae all show overall expo-
EVOLUTION OF BLACK HOLE ACCRETION DISKS. :nential decays (Ld- exp-t/t0, afeature quite difficult to reproduce
C. Luo, Department of Space Physics and Astronomy, Rice : inthe framework of the viscous disk model, which yields powerlike
University, P.O. Box 1892, Houston TX 77251-1892, USA. luminosity decay. Taking into account this observational constraint,
we have studied the temporal evolution of perturbations in the
" Based on previous works on black hole accretion disks, I con- accretion rate, under the assumption that (Iis radial and parameter
. tinue to explore the disk dynamics using the finite difference method dependent. The chosen dependence is such that the model can
tosolve the highly nonlinear problem of time-dependent alpha disk reproduce limit cycle behavior (the system is locally unstable but
equations. globally stable). However, the kind of dependence we are looking
Here aradially zoned model is used to develop acomputational for in ctdoes riot allow us to use the usual Shakura and Sunyaev
"scheme in order to accommodate functional dependence of the procedure in the sense that we no longer can obtain a Iinearized
viscosity parameter alpha on the disk scale height and/or surface :continuity equation without explicit dependence on the accretion
density. This work is based on the author's previous work on the rate. This is sobecause now we cannot eliminate the accretion rate
isteady disk structure and the linear analysis of disk dynamics to try by using the angular momentum conservation equation. In other
to apply to X-ray emissions from black candidates (i.e., multiple- .-,vords, the stress now depends upon the surface density, the scale
height of the disk, and the accretion rate. If we write the viscosity
a 31i28_ parameter as
)'l_states-p_e_c,Utra, inst/a/,bf,i,lfi_ti.ers+, QPOs, etc.).
EVOLUTION OF VAPORIZING PUI_A__RS,. P. McCormick, <z- o_of
Department of Physics and Astronomy, Louisiana State University,
Baton Rouge LA 70803, USA. wherewe have included the r-dependence in etoaridthe p-arameter-
dependence in f,we obtain the linearized angular momentum con-
" - We construct evolutional scenarios for LMXBs using a simpli- servatlon- e_quation
; fled stellar model. We discuss the origin and evolution of short-
" period, low mass binary pulsars with evaporating companions. We
- suggest that these systems descend from low-mass X-ray binaries
fo 3 aRt, gio )
and that angular momentum loss mainly due to evaporative wind
drives their evolution. We derive limits on the energy and angular
momentum carried away by the wind based on the observed low the linearized continuit_ equation =:
eccentricity. In our model the companion remains near contact and
its quasiadiabatic expansion causes the binary to expand. Short- a 1
term oscillations of the orbital period may occur ifthe Roche-lobe ZoO- u = 2--_ aR
overflow forms anevaporating disk.
Acknowledgments= This work hasbeen supported inpart by: and the linearized energy equation-
theU.S. National Science Foundation through gram AST-9020855
and in part by NASA through grantNAGW-2447 ..... _ .
N9 -31129 ( ) a
5'/3 - 73 /,9Z_$ • -8+51_°-313°z+ _" h+3 (l+_o+4_o') _-_)u=
CAN A VARIABLE ALPHA INDUCE LIMIT CYCLE BE- ...
HAVIOR AND EXPONENTIAL LUMINOSI]_+ DECAY _ .... a2 ( +2h_Sf,_+_.
TRANSIENT SOFT X-RAY SOURCES.'? C; Meirelles Filho 2 (5+ i8[3o + 9i3o') (Xofll02 _ t," fo )
and E. P. Liang, Space Physics and Astronomy Department, Rice 3 _ _
University, Houston TX 77251, USA.
- There has been, recently, a revival of the stability problem of 3¢to_ r2 (i +i_o)u + 2 (5[3o-3)h _5.f]
accretion disks. Much of this renewed interest is due to recent _.L foJ
4
Workshop onPhysics ofAccretion Disks
This equation only gives us the local response of the disk tothese the problem under the influence of rotation is made nor the condi-
perturbations, and we see that the a r-dependence plays no role, the i tions under which there will be local energy dissipation and an
major role being locally played by the p_rneter dependence. When - effective Viscosity can be assign_o th_flow. Also, not apparent in
we look for the global response of the disk, this equation no longer : their results areeffects such as inverse energy cascade with conse-
applies, being substituted by the correct and more complicated set quent diminishing of the angular momentum transport efficiency or
of coupled differential equations, which solution is highly depen- even how the spectrum in the inertial zone, i.e., Kolmogorov's
dent on the ¢t radial dependence. spectrum, is affected by rotation. In aprevious papeL[$_ employing
References: [I]Carmizzo J.K. etal.(1982)inPulsationsin results from it]: we have shown that even for Rossby number >l
Classicaland CataclysmicVariables(LP.Cox and C.I.Hanson, turbulence isaffected by rotation, but itsucceeds informing smaller
eds.),Univ.ofColorado,Boulder.[2]LinD.N.C.andTaam R. E. structures, ascompared to the case without rotation, in such away
(1984)inHigh Energy TransientsinAstrophysics(S.E.Woosley, - asto overcome rotational effects. As far as the efficiency of angular
ed.),AIP Conf.Proc.115,83,New York.[3]Huang M. andWheeler - momentum transport is concerned, the value of the viscosity param-
J.C.(1989)Astrophys.J.,343,229.[4]Mineshige S.andWheeler eter is highly affected, even ifthe Rossby number is much greater
J.C.(1989)Astrophys.J.,343,241.[5]HameuryJ. M.etal.(1986) than 1.
Astron. Astrophys., 162, 7!. [6] Hameury J. M. etal. (!988) Astron. _ Such results, however, were derived considering ahot disk, in
Astrophys., 192, 187. [7] Hameury J. M. et al. (1990) Astrophys. J., ",i which opacity is mainly given by electron scattering. In the present
,. N94-31130
353, _85 _._-=w:o-wrkorkforwethheavdeescarpipptliioedn tohfethfeorvmisucloautiso-sntagedevesloolpaerdnebiunlat.heFopllroewviionugs
Wood and Morrill [6] we have used two piecewise continuous
CONVECTIVE SOLAR NEBULA. C. Meirelles Fiiho and M. powerlaws that depend only on the temperature, corresponding to
\
Reyes-Ruiz, Space Physics and Astronomy Department, Rice regions in which opacity is provided either by water ice grains or
University, Houston TX 77251, USA. silicate and Fe grains. It should be remarked,=_h0wever, that by
taking into account the z-structure of the _._sk, there will be, no
Analyzing turbulent flows with rotation, Dubrulle andValdettaro matter the radius, aregion close to the surf_e of the disk, where the
: [I] have concluded that some new effects come into play and may lower-temperature opacity law applies. As we go further out, this
! modify the standard picture we have about turbulence. In that region approaches the midplane of the disk. In the outer regions,
. respect the value of the Rossby number is of crucial importance where the temperature is below the ice condensation point, only the
since itwill determine the transition between regimes where rota- lower-temperature law is applicable. The height of the point sepa-
tion is oris not important. With rotation there will be atendency to rating these regions will becrucial in the determination of anisot-
constrain the motion to the plane perpendicular to the rotation axis ropy factor and the visf_osity parameter as well as in the possible
and as aconsequence the horizontal scale will increase as compared existence of critical pai'ameters for the flow. Although our results
"_to the longitudinal one, which means that the tumover time in this are preliminary compared to other results in the literature, the
direction will increase. The net effect is that the energy cascade efficiency for angidar momentum transport we have obtained is
down process is hindered by rotation. As a matter of fact, when higher. These high values ofct may imply that within this formula-
- rotation ispresent one observes two cascades: An enstrophy (vortic- tion the viscous evolutionary stage of the nebula is shorter. Our
; ity) cascade from large scales to small scales and an inve_e energy formulation also implies aminimum accretion rate to ignite convec-
cascade from small scales to large scales. Since the first process is tive instabilities. Since the mass of the disk is related to the accre-
- not efficient on transporting energy to the dissipation range, what tion r_te the main implication of this is related to the age of the
5 nebula. "
we see isenergy storage in the large structures at the expense of the
small structures. This kind of behavior has been confirmed experi- References: [1]Dubrulle B. and Valdettaro L. (1992) Astron.
mentally by Jacquin et al. [2], who observed that, with rotation, Astrophys., 263, 387. [2] Jacquin L. et al. (1990) J. Fluid Mech.,
Lho,="Ro-_ I..=,where 3'isa parameter that depends on the Reynolds 220, I. [3] Cabot W. et al. (1987)Astrophys. J.. 69, 387. [4] Canuto
= number and measures the influence of rotation on turbulence and R° V. M. and Goldman I. (1984) Phys. Rev. Lett., 54-05, 430.
; is the Rossby number. For a very large 3'we obtain, in the inertial [5] Meirelles C. F. et al. (!993) submitted. [6] Wood and Morrill
: range, aspectrum of k-_ instead of the usual Kolmogomv's k-sis (1988) in Meteorites in the Early Solar System, 329-347, Univ. of
° spectrum. In reality, when rotation is dominant, energy gets stored N94-31131
Arizona.
- in inertial waves that propagate it essentially in the longitudinal
direction. In that case, we can no longer assign just one viscosity to
_the fluid and, what is most important, the concept of viscosity loses ROTATIONAL EFFECTS IN TURBULENCE DRIVEN BY
ks meaning since we no longer have local transport of energy. CONVECTION. C. Meirelles Fiiho, M. Reyes-Ruiz, and C.
,_ccording to Dubrulle [1], Ro = 1is the borderline between these Luo, Space Physics and Astronomy Department, Rice University,
"t_voscenarios: For Ro> 1turbulence is not affected byrotation, for Houston "IX77251, USA.
Ro < ! it will be greatly affected. It is worth mentioning that
compressibility effects will also affect turbulence through the gen- We have treated turbulence with rotation in a thin Keplerian
eration of waves, shocks, etc. These aspects have been underesti- disk. Highlighting implicit assumptions already existent in the _t
mated byCabot et al. [3] in their application of the theory of large- model together with ageometrical but physically reasonable deduc-
° structure turbulence developed by Canuto and Goldman [4] for the "tion of the degrees of freedom of the largest eddies, which is of
turbulence generated by convective instability, in the sense that no paramount importance in our formulation, we were able to obtain
" discussion about the behavior of the characteristic scale lengths in /elations satisfied by parameters of the turbulence, such as turnover