An Analytic Disk Model - Inferences and Logical Structure
An Analytic Disk Model Inferences and Logical Structure R. E. Wilson University of Florida A half-century ago (and further back), a school of thinking disbelieved in OC binaries (W UMa's, etc.), presumably because computation of their light curves was impractical with existing computers So the likely thinking was "if we can't do the computations, the OC model isn't real
This mental barrier delayed meaningful progress on W UMa's and other OC's because the adopted morphology (point contact) was inappropriate Now we have the analogous situation for significantly massive disks in tight binaries - disbelief in self-gravitating (i.e. significantly massive) disks for lack of a way to do the proper computations (light curves, RVs, . . .) The point is NOT that most disks in binaries are significantly massive -- just that SOME very interesting ones may be, and that issue needs investigation This contribution follows a sequence of papers on self gravitating analytic disk models, the latest being ApJ, 869, 19 (2018). Here the underlying concepts are
emphasized and the analysis procedure is made impersonal. Binary Morphology Role of Limiting Lobes Contact means contact with a limiting lobe (not with other star) Detached and SD in the context of beta Lyrae Kuiper (c. 1941) Detached and SD in the context of Algols Kopal (1950s) OC in the context of W UMas Lucy (1968); several others soon after Double contact (super-synchronous rotation) Wilson (1979) See IBVS 5076 (2001) for a brief history of the four categories See ApJ, 869, 19, sec. 5.2 for references to observational examples of double contact
If quantitative modeling for globally self-gravitating disks in binaries is the goal, lets think about the relevant morphology In the garden of binaries, conceptual morphology is the gateway and analytic morphology is the pathway so enter the gateway and follow the pathway In other words -- morphology is fundamental How about -- double contact Why? double contact is a natural consequence of large scale or
long duration mass transfer -- RPMT or long-continued (SPMT) And mass transfer spins up an accreting star Here are two of the many non self-gravitating disk model illustrations in the journals. All are basically the same (fan out with radius, with outer chop). They are also chopped on the inside and axi-symmetric (no tidal stretching). Why might structurally significant disk self-gravity be seriously entertained, considering that massive disks are seldom mentioned?
a) dozens of papers have analyzed disks as optically thick, with no semi-transparency. Semi-transparency can be explored. b) The beta Lyrae disk has been there for two millennia. Why not at least somewhat massive? Lets see what the observations say about disk mass c) substantial mass helps a disk to survive nova explosions that would blow a fluffy disk away (as quantified in terms of energetics by Fig. 7 of ApJ, 869, 19). Recurrent nova CI Aqls disk
survived the outburst of 2000 basically intact If massive disks exist, wheres to look? (kind of binary) Well, W Serpentis stars (like beta Lyrae) have large mass transfer rates, and classical novae transfer at low rates for long times And hows to recognize a massive disk system? Figs. 10 and 11 of ApJ, 869, 19 show dependence of disk thickness on disk mass and several other parameters, although analysis is needed. Surface equipotentials for the self-gravitating disk model for four disk
masses (more massive thicker). Dot on x-axis marks the ring-like mass concentration. Potential includes gravitation of the two star masses and disk mass and centrifugal potential. However serious observational problems stand in the way, such as . . . I. Wild light curve excursions due to disk disturbances II. CVs are mainly observed in and just after outburst, when disks are most disturbed
III. The mass-receiving stars in many systems are hidden within the disk, so unobservable Analytic A-D Disk Model A-D may apply to CVs and W Sers and leans on knowledge about Be stars and beta Lyrae Not for optically thin disks, but semi-transparent edges could be interesting Most light curve analyses for binary circum-stellar disks have been based on ONE model
-- non-SG entirely opaque tiled surface axi-symmetric (many programs, one model) The A-D model naturally produces phenomena characteristic of disks in binaries in particular tidal variation with gravity brightening and an outer null-gravity point -- location now can be computed accurately Subjective fit from 2018 Recent impersonal (Least Squares) Fit
CI Aql V-band light curves by Kent Honeycutt Some numbers for CI Aql (double contact solution) - Star 1 is the white dwarf (from final solution} Inclination Mass ring radius Disk mass/star 1 mass Disk radius (pos. x-axis) Disk mean density (outer part)
Disk T_eff 67.49 deg. 0.0325 a 0.044 0.212 a 3.4 x 10 (-11) g/cm^3 15729 K (from preliminary solutions)
Star 1 T_eff Star 2 T_eff P_orbital A = a_1 + a_2 Star 1 angular rotation/orbital angular rotation 15000 K 6100 K 0.6183619 day 4.5719 R_sun
6000 Summary Model built upon an equipotential structure with gravitation of stars 1 & 2 & disk and disk & star 1 rotations -- disk is a volume emitter with internal attenuation of its own light and the stars light -- can test for fuzzy edges -- output: light curves, RV curves -- finds parameters impersonally, with standard errors
-- suggested applications: classical novae, nova-like variables, and W Serpentis stars that are not too seriously disturbed A plea to observers: observe these systems when they are NOT erupting: Ending Comments Here we have an area of intense interest (classical novae) and cannot agree on a key property (disk masses) within a factor of 1000 3 ingredients are needed a) Appropriate model including disk mass (1981) b) Effective light curve, RV, & analytic algorithms (2018, now)
c) Useful observations (more are needed when not erupting -- shed light on the disk interiors) References (Many more are in ApJ, 869. 19) Abramowicz, M.A.., et al. 1984, MNRAS, 208, 291 (SG disk topology) Bisikalo, D., et al. , A&A, 353, 1009 (disk fluid dynamics)
Bodo, G. & Curir, A., A&A, 253, 318 (SG disk structural model Harmanec, P. 2002, AN, 323, 87 (beta Lyrae review) Kopal, Z. 1955, AnAp, 18, 370 (detached, semi-detached morphology Kuiper, G.P. 1941, ApJ, 93, 133 (early morphlology) Linnell, A.P., Harmanec, P., & Koubsky, P. 2006, A&A, 455, 1037 Sahman, D.I., Dhillon, V.S., Marsh, T.R., et al. 2013, MNRAS, 433, 1588
Van Hamme, W., Wilson, R.E., & Guinan, E.F. 1995, AJ, 110, 1350 Wilson, R.E. 1979, ApJ, 234, 1054 (double contact morphology) Wilson, R.E. 1981, ApJ, 251, 246 (massive disk equipotentials) Wilson, R.E. 2018, ApJ, 869, 2019 (disk model light and RV curves) Wilson, R.E. & Honeycutt, R.K. 2014, ApJ, 795, 8 (observed CI Aql light curves)
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