On vertical structure of accretion disks in type ia supernova progenitors

We study the vertical structure of a thin α–disk [1] in a Type Ia supernova (SN Ia) progenitor system. Accurate equation of state and opacity of solar composition material are used. The results show pronounced features in the disk structure in the regions of ionization and molecule dissociation. We...

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Datum:	2012
1. Verfasser:	Zhiglo, A.V.
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Sprache:	English
Veröffentlicht:	Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2012
Schriftenreihe:	Вопросы атомной науки и техники
Schlagworte:	Section C. Theory of Elementary Particles. Cosmology
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spelling	irk-123456789-1070942016-10-14T03:02:24Z On vertical structure of accretion disks in type ia supernova progenitors Zhiglo, A.V. Section C. Theory of Elementary Particles. Cosmology We study the vertical structure of a thin α–disk [1] in a Type Ia supernova (SN Ia) progenitor system. Accurate equation of state and opacity of solar composition material are used. The results show pronounced features in the disk structure in the regions of ionization and molecule dissociation. We analyze the mass distribution in the disk, aiming to find the system parameters at which this mass distribution could explain the high velocity features (HVF) in SN Ia spectra [2]. We conclude that accretion disks are unlikely candidates for explaining the HVF. Мы изучаем вертикальную структуру тонкого α-диска [1] в системе предшественника сверхновой типа Iа (СН Iа). Использованы точное уравнение состояния и коэффициенты непрозрачности вещества солнечного состава. Результаты демонстрируют выраженные особенности в структуре диска в областях диссоциации молекул и ионизации. Анализируется распределение массы в диске с целью найти параметры системы, при которых это распределение могло бы объяснить высокоскоростные особенности (ВСО) в спектрах СН Iа [2]. Мы делаем вывод, что классические аккреционные диски являются маловероятными кандидатами для объяснения ВСО. Ми вивчаємо вертикальну структуру тонкого α-диску [1] в системі попередника наднової типу Іа (НН Іа). Застосовані точне рівняння стану і непрозорість речовини сонячного складу. Результати демонструють виражені особливості в структурі диску в областях дисоціації молекул та іонізації. Аналізується розподіл маси в диску з метою знайти параметри системи, при яких цей розподіл міг би бути поясненням особливостей з великими швидкостями (ОВШ) в спектрах НН Іа [2]. Ми робимо висновок, що класичні акреційні диски не є правдоподібними кандидатами для пояснення ОВШ. 2012 Article On vertical structure of accretion disks in type ia supernova progenitors / A.V. Zhiglo // Вопросы атомной науки и техники. — 2012. — № 1. — С. 193-197. — Бібліогр.: 18 назв. — англ. 1562-6016 PACS: 97.10.Gz, 97.60.Bw, 95.30.Lz, 44.40.+a, 44.25.+f, 42.25.Bs, 05.70.Ce, 05.20.-y, 02.70.Bf, 02.60.Lj http://dspace.nbuv.gov.ua/handle/123456789/107094 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
topic	Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology
spellingShingle	Section C. Theory of Elementary Particles. Cosmology Section C. Theory of Elementary Particles. Cosmology Zhiglo, A.V. On vertical structure of accretion disks in type ia supernova progenitors Вопросы атомной науки и техники
description	We study the vertical structure of a thin α–disk [1] in a Type Ia supernova (SN Ia) progenitor system. Accurate equation of state and opacity of solar composition material are used. The results show pronounced features in the disk structure in the regions of ionization and molecule dissociation. We analyze the mass distribution in the disk, aiming to find the system parameters at which this mass distribution could explain the high velocity features (HVF) in SN Ia spectra [2]. We conclude that accretion disks are unlikely candidates for explaining the HVF.
format	Article
author	Zhiglo, A.V.
author_facet	Zhiglo, A.V.
author_sort	Zhiglo, A.V.
title	On vertical structure of accretion disks in type ia supernova progenitors
title_short	On vertical structure of accretion disks in type ia supernova progenitors
title_full	On vertical structure of accretion disks in type ia supernova progenitors
title_fullStr	On vertical structure of accretion disks in type ia supernova progenitors
title_full_unstemmed	On vertical structure of accretion disks in type ia supernova progenitors
title_sort	on vertical structure of accretion disks in type ia supernova progenitors
publisher	Національний науковий центр «Харківський фізико-технічний інститут» НАН України
publishDate	2012
topic_facet	Section C. Theory of Elementary Particles. Cosmology
url	http://dspace.nbuv.gov.ua/handle/123456789/107094
citation_txt	On vertical structure of accretion disks in type ia supernova progenitors / A.V. Zhiglo // Вопросы атомной науки и техники. — 2012. — № 1. — С. 193-197. — Бібліогр.: 18 назв. — англ.
series	Вопросы атомной науки и техники
work_keys_str_mv	AT zhigloav onverticalstructureofaccretiondisksintypeiasupernovaprogenitors
first_indexed	2025-07-07T19:29:15Z
last_indexed	2025-07-07T19:29:15Z
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fulltext	ON VERTICAL STRUCTURE OF ACCRETION DISKS IN TYPE IA SUPERNOVA PROGENITORS A.V. Zhiglo ∗ National Science Center “Kharkov Institute of Physics and Technology”, 61108, Kharkov, Ukraine (Received November 21, 2011) We study the vertical structure of a thin α−disk [1] in a Type Ia supernova (SN Ia) progenitor system. Accurate equation of state and opacity of solar composition material are used. The results show pronounced features in the disk structure in the regions of ionization and molecule dissociation. We analyze the mass distribution in the disk, aiming to find the system parameters at which this mass distribution could explain the high velocity features (HVF) in SN Ia spectra [2]. We conclude that accretion disks are unlikely candidates for explaining the HVF. PACS: 97.10.Gz, 97.60.Bw, 95.30.Lz, 44.40.+a, 44.25.+f, 42.25.Bs, 05.70.Ce, 05.20.-y, 02.70.Bf, 02.60.Lj 1. INTRODUCTION Disk structures are ubiquitous in the Universe. They are formed when gas is drifted by gravitational force to the center of attraction, in the process decreas- ing its angular momentum by transporting it to the gas layers farther from the center via some viscosity mechanism. What is loosely called “gas” may in real- ity be plasma, it may contain solid particles, depend- ing on the specific situation. Viscosity is believed to be turbulent/convective eddy viscosity, it may have magnetic origin; microscopic molecular viscosity is negligible to play any role. The heat being released by the viscosity, as well as other heat sources like irra- diation by the central object, hot inner regions of the disk, other objects in the disk environment, is trans- ferred to the disk surface and radiated into space. The heat production in the disk normally leads to the gas temperature increasing towards the disk equato- rial plane; thermal pressure of the gas supports the gas vertical distribution (in z−direction, along the average gas momentum vector, perpendicular to the disk plane of symmetry), prevents it from collapsing to the equatorial plane. Various phenomena in the disks, instabilities of the disks in their environment lead to intricate struc- ture formation (galaxies, protoplanetary disks). Ra- diation from various disk regions is observed by as- tronomers, from subtle spectral features due to rela- tively dim protostellar and circumstellar disks, to ac- tive galactic nuclei and quasars, the brightest objects in the Universe, which are powered by accretion. Different approximations are used for modeling different types of disk systems, or even different re- gions within the same disk, as certain effects impor- tant in one regime (e.g. radiation pressure, radial thermal energy advection, magnetic fields, disk self- gravity, irradiation by the nearby bright sources) are not important in the other ones. In this paper we study vertical structure of circumstellar disks, with parameters typical of the progenitor of type Ia su- pernova (SN Ia) system. Our interest is twofold: 1. Analyzing the role of accretion discs (AD) in high-velocity features (HVF) in the spectra of SN Ia, now considered ubiquitous [3,4]. HVF are absorption lines in the spectrum, in particular CaII infrared (IR) triplet near 800 nm, seen blueshifted at velocities ∼ 17 000... 29 000 km s−1 (up to 40 000 in SN 1994D), higher than the expansion velocity of the photosphere of the SN Ia ejecta. HVF are observed before, and up to ∼a week after SN Ia maximum light, then they fade. Several explanations were proposed for this fea- ture. One generic model [2] not requiring Ca over- production or any modifications to the now standard SN Ia scenarios is that these high-velocity lines are produced in a shell formed from circumstellar mater- ial (CSM) and outermost SN Ia ejecta as the former is overrun by the latter. The circumstellar material is assumed of standard solar composition. This model was successfully tested by several groups against observations. It requires substantial mass of the shell: 5... 7× 10−3M� for SN 2005cg [4], ∼ 0.02M� for SN 2003du [2], 0.1M� for SN 1999ee [5], 0.2M� for SN 2005hj [6]. Large fraction of this mass originates from the CSM located in the vicinity of the SN Ia center, at distances < 1.5× 1015 cm (for SN 2003du [2], from HVF timing considerations). According to a single-degenerate scenario, SN Ia is a result of a thermonuclear explosion of a WD [7] that reached nearly Chandrasekhar mass (MCh ∼ 1.38M�) by accreting mass from a companion star, through Roche lobe overflow. Accretion disk (AD) is thus a natural candidate for the nearby mass. 2. In our simulations we use real equation of state (EOS) and opacities of solar composition gas [8–10], ∗E-mail address: azhiglo@kipt.kharkov.ua PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, 2012, N 1. Series: Nuclear Physics Investigations (57), p. 193-197. 193 as the estimates of the disc mass found in the lit- erature differ significantly, likely depending on the approximations used. As a result we are able to ob- serve interesting features of the disk structure, in par- ticular in the regions where H2 molecules dissociate, where H and He ionize. While we only present our re- sults for the specific value of the central object mass (1.37 M�, slightly under-Chandrasekhar WD) and a range of accretion rates relevant for SN Ia, similar features are observed for other disk parameters, and may have observational consequences. We integrate the structure equations to radii smaller than the WD radius (and a larger envelope around it formed as a result of accreted fuel burning on the WD surface) to spot all these features. 2. THEORY AND NUMERICAL METHOD Circumstellar disks around compact objects with rel- atively low accretion rates are described by a thin α−disk model [1]. Parameter α defines effective kine- matic viscosity coefficient, ν = αcsH , where cs is the sound speed in the disk material, H is a characteris- tic scale height of the disk. This prescription assumes that characteristic turbulent velocity is αcs, and char- acteristic turbulent eddy size is of order H . In orig- inal formulation [1] the vertical structure of AD (i.e. distribution of density ρ, pressure P , temperature T , heat flux F , etc. along vertical z−direction) was not studied in detail. Rough estimate H = cs/Ω was made, where Ω is the Keplerian angular velocity at a given radius r in the disk. We use prescription ν = ε ( 2r3 GM )1/2 P ρ [ 1 + 2GMρ Pr3 z2 ]−1/2 (1) from [11] for direct comparison of the results. The square brackets here seem to take into account scale height (the height above the given point at which pressure changes by a factor of e) decreasing with z, due to increasing gz = GMz/(r2 + z2)3/2, the verti- cal component of gravity of the central object (nearly- Chandrasekhar WD in our study, M = 1.37M�). We used this prescription verbatim, albeit keeping these brackets is inconsistent with the thin disk approxi- mation used, which neglects other effects ∼ (z/r)2. It is claimed in [11] that relating ε to α as α = 3· 2−1/2ε yields description equivalent to original α−model near the disk equatorial plane. We could not reproduce that estimate; instead we get ε = α if H is defined as a scaleheight at z = 0. When original prescription [1] with H = cs/Ω was used in our com- putations (it is used this way by many authors) we really got results close to those with recipe (1) with ε = α. We still define α − ε correspondence below as α = 3· 2−1/2ε in agreement with [11]. α = 0.07 is adopted as the base value, corresponding to ε = 1/30 in [11]; values of α close to this are considered appro- priate for circumstellar disks based on observations. It should be kept in mind that this may correspond to α = 0.033 for the other definition of H used. As cs � Ωr radial pressure gradient is too small to support resting gas in radial graviatational field, dp/dr � grρ. The gas thus rotates with almost Ke- plerian velocity, which by far exceeds its radial drift velocity, vr � vφ. The heat is produced due to vis- cous friction between adjacent differentially rotating layers of gas; this determines vertical heat flux F : dF dz = 9 4 GMνρ r3 ; (2) radial heat flux is neglected in a thin disk. This heat is transported mainly by radiation and convection towards the disk photosphere, and is radiated into space. We use exact solution for the temperature gradient needed for transporting F in the upper ra- diative region of AD [12], in grey atmosphere approx- imation. At large optical depth 1 � τ(z) ≡ ∫ ∞ z κρdz (Rosseland mean opacity κ is used) this simplifies to diffusion approximation often used [11]: dT dz ∣∣∣∣ rad = −3κρF 16σSBT 3 , (3) σSB being Stefan-Boltzmann constant. When the found pure radiative dT/dz exceeds adiabatic gra- dient Chandrasekhar instability drives convection, which transfers the heat in such regions; we set con- vective temperature gradient then as: dT dz ∣∣∣∣ conv = −γ2gzρ T P , γ2 = ∂ ln T ∂ ln P ∣∣∣∣ S . (4) Rosseland mean opacities are taken from [9, 10] for solar composition disc [13]. Equation of state (EOS), including γ2 are taken from [8]. We solve numerically a boundary-value problem for Eqs. (2)–(4) and dp/dz = −gzρ with boundary conditions: F \|z=0 = 0, F \|z=z0 = F0 = 3GMṀ 8πr3 , values for Pz=z0 and Tz=z0 consistent with F0 and τz=z0 = τ0. τ0 was fixed at 10−9, z0 was found by requiring F \|z=0 = 0 when integrating down from z0. 3. RESULTS We varied accretion rate, shown in the figures if dif- ferent from its default value of Ṁ = 10−6M� yr−1; and α, the default value being α = 0.07. We show the results for Ṁ ∈ [4×10−8; 2×10−6]M� yr−1 that cov- ers (still controversial) rates typical of SN Ia progeni- tors [14–16]. α’s in the range we study are used in the literature for various disk systems. Lower α values are seen to produce thicker and more massive disks. α = 0.01 is used for T Tauri stars [17], α = 0.001 was proposed for FU Orionis outbursts. However, larger values of α ∼ 0.07 and above are currently consid- ered appropriate for circumstellar disks in post-main sequence binaries. Fig. 1 shows profile of AD photosphere zτ ≡ zτ=2/3. It is plotted divided by r; zτ/r = const would correspond to conical disk shape. The inner thick disk region is radiation pressure dominated. At r < 4 × 109 cm the disk is predominantly convec- tive, in agreement with [11]. It is mostly radiative at r ∈ [7× 109; 3× 1010] cm; comparable proportions 194 of radiative and convective regions are observed at r ∈ [5 × 1010; 1.2 × 1011]cm. The structure is more complex than in [11], likely due to varying opacity in this region due to lines of heavy elements accounted for in this work. The dip after r ≈ 1.2 × 1011 cm is due to HeIII recombining into HeII, as may be in- ferred from equatorial temperature profile in Fig. 2. The disk becomes convective abruptly, but contrary to [11] it becomes radiative back at r ≈ 4 × 1012cm (where hydrogen has become molecular, after the wide region where H and He recombine and H2 mole- cules form); 3 more transitions occur at larger radii, as hydrogen γ2 changes. The disk regains about a half of its pre-dip slope at r ≈ 1013cm; the slope declines slowly at larger radii through 1016cm we in- tegrated to. Similar features are observed for all Ṁ we tried. Fig. 1. Integral slope of AD photosphere zτ/r, at Ṁ = 10−6M� yr−1 and various α 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 -16 10 -14 10 -12 10 -10 10 -8 10 -6 10 -4 10 -2 α=0.009 α=0.018 α=0.036 α=0.07 α=0.14 α=0.28 m /2 , M su n r, cm 10 10 2 10 3 10 4 10 5 10 6 10 7 10 8 m/2 T z= 0 , K T Fig. 2. Equatorial temperature and half-mass of AD at Ṁ = 10−6M� yr−1. Photospheric tempera- ture T (zτ ) is independent of α 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 2 10 3 10 4 10 5 10 6 α=0.009 α=0.018 α=0.036 α=0.07 α=0.14 α=0.28 0 .5 d m /d S , g cm -2 r, cm Fig. 3. Half surface mass density of AD, 1/2 ∫∞ −∞ ρ(r, z) dz as a function of radius, at Ṁ = 10−6M� yr−1 Fig. 4. Dependence of zτ (r)/r on accretion rate dM/dt (in units of M� yr−1) at α = 0.07 10 6 10 7 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 2 10 3 10 4 10 5 10 6 dM/dt =2.5x10 -7 dM/dt =10 -7 dM/dt =4x10 -8 dM/dt =2x10 -6 Msun yr -1 dM/dt =10 -6 dM/dt =5x10 -7 0 .5 d m /d S , g cm -2 r, cm Fig. 5. Half surface mass density of AD at various accretion rates dM/dt. α = 0.07 Fig. 3 shows surface mass density vs radius. The disk profile and surface density at α = 0.07 and dif- ferent accretion rates are shown in Figs. 4 and 5. 2D distributions of density and temperature in the inner part of the disk are shown in Figs. 6 and 7. It is seen in Fig. 2 that AD radius must exceed ∼ 3 AU for its mass to reach 0.01M�. As the disk ra- dius is smaller that that of the WD Roche lobe, this means that only largest supergiants (SG) could serve as the WD companions for such massive disks. It is still possible to observe sufficient line-of-sight mass density when watching close to the disk equatorial plane — at smaller radii. Fig. 8 shows anisotropy in mass distribution, for 3 radii chosen. Equivalent spherical CSM mass is me(θ) = 2dm/dθ/ cosθ. It is seen that me(0) (twice the value shown in Fig. 9) varies in [4 × 10−3; 9 × 10−2]M� for AD parameters shown, at rAD ≈1 AU. However, anisotropy of the mass distribution disagrees with observations [18]. Fig. 6. Density distribution in the inner part of AD. α = 0.07, Ṁ = 10−6M� yr−1 195 Fig. 7. Temperature in the inner part of AD. α = 0.07, Ṁ = 10−6M� yr−1 Fig. 8. Angular density of the mass distribution. Angle θ of the line-of-sight is measured from the disk equatorial plane. Five sets of disk parameters are shown, differing in accretion rate, indicated in the legend at the respective curves (in units of M� yr−1.) The group labeled “1e − 6α” corresponds to Ṁ = 10−6, α = 0.009; in the rest of the models α = 0.07. 3 curves are shown for each model, for disk radii 1.55×1011, 1.55×1013 and 6.17×1013 cm. Smaller radii correspond to lower curves 10 8 10 9 10 10 10 11 10 12 10 13 10 14 10 -11 10 -10 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 d m /d q � θ = 0 M su n /r ad dM/dt =2x10 -6 , α=0.07 dM/dt =2.5x10 -7 , α=0.07 dM/dt =10 -7 , α=0.07 r, cm dM/dt =10 -6 , α=0.0045 dM/dt =10 -6 , α=0.018 dM/dt =10 -6 , α=0.07 dM/dt =10 -6 , α=0.28 Fig. 9. dm/dθ at θ = 0 as a function of radius. Note that to get an inferred CSM mass of 10−2M� the disk radius must exceed 1012cm even at very low α = 0.0045. For the base model we study (α = 0.07, Ṁ = 10−6) the disk radius should be 1013cm, implying a SG companion 4. DISCUSSION The results for the disk mass distribution are thus hard to reconcile with observed ubiquity of HVF, as- suming ADs the main source of the CSM mass re- quired by impact model [2]. The disks must have substantial radii to have sufficient projected mass density even in their equatorial plane. Disks in bi- naries with Main Sequence stars are too light by a factor of 103... 104. Only SG companions seem to al- low for disks of sufficient radius; such larger disks are pronouncedly flatter, dm/dθ drops by a factor of 10 within ∼ 6◦ off equatorial θ = 0 plane. Such mass distribution is at odds with current observations [18]. Significantly lower α would alleviate both of these discrepancies. Better treatment of convection would alter the results somewhat. Temperature gradient would in- crease, so would the disk mass density; the disk would become flatter at the same time. The difference should not change the conclusions qualitatively, as comparison with radiative regions suggests. The dust was assumed in thermal and hydrostatic equilibrium with gas. If it settles down to z = 0 fast in radiative regions that would decrease opacity, thus the temperature gradient. The disk self-gravity was neglected, as the total disk mass does not exceed a few hundredth of solar mass. Gravity of the companion was found to alter the layers above AD photosphere substantially, but not have much effect on the inner layers and total disk mass. AD irradiation by the WD and its companion was ignored. The bump in the disk photosphere at r ≈ 1.2 × 1011 cm is high enough to shield the outer regions from the central object radiation; ir- radiation effect is insignificant at the bump and at smaller radii. The radiation from the bump (with surface T ≈ 104 K) and from the companion star is intercepted by the disk. Irradiation usually makes disks lighter and geometrically thicker [17]; AD mass is still strongly concentrated towards z = 0. It is unlikely that disk effective opening angle may be made larger due to impact with ejecta, as the lat- ter runs through the disk with highly supersonic ve- locity. The outer, massive disk layers might broaden due to strong radiation from the growing SN Ia pho- tosphere, before being hit by the ejecta. The total disk mass would then have to be of order 0.01M� to lead to the observed HVF; this requires yet smaller α or more extended disk. Under no circumstances a disk in a binary system with a main-sequence star as a WD companion is a plausible candidate for the circumstellar mass sufficient to explain the HVF via mechanism [2]. High temperatures of the gas in the disk at distances of order a few million kilometers would lead to H or He lines visible in early SN Ia spectra, contrary to observations. What the origin of the circumstellar mass in WD–MS binaries is (or whether HVF have some other, not CSM origin) thus remains an open question, requiring further theoret- ical and observational study. References 1. N.I. Shakura, R.A. Sunyaev. Black Holes in Binary Systems. Observational Appearance // A&A. 1973, v. 24, p. 337-355. 196 2. C.L. Gerardy et al. SN 2003du: Signatures of the Circumstellar Environment in a Normal Type Ia Supernova? // ApJ. 2004, v. 607, p. 391-405. 3. P.A. Mazzali et al. High-velocity Features: a Ubiquitous Property of Type Ia Supernovae // ApJ. 2005, v. 623, p. L37-L40. 4. R. Quimby et al. SN 2005cg: Explosion Physics and Circumstellar Interaction of a Normal Type Ia Supernova in a Low-Luminosity Host // ApJ. 2006, v. 636, p. 400-405. 5. P.A. Mazzali et al. High-velocity features in the spectra of the Type Ia supernova SN 1999ee: a property of the explosion or evidence of cir- cumstellar interaction? // MNRAS. 2005, v. 357, p. 200-206. 6. R. Quimby, P. Höflich, J.C. Wheeler. SN 2005hj: Evidence for Two Classes of Normal- Bright SNe Ia and Implications for Cosmology // ApJ. 2007, v. 666, p. 1083-1092. 7. F. Hoyle, W.A. Fowler. Nucleosynthesis in Su- pernovae // ApJ. 1960, v. 132, p. 565-590. 8. F.J. Rogers and A. Nayfonov. Updated and Ex- panded OPAL Equation-of-State Tables: Impli- cations for Helioseismology // ApJ. 2002, v. 576, p. 1064–1074. 9. C.A. Iglesias and F.J. Rogers. Updated OPAL Opacities // ApJ. 1996, v. 464, p. 943-953. 10. J.W. Ferguson et al. Low Temperature Opacities // ApJ. 2005, v. 623, p. 585–596. 11. F. Meyer, E. Meyer-Hofmeister. Vertical struc- ture of accretion disks // A&A. 1982, v. 106, p. 34-42. 12. D. Mihalas. Stellar Atmospheres. 2nd Ed. San Francisco: Freeman & Co., 1978, 632 p. 13. N. Grevesse, A. Noels. Cosmic abundances of the elements // Proc. Symp. “Origin and evo- lution of the elements”. Cambridge: Cambridge University Press, 1993, p. 15-25. 14. R. Sienkiewicz. Stability of White Dwarfs Un- dergoing Spherically Symmetric Steady-state ac- cretion // A&A. 1980, v. 85, p. 295-301. 15. K. Nomoto. Accreting white dwarf models for type I supernovae. I. Presupernova evolution and triggering mechanisms // ApJ. 1982, v.2̇53, p. 798-810. 16. S.-C. Yoon, N. Langer, S. Scheithauer. Effects of rotation on the helium burning shell source in accreting white dwarfs // A&A. 2004, v. 425, p. 217-228. 17. P. D’Alessio, J. Canto, N. Calvet, S. Lizano. Accretion Disks around Young Objects. I. The Detailed Vertical Structure // ApJ. 1998, v. 500, p. 411-427. 18. M. Tanaka, P.A. Mazzali, K. Maeda, K. No- moto. Three-dimensional Models for High- Velocity Features in Type Ia Supernovae // ApJ. 2006, v. 645, p. 470-479. � �� α�� ! ��"# $�� %��% � �&''�(�� )�� # �� +�� ,�� ,�� %� ��(��(�� (��# -��% �� (�� . �� &�� ,� �,/%�� ,�� 0 1" �� ! �� 2�# �� . �� (�� % �%��% �� %�� % �,/%��% 0 1# �� 3 � �� α�� 4 �� 5 �� !! ��"# 6�� 4 �� 4 �%��% �� 4 ��4�� %�� # �� +��4 ��,�� 4 �� 4 �� ,��%� ��(4�(45 �� 4��4��(45# -��4� ��3��% ��4� �� . �� % �� (�� 4� 4� ,� ,�� %��% ��,�� % � �107" �� !! �� 2�# �� ,� � �� . )� ��4 � ��(4��4 �� 3 �� 4,�� % ��%��% 107# �89

On vertical structure of accretion disks in type ia supernova progenitors

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