Emission lines formed in the circumstellar envelopes of several type of stars
can be modeled using first principles of line formation. We present simple ways
of calculating line emission profiles formed in circumstellar envelopes having
different geometrical configurations. The fit of the observed line profiles
with the calculated ones may give first order estimates of the physical
parameters characterizing the line formation regions: opacity, size, particle
density distribution, velocity fields, excitation temperature.Comment: 3 pages ; to appear in the proceedings of the Sapporo meeting on
  active OB stars ; ASP Conference Series ; eds: S. Stefl, S. Owocki and A.
  Okazak

Arias, M. L.

Frémat, Y.

Zorec, J.

English

arXiv

3 pages ; to appear in the proceedings of the Sapporo meeting on active OB stars ; ASP Conference Series ; eds: S. Stefl, S. Owocki and A. OkazakiEmission lines formed in the circumstellar envelopes of several type of stars can be modeled using first principles of line formation. We present simple ways of calculating line emission profiles formed in circumstellar envelopes having different geometrical configurations. The fit of the observed line profiles with the calculated ones may give first order estimates of the physical parameters characterizing the line formation regions: opacity, size, particle density distribution, velocity fields, excitation temperature

Arias, M.L.

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Circumstellar rings, flat and flaring discsM.L. Arias, J. Zorec, Y. Fre´matTo cite this version:M.L. Arias, J. Zorec, Y. Fre´mat. Circumstellar rings, flat and flaring discs. 3 pages ; toappear in the proceedings of the Sapporo meeting on active OB stars ; ASP Conference.. 2006.<hal-00016425>HAL Id: hal-00016425https://hal.archives-ouvertes.fr/hal-00016425Submitted on 4 Jan 2006HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.ccsd-00016425, version 1 - 4 Jan 2006**FULL TITLE**ASP Conference Series, Vol. **VOLUME**, **YEAR OF PUBLICATION****NAMES OF EDITORS**Circumstellar rings, flat and flaring discsM.L. Arias1, J. Zorec2, Y. Fre´mat31 Facultad de Ciencias Astrono´micas y Geof´ısicas, UNLP, Argentina2Institut d’Astrophysique de Paris, UMR7095 CNRS, Univ. P&M Curie3Royal Observatory of BelgiumAbstract. Emission lines formed in the circumstellar envelopes of severaltype of stars can be modeled using first principles of line formation. We presentsimple ways of calculating line emission profiles formed in circumstellar envelopeshaving different geometrical configurations. The fit of the observed line profileswith the calculated ones may give first order estimates of the physical param-eters characterizing the line formation regions: opacity, size, particle densitydistribution, velocity fields, excitation temperature.1. Rings and flaring discsIn optically thick regions, more than 90% of the emitted energy in a given linecan be considered produced in a limited region of the circumstellar disc. Thisis the case of Fe ii in Be stars (Arias et al. 2005), but also hydrogen Balmer,Paschen series if their formation region has the aspect of an expanding ring. Inboth circumstances, the emitted radiation can be estimated using an equivalentisothermal ring with uniform semi-height H, whose surface density equals theradial column density. If the particle density has a distribution N(R)∼ R−β,the radius of the ring is then Rr/R∗ = [(1 − β)/(2 − β)][1 − (Ri/Re)β−2]/[1 −(Ri/Re)β−1], where Ri,e are the internal and external radii of the line formingregion. The ring can be considered having expansion Vexp and rotation VΩvelocities, both represent averages of the respective velocity fields (Arias 2004).The emitted flux is simply Fλ =∫S(i) Iλ(x, y)dxdy where S(i) is the aspect-angleeffective emitting surface projected on the sky and Iλ(x, y) is:Ia(x, y, v − vr) = I∗(x, y)e−τf (v−vr)µ(x,y) + S[1− e−τf (v−vr)µ(x,y) ](stellar emission absorbed by the front side)+(front side emission)Ib(x, y, v − vr) = S[1− e−τt(v−vr)µ(x,y) ]e−τf (v−vr)µ(x,y) + S[1− e−τf (v−vr)µ(x,y) ](rear emission absorbed by the front side)+(front side emission)(1)with τv= τoΦ(v−vr) and vr(x, y)= ±{Vexp(R)[1−(xR)2]12±VΩ(R)xR} sin i, where(f, r) stand for ‘front’ and ‘rear’ sides of the ring. The signs in the radial velocityvr are chosen according to the quadrant; v is the Doppler displacement in theobserved emission line profile, µ(x, y)= cos(ring-normal;observer), i inclinationof the ring-star system, τo is the radial opacity of the ring in the line center and12 Arias et al.-300 -200 -100 0 100 200 300V (km s-1)0.60.70.80.91.01.11.21.3i = 45o= 1.5S/F = 0.17H = 1.0R = 3.5Vexp = 0 km/sV = 300 km/s= 3.0= 2.0= 1.5= 1.0= 0.5= 0.25-300 -200 -100 0 100 200 300V (km s-1)1.01.11.21.31.4 Vexp = 150 km/sV = 300 km/s-400 -300 -200 -100 0 100 200 300 400V (km s-1)-0.20.00.20.40.60.81.01.2= 15oR = 5.9S/F = 0.08= 0.7Vexp = 0 km/sV = 185 km/s= 1.0= 0.5= 0.1= -0.5H ( Eri)1994Figure 1. a) Line profiles for a ring with Vexp=0 and the indicated param-eters. b) ’Steeple’ line profiles produced by rings with same parameters asin a) but Vexp 6= 0. c) Line profiles due to flaring discs treated as rings, forseveral β and opening angle φ=15o. β= 0.1 closely fits Hα of α Eri in 1994(a flat ring would require H=3.8; β=−0.1)-600 -400 -200 0 200 400 600V (km s-1)V =150 km/so = 1.0H = 0.5R*(So/F*)R2r = 4.5Vexp=0 km/s60 km/s120 km/s240 km/s320 km/s0.1-600 -400 -200 0 200 400 600V (km s-1)Vexp=150 km/sV =0 km/s80 km/s140 km/s260 km/s340 km/s0.1-600 -400 -200 0 200 400 600V (km s-1)V =VexpV =0 km/s80 km/s140 km/s260 km/s340 km/s0.1Figure 2. Three-peak line profiles produced by rotating+expanding ringsΦ(v) is the intrinsic absorption line profile. The line source function is: Sλ(τo)=So for τo ≤ 1; Soτpo for τo > 1 [p ≃ 1/2 for Gaussian Φ(v)] and Bλo(Te) forτo≥ (Bλo/So)2 (Mihalas 1978, Chap.11). So depends on the nature of the linetransition: collision-, photoionization-, mixed-dominated. Using So as done inCidale & Ringuelet (1989) we can determine the excitation temperature (Ariaset al. 2005). Thus, the free parameters to fit the observed emission line profilesare: So/F∗, τo, Rr, H, i, VΩ, Vexp and density distribution β (or α= 2−β). Theshape of the line profiles reduce strongly the space of free parameters, mainlythose of the velocity field and the ratio between τo and H. Line intensitiesare sensitive to (So/F∗)R2r and Rr to the temperature, which in turn determinesSo/F∗. Figure 1a shows line profiles obtained for the indicated parameters of thering with Vexp=0, which are typical for ‘shell’ lines. The same ring parametersare used for Fig. 1b, but Vexp= 150 km/s. The line profiles are of the ‘steeple’type seen frequently in Fe ii lines. Flaring discs can be treated in the same wayas cylindrical ones, except that the surface density, and hence τo depends onthe coordinate perpendicular to the equator (Vinicius et al. 2005). A fit of theHα line of α Eri in 1994 with a flaring disc of opening angle φ = 15o is shownin Fig. 1c, where are also shown line profiles for different β-values. Severalthree-peak emission line profile are shown in Fig. 2 produced in regions treatedRings and discs 3-300 -200 -100 0 100 200 300V (km/s)0.81.01.21.41.61.82.02.22.4(a)= 1.5o = 1.0S/F = 0.3H = 1.0R = 3.5Vexp = 150 km/sV = 300 km/si = 5oi = 10oi = 20oi = 30oi = 50oi = 70o-300 -200 -100 0 100 200 300V (km/s)0246810(b)= 2.0o = 10S/F = 0.3R = 5Vexp = 0 km/sV = 300 km/si = 10oi = 20oi = 30oi = 50oi = 70o-400 -300 -200 -100 0 100 200 300 400V (km/s)0.30.40.50.60.70.80.91.01.11.21.3o = 1.0= 1.5S/F = 0.17H = 1.0R = 3.5Vexp = 0 km/sV = 300 km/si = 5oi = 10oi = 20oi = 30oi = 50oi = 70oi = 85o(c)Figure 3. Emission line profiles obtained with discs. a) P Cyg like profiles.b) Bottle shaped. c) Broadening due to v1 at i→ 90oas equivalent expanding rings. Due to the Doppler shifts, the central emissioncomponents are produced by the front and rear sides of ring sectors where theradial velocity is vr ≃ 0.2. DiscsThe main difference in the treatment of discs with respect to that for rings is inthe velocity dependence of the intrinsic absorption line profile. It has been shownby Horne & Marsh (1986) that for a Gaussian Φ(v) the Doppler width of theprofile is enlarged by a “turbulent” term due to the differential rotation in thedisc towards the observer’s direction. The wavelength dependent opacity is thenproportional to exp{−(1/2)[(λ − λD)/(∆D × δ)]2}, where λD= λo(vo/c) and:vo = [VΩ(R) sin θ + Vexp(R) cos θ] sin iδ = [1 + (λov1/c∆D)2]1/2v1 = [12VΩ(R) sin θ + Vexp(R)(2− β) cos θ] cos θ tan i sin i (2)where θ is the azimuthal angle. For large values of H, v1 acts as a non-negligiblebroadening agent of the effective Doppler line width. Different examples ofline profiles obtained with discs seen at several inclination angles are shownin Fig 3. The parameters used in Fig 3a can suite for P Cyg type line pro-files, while Fig 3b reproduce the bottle shaped emission line profiles seen fre-quently in Be stars. The ‘bottle’ shaped profiles can be obtained also with rings.They are produced by the τpo opacity dependence of the source function dueto its non-local energy supply. The broadening of the effective Doppler lineby v1 is depicted in Fig 3c (i = 85o). Other related subjects can be found inhttp://www2.iap.fr/users/zorec/.ReferencesArias, M.L. 2004, PhD Thesis, University of La Plata, ArgentinaArias, M.L., Zorec, J., Cidale, L., Ringuelet, A. 2005, A&A, submittedCidale, L.S, & Ringulete, A.E. 1989, PASP, 101, 417Horne, K., Marsh, T.R. 1986, MNRAS, 218, 761Mihalas, D. 1978, Stellar Atmospheres, FreemanVinicius, M.M.F., Zorec, J., Leister, N.V., Levenhagen, R. 2005, A&A, in press

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