Modelling Variability in Hot-Star Winds

Mo delling Variability in Hot-Star Winds 1 Stanley P.Owocki Bartol Research Institute University of Delaware, Newark, DE 19716 USA Abstract. I review 2-D hydro dynamical simulations of rotating hot-star winds with azimuthal structure induced by mo dulation of the radiative driving force near the wind base. As a rst step toward examining more realistic p erturbation mechanisms (e.g., nonradial pulsations, or magnetic elds), the driving mo dulation here is taken to arise from bright and dark sp ots in the stellar photophere. These sp ots induce decreases or increases in wind ow sp eed, and as the star rotates, spiral \Co-Rotating Interaction Regions" (CIRs) form, much as in the solar wind, from from interaction b etween fast and slow ow streams. A new feature unique to line-driven owisavelo city-gradient kink that propagates inward from interaction fronts at a fast radiative-acoustic mo de sp eed. The slowly evolving velo city plateaus that form b ehind suchkinksgiveriseto absorption features with a slow apparent acceleration, muchlike the Discrete Absorp- tion Comp onents (DACs) often observed in UV wind lines from hot-stars. In simulation mo dels with base driving sinusoidal ly mo dulated b etween increases and decreases, there arise alternating spiral streams of enhanced or decreased density, asso ciated resp ec- tively with decreased or increase ow sp eeds. These sp eed variations have substantial impact on the line pro le, and so these dynamical simulations are not as successful as analogous kinematic mo dels of corotating density streams in repro ducing the \phase- bowing" of p erio dic absorption mo dulations observed in the recent IUE `Mega' pro ject. 1 Intro duction Several pap ers at this meeting (e.g. by Prinja, Kap er, Kaufer, Massa, and Wolf ) have summarized the extensive observational evidence for explicit variability, cyclical or otherwise, in the winds from hot, luminous, early typ e (OB) stars. A general challenge for theory is to understand the nature of the physical changes and/or structures asso ciated with this variability.To b e visible as direct variations in line-pro les formed from globally integrated radiative ux, the asso ciated ow structure must b e on a relatively large scale, on order the stellar radius. This makes it unlikely that suchvariations could stem from pro cesses entirely intrin- sic to the wind out ow, such as the inherent instability in the line-driving of the wind to small-scale p erturbations (Rybicki 1987; Owocki, Castor, and Rybicki 1988; Owocki1994b). The dynamical evolution of such large-scale structure can be simulated using the lo cal, computationally ecient, CAK/Sob olev expres- sions for the line force (Castor, Abb ott, and Klein 1975; Sob olev 1960), making it feasible to carry out multidimensional simulations of the wind structure resulting from large-scale p erturbations from the underlying, rotating star. In this review, I will fo cus on recent e orts to develop initial dynamical mo dels for two distinct classes of suchvariability, namely the `classical' Discrete 2 Stanley P.Owocki Absorption Components (DACs) and the more recently identi ed Periodic Ab- sorption Modulations (PAMs) discovered in the IUE `Mega' pro ject (Massa et al. 1995). Unlike the quasi-episo dic, slowly evolving, net absorption enhancements that characterize most DACs, the PAMs recur regularly at p erio ds a loworder fraction of the rotation p erio d, include b oth reductions and enhancements of absorption, and evolve relatively quickly over the line pro le. Indeed, in contrast to the slow blueward evolution of DACs, the PAMs in one case (BO I star HD 64760) show a \phase-b owing" that re ects apparentredward as well as blueward propagation (Owocki, Cranmer, & Fullerton 1995; ; Fullerton et al. 1997). These distinct observational characteristics likely re ect di erences in the underlying p erturbation mechanisms, p erhaps, for example, with the more sto chastic DACs b eing induced by magnetic activity, and the regular PAMs b eing initiated by Non-Radial Pulsations (NRPs). But given the present uncertainty, the initial simulations here simply induce wind variations rather arti cially, through direct mo di cation of the radiative driving in the inner wind, much as might o ccur from \sp ots" on the underlying star (Cranmer and Owocki 1996, hereafter CO). I rst (x 2) describ e the e ect of isolated sp ots, b oth brighter and darker than the ambiant photophere. As the star rotates, Co-rotating Interaction Regions (CIRs) form along spiral patterns by collision b etween faster and slower wind streams originating from di erent longitudes relative to the sp ot. These simulations thus represent the rst dynamical test of the original prop osal by Mullan (1984a,b; 1986) that the wind density enhancements in such CIRs could cause the DACs. A central goal here is to determine whether key characteristics of observed DACs, particularly their apparent slow acceleration, can b e repro duced in synthetic line-pro les generated from dynamical mo dels with CIRs. I also examine (x 3) the e ect of a sinusoidal modulation of the radiativedriv- ing near the wind base, assuming a xed number (m = 4) no des around the star. This is intended as a dynamical version of the simple kinematic picture prop osed to explain the \phase b owing" of the PAMs in HD 64760 (Owocki, Cranmer, & Fullerton 1995.) In this picture the PAMs arise from corotating streams of alternating increased or decreased density, within the key simpli cation that the velo city is xed to a sp eci c law, una ected by the density p erturbations. The dynamical simulations here self-consistently include suchvelo cityvariations, and so allow us to examine their e ect in the line-formation. 2 CIRs Induced by Isolated Sp ots Let us rst review the CO simulations of wind structure induced by isolated sp ots on a rotating hot-star. The aim is to mimicphysical pro cesses { e.g. magnetic eld, NRPs { that might increase or decrease the mass ux emerging from some lo calized region of the star, and then study howsuchvariations are prop- agated through the radiatively driven stellar wind. To reduce the complexity and computational costs, the simulations are con ned to 2-D variations in radius and azimuth (r , ) within the equatorial plane. The line-driving force is computed using the standard CAK/Sob olev formalism (Castor, Abb ott, Klein Mo dellin g Variability in Hot-Star Winds 3 Fig. 1. Grayscale p olar plots showing the spatial dep endence of the deviations from a steady mo del for a. density, b. radial velo city,c.azimuthal velo city, and d. Sob olev optical depth. 1975; Sob olev 1960), mo di ed by the nite-disk correction factor for a spherical out ow(Friend and Abb ott 1986; Pauldrach, Puls, and Kudritzki 1986). This ignores the azimuthal force that should arise from sideview p ersp ectives of the sp ot, and simply mo di es the radial force by a xed enhancement/reduction factor determined by the relativeproximity to the sp ot. The sp ot parameterization allows sp eci cation of b oth a longitudinal width and an amplitude A, with 1 <A<0 for dark sp ots and A>0 for bright sp ots. Of the mo dels listed in Table 1 of CO, I con ne attention here to the rst o two, for which =20 and A = 0:5, representing a standard bright and dark sp ot. The stellar parameters represent those for the canonical O-typ e sup ergiant Puppis, with a rotation sp eed V = 230 km/s, corresp onding to a rotation rot p erio d of P 4:2days. For convenience, let us assume two identical sp ots p ositioned on opp osite hemispheres, allowing restriction of the computation to o an azimuth range of just 180 with p erio dic b oundary conditions. For the bright sp ot case, gure 1 shows grayscale plots of the resulting density, radial velo city, azimuthal velo city, and radial Sob olev optical depth, all relative to values in the corresp onding steady, spherically symmetric, CAK wind mo del without anyspot.Thespothereiscentered on the x-axis, at the origin the spiral pattern of enhanced densitythatcharacterizes the resulting CIR. Note that regions of enhanced density generally corresp ond to regions of lower radial velo city. Because of the enhanced brightness over the sp ot, the wind driven from there initially has a higher mass ux, and thus higher density. As the enhanced brightness fades with increasing heightabove the sp ot, the higher densityofthis 4 Stanley P.Owocki Fig. 2. left panels: Radial variation of velo city (upp er panel) and density (lower panel) along selected, xed azimuthal angles in the bright sp ot mo del. Fig. 3. right panels: Same as g. 2, but for the dark sp ot mo del. material makes it harder to accelerate, re ecting the characteristic scaling of the line-acceleration with the inverse of the density , 1 @v r g (1) lines @r where is the usual CAK exp onent. The lower velo city gradient @v =@ r asso- r ciated with the lower acceleration also contributes, through eq. (1), to a further reduction in the acceleration. As the stellar rotation brings this higher-density, lower-sp eed material into interaction with faster ambient wind originating away from the sp ot, there results a sho ck compression of the gas into the dense spiral stream that characterizes the CIR. Though the general CIR formation here is analogous to that o ccuring in the solar wind (Hundhausen 1972; Zirker 1977), there are imp ortant di erences.

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