The Be Star Newsletter, Volume 36 - December 2002

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Pulsationally-Induced Shocks in BW Vulpeculae One of a series of invited articles currently appearing in the Be Star Newsletter Myron Smith Computer Sciences Corporation, Space Telescope Sciences Institute e-mail: msmith@stsci.edu Received: October 31, 2002

A variable star astronomer doesn't need to work on B star pulsators for a living to know something about BW Vulpeculae (B1V-B2III). This  Cephei star is perhaps the most energetic regularly pulsating star known in the Galaxy. The nonlinearities associated with its radial pulsations are so pronounced as to cause predictable "standstills" in its velocity and optical and UV light curves during its 0.201 day cycles. It has long been recognized that in each cycle two "shocks" occur (defined by a "velocity discontinuity," if not by H emission) each having amplitudes of several times the atmospheric sound speed. We designate the first of these as the primary shock, which represents the emergence of the wave into the visible atmosphere. The second shock has been the subject of several proposed scenarios. Herein, we follow the recently-evolved picture summarized by Mathias et al. (1998) in which this second shock is produced by the cascade of the upper atmosphere to the lower layers, some 0.8 cycles after its initial ejection by the primary shock. Beyond this general description, there isn't much qualitative agreement that can lead yet to a standard picture of the effects of the shock kinematics on the star's atmosphere. One of the problems is that the BW Vul's pulsations are so much more energetic than in other  Cep stars that it is difficult to find other stars for which comparable spectroscopic signatures occur. Consequently, it is sometimes difficult to identify what the processes are in BW Vul, let alone to quantify their effects. Aside from its enormous velocity amplitude of 200-250 km s-1 (variable), the lines undergo large variations in strength, position, and shape. The latter can take the form of line doubling and extreme changes in width, making measurements throughout the cycle daunting. In this article, I summarize recent findings by Smith and Jeffery (2003) based on three nights (21-23 September 2000) of McDonald Sandiford-echelle observations of this star over the wavelength region 5510-6735. Our interpretation of these observations has resulted in a picture that challenges two long-standing views of the dynamical processes at work in this atmosphere. The first claim, hitherto untested, was an interpretation by Young, Furenlid, & Snowden (1981) that variations in the equivalent widths of certain lines, notably the CII 6678-83 doublet ( = 14.5 eV; gf ratio, 2:1) are an effect of the distension of the atmosphere on line formation. These authors reported that this doublet reaches its maximum strength outside the shock passage intervals. They further suggested that these changes are due to an increase in continuous opacity. If the continuous opacity decreases (because the gas density decreases), while the number of line absorbers remains the same, the depth of an unsaturated line and hence line strength will increase. This effect would cause lines of all ions to increase more or less uniformly. According to this explanation, the CII lines should become abnormally strong during the "distension" (nonshock) phases and should be "normal" during the shock phases. As noted below, this actually seems not to be the case. In addition, there is a priori reason to question the continuous opacity interpretation. In considering the effect of continuous opacity on atmospheric structure, the key question is how the total continuous opacity per gram of material (that is, mean atomic particle) varies. In a simple pure hydrogen atmosphere, the mean atomic particle is of course a hydrogen atom. The line absorption is ultimately referred to this same fictitious particle because it is the ratio of the line and continuous coefficients that determines the fractional flux absorbed by the line. If the density of a hydrogen atmosphere changes (H is already highly ionized in BW Vul's atmosphere), the effects on the line to continuous atmosphere are generally indirect and unimportant. The Young et al. idea has validity in atmospheres of stars situated in at least two other places on the H-R Diagram. The first place is among cool main sequence stars, for which the continuous opacity, due to H-, depends directly on the electron density. Thus, changing the density of electrons indeed affects the continuous opacity per mean atomic particle. The second case for which the continuous opacity-line strength equivalence holds is for hot supergiants and hypergiants. In the atmospheres of these stars, the dominant opacity is a combination of electron scattering and hydrogenic bound-free absorption. As the atmospheric density changes, the relative balance between these two absorbing changes can shift decisively from one of these contributors to the other. However, judging from the observed absence of metastable effects in shell or HeI triplet lines, the density of the atmosphere of BW Vul does not get low enough during its cycle for it to enter the supergiant regime. Model atmosphere computations bear out this reasoning. Using Kurucz (static!) models, one derives from a line synthesis code (e.g. Hubeny's SYNSPEC) that the mean equivalent width of CII 6578 from a Teff = 23,000K, log g ~ 4 model is 0.22Å and that the 6578/6583 ratio is 1.14. The results for a log g ~ 3 model are virtually indistinguishable from the log g ~ 4 case. These results are likewise insensitive to temperature in the Teff range 20,000-25,000K. Figure 1 exhibits our measured equivalent widths for the 6583 line for all three nights of our observations. In these plots the equivalent widths of 6578 are also plotted by scaling the 6578 results by factors of 1.3, 1.1, and 1.2. These ratios do not perceptibly change during shock phases, and they are also in quantitative agreement with the model computations. Perhaps most importantly, the computed ratio agrees with those found outside the shock windows. Altogether, these results are consistent with the CII strengths being normal for a B1IV spectrum during shock passages. Note that the lines are not "weaker" in the curve of growth sense because they are no less optically thick. Figure 1. CII 6578Å,6583Å equivalent width curves with pulsation phase for the 3 nights of this study. Although several authors have monitored the H line of BW Vul, no studies have been published of the behavior of the red HeI lines (singlet, 6678 and 5876). It was the omission of these critical lines in earlier investigations that prompted our McDonald observing program. In measuring the equivalent widths of these two lines, Simon and I discovered that their ratio remained close to 1.1 except during the phases of the infall shock passage. Interestingly, Young et al. had found evidence of shock heating from a temperature sensitive line ratio. Similarly, Simon and I discovered through the SiIII 5740/SiII 6371 ratio that the atmosphere appears to heat by about equal amounts during the transits of the two shocks. However, even though the two HeI lines are singlet-triplet analogs of each other, and their equivalent widths tracks each other closely during most phases, the 5876 line appears relatively strong during one of the two shocks, during the infall phase. Given the equality of the two shocks, it appears that heating alone cannot be the cause of the increased strength of the 5876 line. Inspection of Figure 2 show that shapes of the two lines during the infall-shock phase do not match: the blue absorption lobe of the 5876 line is much more developed than for 5876. We found that this is a persistent characteristic over all cycles monitored, corresponding to the infall shock passage and lasting some 0.09 cycles. At first blush, the dissimilar shapes of these lines at the same time presents a puzzle. What could be the cause? The culprit cannot be a metastability effect involving the triplet line because at these phases the gas is shock compressed, not distended. Figure 2. Profile for the HeI 5876Å (dashed)and 6678Å (solid) lines at an infall phase, near  = 0.90 on each of three nights, where  = 0 is reckoned from light maximum and approximately the midpoint of the velocity standstill. Also depicted is the 6678Å feature scaled by a factor of 2 (dotted line), as well as this same feature (thick dot-dashed) scaled by the indicated scale factor. This figure shows an "excess absorption" of the blue lobe of both lines to the left of the solid dot. The lines seem to be strictly optically thin (ratio of 2) for velocities less than -30 km s-1 on "Night 3." Simon and I believe the answer to this dilemma is that the presence of a newly formed optically thin column of excited HeI absorbers at rest with respect to the star (center) and external observer. This column has just begun to form and therefore does not yet contain enough excited HeI atoms to be optically thick in the 5876 and 6678 lines. Because these lines have a gf ratio close to 2, in Fig. 2 I have scaled the strength of the of the 6678 profile by 2 to approximate how 5876 would appear if the gas at these velocities were perfectly optically thin. One can compare this in the figure with the observed profile of the stronger 5876 line. The plots also indicate what factor one would actually have to apply to 6678-blue in order for this feature to match the blue lobe of the 5876 profile. A fair conclusion from this diagram is that during the infall shock phases the blue lobe of the 5876 profile has somehow been strengthened by factors of 1.3-2.0 during infall phases - and only at infall phases. Thus, the effect is consistent with heating (excited HeI atoms) in a limited region of the atmosphere just above the shock front created by the returning gas.1 If this is the case, the fact that these lines arise from highly excited lower levels, suggests that the upper regions of the atmosphere have been heated, hence the added "new column." The above picture is so far still only a hypothesis, and one has to be a little careful in advancing it for a few reasons. First, one has to think "globally" about what is going on. Figure 3, courtesy of Simon, is a colorized cartoon to show how the upper atmosphere returns to the "surface" over the phases indicated.2 The effects of infall with height are shown together with the creation of a new, optically-thin blue lobe in the line profile. Notice that as the infall proceeds the optically thin region moves upward (Eulerian coordinates, relative to star center). At this time the atmospheric stratum at which  (for negative and rest velocities) finally merges with the column, and the blue lobe becomes optically thick. At this point, the excess absorption in 5876 disappears - actually, by virtue of the blue lobe absorption of 6678 catching up. The two profiles have then become morphologically indistinguishable once again. Note in our picture the blue lobe is formed at the base of the infall, where the infall has suddenly come to rest, and in atmospheric strata below where the optically thick red lobe forms. This brings us to a second point where care must be taken. In Fig. 3 Simon and I have taken it on faith that the effective line width of the local intensity profile is narrow enough that the wings from the optically thick red lobe do not extend to the blue lobe - if the optical thickness from the red lobe extended to the blue lobe then the blue lobe would be formed at higher regions in the atmosphere and one could not see down to the infall shock front. This fine point remains to be tested by modeling of the photon redistribution process of this line, and, especially, under these dynamic conditions. Figure 3. Cartoon of the formation of the HeI 5876Å line profile as it evolves through radius minimum. The five bottom panels approximate line profile as it evolves through radius minimum. The top panel shows the variation of the stellar radius. The five bottom panels approximate the observed line profile at five specific phases during the infall period. The center of each panel corresponds to the rest wavelength of the line (tick marks). The composite line profiles (black solid) are decomposed into red-shifted (red), blue-shifted (blue) optically thick components and the unshifted optically thin component (dotted green). The five vertical panels in the center illustrate (i) the relative positions (z: horizontal lines) and (ii) motions (vectors) of six specific Lagrangian zones in the atmospheres, (iii) the position relative to these layers where the monochromatic optical depth (black dotted line) equals 1, and (iv) the location where each component of line absorption is likely to be strongest (green and red rectangles). Thus, for  = 0.86, the optically thin stationary component (green) is formed below the optically thick redshifted component. A third point of care is to ensure that our picture is not contradicted by the behavior of other lines during the infall. We remind the reader that various spectral line ratios clearly show that atmospheric heating is produced during both the primary and infall shock phases. This point is consistent with our explanation of the extra blue lobe in 5876 during infall. However, recall that our models show that heating should produce little change in the equivalent widths of the CII doublet. Fig. 1 demonstrates that the lines weaken during the shock intervals (cf. Young et al.). Moreover, the line strength ratio (a measure of their consistent optical thickness and position on their curves of growth) is the same, whether during the shock intervals or otherwise. How then can the lines' obvious weakenings be understood? The apparent enigma can be reconciled by postulating that the atmospheric temperature gradient has become shallow. If the line source functions are essentially formed in LTE, the lines will respond to this change by weakening and this change will affect all lines formed in this region. Thus, the riddle of the CII large line strengths posed by Young et al., restated here as weakened lines during shock phases, can be reconciled in our picture of a flattened temperature gradient. This gradient is plausibly flattened by heating over a range of strata during the infall shock - that is, by a shock distributed in height. One may similarly assume that during the primary, upward-moving shock, the line formation region is rendered more nearly isothermal, as indeed was assumed in early shock simulations for this star by Stamford and Watson (1978). I began this article by stating that Simon Jeffery and I would challenge two widely held views advanced in the literature. The first relates to the variations of the CII line strengths. The second claim is that the progress of the pulsation wave upward through the photosphere of BW Vul can be discerned by time delays of the wave as it moves upward through atmospheric strata. This so-called "Van Hoof effect" has been reported by several authors over the years. Typically, investigators discover among various lines at some given moment that the blue-lobe strengths of various lines are different. The most recent report was in the fine paper by Mathias et al. (1998), in which a phase delay was noted between a SiIII line and H. In interpreting a profile difference as a difference in the evolution of the profiles with phase, one must appeal to the shock traversing a long distance, typically some 1% of BW Vul's radius. Absent dynamical models, we do not know that the full line formation region of the photosphere is really this extensive. But even if this is so, some readers may share my skepticism that a difference in mean depth of formation of two lines can be this large in the atmosphere of even a dynamic B III-V star, particularly at the time the atmosphere is approaching its maximum compression state! I believe a more reasonable expectation is that the difference in blue lobe strengths, from which the "phase difference" is derived, is actually due to the optically thin column formed by selected lines, as in Fig. 2. In our picture, shock-heating will affect those atomic species in which the ensuing ionization brings the dominant ion into the greatest new visibility. In the case of silicon, this would be SiIII. Meanwhile, hydrogen is essentially already ionized. An optically thin column in H must therefore be harder to build, and the infall has to proceed longer before one can see a developed blue lobe in H. So, the Van Hoof effect is more likely in our view to be an artifact of the transient heating of a optically thin column of gas just above the shock. Many of the ideas are conjectural, but so far they have the advantage of explaining the qualitative behavior of a large number of types of optical (and ultraviolet resonance) lines. In future studies we will attempt to validate these ideas based on ad hoc ("toy") atmospheres with artificial density and temperature gradients. However, a firm understanding even at a qualitative level will also depend upon the discovery of other extreme-amplitude pulsators in which the strengths of the pulsations vary just enough to cause large differences in delays of the infall shock. Such phase delays are apt to cause large changes in the amounts and the distribution of heating through the atmosphere. Thus, additional BW Vul-like stars will provide the diversity of conditions needed to test these new ideas. 1We should also point out that in IUE data the CIV 1548 shows similar "excess absorption" relative to the other doublet member, 1552, at the same phases. This strong absorption mimics a fluctuation in wind absorption and was the basis for Burger et al.'s (1983) suggestion that the wind outflow is modulated by the pulsation cycle. We prefer our picture to their inference because it requires only one process to operate at the same place and time to explain the same morphology for both the UV resonance and red HeI lines. 2By convention, phase zero corresponds to the light maximum and maximum atmospheric compression, so the process depicted occurs nearly a full cycle after the emergence of the primary pulsation-wave shock and just prior to its reoccurrence in the new cycle. REFERENCES Burger, M., de Jager, C., et al. 1983, A&A, 109, 2890 Mathias, P., Gillet, D., et al. 1998, A&A, 339, 525 Owocki, S. & Cranmer S. 2002, IAU Colloq 185, ASP Conf Ser. 259, 512 Smith, M. A. & Jefferys, C. S. 2003, MNRAS, submitted (astro-ph/0210189) Stamford, P. A. & Watson, R. D. 1978, Proc. Astron Soc. Australia, 3, 275 Young, A., Furenlid, I., & Snowden, M. 1981, ApJ, 245, 998