SiO maser movies

New Astronomy 5 (2000) 155–162 www.elsevier.nl / locate / newast

SiO maser movies

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M.D. Gray a,1 , E.M.L. Humphreys b,2 a

Department of Physics and Astronomy, University of Wales, Cardiff, P.O.Box 913, Cardiff, CF24 3 YB, UK b Onsala Space Observatory, S-43992 Onsala, Sweden Received 21 September 1999; accepted 2 December 1999 Communicated by P.S. Conti

Abstract We show how the intensity and spatial distribution of silicon monoxide masers varies with time according to the parameters of a current model. The variation of the masers at 43 GHz in the v 5 1 vibrational state is presented as an animation. Where possible, comparisons are drawn with a similar animation of the real Mira variable TX Cameleopardalis.  2000 Elsevier Science B.V. All rights reserved. PACS: 97.10.Fy; 97.60.-s; 97.30.-b; 95.30.Ky Keywords: Masers; Stars: AGB and post-AGB; Circumstellar matter; Radio lines: stars; Stars: individual: TX Cam

1. Introduction It is now well known that when resolved, the appearance of SiO maser emission from the circumstellar envelopes of Mira variable stars takes the form of a broken ring of emitting clumps (Diamond et al., 1994; Greenhill et al., 1995; Miyoshi et al., 1995). The approximate radius of the ring lies in the range 1.5-4.0 stellar radii, and depends on the host star and the stellar phase (Boboltz et al., 1997). Typical linear sizes for resolved maser clumps are of order 5 3 10 9 m. Recently, observations of the Mira variable TX Cameleopardalis (TX Cam) have fol-

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With thanks to P. Diamond, J.Yates & D. Field. E-mail addresses: [email protected] (M.D. Gray), [email protected] (E.M.L. Humphreys) 1 Thanks to the Royal Society for support. 2 EMLH would like to thank the Swedish Foundation for International Cooperation in Research & Higher Education for financial support.

lowed the motions of its circumstellar SiO maser clumps for more than one full stellar period. The results of this set of observations have been developed as an animation (Diamond & Kemball, 1998). It is therefore timely to produce a theoretical / computational counterpart to this animation, which shows how a combination of hydrodynamic calculations and maser amplification codes can reproduce many of the basic features of the observations, whilst failing to explain some of the details. The Mira model (see Section 2) simulates a star pulsating in its fundamental mode. Opinions vary regarding the mode of pulsation of Miras with some authors favouring the fundamental mode (Wood & Sebo, 1996; Ya’ari & Tuchman, 1999), whilst others opt for pulsation in the first overtone, for example (Feast, 1996). The controversy appears to be dominated by an apparent agreement of measured stellar sizes with model predictions for the first overtone, coupled to problems in generating envelope dynamics of sufficient vigour with this mode. It is quite

1384-1076 / 00 / $ – see front matter  2000 Elsevier Science B.V. All rights reserved. PII: S1384-1076( 00 )00020-8

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possible, however, that we observe examples of both ` 1998; Bedding & Zijlstra, 1998; van modes (Bartes, Leeuwen et al., 1997), and that a Mira, as it evolves can switch pulsational modes (Bedding et al., 1998), perhaps more than once. The subject of the long time-series observations (TX Cam) has a rather long period for a Mira with an oxygen-rich envelope, at 557 d (Kholopov et al., 1985). Miras with such long periods appear more likely to be fundamental mode pulsators (van Leeuwen et al., 1997) which is likely to put TX Cam in agreement with the model in this respect. Evolution of a star along the Asymptotic Giant Branch (AGB) is dominated by a series of thermal pulses (Iben & Renzini, 1983), interspersed with quiescent periods where we observe the stars as Miras with a fairly steady period. For the purposes of the present work, the most important effects are a general lengthening of the pulsation period (disturbed by each thermal pulse) (Vassiliadis & Wood, 1993) as the star follows a Whitelock evolutionary track (Whitelock & Feast, 1991), an increasing mass-loss rate as the star tends to develop a ‘superwind’ (Bowen & Willson, 1991; Vassiliadis & Wood, 1993), and if the star is sufficiently massive, a change of the envelope composition from an oxygenrich state, in which most carbon is bound as CO, to a carbon rich state where the CO binds almost all the oxygen, and there is an excess of carbon to react with other species. The model which we use has an oxygen-rich envelope and a modest mass-loss rate. We have already noted that TX Cam has a rather long period for an O-rich Mira, and it does indeed show observational features that indicate it is highly evolved, and that its envelope is becoming contaminated with C-rich material. Both the absence of OH and H 2 O masers (Dickinson, 1976) and the presence of CN (Olofsson et al., 1991) support the idea of TX Cam as an aging object approaching the C-rich stage. An observed feature of the SiO maser emission from TX Cam and many other AGB stars is polarization, usually linear at the level of 30–40%, possibly much higher in line wings (Cernicharo et al., 1997). In the case of TX Cam, observations have been carried out for all Stokes parameters at VLBA resolution (Kemball & Diamond, 1997) The model does not treat polarization at all, but we note that polarization-sensitive observations may be important

in helping us to fix the phase-shift between the observational and model phases because the passage of a shock is likely to change the magnetic field direction, and hence the plane of polarization, significantly (Gray, 2000).

2. The model The composite model used to simulate the maser emission falls neatly into two separate parts. Envelope motions are predicted by code developed by Prof. George Bowen of the University of Iowa. This model of a pulsating envelope is described in Bowen (1988, 1989) and its application to the SiO maser problem in Miras appears in Humphreys et al. (1996). We note that more recent models of pulsating ¨ AGB stars (Fleischer et al., 1995; Hofner et al., 1995) have not been adopted because these latter models are based on carbon-rich stars, whilst the work in Bowen (1988) pertains to oxygen-rich envelopes as required for Mira variables with SiO masers. The maser model has also been extensively described elsewhere, with basic amplification theory in Field & Gray (1988); Field & Richardson (1984) and application to late-type stars in Doel et al. (1995); Humphreys et al. (1996). We adopt the usual decoupling of pump and maser, such that the saturating action of any maser(s) does not significantly affect the radiation transfer in the infrared lines (at 4 and 8mm) which form part of the pumping mechanism. The radiation transfer in infrared lines is handled via the Sobolev or LVG approximation. Although this approximation is rarely truly appropriate, and will be replaced in future work, we note that there are large velocity gradients in the model, and in real Mira envelopes (Hinkle et al., 1997; Wood, 1990) especially in the radial direction. The Sobolev approximation also has the advantage, for this work, in that it provides a shape and size for the maser region, which can be roughly equated to an observational clump and is independent of other parts of the envelope. More exact radiation transfer solutions would yield an unbroken ring of emission if spherical geometry were used. Propagation and saturation of the partially coherent maser radiation is dealt with using the semi-classical approximation

M.D. Gray, E.M.L. Humphreys / New Astronomy 5 (2000) 155 – 162

including all processes of competitive gain Doel et al. (1995); Field & Gray (1988). The other part of the maser pump is provided by collisions of the SiO with a dominant partner molecule. This molecule is taken to be H 2 , but we note that the rate-coefficients were originally developed for He (Bieniek & Green, 1983a; Bieniek & Green, 1983b). A correction has been introduced for the different reduced mass of the H 2 –SiO system, but the rate-coefficients are likely to be poor approximations to the behaviour of rotationally excited H 2 . High temperature regions are also present in the model envelope which may lead to a significant population of H-atoms. Observational evidence remains divided on this issue (Beach, 1990; Chapman & Rudnitskij, 1998). The behaviour of the H–SiO system has recently been shown to be very different from the He–SiO system (Jimeno-Cuellar et al., 1999), and this may lead to significant errors at some radii and some phases. In future work, the rate-coefficients used here will be augmented with new sets from modern close-coupled calculations of both the SiO–H and SiO–H 2 systems (Jimeno-Cuellar et al., 1999, 2000). The advantage of the Sobolev approximation, other than the sheer computational speed advantage, is that it allows us to study small isolated regions of the envelope which are radiatively decoupled (in the pumping and maser lines) from the rest of the envelope. Obviously, in the observations we are faced with a problem in which the spherical symmetry of the envelope has been broken as far as the maser emission is concerned. Some parts of the envelope are more favoured in terms of their ability to emit, than others at the same radius and aspect to the observer, and unfortunately we do not know why. Several possibilities have been suggested, including thermal and thermochemical instabilities (Cuntz & Muchmore, 1994; Muchmore et al., 1987) or the magnetohydrodynamic Parker instability (Hartquist & Dyson, 1997). It is not clear which of these, or perhaps some alternative process, is dominant so we have adopted a scheme of extreme simplicity to break the spherical symmetry. Essentially we view the clump-phase as containing a much higher proportion of SiO than the background phase. We choose the clump positions at random and then let the clump positions be adjusted according to the underlying envelope model. Obviously, the chosen positions are

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only truly random at the zero phase of the model. Unfortunately, we do not yet know accurately how the model phase (zero for maximum outward velocity of the sub-photospheric piston) relates to the optical phase where zero corresponds to maximum light. We note that significant radiation transfer interplay between 28 SiO and the minor isotopomers 29 SiO and 30 SiO is likely to be responsible for several masers in ´ higher vibrational states of 28 SiO (Gonzalez-Alfonso & Cernicharo, 1997). However, in this work, we are primarily interested in low-lying J-lines in the v 5 1 and v 5 2 vibrational states, and the influence of the rare isotopomers has been ignored.

3. Construction of the animation Output from the SiO maser programs provides, for each of 20 equally spaced phases covering the full stellar period, an (x,y,z) ASCII file for each maser transition. In every file, x and y are sky coordinates, representing positions that would be seen by a distant observer viewing the model. The z-entries are the maser intensities, integrated across all velocity bins, at the corresponding position. The first operation is to read one of these ASCII files, and process it into a form which can be read by the AIPS software package. The x- and y-values in cm were converted into AIPS pixels by choosing the map side to be 10 stellar radii (see Table 1) and scaling this to be equal to 1024 pixels on the AIPS TV window. To improve comparison with observations, the map was then convolved with a circular gaussian of FWHM equal to 12 AIPS pixels. This corresponds to resolving objects of linear size equal to 2.0 3 10 10 m, chosen to be comparable to the performance of the VLBA at 43 GHz, assuming TX Cam to be at a distance of 696 pc (see Table 1). If TX Cam is actually at the lower distance of 317 pc, then the linear resolution of the model is poorer than that of the VLBA by a factor of 2.2. The resulting scaled (x,y,z) data are then written into a data-file which can be read by the AIPS task ‘FETCH’. The twenty available images from the calculations were augmented by interpolating two additional frames between every calculated pair, using the AIPS task ‘COMB’. Finally, the 60 resulting frames were combined into an AIPS anima-

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Table 1 Stellar parameters for TX Cam and the model

colm.Gray / sio / siomed.gif . Slower and faster versions of the model animation are also available.

Object

TX Cam

Model Mira

Mass (M ( ) Period (d) Mode Radius (R ( ) ~ (M ( yr 21 ) M Distance (pc)

1.5 557 Fundamental? 474 a 1.1 3 10 26 b 317 c

1.0 332 Fundamental 244 1.8 3 10 27 N /A

a

This value is the arithmetic mean of the estimates by (Cahn & Elitzur, 1979) and (Pegourie, 1987). b From (Knapp & Morris, 1985). c From (Patel et al., 1992) but note that Cho et al. (1996) calculate a distance of 696 pc.

tion via the task ‘MCUBE’. Subsequently copies of the movie have been developed to run under different formats, notably as an MPEG via the STARLINK routine ‘FITSTOMPEG’, and a gif89 version for World-Wide-Web (WWW) browsers.

4. Comparison of the model and TX Cam Our model is not specifically a model of TX Cam. For a comparison of several important stellar parameters, see Table 1. We note that several quantities are markedly different, notably the pulsation period and the mass-loss rate. Nonetheless, we offer the reader a comparison between the animations which currently exist, and derive some observationally relevant statistics from the model animation in Section 5 below. The TX Cam animation is available, courtesy of Dr. Phil Diamond at the following WWW site: http: / / www.jb.man.ac.uk / |pdiamond / txcam2.html . The animation for the model star is submitted as part of this work, and is also available at a WWW site with URL: http: / / www.astro.cf.ac.uk / pub / Mal-

5. Results The variation of the intensity and the spatial behaviour of the SiO emission in our model circumstellar envelope is displayed in the gif89 animation, as submitted. Certain useful statistics have been derived from the animation, and all relate to the averaged behaviour of the population of modelled maser clumps. The usefulness of a given statistic in this work, depends on whether it can be directly compared with the observational data from TX Cam. We reserve calculation of statistics which relate purely to the model (the mean temperature for bright objects at 43 GHz for example) and cannot be directly related to observation, for a more detailed publication (Humphreys et al., 2000). We have chosen to record the following observation-related statistics: the mean proper motion, mean expansion velocity, mean ring radius, mean ring thickness and mean velocity in the line-of-sight. All these statistics relate to averages over the fifty brightest maser objects in a given transition. The object lists are significantly different for different masing transitions, and for a given transition are determined by averaging over all phases. We have recorded grand averages (over objects and phases) for three transitions (v 5 1,J 5 1–0, v 5 2,J 5 1–0 and v 5 1,J 5 2–1) in Table 2. Phase dependence of the statistics, with the exception of the proper motion, is shown in Fig. 1 to Fig. 4. The obvious features of Fig. 1 are that all three transitions behave similarly over the stellar period, with a small initial contraction of the maser ring, followed by a larger shock-driven expansion. At high

Table 2 Statistics derived from the model Statistic

v 5 1,J 5 1–0

v 5 2,J 5 1–0

v 5 1,J 5 2–1

Mean proper motion (AU) Mean ring radius (AU) Ring thickness (AU) Mean expansion velocity (km s 21 ) Mean line-of-sight velocity (km s 21 )

0.45160.069 2.13160.133 2.035 0.87663.561 20.05160.259

0.50060.087 1.95660.147 0.914 1.14063.633 20.02160.448

0.44660.036 2.17160.133 0.704 0.85963.690 20.00960.153

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Fig. 1. The mean radius of the fifty brightest maser features, generated by the model Mira variable, as a function of stellar phase. Twenty epochs is equal to one stellar period. Epoch one corresponds to phase zero, where this origin of the phase is based on the modeller’s definition, see Section 2.

epochs, expansion is halted by gravity, and a slow contraction begins. The maser zones for the v 5 1 lines are closely coupled, with a ring of similar size, but the ring of v 5 2,J 5 1–0 masers should lie significantly inside the others at all phases. Error bars, based purely on the statistical scatter of the spots, are about 0.13 AU in all cases, but have been

omitted for clarity. The likely effects of modelling errors, such as uncertainties in the rate-coefficients, and the use of the Sobolev approximation are discussed elsewhere (Humphreys et al., 1996). In Fig. 2, the grouping of the transitions is rather different. The maser ring of the v 5 1,J 5 1–0 line is always thick, about double the thickness of the other

Fig. 2. As for Fig. 1, but displaying the ring thickness. This is defined, at any phase as the difference between the outermost and innermost contributing spot from the 50 brightest.

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Fig. 3. As Fig. 1, but showing the mean expansion velocity of the ring.

two. This indicates that a much wider range of physical conditions will support the pump in the v 5 1,J 5 1–0 transition. The v 5 2,J 5 1–0 transition is also odd in thickening to a maximum near epoch 5, whilst the other two lines thin steadily to a minimum near epoch 9 (phase 0.45). Fig. 3 principally shows the effect of the outwardmoving shock on the maser ring. The v 5 2,J 5 1–0 maser ring, which has the smallest mean radius is affected first, but the pattern is similar for all three

transitions. A rapid outward acceleration, provided by the shock appears between epoch 0 and epoch 6, producing a peak expansion velocity in the plane of the sky of about 6 km s 21 . Subsequently, this velocity slowly decays under gravity, but only the v 5 2,J 5 1–0 ring is clearly infalling again at the end of the period. The data in Fig. 4 are probably most easily compared with a single-dish spectrum than with an interferometer map, but again there are clear predic-

Fig. 4. As Fig. 1, but showing the mean line-of-sight velocity.

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tions. Part of the cycle is dominated by blue-shifted emission, and this corresponds roughly to the period where the maser rings are expanding (see Fig. 1). This can be rationalized on the basis that a few of the masing objects from the back-hemisphere of the envelope are occulted by the star. Also, there is a clear prediction that the excursion to the red during the contraction phase should be significantly more extreme in the v 5 2,J 5 1–0 transition. Error bars on these values, which give an idea of the line-width produced by the very bright objects have similar values for all three lines, but show considerable variation with phase. Peak dispersions of | 2.5 km s 21 appear near epoch 5, whilst the narrowest distributions of | 0.5 km s 21 appear near epoch 16. We note that the grand-average line-of-sight velocity is always mildly blue for all the lines studied here.

6. Discussion We discuss here general points of similarity and difference between the modelled circumstellar masers, and those observed in TX Cam. Both objects show a ring-like distribution of masing objects, which show significant proper motion over one stellar period. In both cases, the proper motion is dominated by expansion, but infalling motions are apparent. In the case of the model, there is a clear phase of infall, and following acceleration by the shock, the outflow decelerates under gravity. In the case of TX Cam, the picture is more complex: some objects appear to behave in a way similar to those in the model, with a decelerated outflow. However it is not clear whether the dominant deceleration mechanism is gravitational, or whether it is collision with an overlying layer of the atmosphere. Another population of objects appear to move outwards with almost constant velocity (P.J. Diamond, private communication). It is not clear how the velocity of these objects is maintained, but one possibility is an increase in radiation pressure on the masing objects as dust begins to condense within them. Ring radii and thicknesses appear consistent with those in TX Cam, given the differences in stellar parameters, and allowing for the fact that there are clearly nonspherical components to the motions in the real star. In the model animation, there is a range of phase,

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from model phase | 0.25 to | 0.6 where the emission is very dim, and though far from zero, is too dim to see given the dynamic range of the movie. In fact the ratio of frequency and spot integrated intensity for the brightest and dimmest epochs is about 500 for the model. This figure is far lower for TX Cam, but looking at the animation for the real star, it is noticeable that there are large arcs of the source that do become dim at some phases, and we suggest that the asphericity of the TX Cam envelope may smear out the phase effect on the intensity, so that there is always some fraction of the maser zone which supports bright maser features. It is tempting to attempt to draw strong conclusions from the line-of-sight velocities, but some observational considerations indicate that some of these are unwise. Our data, averaged over the 50 brightest objects, and all phases, show a slight dominance in blue-shifted emission, but it is very small in all cases and vastly smaller than the statistical scatter. We know that Mira variables can shift from period to period between red and blue dominated spectra (Nyman & Olofsson, 1986). Also, there is a considerable contribution to the wings of spectral lines from weaker emission, which is not visible in the interferometer maps. The only strong conclusion here is the differential shift between the v 5 1 and v 5 2 transitions: for at least part of the cycle, we expect the v 5 2,J 5 1–0 line to be significantly more red-shifted than the other two studied. Analysis of the model provides clear observational predictions for transitions which have not yet been studied in the same detail as the v 5 1,J 5 1–0 line. We suggest that the behaviour of the v 5 1,J 5 2–1 transition at 86 GHz should closely follow that of v 5 1,J 5 1–0, with the exception of the ring thickness. In this respect, we expect a thinner, better defined ring because this transition appears to be generated by a subset of the conditions that give rise to v 5 1,J 5 1–0. We contrast this with the expected behaviour of the v 5 2,J 5 1–0 transition, which we would expect to exhibit a significantly smaller ringsize at all phases, though with some overlap with the other lines. We also expect a delay in expansion velocities between the v 5 2,J 5 1–0 line and the v 5 1 pair, with this latter pair lagging by 0.1–0.2 of a period.

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In future work, we hope to be able to model specific stars with improved radiation transfer methods, and improved rate-coefficients for collisions between SiO and both atomic and molecular hydrogen.

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