Vla Observations of Aurigae: Confirmation of The

VLA OBSERVATIONS OF AURIGAE: CONFIRMATION OF THE SLOW ACCELERATION WIND DENSITY STRUCTURE Graham M. Harper, Alexander Brown, and Philip D. Bennett Center for Astrophysics and Space Astronomy, 593 UCB, University of Colorado, Boulder, CO 80309-0593; [email protected], [email protected], [email protected] Robert Baade Hamburger Sternwarte, Universita¨t Hamburg, Gojenbergsweg 112, 21029 Hamburg, Germany; [email protected] Rolf Walder Steward Observatory, University of Arizona, Tucson, AZ 85721; [email protected] and Christian A. Hummel European Southern Observatory, Casilla 19001, Vitacura, Santiago 19, Chile; [email protected] Receivved 2004 June 21; accepted 2004 October 20

ABSTRACT Studies of the winds from single K and early M evolved stars indicate that these flows typically reach a significant fraction of their terminal velocity within the first couple of stellar radii. The most detailed spatially resolved information of the extended atmospheres of these spectral types comes from the Aur eclipsing binaries. However, the wind acceleration inferred for the evolved primaries in these systems appears significantly slower than for stars of similar spectral type. Since there are no successful theories for mass loss from K and early M evolved stars, it is important to place strong empirical constraints on potential models and determine whether this difference in acceleration is real or an artifact of the analyses. We have undertaken a radio continuum monitoring study of Aurigae (K4 Ib + B5 V) using the Very Large Array to test the wind density model of Baade et al. that is based on Hubble Space Telescope (HST ) Goddard High Resolution Spectrograph ultraviolet spectra. Aur was monitored at centimeter wavelengths over a complete orbital cycle, and flux variations during the orbit are found to be of similar magnitude to variations at similar orbital phases in the adjacent orbit. During eclipse, the flux does not decrease, 3 3 showing that the radio emission originates from a volume substantially larger than RK (150 R) surrounding the B star. Using the one-dimensional density model of the K4 Ib primary’s wind derived from HST spectral line profile modeling and electron temperature estimates from previous optical and new HST studies, we find that the predicted radio fluxes are consistent with those observed. Three-dimensional hydrodynamic simulations indicate that the accretion flow perturbations near the B star do not contribute significantly to the total radio flux from the system, consistent with the radio eclipse observations. Our radio observations confirm the slow wind acceleration for the evolved K4 Ib component. Aur’s velocity structure does not appear to be typical of single stars with similar spectral types. This highlights the need for more comprehensive multiwavelength studies for both single stars, which have been sadly neglected, and other Aur systems to determine if its wind properties are typical. Key words: binaries: eclipsing — radio continuum: general — stars: individual ( Aurigae) — stars: mass loss — supergiants — techniques: interferometric

1. INTRODUCTION transitions of sufficient opacity to provide absorption and scattering diagnostics (Hempe & Reimers 1982). Optical studies Aurigae systems are detached eclipsing binaries in which a have mostly concentrated on the K star’s chromosphere, where hot main-sequence star (typically of spectral type B) moves larger column densities allow the use of numerous weaker metal through the partially ionized wind of an evolved late-type su- absorption lines as atmospheric diagnostics (Wright 1970). How- pergiant (Hack & Stickland 1987). These systems are of great ever, only a few optical transitions are strong enough to be importance to the study of late-type stellar atmospheres, be- opaque in the lower density winds, and these turn out to be of cause in the ultraviolet (UV) the B stars act as sensitive probes very limited utility (see x 2). Aurigae (K4 Ib + B5 V) is the of the K star’s atmospheric structure. Near eclipse the B star eponymous binary and has been the subject of intensive UVand provides spatial information about the K star atmosphere, al- optical observing. The stellar parameters and orbit are accu- beit modified by the companion star, as the lines of sight pass rately determined (Bennett et al. 1995, 1996) and allow quan- through successive projected heights above the K star limb. titative analysis of other aspects of the system, e.g., the wind Eclipsing systems provide rare opportunities to obtain direct momentum equation because the stellar radius and gravity are height-resolved dynamic and thermodynamic information for known. late-type stars, and it allows us to study the atmospheric energy The specific mechanisms responsible for mass loss from the K and momentum balance. These systems have been extensively and early M evolved stars remain unknown, and understanding studied with International Ultraviolet Explorer (IUE) and the them is one of the challenges of stellar atmosphere studies. The Hubble Space Telescope (HST ) in the UV, where hot stars dom- detailed thermodynamic information gleaned from the Aurigae inate the observed flux and the late-type stellar winds contain binaries provides the basis for studies of the momentum balance 1018 VLA OBSERVATIONS OF AURIGAE 1019

(Eaton & Bell 1994) and mass-loss mechanisms (Kuin & law model: V(R) ’ V1(1 R=R) ,where is a wind accelera- Ahmad 1989). However, our understanding from these systems tion parameter. Here rapid and slow wind acceleration corresponds must be tempered by the very nature of the binary systems. The to 1 and 3, respectively. masses of the two components are similar, and the orbital separation occurs within the wind acceleration region, where the 2.1. Binary Systems radial wind velocity is similar to the stars’ orbital velocities. Flow The most detailed spatial information on this acceleration perturbations are to be expected, and wind accretion phenom- region covering 1 < R=R < 5 has come from studying multiple ena may occur (Chapman 1981; Che-Bohnenstengel & Reimers lines of sight in Aurigae systems. These were first studied in 1986; Walder & Harper 1996). Indeed, one of the puzzles that detail with IUE HIRES spectra (see Hack & Stickland 1987 and has arisen out of wind studies of the single and Aurigae pri- references therein). The radiative transfer modeling of these sys- mary stars is that the wind acceleration from single stars gen- tems has been pioneered by the Hamburg group (D. Reimers, erally appear more rapid than for Aurigae stars. In addition, A. Che, K. Hempe, and R. Baade). Initial studies adopted a fast Ahmad & Stencel (1988) noted that the wind acceleration in wind acceleration ( 0:5; Che et al. 1983), but later models Aurigae systems appears to continue beyond the orbital sep- that considered lines of sight closer to the primary derived a more aration (typically 6 supergiant radii), whereas the Alfveń slowly accelerating wind ( 2:5 3:5), e.g., Schro¨der (1985) wave models suggest that the wind is close to its terminal ve- and Kirsch & Baade (1994). locity at this distance (6R). The general feature of Alfveń These large values of are in strong contrast to those found wave–driven wind models that is pertinent here (Hartmann & from, albeit less detailed, studies of single stars, which indicate MacGregor 1980; Holzer et al. 1983) is that the Alfveńwaves rapid acceleration. Next, we briefly review some studies of sin- must be damped on scales of order the stellar radius; otherwise, gle stars and their limitations to place the results from detailed the predicted terminal wind velocities are higher than observed. Aurigae models in context. For current theoretical models of steady Alfveń wave–driven wind models, this leads to a rapid wind acceleration. 2.2. Singgle Stars

Observationally there appears to be a significant difference Here we consider the K4 Ib stars whose V1=Vesc ratio is between the wind flows inferred from the study of Aurigae characteristic of most noncoronal cool evolved stars. Some systems (slow acceleration) and those from studies of single hybrid bright giants of slightly earlier spectral type show evi- stars of similar spectral types (rapid acceleration). The goal of dence of terminal velocities comparable to the escape speed this radio study is to independently test the wind acceleration V1=Vesc 1. For example, Aqr (G2 Ib; Dupree et al. 1992b) model derived from UV line profile analyses and see if the slow and TrA (K3 II) have been observed infrequently to show wind acceleration in Aur is real or an artifact from a systematic such a high-velocity wind component in addition to the slower error in the analysis techniques. The radio observations provide persistent wind flow (Hartmann et al. 1985; Brown et al. 1996). an orthogonal diagnostic to the UVanalyses: they are primarily The metal-deficient field giant HD 6833 (G9.5 III) also shows a sensitive to the density of ionized gas and only weakly sensitive fast wind (Dupree et al. 1992a). These stars also appear to have to the complex atmospheric velocity fields. fast wind acceleration but are not the subject of this paper. In x 2 we discuss the importance of wind acceleration and the apparent differences observed in single evolved cool stars and 2.2.1. Singleg Stars: UV Line Profiles in Aurigae primaries. In x 3 we discuss the diagnostic poten- UV line profile analyses have focused on the strong Mg ii h tial of radio observations, and in x 4 we briefly discuss the pre- and k kk2795, 2802 (air) resonance doublet or the numerous vious radio nondetection. In x 5 we present the observations and Fe ii line profiles. Drake (1985) modeled Boo (K2 III) using results of our long-term monitoring of Aur with the NRAO1 a partial redistribution treatment of Mg ii and derived a rapid Very Large Array (VLA). In x 6 we discuss and compare radio wind acceleration, and Harper et al. (1995) performed a simpler predictions from one-dimensional models based on UV line pro- wind scattering model for TrA (K3 II) and also found a fast file analyses and then discuss the effects of the orbital pertur- acceleration with 1. The derived acceleration in these Mg ii bations based on three-dimensional hydrodynamic simulations studies depends on the ionization structure of the wind above in x 7. In x 8, the results of this study of Aur are compared with 15,000 K. The lower level of the h and k lines is the Mg ii findings for single evolved K stars. The conclusions are pre- ground state, and in cool stellar atmospheres Mg i is photo- sented in x 9. ionized to Mg ii. However, if the wind becomes warmer than 15,000 K, it starts to become collisionally ionized to Mg iii:a 2. WIND ACCELERATION slower wind acceleration with a significant gradient in the Mg iii Although the mechanisms that drive mass loss from non- abundance can mimic a fast wind acceleration if Mg ii is as- coronal K and early M evolved stars are poorly understood, one sumed to dominate throughout. Another systematic bias, af- well-defined characteristic of the winds from these stars is that fecting both single stars and Aurigae binaries, results from the their terminal velocities, V1, are typically 0.2–0.6 of the sur- presence of gradients in the turbulence and affects the apparent face escape speed Vesc; e.g., Aur is ’0.57. Most of the energy acceleration of the mean flow. The turbulence gradient has yet 2 2 input into the wind (/Vesc þ V1) goes toward overcoming to be reliably determined for any single star. Another impor- the gravitational potential, and a smaller amount resides in the tant limitation of using the Mg ii doublet is that, unlike hot star wind’s final kinetic energy. Most of the energy is deposited winds, the wind turbulence at the base of the flow (assuming it is close to the star in the acceleration region, where the mechanisms similar to chromospheric turbulence) is of order the wind speed, that drive mass loss are most manifest (Holzer & MacGregor so there is little independent information to be gleaned from dif- 1985). The wind velocity law is often described using a power- ferent parts of the emission profiles of one or both resonance doublet line profiles [(k) ¼ 2(h)]. 1 The National Radio Astronomy Observatory is a facility of the National To have a hope of reliably inferring the wind velocity struc- Science Foundation operated under cooperative agreement by Associated Uni- ture from single stars requires the use of many lines of different versities, Inc. optical depth. Fe ii is the only diagnostic with this potential 1020 HARPER ET AL. Vol. 129 because it is a dominant ionization state in warm partially range of different radii (equivalent to the multiple lines of sight ionized winds, i.e., Twind < 15;000 K, of single stars, with UV in Aurigae systems). To disentangle the line formation prob- emission lines covering over 3 orders of magnitude in optical lem and its attendant uncertainties from the desired velocity depth, thus sampling the entire wind acceleration region. The information, these diagnostics should preferably be from a dom- lower levels have the same parity as the ground and are meta- inant ionization state, either in the ground or metastable states of stable. For k Vel (K4.5 Ib; Keenan & McNeil 1989), which has low excitation energy. Ground-based diagnostics are not suited a similar spectral type to Aur, Sobolev with Exact Integration for this specific problem. Although quantitative studies of single- line profile modeling of Fe ii by Carpenter et al. (1999) also star winds are in their infancy, the preponderance of evidence suggests rapid wind acceleration. gathered so far from both UV and optical studies of evolved K stars is that these stars typically have rapid wind acceleration. 2.2.2. Singgle Stars: Optical Line Profiles There are even fewer M supergiant studies, and we note that the 1. H: Studies of H asymmetries in evolved cool stars matching of Fe ii wind absorption features with the density often show the presence of blueshifted (outflowing) absorption structure of Betelgeuse (M2 Iab) suggests a significantly slower cores. Mallik (1982) found that for late G and K supergiants acceleration, V(15R)=V1 0:5 (Harper et al. 2001). the H absorption core was formed in a region where the velocity is increasing radially outward. This, and subsequent stud- 3. RADIO CONTINUUM DIAGNOSTICS ies (Mallik & Mallik 1988), explored the influence of different Although absorption- and emission-line studies are very sensi- assumed temperature structures and velocity structures on the tive to the details of the mean flow and turbulent velocity fields, H profile. These studies showed not only the sensitivity of the free-free centimeter radio continuum emission is insensitive to deduced mass-loss rates to the completeness of the hydrogen these properties. Instead, it is sensitive to the density of ionized atomic models and the general radiative transfer problem itself, gas. For single late-type stars when the gas is cool, T < 5000 K, but also to the unknown thermodynamic conditions, rendering e the ionization balance is determined by the photoionization of H a poor diagnostic for quantitative study of wind acceleration. metals by the stellar continuum, whereas for T > 15;000 K hy- Mallik (1993), adopting schematic temperature and density e drogen becomes collisionally ionized. For binary systems with structures, found models in which the wind velocity reached a hot companion there may also be additional photoionization. 10–25 km s1 at 2R . A comparison with Figure 4 of Reimers When the gas is partially ionized, the radio opacity is very sensi- (1977), showing terminal wind speeds typically between 27 and tive to the electron temperature (T ) and weakly sensitive to com- 54 km s1, hints that the winds from K supergiants are accel- e plex velocity fields through the radiative transfer of H i Ly. erated rapidly and reach a significant fraction of their terminal The source function for the radio emission is thermal, on the velocity within one stellar radius of the surface. Rayleigh-Jeans tail, and thus linear in T . 2. Ca ii K emission-line shifts: Following preliminary anal- e In spectral line analyses of Aurigae binaries, the line-of- ysis by Wilson & Bappu (1957), Wilson (1960) found small blue- sight absorption features are necessarily sensitive to very small shifts in emission cores of the optically thick chromospheric Ca ii volumes of the total wind. For example, for Aur the angular K lines, suggestive of chromospheric outflows. Note that these diameter of the B star (0.16 mas) is small compared with the putative outflows of 2–6 km s1 are not seen in HST Goddard K star (5.27 mas) and is very small compared with the orbital High-Resolution Spectrograph (GHRS) spectra of the optically scale of 16.2 mas (Bennett et al. 1996). Inhomogeneities on thin C ii] k2325 emission multiplet; instead, these lines are typi- scales comparable to the hot-star diameter are therefore likely cally slightly redshifted. Applying these Ca ii flow velocities to to reveal themselves as variations in absorption-line profiles. estimates of mass loss for K Ib supergiants give values larger The associated P Cygni wind scattering is global in nature: The than those for other well-studied K supergiants and rates orders blueshifted scattering emission is weighted toward the hemi- of magnitude larger than observed for K giants (Reimers 1973). sphere between the B star and the observer, whereas the red- Since the Ca ii K line is the only optical/UV emission line that shifted emission is weighted toward the far K star hemisphere, appears to be collisionally excited within the accelerating flow, where the wind is flowing away from the observer. The wind’s high signal-to-noise ratio (S/N) and high spectral resolution ob- line-of-sight absorption is superposed on the blueshifted emis- servations are needed to establish the underlying structure of the sion. The centimeter radio continuum emission does not have resolved Ca ii HandKlineprofiles. a significant scattering contribution and is therefore dominated 3. He i k10830 wind absorption: Although this diagnostic has by the hemisphere between the K star and the observer and thus been used to search for warm/hot winds from evolved stars, e.g., samples the extended atmosphere, which is responsible for the Smith et al. (2004), it is not a good diagnostic for wind accelera- blueshifted P Cygni line emission and line-of-sight absorption. tion. The lower level of the transition is metastable but very high Thus, radio observations are an excellent complement to P Cygni lying (19.8 eV). Its population depends strongly on the unknown line analyses and can provide a test of models based on UV and complex thermodynamic atmospheric structure (Sasselov & diagnostics. Here we directly compare our new radio results with Lester 1994). Unfortunately, this diagnostic does not provide the most detailed model derived from UV analyses. much information about relevant gradients. Other similar binary systems with an evolved late-type star 4. Circumstellar absorption features: Blueshifted wind ab- and a compact hot companion (a source of photoionization) are sorption features might appear to be good diagnostics for ac- the VV Cephei binaries (Hjellming 1985) and symbiotic sys- celeration, with different species forming at different radii and tems. VV Cephei systems are similar to Aurigae systems ex- velocity shifts. However, Ca ii is ionized to Ca iii by H Ly in the cept that the evolved primary has later spectral type, e.g., VV acceleration region, and, like Na i and K i,Caii forms by re- Cep (M2 Iab + B0.5 V) and Sco(M1.5Iab+B3V).Symbi- combination in the adiabatically cooling circumstellar shell when otic systems have an M-type evolved companion, a lower mass the wind is already close to its terminal velocity. giant, with a white dwarf hot companion (Seaquist et al. 1984). In summary, quantitative measures of wind acceleration for The winds of late K and early M giants and supergiants are single stars require multiple diagnostics that are sensitive to a expected to be weakly ionized in the absence of additional No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1021

TABLE 1 Adopted System Parameters for Estimating Radio Contribution from the B Star H ii Region

Property Value Notes/Source

B star: Teff...... 15,200 200 K Bennett et al. (1996) ...... 0.16 mas Angular diameter; Bennett et al. (1996)

R*...... 4.5 0.3 R Bennett et al. (1996) 42 1 NLyc...... 1.3 0.4 ; 10 s Aufdenberg et al. (1999) K star: Teff...... 3960 100 K Bennett et al. (1996) Tmin...... 3090 K Assumed to equal 0.78Teff TBalmer ...... 3322 K Carpenter et al. (1999) ...... 5.27 mas Angular diameter; Bennett et al. (1996)

R*...... 148 3 R Bennett et al. (1996) model: ˙ 9 1 M ...... 5 ; 10 M yr Baade et al. (1996) 1 V(5R*)...... 32 km s Baade et al. (1996) 1 V1 ...... 70 km s Baade et al. (1996) 4 ne/nH ...... 3.6 ; 10 Photoionization of metals ...... 1.4 Mean mass per hydrogen nucleus (in hydrogen masses); assumed Twind (initial)...... 12,500 K Initial estimate for wind Te; Eaton & Bell (1994) Twind (final)...... >15,000 K Final estimate for wind Te; this work Aur (A+B) orbital parameters: Distance...... 261 3 pc Bennett et al. (1996) and references therein Semimajor axis (a)...... 908 10 R Bennett et al. (1996) and references therein Eccentricity ...... 0.40 Bennett et al. (1996) and references therein sin i ...... 87 Bennett et al. (1996) and references therein Period ...... 972.183 days Bennett et al. (1996) and references therein Periastron passage...... JD 2,441,373.6 Bennett et al. (1996) and references therein Mideclipse...... JD 2,438,386.540 Bennett et al. (1996) and references therein ionization sources, whereas for mid- and early K bright giants neglected, is controlled by the ratio X (Seaquist et al. 1984; the situation is less clear. k Vel (K4.5 Ib) has a wind temperature Nussbaumer & Vogel 1987): 10,000 K (Carpenter et al. 1999), whereas the hybrid bright 2 2 2 giant TrA (K3 II) appears to have a hotter wind (17,500 K) 4 mH Vwind X ¼ RKB NLyc ; ð1Þ that is collisionally ionized even in the absence of additional B M˙ photoionizing sources. In the following we draw on analytical results from previous studies of symbiotic and single stars and where NLyc is the total number of B star photons emitted H ii regions, e.g., Hjellming & Newell (1983), Drake & Linsky shortward of the Lyman continuum edge at 912 8 per second, (1986), and Brown (1987). M˙ is the K star mass-loss rate, Vwind is the K star wind velocity at the position of the B star, m is the mean mass per H nucleus 3.1. Potential Orbital Modulation of the B Star’s H ii Reggion H (in grams), RKB is the radial separation of the stars, and B is the The radio flux from Aurigae systems comes from the K star’s case B H recombination coefficient. The shape and size of the partially ionized atmosphere, with a potential contribution from H ii region is governed by the parameter X, which changes with a region of fully ionized hydrogen surrounding the compact RKB during the orbit: B star (H ii region). Here we refer to an H ii region as a region of X < 1.—The H ii region is a confined ‘‘bubble’’ around the plasma where hydrogen is photoionized by the hot star’s Lyman 3 Bstar. continuum, which would otherwise be mostly neutral. In these 1 < X < 1 .—The H ii region is a cone opening to infinity binary systems, the H ii region would form within the winds of the 3 4 away from the K star. evolved late-type star. If the K star wind is only partially ionized, 1 luminosity and the For Aur in particular, using the system parameters in Table 1, density of the K star wind, the shape and size of the H ii region we find X ¼ 2:6 at a distance of the semimajor axis (R ¼ 6:1R) can be (1) a localized bubble around the B star, e.g., the Sco adopting an initial wind temperature of Te 12;500 K, charac- system (Hjellming & Newell 1983), (2) an open cone extend- teristic of the outer chromosphere near 2.5R (Eaton 1993). [Here 13 4 0:75 3 1 ing to infinity away from the K star but still bounded toward the we adopt B ¼ 2:6 ; 10 (Te=10 ) cm s ; Osterbrock K star, and (3) a large volume that essentially envelops the K star. 1974]. The B star effective temperature is well determined (TeA ¼ Since Aurigae systems have periods of a few years, in case (2) 15;200 K; Bennett et al. 1995), but the number of Lyman contin- 42 at sufficiently large distances from the K star, the H ii recombi- uum photons (NLyc ¼ 1:3 ; 10 ) is a sensitive function of Teff, nation time will exceed the orbital period and a permanently and there is some uncertainty in NLyc from the theoretical mod- ionized toroidal outer zone will form (Seaquist et al. 1984, 1987). els. The adopted value of NLyc is taken from PHOENIX mod- The shape of the H ii region in a highly idealized, spheri- els that included non-LTE H and He and included iron line cal, weakly ionized (ne=nHT1) K star wind in a long-period blanketing computed in LTE (J. P.Aufdenberg 2002, private com- binary, for which time-dependent ionization effects can be munication; see also Aufdenberg et al. 1999). We thus expect 1022 HARPER ET AL. Vol. 129

ii rad under these conditions that the H region will be mostly open, wind that is still accelerating in the 1 region. Underpin- as found by Kirsch & Baade (1994). ning the derivation of equation (2) is an expression for the ra- Earlier estimates of Aur’s parameters had a slightly cooler dius in which the radial optical depth ¼ 1: B star and a slightly more massive, slower wind, e.g., (Hu¨nsch ˙ ; 9 1 0:45 0:7 & Reimers 1993) TeA ¼ 15;000 K, M ¼ 6:3 10 M yr , Te 1=3 1 1 RRðÞ¼ 1:72 ( fion fele) and v1 30 km s (Schro¨der 1985). This gives X 0:5 3 < 104 5 GHz 1 ii ! X < 4 with a partially open H region. In the first UV 2=3 studies the B star was thought to be significantly cooler, i.e., M˙ 10 km s1 1:4 R 1 ; : TeA ¼ 13;000 K (Che et al. 1983), which would have resulted in 109 M yr1 v 148 R a bound H ii region. 1 The orbit of Aur is eccentric (e ¼ 0:40), and the separation ð4Þ of the two stars (RKB) constantly changes with orbital phase. Potentially this can lead to a change in shape and size of the H ii This expression should be used to test whether equation (2) is a region, which may lead to orbital modulation of radio fluxes in valid approximation. For the parameters in Table 1 this gives rad an otherwise steady K star wind, especially near B star eclipse. R( 4:86 GHz ¼ 1) ’ 1:3R. The most detailed UV line profile analysis of Aur, based on HST GHRS spectra by Baade et al. 4. PREVIOUS RADIO OBSERVATIONS (1996), shows a slow wind acceleration and suggests that at this A VLA survey of 10 Aurigae binary systems during 1985 radius the wind is far from its terminal velocity. The density at a and 1986 was conducted by Drake et al. (1987) at 6 cm with given radius is underestimated, since the assumed velocity in 100 MHz bandwidth. They detected two systems: 31 Cyg (K3 equation (2) is too high. The radio opacity is proportional to the Ib–II + B3.5 V) at 0.36 mJy and 47 Cyg (K2 Ib + B3 V) at product of the electron and proton densities, so that the opacity 0.50 mJy, a 3 detection for Pup (K3 Ib + B2–B3 V) at at a given radius can be significantly underestimated, leading to 0.17 mJy, and a 3 upper limit for Aurof0.17mJy.They an effective source size, and radio flux, which is too small. Note found that the detected sources correlated with B star compan- also that the small density scale heights associated with a wind ions of earlier spectral type, which, hence, were more luminous accelerating region lead to the flux being a stronger function of 0.6 in the H Lyman continuum. Using a simple constant-velocity than the given by equation (2). Our preliminary models wind model to estimate the wind volume emission measure for Aur, which allowed for the effects of wind acceleration and (Moran 1983), they found that for 31 Cyg and Pup the B star intrinsic K star wind ionization, indicated that Aur should companions could ionize the K star winds, whereas for 47 Cyg indeed be detectable with the VLA. an extra source of ionization was required. 5. NEW VLA OBSERVATIONS OF AURIGAE If Aur’s K star wind is fully ionized by the B star and the wind is assumed to have constant velocity, we can use the an- We observed Aur with the VLA on 15 dates during the alytical expression developed by Wright & Barlow (1975), interval 1995–1998. These were the result of three separate VLA Olnon (1975), and Panagia & Felli (1975) programs: AH546 provided the first detection and constrained the spatial size of Aur, AH603 commenced the orbital moni- T 0:1 0:6 toring, and AH649 covered the eclipse of the B star. These obser- F ðÞ¼mJy 0:60 e ðÞf f 2=3 104 5 GHz ion ele vations were primarily at 8.46 GHz (X band: 3.54 cm, referred ! to here as 3.5 cm) and 4.86 GHz (C band: 6.17 cm, referred to 4=3 ˙ 1 2 here as 6.2 cm), with a single observation obtained at 14.94 GHz ; M 10 km s 1:4 100 pc 109 M yr1 v D (U band: 2.01 cm, referred to here as 2.0 cm). All the obser- 1 vations were recorded with a total bandwidth of 100 MHz cen- ð2Þ tered on the given frequency. During this period the VLA was in a range of different array configurations. For all observations, to estimate the resulting radio flux. This expression uses the Aur was shifted several beamwidths away from the phase cen- free-free Gaunt factor from Mezger & Henderson (1967), which ter to avoid contamination by any phase center artifacts, which can is based on Altenhoff et al. (1960): be caused by baseline-dependent additive errors in the visibilities. 0:15 However, no such artifacts were seen in any of the resulting maps. Te 0:1 The data were calibrated and reduced using the AIPS data gA ’ 5 : 104 5GHz reduction software package. Phase calibration was performed using the VLA calibrator 0423+418, except for the first observa- The opacity corrected for stimulated emission is given by tion on 1995 February 20, when 0432+416 was used. 0423+418 is not resolved in any VLA configuration. 3C 48 (J2000: 0137+ 3 3 1 ne(cm )nion(cm ) 331) was the primary flux calibrator with assumed flux densities cm ’ 0:212 0:1 1:35 : ð3Þ (Hz)Te (K) of 5.63, 3.29, and 1.81 Jy at 4.86, 8.46, and 14.94 GHz, respectively (the VLA Calibrator Manual 1995.2 values). 3C 48 is Using the system parameters compiled in Table 1 and assum- known to vary by 2%–3% over several year timescales. ing Te ’ 12;500 K, equation (2) gives a 6 cm flux of 0.06 mJy, Maps of the regions surrounding Aur and 0423+418 were which is below the observed upper limit of Drake et al. (1987). created using the task MX and the source flux densities measured We assumed that hydrogen is the dominant source of electrons using the JMFIT and IMEAN tasks. The measured flux densities and positive ions (protons), i.e., ne ¼ nion ¼ felen H ¼ fionn H, with from the combined JMFIT and IMEAN results and the 1 error fion ¼ fele ¼ 1 and helium is neutral. bars measured from adjacent background regions are given in Equation (2) is based on the assumption that the wind has Table 2. On one date (1998 May 18), using the A configuration, constant velocity, constant temperature, and constant ionization we were unable to make acceptable maps because of rapid var- fraction. However, this expression underestimates the flux of a iation in atmospheric phase that prevented accurate calibration. No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1023

TABLE 2 VLA Observations of Aurigae

Aur Phase Calibrator 0423+418

Orbital Phase 2.0 cm 3.5 cm 6.2 cm 3.5 cm 6.2 cm Date Program ID VLA Config. () (mJy) (mJy) (mJy) (Jy) (Jy)

1995 Feb 20...... AH 546 D 0.708 ... 0.35 (0.02) 0.25 (0.02) ...... 1995 Aug 20...... AH 546 A 0.894 ... 0.30 (0.01) ... 1.391 (0.001) ... 1997 Jan 18...... AH 603 A!B 0.426 ... 0.29 (0.02) 0.18 (0.03) 1.038 (0.003) 1.205 (0.003) 1997 Mar 15 ...... AH 603 B 0.484 0.31 (0.08) 0.25 (0.02) ... 1.067 (0.003) ... 1997 May 15...... AH 603 B 0.547 ... 0.18 (0.02) 0.18 (0.02) 1.105 (0.002) 1.295 (0.002) 1997 Jul 22 ...... AH 603 C 0.616 ... 0.30 (0.02) 0.18 (0.03) 1.185 (0.004) 1.382 (0.003) 1997 Sep 25...... AH 603 DnC 0.683 ... 0.14 (0.04) 0.11 (0.04) 1.217 (0.001) 1.390 (0.001) 1997 Dec 1 ...... AH 603 D 0.752 ... 0.25 (0.02) 0.14 (0.02) 1.184 (0.001) 1.385 (0.001) 1998 Jan 27...... AH 603 D 0.811 ... 0.26 (0.02) 0.19 (0.03) 1.200 (0.001) 1.400 (0.001) 1998 Mar 6 ...... AH 603 A 0.850 ... 0.23 (0.02) 0.19 (0.02) 1.144 (0.006) 1.281 (0.008) 1998 Jun 18 ...... AH 649 BnA 0.957 ... 0.27 (0.02) 0.21 (0.02) 1.119 (0.005) 1.307 (0.005) 1998 Jul 6 ...... AH 649 B 0.975 ... 0.31 (0.02) 0.23 (0.02) 1.225 (0.004) 1.311 (0.003) 1998 Jul 26 ...... AH 649 B 0.996 ... 0.36 (0.02) 0.25 (0.02) 1.232 (0.004) 1.367 (0.002) 1998 Aug 18...... AH 649 B 0.020 ... 0.37 (0.02) 0.24 (0.02) 1.265 (0.002) 1.399 (0.002) Mean/ ...... 0.31 (0.08) 0.28 (0.07) 0.20 (0.04) 1.182 (0.092) 1.338 (0.006)

The larger error bars for 1997 September 25 are a result of 10 calibrator, as this provides a check source for systematic errors missing antennas during the array reconfiguration (DnC). in the data reduction process. The flux constancy of 0423+418 The location of Aur measured on 1998 March 6 in the is not known, but the variations observed in Aur do not closely A configuration at 3.5 cm is (J2000) ¼ 05h02m28s:686, ¼ follow the relative magnitude or pattern of the phase calibrator þ4104033B08, which is within 45 mas of the proper motion– flux throughout the observing sequence, lending credence to the corrected Hipparcos optical position. This observation provides reality of the variations observed in Aur. the best spatial resolution (240 mas) and position: the source is During the eclipse of the B star (phase 1.0), which is close to unresolved and within a small fraction of the beamwidth of its central, the radio flux increases slightly. This shows that the expected location. Relative to the K star, the B star sweeps out radio emission is not dominated by an H ii region of volume 3 3 an angle of 20 mas in the sky, so the radio emission from the RK ’ (150 R) surrounding the B star, which would be oc- system is expected to be unresolved. culted by the K star photosphere at this time. The data cover, We searched for potential circular polarization from Aur, albeit sparsely, one complete orbital cycle with a small overlap and, because of the low S/N, we used the combined 1998 B in orbital phase. There are no observations for phases between configuration 3.5 cm data sets. We find a 3 upper limit of 8.4% 0.02 and 0.42, which span periastron at phase 0.071. It can be for the fractional circular polarization. The absence of signif- seen from Figures 1 and 2 that the variations within the orbit, icant polarization and the positive spectral index of the source where it is well sampled, are of the same magnitude as varia- indicates that the centimeter radio emission is most likely ther- tions at different times but with similar orbital phase. The ob- mal. The 1986 nondetection at 6.2 cm (Drake et al. 1987) is con- served variations are not a simple function of orbital phase, and sistent with the values we observe. The 6.2 cm flux has been near orbital modulations of the H ii region are not apparent. The 1995 and dipped below 0.17 mJy on several occasions. The increased observations (red ) show slightly higher fluxes than similar phases sensitivity of our observations compared with those reported by during the next orbit. The 1997 observations (green) show a fairly Drake et al. (1987) is primarily due to deeper exposures. constant 6.2 cm flux, whereas the 3.5 cm flux is more variable, giving rise to a significant change in the spectral index. A charac- 5.1. Results of VLA Observvations teristic timescale ( var) for radio variability is the crossing time for 1 The results of the combined programs are shown in Figures 1 R ¼ RK . Adopting a propagation speed of 15 km s , which is and 2. Different symbols show the different years, and the array approximately equal to both the thermal hydrogen velocity and configurations are given above the symbols. Figure 3 shows the the wind velocity at 2.8RK, var 80 days. This is a typical in- actual and apparent orbital positions at the phases of the VLA ob- terval in our temporal sampling. The 6.2 cm flux is formed further servations. The average fluxes and standard deviations from the out from the K star, and the 3.5 cm variability may reflect dy- mean value are 0:28 0:07 mJy at 3.5 cm and 0:20 0:04 mJy namical changes in the acceleration region. at 6.2 cm. The single 2.0 cm observation gives 0:31 0:08 mJy. 6. MODELING AURIGAE’S RADIO FLUX The flux variations do not correlate with the different array configurations and are consistent with an unresolved binary source Aur has now been detected at three wavelengths, and the with no nearby confusing objects. Periods of low flux are not system can be analyzed in more detail. First, however, we correlated with the extended arrays, which sometimes suffer consider a very simple model. One could consider that the ra- from poor phases. The empirical spectral index, defined as ¼ dio emission from such a system would be a combination of d log F=d log , derived from the 3.5 and 6.2 cm fluxes ranges the thermal emission from the stellar photospheres with addi- from 0.0 to 1.1 with a mean of 0.6, the implications of which are tional emission from an H ii region in the K star wind near the discussed in x 6.3. Bstar. No suitable check source is present within the region mapped An upper limit to the radio flux from the H ii region is given by around Aur itself, so we show the flux variations of the phase assuming that all B star Lyman continuum photons are absorbed Fig. 1.—Fluxes at 3.5 cm from VLA monitoring programs AH546, AH603, and AH649 obtained between 1995 February and 1998 August. Red circles, green squares, and blue triangles are observations made in 1995, 1997, and 1998, respectively. The red shaded region indicates when the B star is eclipsed by the K star photosphere. The observations are wrapped in orbital phase (period 972.183 days), but most observations occurred during one cycle. Periastron is at phase 0.071. The VLA configurations are shown above each datum. The variability of Aur (top) is not well correlated and is greater than that of the phase calibrator 0423+418 (bottom). This indicates that the variability of Aur is not instrumental in origin.

Fig. 2.—Same as Fig. 1, except for 6.2 cm. VLA OBSERVATIONS OF AURIGAE 1025

Fig. 3.—Actual and apparent orbit of Aur, showing the phases when the VLA data were obtained, as well as the epochs when HST GHRS spectra were also obtained. The orbit and K star sizes are to scale, and the B star size has been enlarged to enhance visibility. The VLA epochs correspond to the entries in Table2.Theline of sight to the Earth is indicated by the dotted line. The orbital positions where HST GHRS spectra were obtained are also shown; their number convention is adopted to be consistent with previous publications. The chromospheric temperature model is constrained by GHRS epochs 4 and 5, and eclipse spectra were obtained at GHRS epoch 8. within the K star atmosphere and wind and the whole region is utes little to the total flux because of its very small angular size, optically thin to the radio: whereas the H ii region dominates. The total from this model (hereafter known as model 1) is 0.23 mJy. The total is slightly 0:1 F (mJy) ¼ 1:18 ; 1042N less than that observed (0:31 0:08 mJy). Lyc 5 GHz The number of Lyman continuum photons required to ionize 0:4 2 the volume emission measure of a constant velocity and Te wind ; Te 100 pc 4 : ð5Þ is, following (Moran 1983), 10 D T 0:75 N ¼ 1:46 ; 1042 e Here we have used a power-law expression for the case B hy- Ly 104 drogen recombination rate. At 2.0 cm, where the H ii region has ! 2 its lowest opacity, the flux would be 0.22 mJy. M˙ 10 km s1 1:4 148 R ; : ð7Þ The contributions from the naked B and K star photospheres 109 M yr1 v R can be evaluated using the opaque disk model with angular 1 diameter and brightness temperature T : Br There are sufficient B star Lyman continuum photons to ionize a significant fraction of the wind, in accord with the opening angle 2 2 8 estimate in 3.1. A fraction of the B star Lyman continuum pho- FðÞ¼mJy 1:42 ; 10 TBr : ð6Þ x 5 GHz mas tons will be lost to the system, so the contribution from the H ii region in model 1 will be overestimated. If the total radio flux is At 2.0 cm, the B and K stars contribute 5:0 ; 105 and dominated by optically thin emission, then / 0:1, whereas 1:4 ; 102 mJy, respectively (assuming the disk sizes in Table 1, the observations indicate optically thick emission, which leads which radiate at Teff). The B star’s naked photosphere contrib- model 1 to further overestimate the escaping radio flux. 1026 HARPER ET AL. Vol. 129

6.1. Density and Temperature Models The relationship between tangential and radial column den- A realistic estimate of the radio flux from the K star’s ex- sity at a projected radius from the center of the K star R ¼ b (b is called the impact parameter) can be approximated to within panding wind requires knowledge of the density and tempera- 50% by ture structure. The ionization problem can then be solved and the radio opacity found. The radio fluxes can then be found by pffiffiffiffiffiffiffiffiffiffiffiffiffiffi tang rad solving the radiative transfer equation. The detailed structure N H ðÞb N H ðÞb 4H=b; ð9Þ models adopted are described in the following subsections. where H is the density scale height at b, which can be derived 6.1.1. Density Model tang from the observed change of N H with b,i.e.,byobserving The most detailed velocity and density model is that of different impact parameters typically during ingress. This ap- Baade et al. (1996), who derived a mean one-dimensional proximation is valid for wind density distributions ranging from model for Aur on the basis of the analysis of HST GHRS Fe ii quasistatic exponential Menzel (1931) to power-law atmospheres, spectra using a combination of curve of growth for the inner including a constant wind velocity. wind region and two-dimensional P Cygni line profile calcu- In this work we adopt a temperature structure based on a com- lations for the outer wind region. In the inner regions the wind bination of optical and GHRS data. Although the radio emission velocity is deduced from the line-of-sight absorption columns at the VLA wavelengths is not sensitive to the deep chromo- and the continuity equation, whereas the faster wind is modeled sphere, we adopt a density and temperature model that runs to the from P Cygni profiles, which give the mass-loss rate and ve- temperature minimum. The radio emission is solved as a radia- locity in the outer reaches. The constraints from the outer region tive transfer problem, with the temperature minimum region pro- are probably more reliable, since they use both column density viding a suitable boundary condition, and permits radio fluxes and velocity information, whereas the low-speed wind region is computed at shorter wavelengths. We adopt Tmin ¼ 0:78TeA ¼ inferred from and depends strongly on the poorly understood 3090 K for TeA ¼ 3960 K from Bennett et al. (1996). The tem- turbulence. perature near 1.1R is from a new curve of growth fitted to the The velocity model is given by optical spectrum of the 1987 eclipse (Griffin et al. 1990). We derive Te ¼ 5000 K, in good agreement with the published result 8 þ1000 of T 5500 K (Schro¨der et al. 1990). > R 1 e ¼ 2000 > The temperature between 1.2 and 1.5R is constrained by >VðÞ1 1 for R=R 5; < R two observations with the HST GHRS. Observed line profiles VRðÞ¼ ½VðÞ1 VðÞ5R ð8Þ were converted to monochromatic optical depths, monochro- > > 2 matic (v), assuming the line formation is well approximated > R : ; 1 þ V ðÞ5R for R=R > 5; by pure absorption, and then hydrogen column density pro- R 4R files were derived assuming solar abundances and that ions are singly ionized. The level populations were assumed to have a 1 Boltzmann distribution. Each line of sight was assumed to be where 1 ¼ 3:5, 2 ¼ 1:5, V1 ¼ 70 km s , and the velocity 1 characterized by a single temperature, which was optimized by at 5R is 32 km s , which is just less than half the terminal velocity. The density is then given by the mass-loss rate (5 ; a least-squares fitting procedure that minimized the deviations 9 1 in derived column density from the mean profile. The temper- 10 M yr ) and the spherical continuity equation, assuming a mean mass per hydrogen nuclei () of 1.4 proton masses. ature sensitivity arises because most of the lines are from ex- (Baade et al. [1996], in their UV line profile analysis, invoked cited levels. This analysis gave temperatures of 8300 1000 ad hoc Fe ii ionization sectors in the wind to bring the densities and 11; 000 1500 K for 1.18 and 1.48R (GHRS epochs 5 and into agreement with those derived from curve of growth.) 4; PI A. B., GO-3626 visits 4 and 5), respectively. These 1993 March values are slightly higher than those found by Eaton 6.1.2. Temperature Model (1993) for earlier eclipses at similar projected heights above the From spectral synthesis modeling of line-of-sight absorption K star limb. The general trends are similar to those inferred from observed in IUE spectra, Eaton & Bell (1994) found a common the previous IUE analysis but differ in detail. relation among Aurigae systems between the characteristic Here the electron temperature Te(K) is characterized in terms of the normalized stellar radius Z ¼ R=R: chromospheric excitation temperature (Texc) and the tangential column density. This relation shows an increase in Texc with ( radius, reaching about 12,500 K in 31 Cyg, 32 Cyg, Aur, and 0:9198 AL Vel. This trend is expected to translate into a common re- TeðÞ¼Z min 3085:4 þ 5656:9Z lationship between Te and radial column density. "# ) 2 The relationship between Texc and Te depends on the diagnos- Z 1 ; tanh ; T max ; ð10Þ tics considered. For the electron densities and temperatures en- 0:1413 e countered in the chromosphere and inner wind, metastable atomic energy levels (i.e., those with the same parity as the ground state) should have Boltzmann populations, to a good approximation. where we truncate the temperature rise with different values of max Since nearly all of the UVabsorption arises from these levels, we Te . The significant figures for the coefficients above are the assume that Te ’ Texc. Beyond the chromosphere, Texc appears as result of a model fit and have no implied physical meaning. an extension of the trends found closer to the photosphere but with Figure 4 shows the adopted temperature structure for dif- more scatter, reaching 17,000 K for 32 Cyg, 15,000 K for 31 Cyg, ferent values of Tmax. We find from the radio model that the and 12,500 K for Aur. Here we extrapolate the chromospheric interpretation of the 3.5 and 6.2 cm radio fluxes is insensitive to values guided by these values and explore different maximum the temperature structure of the chromosphere and relatively wind temperatures. insensitive to the temperature in the outer region as long it is No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1027

We include advection in the solution of the hydrogen rate equations, assuming a steady spherical outflow with the velocity model described above. For the photoionized metals, we assume that those with a first ionization potential less than 4 13.6 eV are singly ionized, leading to ne=nH ¼ 3:6 ; 10 .We find that the radio fluxes can only be reproduced if the wind acceleration is slow and the wind is hot enough that collision ionization dominates. The model radio fluxes are therefore rather insensitive to uncertainties in the Te and ionization structure. 6.3. Properties of the Radio Model The radio fluxes were calculated from the ionization model described above by solving the radiative transfer problem for spherically symmetric one-dimensional atmospheres, i.e., the K star wind dynamic and thermodynamic properties are described by a single radial coordinate. The details of the one-dimensional code are given in Harper et al. (2001), but here we do not include dust opacity. The core of the code is the geometry module of Fig. 4.—Adopted electron temperature models for the Aur radio flux calculations. The outer regions have different maximum temperatures, whereas the S-MULTI (Harper 1994). We consider system-induced asym- inner regions have the same Te distribution. metries in x 7. The fluxes for the models described below are given in Table 3 at the observed VLAwavelengths and for 0.7 cm max (Q band), 1.3 cm (K band), and 20 cm (L band) for completeness. ionized or Te > 15;000 K, i.e., when hydrogen becomes collisionally ionized in the absence of the B star. For the sequence of models [models 2(a) and 2(b), 3(a) and 3(b), 4(a) and 4(b), and 5(a) and 5(b)] we use the system param- 6.2. Ionization Structure of the K Superggiant Wind eters described above and vary the maximum of the K star wind temperature to be T ¼12;500, 15,000, 20,000, and 25,000 K. In single evolved late-type stars the chromosphere and wind max The four different Te profiles are shown in Figure 4. The (a) mod- electron density have contributions from photoionized metals els have an ionization balance representative of that intrinsic to an and from hydrogen. Hydrogen is ionized by a two-step process isolated K supergiant, whereas the (b) models have fully ionized of excitation of the n ¼ 2 level by electron collisions and scat- hydrogen representing the extreme case in which the B star has tering in Ly, followed by photoionization by the optically thin aenvelopingHii region (X > 1 ). These are generalizations of 4 K star Balmer continuum. In Aur the B star presents additional equation (2) in which we have now solved for the detailed den- photoionization of hydrogen through the formation of a po- ii sity and temperature structure, and the (b) models also reflect a tential H region and the presence of an additional source of more realistic estimate than model 1 in that not all B star Lyman Balmer continuum. continuum photons are reprocessed in the K star wind and some We can represent the mean intensity of the Balmer continuum escape the system, and optical depth effects are included. in a location between the two stars, separated by a distance s,as For models with lower T , the differences in fluxes between max s(1 x) sx the (a) and (b) models are the most significant. In models 2(a)– J ¼ W BðÞþ3320 K W BðÞ15;200 K ; 5(a), the ionization is extremely sensitive to Te through the col- RK RB lisional population of the H i n ¼ 2 level, which leads to a mod- ð11Þ est sensitivity in the radio flux. The less ionized atmospheres appear more compact in the radio and thus have smaller fluxes, where W is the radiation dilution factor, x is the fractional length since the thermal source terms are the same in both the (a) and from the B star, and the radiation temperatures are estimates for (b)models.FormodelswithT max ¼ 20;000 and 25,000 K, the Balmer continua (see below). The contributions become collisions dominate the ionization of hydrogen beyond R > equal, at the Balmer edge, near 1 x ¼ 0:23, i.e., the B star 2:5R, and the concept of the H ii region surrounding the B star makes a significant contribution to the Balmer continuum in the is no longer well defined. The fluxes for the longer wavelengths wind acceleration region. Guided by the observation that the ra- are therefore similar for models (a) and (b). In the absence of dio flux does not decrease during eclipse, we neglect the explicit photoionization the balance between collisional ionization and contribution of the B star’s Balmer continuum in the ionization radiative recombination leads to hydrogen being 50% ionized at of hydrogen. 15,340 K (Arnaud & Rothenflug 1985). Above this temperature At a distance of R ’ 18R, the hydrogen recombination time the inherent uncertainties present in the calculation of the two- in the K star wind equals the orbital period (8:4 ; 107 s). Outside stage hydrogen ionization become unimportant, as collisional this radius, hydrogen ionized by the B star is advected outward processes dominate and depend only on Te. The radial distance 1 and cannot fully recombine before the B star returns to the same at which ¼ 3 occurs for 3.5 cm are also given in Table 3. This relative position. Essentially, the outer wind is fully ionized irre- indicates the layers of the K star atmosphere to which the ob- spective of the electron temperature. We find that this region con- servations are sensitive. The 3.5 cm observations reported here tributes little to the integrated radio fluxes. are sensitive to R 2:5R, i.e., the layers where Te is not em- For Aur, we estimate the ionization balance within the K pirically well constrained. supergiant wind using a collisional and radiative model for The fully ionized models 2(b)–5(b) show that the flux has a hydrogen and using escape probabilities for the Ly and Lyman weak sensitivity to Tmax and the models shrink slightly with continuum radiative transfer. We include photoionization from increasing Tmax. This phenomenon is expected and well under- the K star Balmer continuum, where we have taken the K star stood: when hydrogen is fully ionized, the opacity at centimeter 1:35 photoionization rates from k Vel (K4 Ib; Carpenter et al. 1999). wavelengths / nenionT e ,soasTmax increases, the source 1028 HARPER ET AL. Vol. 129

TABLE 3 Aurigae Model Radio Fluxes

rad 1 Model Notes 0.7 cm 1.3 cm 2.0 cm 3.5 cm 6.2 cm 20 cm R( = 3 ) (3.5 cm) Observed ...... 0.31 0.08 0.28 0.07 0.20 0.04 ...... 1...... Simple Approximation ...... 0.23 ...... 9 1 Tmax-sensitive: M˙ ¼ 5 ; 10 M yr 2(a) ...... Tmax = 12,500 K 1.29 0.45 0.23 0.10 0.04 0.01 2.16 2(b) ...... Tmax = 12,500 K 1.76 0.71 0.41 0.20 0.11 0.03 2.75 3(a) ...... Tmax = 15,000 K 1.43 0.58 0.33 0.16 0.08 0.02 2.38 3(b) ...... Tmax = 15,000 K 1.79 0.75 0.44 0.22 0.12 0.03 2.64 4(a) ...... Tmax = 20,000 K 1.45 0.63 0.40 0.22 0.12 0.04 2.45 4(b) ...... Tmax = 20,000 K 1.79 0.75 0.45 0.23 0.13 0.04 2.55 5(a) ...... Tmax = 25,000 K 1.45 0.63 0.40 0.22 0.12 0.04 2.41 5(b) ...... Tmax = 25,000 K 1.78 0.74 0.44 0.23 0.13 0.04 2.54 M˙ -sensitive: Tmax = 20,000 K 9 1 6(a) ...... M˙ ¼ 7:5 ; 10 M yr 1.95 0.89 0.57 0.31 0.17 0.05 2.79 Velocity-sensitive: Tmax = 20,000 K 9 1 7(b) ...... M˙ ¼ 7:5 ; 10 M yr 0.75 0.40 0.28 0.18 0.12 0.05 2.00

Notes.—Fluxes are in millijanskys. The observed values are the mean and standard deviations. becomes warmer but the optical depth scale and hence the ap- the mass-loss rate further and lowering the temperature, the parent size decreases. The product of the two leads to the relative wind would become weakly ionized, and eventually an H ii re- insensitivity of the total flux to Tmax. Expressed another way, if gion would form near the B star and pronounced orbital mod- the radio emission were optically thin, then from Kirchoff’s law ulation would be expected. 0:35 the emissivity would be /Te . The real ionization balance is likely to be between the two limiting cases of models (a) and (b). 6.3.1. Notable Discrepancies in Radio Fluxes The best overall agreement with the observations occurs for The predicted radio fluxes are in fair agreement with the ob- T max > 15;000 K, where the 3.5 and 6.2 cm model fluxes are servations, but they do not provide a very close match and sug- within the observed range of variability shown in Figures 1 and gest that the adopted atmospheric structure may require revision, 2. However, models 2–5 underestimate the mean 6.2 cm flux. as suggested by a systematic difference between the computed The 2.0 cm model fluxes are too large compared with our single ( ’ 1) and observed ( ’ 0:0 1:1) spectral index and the ex- observation. Overall the results suggest that the adopted density cess 2.0 cm model flux. In particular, if we allow a small increase model works well if T max 15;000K.Inthisregionofpa- in the mass-loss rate to increase the match to the 6.0 cm flux [i.e., rameter space the results are insensitive to uncertainties in the model 6(a)], the 2.0 cm flux continues to be too high. The inner hydrogen ionization caused by the presence of the B star. Per- wind region is less well constrained by the UV line profile anal- haps the largest difference between the model and observations ysis (i.e., a curve of growth), and the region R < 2R requires is the 6.2 cm flux. Increasing Tmax does not change the flux, but more study. Radio observations at 0.7 and 1.3 cm would provide increasing the overall density does increase the opacity and size clarification and a valuable test of this inner region. of the source. We therefore repeated model 4(a) but increased 9 1 6.3.2. Effects of Gradients on Spectral Index the mass-loss rate by 50% to M˙ ¼ 7:5 ; 10 M yr ,which defines model 6(a). This represents a small adjustment to the One point of particular note is that the mean observed spectral originally derived mass-loss rate when compared with typical index is ¼ 0:6, which might naively be interpreted as showing uncertainties of factors of 5 in estimates of mass-loss rates of that Aur has a constant-velocity (i.e., very rapidly accelerating) single stars. The 6.2 and 3.5 cm model fluxes are now within 1 wind with constant ionization and Te structure. For isothermal of variations about the observed mean, but the 2.0 cm model winds, monotonic acceleration increases because the apparent flux is larger than for models 2–5 and significantly larger than size of the system decreases more slowly as increases than for a observed. constant-velocity wind. As the density scale heights get smaller If the wind of Aur had a rapid acceleration, then the radio close to the star, eventually ! 2, which is the fixed angular fluxes would be reduced, because the density and hence opacity diameter blackbody limit. Why then is the observed mean value at a given radius would be lower. To investigate the magnitude of 0.6 even though the wind is accelerating? The presence of a this effect, we repeated model 6(a) with its enhanced mass-loss positive Te gradient with radius produces the countering effect. rate but with a rapid acceleration, and we also fully ionized the At higher frequencies the radio emission samples increasingly wind to maximize the radio flux, creating model 7(b). We used cooler layers closer to the photosphere. The resulting effect is to the power-law model with ¼ 1, i.e., similar to k Vel and balance the increase in from the wind acceleration. The pres- TrA. The fluxes and characteristic formation radius are signifi- ence of a temperature rise in the acceleration region is probably cantly smaller, except for 20 cm, which is formed near R 5R, associated with energy being deposited while the momentum and the 2.0 cm flux, which is now close to that observed. is also deposited. This may be a common occurrence among These radio models confirm the Baade et al. (1996) one- evolved late-type stars and thus render the spectral index, when dimensional wind density model for R > 2R as long as used in isolation, of little diagnostic value. T > 15;000 K, which is in accord with our expectations of max 7. BINARY-INDUCED DENSITY STRUCTURE the wind temperatures of Aurigae systems, e.g., Eaton & Bell (1994), and the absence of orbital induced variations near Thus far we have used one-dimensional models to compute eclipse. If one tried to match the total radio flux by increasing the radio fluxes from Aur. This is, in part, because the density No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1029 model of Baade et al. (1996) is a mean one-dimensional rep- of mass of the stellar system was placed at the center of the cube. resentation with some non–one-dimensional character intro- Depending on the orbital phase, the separation of the stars cor- duced by the addition of Fe ii–Fe iii ionization zones induced by responds to between 1/5 and 1/10 of the length of the cube. In this the B star. Some of the observed radio flux variations are likely way, the matter always flows supersonically outward through the due to some of the temporal and spatial complexities of the boundaries of the cube, ensuring that the outer boundary does not binary. Now we consider, in an exploratory manner, the mod- affect the simulation within the cube. ifications to the density distribution that result from the binary Perhaps the greatest simplification we make in these dynam- nature of Aur. The two components of Aurigae systems ical simulations is to assume that the wind from the K star is typically have similar masses, and, although the chromospheres accelerated rapidly to its terminal speed just above the photo- of the evolved components appear similar to those of single sphere. Given the absence of a description of the wind accel- stars with similar spectral types (Eaton 1992), at some radius eration force, this assumption was imposed to restrict the very the gravitational effects of the B star and the orbital motions large density range within the computational domain that would must modify the K star wind. At typical orbital separations, the have made the computations prohibitive. Therefore, at the wind- orbital and K star wind velocities are similar. shedding boundary of the K star we simply set, for each boundary Here we describe three-dimensional hydrodynamic simulations cell, the wind solution before each time step: initiated at the onset of our VLA study that adopt a faster wind acceleration than indicated in the Baade et al. (1996) model. They M˙ ðÞ¼R ; ð12Þ do, however, represent the only detailed study of the influence of K 2 4RK V1 the eccentric binary orbit and B star’s gravitation potential on the

K star wind. Selected results were reported in Walder & Harper V(RK ) ¼ V1 þ VKorbit ; ð13Þ (1996). and set the wind gas temperature to T and then follow the tem- 7.1. Model Parameters eff perature adiabatically. Here RK denotes the radius of a bound- For these exploratory, yet challenging, hydrodynamic simu- ary cell. Since the imposed velocity is supersonic, the flow will lations, we have chosen a simplified model for the system. We be shed smoothly from the K star. solved the pure adiabatic Euler equations with a polytropic The boundary at the B star is difficult to apply for two rea- equation of state, using eth ¼ p=( 1), where eth denotes the sons. First, the radius of the B star is small compared with all thermal energy density and p the total gas pressure. We chose the other spatial scales of the system. Second, the strong radiation polytropic index ¼ 5=3. Radiative transfer, ionization, and ra- field of the B star certainly affects the momentum and energy diative cooling were not considered. These simplifications make equilibrium of the flow. We neglected these complications in our model rather poor in describing the flow in the vicinity of this study by applying so-called all-absorbing boundary con- the accreting B star, which includes an accretion shock. How- ditions (Tam & Fryxell 1989; Ruffert & Arnett 1994; Zarinelli ever, by additional simulations we find that this will probably et al. 1995), which essentially assume that all material and an- affect neither the overall accretion rate nor the large-scale struc- gular momentum within a certain sphere around the B star even- ture of the flow. tually falls on the B star. We adopted a radius of 18 R for this For these simulations we adopted a mass-loss rate for the sphere. 9 1 K star of M˙ ¼ 4 ; 10 M yr , a terminal wind velocity of 1 v1 ¼ 55 km s , and an initial wind temperature of 4000 K. 7.2.3. Meshes and Discretization 1 The K star has a v sin i ¼ 8:5kms (N. Piskunov 1995, private The computational box was discretized by a basic mesh of communication; see also Griffin et al. 1990), which is smaller 40 ; 40 ; 40 cells. To improve the resolution, subsequent finer than both the final wind velocity and the orbital velocity. Here we and finer meshes were constructed in the vicinity of the accret- assume the K star is nonrotating, but since the rotation speed is ing star. Six levels of refinement were chosen, leading to a finest of order the chromospheric wind velocities, future work is re- mesh of 25 ; 25 ; 25 cells having each a size of 3:9 ; 1011 cm. quired to assess the potential for aspherical mass loss. The all-absorbing sphere has a diameter covered by seven cells. 7.2. Numerical Method, Discretization, The orbit and the shedding of the K star wind was covered by 12 and Boundary Conditions mesh cells of 1:56 ; 10 cm. We have integrated the system over two binary orbits to eliminate traces of the imposed initial 7.2.1. Numerical Method conditions. The hydrodynamic simulations were performed with the AMRCART code2 (Walder & Folini 2000). It consists of a mul- 7.3. Implications for the Radio Fluxes tidimensional high-resolution finite volume integration scheme The radio intensity and opacity are sensitive to the square of (Colella 1990) based on an adaptive Cartesian mesh (Berger the density, and since our analysis in x 6.3 suggests that the 1985). wind is mostly ionized, it is relatively insensitive to Te.For 7.2.2. Computational Domain and Boundary Conditions orbitalR phases ¼ 0:737 and 0.086 we computed the integral 2 5 nH(z) dz (cm ) along the line of sight (z) to examine de- The simulation, performed by R. W., occurs within a fixed partures from a purely spherical wind in the plane of the sky. At 15 cube with an edge length of 10 cm. The stars were moved phase ¼ 0:737 the B star and K star are close to the plane of through the mesh along their eccentric orbital paths. The center the sky and have their maximum projected separation, whereas ¼ 0:086 is close to periastron, shortly after egress, and the B star accretion flows are more prominent. Figure 5 (left) shows the 2 AMRCART is part of the A-MAZE code package, which consists of adaptive mesh three-dimensional magnetohydrodynamic and radiative transfer contour plots of this integral evaluated through a region of com- codes. It is publicly available at http://www.astro.phys.ethz.ch/staff/walder/ putational domain near the binary pair. Significant departures walder.html. from spherical symmetry are small except near the B star. 1030 HARPER ET AL. Vol. 129

R 2 Fig. 5.—Three-dimensional hydrodynamic simulations at orbital phases ¼ 0:737 (top)and ¼ 0:086 (bottom). Left panels show the integral nH(z) dz along the line of sight (z) through the computational domain. Right panels show the logarithmic brightness temperature TBr under the additional assumptions that the plasma is fully ionized and has a constant Te ¼ 15;000 K with a 3 K Galactic background. These are shown to illustrate the effect on the specific intensity in the presence of binary-induced complex flow patterns. The perturbation from a purely spherical K star outflow can be seen in the accretion zones near the B star. This region is optically thin at ¼ 0:737 and does not contribute significantly to the total system radio flux. Near periastron at ¼ 0:086, there is a small region that has moderate optical depth; however, the angular extent is small. The B star accretion zone is expected to be a minor contributor to the total radio flux.

Although the B star photosphere has a negligible contribution ness temperature, which for constant Te with a Galactic back- to the radio flux, there are density enhancements present in the ground of Tbck 3Kis accretion zones near the B star. The characteristic radio formation radius at 3.5 cm will be similar to model 7(b), which has a TBr ’ Te½1 exp ()þTbck exp (): ð14Þ fast acceleration, i.e., 2R. In the unperturbed flow the total rad 1 line-of-sight radio optical depth through the atmosphere for a Toward the K star, TBr 15;000 K near 3.ThenTBr can general impact parameter, b,is(3=2)rad, where rad is the be estimated for regions near the B star from the maps of the optical depth toward the K star at radius R ¼ b. For thermal radio hydrodynamic simulations (Fig. 5, left), which provide infor- emission the specific intensity is proportional to the radio bright- mation on the wind flows and the resulting density distribution No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1031 induced by the binary nature of the system. The adopted energy equation, however, is not expected to be realistic, so in Fig. 5 (right) we have imposed the following empirically constrained assumptions to provide a sense of the variation of TBr in the sky: (1) hydrogen is predominantly ionized, and (2) Te ¼ 15;000 K. Using equation (3), 2:1 T 1:35 ¼ 3:6 ; 1027 e 5 GHz 4 Z 10 K ; 2 5 nH(z) dz (cm ): ð15Þ R 2 Near the B star at phase 0.737, where nH dz peaks at 26 5 10 cm , TBr is 1000 K over a very small solid angle. 25 5 There is a larger zone of TBr 250 K within the 2:5 ; 10 cm contour where the ambient K star wind column is 6:5 ; 1024 cm5 or TBr 65 K. The accretion columns are larger at ¼ 0:086, where the wind densities near the B star are larger and the K star wind speed is lower. The radio optical depth is close to ¼ 1; Fig. 6.—Al ii] k2669.155 chromospheric emission from Aur and k Vel. The however, the solid angle is extremely small. Even though the observed fluxes have been scaled to surface fluxes using the angular diameters given in the text. The Aur spectra were obtained at GHRS epoch 8 during density is enhanced locally in the accretion flow, any associated eclipse. k Vel traces the lower bound of the Aur spectrum. The Al ii] surface increase in Te will reduce its opacity. The locally heated region fluxes and line shapes are remarkably similar. The strong scattering lines are near the B star is therefore expected to provide a small and varying Fe ii kk2666.64 and 2664.66, and the weak emission on the blue shoulder of the Al ii]isCrii k2668.71. There may be a small broad wind-scattering component contribution to the total system flux. Density enhancements in the ii plane of the orbit have a small projection in the plane of the sky, to the Al ]line. and the radio observations are not sensitive to them. GivenR the small solid angle and low to moderate optical depths 2 (1999). k Vel traces the lower bound of the Aur spectrum, and in the nH dz enhancement computed in this model, the pertur- the similarity of the Al ii] profiles is apparent. The broad shoulder bation to the integrated fluxes predicted from the one-dimensional on the blue wing of the Al ii] line in Aur is likely due to Cr ii model are not expected to be significant. Unfortunately, our radio k2668.707, which is formed by scattering of B star photons in monitoring does not adequately sample periastron, and physically the wind of Aur and is not seen in k Vel. Si ii] k2350.173 and the more complete dynamical simulations are also required for further C ii] kk2323.501, 2324.689 lines from the ne-sensitive 2325 8 detailed comparisons. multiplet also show close agreement between their surface fluxes. 8. DISCUSSION Semiempirical radiative transfer models of the earlier spectral type Aurigae systems HR 6902 (G9 II) and 22 Vul (G6 Ib–II) Although the eclipsing nature of Aurigae systems has also agree with empirical models based on eclipse curve-of- provided the most detailed spatial description of the thermody- growth data (Marshall 1996). namic and dynamic conditions in evolved late-type star atmo- It is known, however, from optical studies in which the K star spheres, they are not single stars. The presence of the B star can be observed out of eclipse that additional photoexcitation companion may have significant consequences for both the of the chromosphere occurs in the illuminated hemisphere. Si i chromospheric and wind temperature structure and the mass- k3905 emission is observed when the substellar point is visible loss process. (Christie & Wilson 1935; see also Griffin & Griffin 2000), and this emission probably forms deep in the chromosphere and up- 8.1. Chromospheric Heatingg per photosphere. Walter (1937) found an increase in Ca ii emis- Evidence suggests that the chromospheres on the hemi- sion that correlates with the B star illumination. Although there spheres not illuminated by the B stars are indeed typical of single is direct evidence for the influence of the B star on the chromo- stars. K star chromospheric emission lines that are thermally and spheric emission, it has yet to be quantified; the major cool- photoexcited have surface fluxes typical of these spectral types ants occur in the UV, and the spectral signatures are swamped (Eaton 1992). UV eclipse spectra of Aurigae systems mostly by the B star when observed out of eclipse. The K star rotation show light scattered from the B star by opacity from singly and orbital periods are very similar, so the B star illuminates only ionized metals in the K star wind. In a few spectral regions that a part of the K star chromosphere. Furthermore, the timescales are dominated by opacity from neutrals or intercombination for atmospheric cooling in the chromosphere are very short com- lines from single ionized species, the intrinsic K star spectrum is pared with the orbital period, so the nonilluminated hemisphere observed. In Figure 6 we show HST GHRS spectra of Al ii] is expected to relax to a ‘‘single-star’’ state. In the lower density k2669.155 (wavelengths greater than 2000 8 are given in air) regions in the wind, the additional heating from the B star may for k Vel and Aur during eclipse (GHRS epoch 8; PI: A. B., play an important role in raising the wind temperature. GO-6068 visit 2). The observed fluxes have been scaled to 8.2. Mass Loss surface fluxes using the angular diameters: for k Vel we adopt 11.1 mas (Blackwell & Shallis 1977). No interstellar medium One difference between single stars and the evolved primaries (ISM) reddening correction has been applied here, since it is ex- that can be quantified to some degree is the wind acceleration. In pected to be similar for both sources, i.e., E(B V ) ’ 0:08. The single evolved K stars it is now becoming clear that the wind spectra are also shifted to the photospheric rest frame for each acceleration is rather rapid, e.g., k Vel (K4 Ib; Carpenter et al. star. The k Vel observations are described by Carpenter et al. 1999) and TrA (K3 II; Harper et al. 1995). Other late-type 1032 HARPER ET AL. Vol. 129

TABLE 4

Radio Angular Sizes of Evolved K Stars, radio

Flux a Distance V1 * Twind 3.5 cm radio 1 Star Spectral Type (pc) (km s ) (mas) (K) (mJy) ()

k Vel...... K4.5 Ib 176b 30d 11.1 10,000d 0.14 1.7 TrA...... K3 II 127b 100e 9.6 17,500g 0.28 2.0 Aur ...... K4 Ib 261c 70c 5.3 20,000 0.28 3.5 Tau ...... K5 III 20b 30f 21.2 5000h 0.30 1.8

a Very rough estimates for chromospheric/wind temperatures. b Perryman et al. 1997, Hipparcos. c Bennett et al. 1996. d Carpenter et al. 1999; Twind suggested by radio flux. e Harper et al. 1995; V1 of most persistent state. f Reimers 1977; Ca ii wind absorption variable, not always present. g Harper 2001. h Harper et al. 2004. giants also appear to possess a rapid wind acceleration (Carpenter diation pressure on atoms and molecules, and these stars show et al. 2001). little evidence for coherent pulsations such as those observed We can adopt a more empirical approach to this question in Mira variables. Almost by default, researchers believe that by comparing the ratio of Aur’s apparent radio size to its some form for magnetohydrodynamic waves drive the mass photospheric angular diameter with ratios from other evolved flows. However, no satisfactory model has yet been constructed. Kstars:k Vel ( K4.5 Ib), TrA (K3 II), and Tau (K5 III). In Alfveń wave–driven wind models provide the correct magnitude Table 4 we have crudely estimated the wind temperatures for of wave energy fluxes for magnetic fields of B 1 10 G at mid- these stars, e.g., from Harper (2001), and presented radio fluxes chromospheric gas pressures. However, the predictions for the obtained by us with the VLA and the Australia Telescope Com- wind heating (Hartmann & MacGregor 1980; Holzer et al. 1983; pact Array. Using the simple opaque disk model, equation (6), Harper 1989) are not empirically borne out, e.g., optically thin we can compare the apparent radio sizes. Aur is signifi- emission lines from a range of excitation energies are not ob- 9 1 cantly larger than both k Vel, which has M˙ 3 ; 10 M yr served to be blueshifted, and the electron densities are too low. (Carpenter et al. 1999), and TrA, which has a smaller and less This problem can be overcome, in principle, by restricting the 9 1 well constrained mass-loss rate (M˙ 10 M yr ). (These wind filling factor within the chromosphere and having flux stars also have similar stellar radii, using Hipparcos distances tubes expand outward until they become radial, e.g., Hartmann & [Perryman et al. 1997] and photospheric angular diameters MacGregor (1982) and Jatenco-Pereira & Opher (1989). This from the literature; k Vel, R ¼ 210 R [Blackwell & Shallis would reduce the wind emission measure and make it much 1977], and TrA, R ¼ 131 R [Cohen et al. 1996] compared harder to detect the wind signature in disk integrated emission-line with Aur, R ¼ 148 R. Tau is a lower mass giant with profiles. R ¼ 46 R [Mozurkewich et al. 1991].) Empirically Aur Although direct evidence for surface magnetic fields is miss- stands out from the other stars. A difference in ionization state ing, radio maser observations of the Mira TX Cam (Kemball & alone, through the wind temperature, does not appear be the Diamond 1997) and the supergiant VX Sgr (Chapman & Cohen cause, cf. TrA, and the mass-loss rates alone do not seem 1986) indicate circumstellar magnetic fields, which, if extrapo- to be the cause, cf. k Vel, but cannot be ruled out because of lated back to the stellar surfaces, yield magnetic fields of the the uncertainty in single-star mass-loss rates. Aur may have a appropriate strength for Alfveń wave–driven winds. The dis- large radio= ratio because of a larger ionized mass-loss rate covery of C iii k977.020 and O vi emission on Tau with the and a slower wind acceleration. Far Ultraviolet Spectroscopic Explorer (FUSE) principal inves- In the atmospheric models constructed here that roughly tigator (PI) science observations now provides indirect spectro- match the observed radio fluxes, the B star does not appear to scopic evidence for surface magnetic fields for at least some have a direct effect on the K star’s ionization in the outer layers evolved K stars (Ayres et al. 2003). The O vi kk1031.926 and because Te is sufficiently high for collisional ionization. In this 1037.617 resonance doublet is collisionally excited by electrons case the B star’s Lyman and Balmer continua helps to ionize the in hot (300,000 K) plasma that is thought to require magnetic cooler chromospheric layers closer to the K star. The radio heating. If the 300,000 K plasma is heated by conduction from signature of these effects is more pronounced at shorter wave- the corona, then magnetic fields are required, since acoustic lengths, and a search for radio modulation during eclipse is heating is insufficient to explain stellar coronae (Stepien´ & worthwhile.However,adirect effect of the B star, which we Ulmschneider 1989). Extremely strong acoustic shocks, while in have not quantified, is photoelectric heating, which increases Te principle capable of reaching over 100,000 K, are expected to be and therefore indirectly affects the ionization state of the inner rare (Cuntz 1987), and there are no existing acoustic heating wind. The wind may have sufficient additional heating to lo- models that predict the observed O vi fluxes and line widths. C iii cally raise the wind temperature and become collisionally ion- and O vi emission have recently been detected with FUSE3 in the ized. This may have an impact on the mass-loss process. spectrum of k Vel. Figure 7 shows the O vi emission from k Vel The mechanisms that drive mass loss from evolved late K and early M stars remain poorly understood. They have little or no 3 Based on observations made with the NASA-CNES-CSA Far Ultraviolet dust, and when dust forms it is too far from the stellar surface to Spectroscopic Explorer. FUSE is operated for NASA by Johns Hopkins Uni- drive a wind, e.g., Danchi et al. (1994). There is insufficient ra- versity under NASA contract NAS5-32985. No. 2, 2005 VLA OBSERVATIONS OF AURIGAE 1033

dynamic simulations that include more mass-loss physics and more complete energy equations. Observations of other systems are required to clarify whether Te is controlled by wind heating or photoelectric heating and whether the wind acceleration correlates with binary separation.

9. CONCLUSIONS Our observations and models indicate that the wind from Aur does not accelerate as fast as those inferred in single stars of similar spectral type. The radio continuum observations provide orthogonal diagnostics to UV line profile analyses and allow an almost independent test of the density model, which is essentially confirmed by this work. Tighter constraints on the Te structure near 2R would remove some of the remaining uncertainty. This study provides clarification on the nature of wind acceleration for theoretical studies of evolved late-type stars, and we must now endeavor to study single stars in as much detail as Fig. 7.—FUSE spectra of the O vi kk1031.926 and 1037.617 emission lines possible. One very real problem is that most single-star studies from k Vel that are collisionally excited near 300,000 K. The C ii lines have lower levels in the ground term and are present in the stellar spectra and as ISM absorp- have relied on the power-law velocity model, which, aside tion. The O vi emission is an indirect indicator for magnetically heated plasma. from the terminal velocity, which can usually be accurately measured, has only one adjustable parameter. The very use of the power-law model may be skewing our interpretation of obtained during a 21 ks orbital night exposure. The spectra ob- wind flows and should be relaxed where possible. Modeling tained from program C023 (PI G. H.; observation C0230501) single stars with such an inflexible velocity law may be mis- will be described in detail elsewhere. Given the established similarity of k Vel’s and Aur’s chromospheric heating rates, the leading us into an artificial divide between slow and fast acceleration. It is noteworthy that the more direct empirical wind discovery of O vi on k Vel suggests that magnetic fields are likely velocity laws derived from symbiotic systems differ markedly present in the atmospheres of late K Ib stars. If the wind is driven by Alfveń waves and the dominant wave from the power law, e.g., Vogel (1991); whether this is also a result of binarity remains to be seen. The Fe ii UV emission damping is from ion-neutral collisions (Holzer et al. 1983), line diagnostics appear to be a way forward for single-star stud- then the presence of the B star may change the damping length ies, potentially providing sufficient independent radial infor- (L) through a change in the ionization state of the wind. Ions in mation to derive a more realistic velocity description. The line the wind move with the Alfveń waves and are damped by fric- profile analysis does, however, require intensive radiative trans- tion with the neutrals. In the partially ionized winds of evolved fer calculations. late K and early M stars the sources of ions are single ionized Useful future radio observations would include an eclipse/ metals with low ionization potentials and protons. The metals periastron study at higher frequencies, as described above, and a are photoionized by the chromospheric radiation field, and study of Aurigae systems with a range of early-type com- hydrogen is photoionized by excitation of the n ¼ 2 level followed by photoionization in the Balmer continuum. The domi- panions to help assess the role of wind ionization and heating by the compact hot source. The forthcoming VLA upgrade, the nant neutral components of the chromosphere are hydrogen and EVLA, will provide the increased sensitivity required to exam- helium. The presence of the B star slightly increases the abun- ine a range of such systems. dance of metal ions (N, O) but also liberates protons at the expense of neutral hydrogen. For small-amplitude waves with periods that are long compared with the ion-neutral collision time, the increase in hydrogen ionization increases the damping We thank the VLA for providing observing time that al- length of the waves, which in turn leads to an increase in the lowed the extensive monitoring of Aur. We thank the referee, terminal wind speed (Holzer et al. 1983). However, the mass- Stephen Drake, and R. Harper for suggestions that improved this loss rate and base wind structure are relatively insensitive to manuscript. This research was funded by NASA LTSA grants changes in damping length as long as L R (Hartmann & NAG5-4804 and NAG5-3226, FUSE NAG5-12438 (G. M. H.), MacGregor 1980). The additional ionization will modify the and NSF grant 0206367, and the hydrodynamic study was sup- gas density structure, but since the nonthermal terms dominate ported in part by the Scientific Discovery through Advanced the momentum balance, it is not clear that this effect signifi- Computing (SciDAC) program of the DOE, grant DE-FC02- cantly changes the wind acceleration profile. 01ER41184. This paper also uses observations from HST proj- We note that the slow Aur acceleration could represent the ects GO-3626 and GO-6069, which was supported by grants interaction of an intrinsic single K star wind with the binary na- GO-0326.01-91A and GO-06069.01-94A from the Space Tele- ture of the system, e.g., wound-up magnetic field lines. Further scope Science Institute. This research has made extensive use of progress here requires a new generation of three-dimensional NASA’s Astrophysics Data System Bibliographic Services.

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