the astrophysical journal,543:868 879,2000november10...

THE ASTROPHYSICAL JOURNAL, 543 :868È879, 2000 November 102000. The American Astronomical Society. All rights reserved. Printed in U.S.A.(

MID-INFRARED INTERFEROMETRY ON SPECTRAL LINES. III. AMMONIA AND SILANE AROUNDIRC ]10216 AND VY CANIS MAJORIS

J. D. MONNIER,1 W. C. DANCHI,2 D. S. HALE, P. G. TUTHILL,3 AND C. H. TOWNES

Space Sciences Laboratory, University of California at Berkeley, Berkeley, CA 94720-7450Received 2000 January 10 ; accepted 2000 June 14

ABSTRACTUsing the University of California Berkeley Infrared Spatial Interferometer with a radio frequency

(RF) Ðlter bank, the Ðrst interferometric observations of mid-infrared molecular absorption features ofammonia and silane with very high spectral resolution (j/*jD 105) were made. Under the(NH3) (SiH4)assumptions of spherical symmetry and uniform outÑow, these new data permitted the molecular stratiÐ-cation around carbon star IRC ]10216 and red supergiant VY CMa to be investigated. For IRC]10216, both ammonia and silane were found to form in the dusty outÑow signiÐcantly beyond boththe dust formation and gas acceleration zones. SpeciÐcally, ammonia was found to form before silane ina region of decaying gas turbulence while the silane is produced in a region of relatively(Z20R

*),

smooth gas Ñow much farther from the star The depletion of gas-phase SiS onto grains soon(Z80R*).

after dust formation may fuel silane-producing reactions on the grain surfaces. For VY CMa, a com-bination of interferometric and spectral observations suggest that is forming near the terminationNH3of the gas acceleration phase in a region of high gas turbulence (D40R

*).

Subject headings : circumstellar matter È instrumentation : interferometers Èinstrumentation : spectrographs È molecular processes Èstars : AGB and post-AGB È turbulence

1. INTRODUCTION

Both high- and low-mass stars near the end of their livesare known to emit copious amounts of material, with thehigh mass-loss rates critically dependent on the formationof silicate or carbonaceous dust grains within a few stellarradii of the red (super-) giant photosphere. Stellar photonsboth impart momentum to the dust particles throughabsorption and scattering (which drive a wind) and heatdust close to the star to temperatures of up to 1200È1500 K(e.g., Lafon & Berruyer 1991). Thermal radiation from thesehot dust grains peaks in the near-infrared (1È5 km), whilemore distant and cooler (500 K) grains emit mostly in themid-infrared (5È20 km).

Although the physical sizes of these evolved stars areimpressive AU), their galactic paucity means that(R

*Z 1

even the closest examples lie at distances greater than 50 pc.Thus, the characteristic size scale for dusty circumstellaremission at a few stellar radii is generally a small fraction ofan arcsecond, too small to be resolved using standardobserving techniques from ground-based telescopes limitedby telescope di†raction (in the mid-IR) and/or atmosphericturbulence (for shorter wavelengths). However, long-baseline interferometry in the infrared can directly detectand measure the morphologies of these envelopes.

The high densities of heavy elements and the mild tem-peratures around evolved stars encourage the formation ofmyriad diatomic and polyatomic molecules in addition todust grains. For instance, over 50 molecular species havebeen found around the prototypical carbon star IRC]10216 (see review by Glassgold 1998). Attempts to under-

1 Current address : Smithsonian Astrophysical Observatory, MS 42, 60Garden Street, Cambridge, MA, 02138.

2 Current address : NASA Goddard Space Flight Center, InfraredAstrophysics, Code 685, Greenbelt, MD 20771.

3 Current address : Chatterton Astronomy Department, School ofPhysics, University of Sydney, NSW 2006, Australia.

stand the density, temperature, and velocity distributions,as well as the formation mechanisms of these molecules,have contributed to the development of the Ðeld of astro-chemistry.

Using estimates of the temperature, atomic abundances,and gas density in and above the photosphere, predictionsof molecular abundances can be made through detailed cal-culations of a network of chemical reactions. By assuminglocal thermodynamic equilibrium (LTE), various moleculesare said to ““ freeze out ÏÏ in the stellar wind. The decreasingtemperatures and densities cause reaction rates to fallquickly, locking the atoms in certain energetically favorablemolecules. Frozen equilibria models have proven useful inexplaining the abundances of many molecules observedaround asymptotic giant branch (AGB) stars (e.g., Lafont,Lucas, & Omont 1982) ; however, additional chemical pro-cesses are needed to explain some detected species. Forinstance, penetration of interstellar UV radiation catalyzesphotochemical reactions in the outer envelopes of AGBstars (e.g., Cherchne† & Glassgold 1993), while other mol-ecules may be produced under nonequilibrium conditionsassociated with shocks (Willacy & Cherchne† 1998). Partic-ularly relevant here is the fact that negligible amounts ofsilane and ammonia are predicted by most freeze-outmodels, yet they have been detected with some abundancein circumstellar envelopes (e.g., Keady & Ridgway 1993,hereafter KR93) ; their formation is hypothesized to be cata-lyzed on the surfaces of dust grains in the Ñow. In addition,recent discoveries of brown dwarfs and extrasolar planetshave catalyzed interest in the chemistry of cool stellar atmo-spheres (e.g., Burrows & Sharp 1999), leading to newinsights into molecular formation mechanisms in theseenvironments. Since it is often difficult or impossible toexperimentally reproduce the physical conditions of cir-cumstellar and interstellar space, molecular observationsare critical to test and guide relevant theories.

This paper is the third in a series on the spatial distribu-

868

MID-IR INTERFEROMETRY ON SPECTRAL LINES. III. 869

tions of dust and molecules in the inner envelopes of nearbyred giants and supergiants. Paper I (Monnier et al. 2000b)discussed the hardware implementation of this experiment,while Paper II (Monnier et al. 2000a) discussed recent visi-bility data at 11.15 km and presented the appropriate dustshell models for IRC ]10216 and VY CMa. This paper(Paper III) makes use of these results, as well as the Ðrstmid-IR visibility data ever reported on spectral lines, pro-viding critical new information on the molecular stratiÐ-cation around these stars.

The methods used in this work are technologically chal-lenging and represent signiÐcant advances in infrared inter-ferometry. By combining the high spatial resolution oflong-baseline interferometry with the high spectralresolution of heterodyne spectroscopy (Paper I), this workhas, for the Ðrst time, probed the brightness distribution onand o† spectral absorption features as narrow as D1 kms~1 (j/*jD 105). This allows the absorbing regions of poly-atomic molecules to be directly measured, setting stronglimits on the formation radii. Such measurements areimportant for determining the formation mechanism, sincethere is at present no good theory to explain the observedhigh abundance of certain molecular species (e.g., andNH3SiH4).

2. MODELING

The observing methodology for extracting visibility dataon and o† spectral lines with the Infrared Spatial Interfer-ometer (ISI) has been discussed in detail in Paper I andMonnier (1999). New dust shell models of IRC ]10216 andVY CMa have been developed in Paper II. However, inter-preting spectral line observations requires modeling of thedistribution of circumstellar molecules as well as dust.

As for observations of continuum radiation with the ISI,it is rarely possible to directly reconstruct an image of theastrophysical source, due to the sparse sampling of theFourier plane a†orded by a two-element interferometer.This limitation necessitates the use of radiative transfermodels for interpreting the line data. This section discussesthe assumptions used in creating models of the molecularenvelopes around AGB stars, the numerical code, and thescientiÐc goals of subsequent analyses.

2.1. Simple ModelsPaper II adopted assumptions of a spherically symmetric

and uniform outÑow of dust embedded in the stellar winds,approximations that have been extended to include the dis-tribution of molecular material. As with the models of thedust shells, the molecular envelope was characterized by theinner formation radius and overall abundance factor, freeparameters in Ðtting models to the molecular line data.

Observations have shown that the line shapes of SiH4and around AGB stars typically show emission in theNH3red wing and absorption in the blue (e.g., Goldhaber 1988,hereafter G88). This kind of proÐle is expected for molecularemission and absorption in an expanding envelope (e.g.,Shu 1991). Figure 1 shows a theoretical line proÐle similarto those actually observed. The bulk of the absorption isblueshifted with respect to the star at the speed of theoutÑow. This is because the entire column of molecular gasalong the line of sight connecting the observer and the staris at the same relative velocity assuming uniform([voutflow),outÑow; hence, there is a large optical depth, at thisqline,frequency, and self-absorption is observed. On the otherhand, lines of sight that penetrate the molecular gas

FIG. 1.ÈExample of a theoretical spectral line shape using radiativetransfer calculations from the Keady (1982) code.

envelope at impact parameters o† the observer-star axisencounter parcels of gas at a variety of relative Dopplershifts. The optical depth at any particular frequency is hencegenerally low, allowing emission from deeper layers of hotdust to escape and to be observed without signiÐcantmolecular absorption. The low-level emission observed atboth blue- and redshifted velocities arises from the relax-ation of IR-pumped and collisionally excited transitionsinto higher energy vibrational states. Note that absorptionin the line core occurs primarily because of the large opticaldepth at that frequency, combined with the fact that thetemperature decreases with increasing distance from thestar. Hence, absorption under these conditions would occureven when the molecules are in local thermodynamic equi-librium (LTE) with the dust and radiation.

For the AGB stars studied here, the source of most of themid-IR Ñux is thermal emission from the dust envelope(Danchi et al. 1994), not from the star itself. Since the blue-shifted absorption features indicate that most of the absorp-tion is occurring along the direction toward the center ofdust envelope, an interesting measurement that can bemade with an interferometer is the size of the absorptionregion. This measurement yields direct information on theapproximate location of the surface, which can beqlineD 1used to determine the abundance and inner radius of molec-ular formation. However, this method is insensitive to mol-ecules that may exist right at the inner radius of the dust, ifthey are in LTE. This is because there is no signiÐcantbackground source of radiation to absorb. These com-plications require the use of a sophisticated spectral linecode to quantify the sensitivity of this method to moleculesforming near the inner radius of the dust shell. Such a codehas been used, and is described in the next section.

Previous spectral line work (Betz, McLaren, & Spears1979, hereafter B79 ; McLaren & Betz 1980 ; Goldhaber &Betz 1984 ; G88 ; KR93) has shown that ammonia and silaneexist around AGB stars at up to 104 times the abundancespredicted by equilibrium calculations of expanding out-Ñows (for more recent work under somewhat di†erentphysical conditions, see Burrows & Sharp 1999). It has beensuggested that dust catalyzes the formation of these mol-ecules through chemical reactions on grain surfaces. If thisis the case, one might expect the inner radius of molecularformation to coincide with the dust formation radius.However, atoms and molecules generally have low sticking

870 MONNIER ET AL. Vol. 543

efficiencies at high temperatures, elastically scattering o†the grain surfaces (e.g., Leitch-Devlin & Williams 1985).This fact, and the lack of known chemical pathways for theformation of molecules such as ammonia and silane, makedirect measurements of molecular formation radii impor-tant, and this is one of the primary goals of the Ðlter-bankproject of the ISI.

2.2. Radiative Transfer CalculationsRadiative transfer in spectral lines often is accomplished

by applying the Sobolev approximation (e.g., G88 ; Shu1991), which assumes that large-scale velocity gradientsessentially radiatively decouple parcels of molecular gas. Toaccurately calculate the radiative transfer in a spectral line,the Sobolev approximation requires the natural line width,in this case determined by microturbulence (for cold gas) orthermal motions (for hot gas), to be much smaller than theexpansion velocity. While this condition is reasonably satis-Ðed for the narrowest lines it is(voutflowD 15 *vline width),only weakly so for the broadest ones (voutflowD 4 *vline width).In order to avoid this uncertainty, all radiative transfercalculations in spectral lines were performed using a codedeveloped by J. J. Keady (Keady 1982), based on themethod of Mihalas, Kunasz, & Hummer (1975). It accu-rately calculates line proÐles as well as frequency-dependentemission proÐles, from which visibility curves can be com-puted on and o† spectral features. This code was developedto treat the case of molecules embedded in an expandingÑow, even when the absorbing molecules are comingledwith continuum-emitting sources. This is likely the case forAGB stars, where thermal emission by dust is believed to be““ Ðlling-in ÏÏ the absorption features. The program, writtenin Fortran, formally solves the observerÏs frame transportequation, which is necessary to correctly account for thepropagation of line radiation through an expanding Ñow,thus avoiding the questionable Sobolev approximation.Keady has allowed his code to be used for the analyses thatfollow, and has assisted in porting the Fortran code to rununder Solaris. This code has been extensively tested, havingbeen used for over 15 yr (Keady 1982 ; Keady, Hall, &Ridgway 1988 ; KR93 ; Winters et al. 1998). While the codewas already able to be used with spherical top molecules(e.g., the appropriate partition function and sta-SiH4),tistical weights had to be programmed for (a sym-NH3metric rotor). A nice summary of the mid-IR molecularproperties of both and can be found in chapter 5SiH4 NH3of G88. Readers interested in the numerical details of theradiative transfer calculation should consult Keady (1982)and Mihalas et al. (1975) for further details.

2.3. Assumptions2.3.1. Dust

The source function used for radiative transfer in KeadyÏscode assumes a single dust grain size and temperature at agiven radius from the star. The code (WolÐre & Cassinelli1986) that was used for Ðtting the ISI continuum visibilitydata in Paper II utilized the full MRN (Mathis, Rumpl, &Nordsieck 1977) distribution of grain sizes, and hence somemodiÐcation must be made to adopt our previous modelsfor use by KeadyÏs algorithm. The average cross section ofthe MRN distribution was used as input to the Keady code,along with the size-averaged dust temperature. This neces-sary simpliÐcation resulted in a slight misÐt to the ISI con-tinuum visibility data, which was compensated for by

empirically adjusting the overall value of the single grainsize dust opacity change).([30%

2.3.2. Temperature(s) of the Gas

In addition to spherical symmetry and uniform outÑow,other assumptions are also generally made for line calcu-lations. Most important is the assumption that theoccupation of various rovibrational states of the polyato-mic molecules can be approximated by a Boltzmann dis-tribution using separate vibrational and rotationaltemperatures, and Ideally, the populations of theTvib T rot.various states should be calculated using a multilevel modelmolecule. However, the collisional excitation constants arepoorly known for and and the large number ofSiH4 NH3,(far-IR) rotational transitions make for a difficult anduncertain result.

G88 (p. 103) considered this question in some detail forIRC ]10216, and we summarize his conclusions here. Forsufficiently high molecular densities, both mid- and far-IR(i.e., rovibrational and pure rotational) transitions will beoptically thick, trapping line radiation. In this case, col-lisional excitation and de-excitation will have a strong inÑu-ence on the level populations, equilibrating the vibrationaland rotational temperatures with the gas (kinetic) tem-perature. However, the molecules under consideration hereare not found at sufficiently high densities for this to apply.

At the somewhat lower densities encountered forammonia and silane, the mid-IR (rovibrational) transitionsbecome optically thin. In terms of excitation mechanism,this allows IR pumping of the vibration-rotation transitionsto dominate (over collisions) within about while rota-70R

*,

tional relaxation in the pure rotational transitions (far-IR)dominate in the outer envelope (where these transitionsbecome optically thin). Collisional excitation and de-excitation never play a dominant role. Hence, andTvib Trotshould be close to the radiation/dust temperature, Tdust,suggesting that is a good starting point.Tvib\ Trot \ TdustThe radial dependence of the rotational and vibrationaltemperatures usually need slight adjustment during themodeling process to reproduce the relative depths of high-and low-excitation lines.

One interesting exception applies to the J \ K states ofThe rotational dipole moment along the symmetryNH3.axis (z-axis) of is equal to zero ; hence, the *K \ 0NH3selection rule must apply for all radiative (dipole) tran-

sitions (see Townes & Schawlow 1975). Therefore, a mol-ecule rotating in the J \ K state cannot radiativelyde-excite to a lower energy (lower J) state. Hence, the equi-librium population of J \ K states is not determined by theradiation temperature, but by collisions with the ambientgas (mostly the rotational temperature of these statesH2) ;should be in equilibrium with the gas (kinetic) temperature.However, a strong (parallel-type) vibrational band at 6.1km does allow *K \ ^1 transitions, thereby allowingK-ladders to come into equilibrium if sufficiently excited bythe radiation Ðeld. Sufficient IR pumping in this band islikely to dominate over collisional processes out to a fewhundred although a detailed calculation is lacking (seeR

*,

G88).

2.3.3. Molecular Constants

The polyatomic molecules of and have beenSiH4 NH3modeled using physical constants (see Table 1), includingthe moments of inertia and vibrational energy levels,

No. 2, 2000 MID-IR INTERFEROMETRY ON SPECTRAL LINES. III. 871

TABLE 1

MOLECULAR CONSTANTS ASSUMED IN THE

MODEL CALCULATIONS

Parameter Value Source

SiH4B . . . . . . . . . . . 2.8591 cm~1 1l4 . . . . . . . . . . 913.473 cm~1 1k4 . . . . . . . . . . 0.247 D 2

NH3B . . . . . . . . . . . 9.9466 cm~1 3C[ B . . . . . . [3.7199 cm~1 3l2 . . . . . . . . . . 932.434 cm~1 3k2 . . . . . . . . . . 0.24 D 4

NOTE.ÈMost of these parameters wereoriginally collected in Goldhaber (Table V.1in G88). The rotational constants (B and C)are given for the vibrational ground state,along with the appropriate vibrationaldipole moment and origin frequency(k

n) (l

n).

REFERENCES.È(1) Gray, Robiette, & Johns1977 ; (2) KR93 ; (3) Urban et al. 1983 ; (4)Nakanaga, Kondo, & Saeki 1985.

adopted from KR93 and G88. Readers interested in learn-ing more about molecular spectroscopy should consultthese sources ; a rigorous and complete treatment of thesubject can be found in Microwave Spectroscopy by Townes& Schawlow (1975).

2.4. Analysis MethodFor each star and target molecule, the analysis strategy

for ISI spectral line data was straightforward and had threemajor steps.

1. The dust shell was modeled in order to have a reason-able approximation of the continuum source. This has beendone in Paper II, where coeval continuum visibility datawere used to create appropriate dust shell models of theastrophysical sources under study.

2. Molecules were assumed to form at a given radiusfrom the star and to Ñow out uniformly. Theoretical spec-tral line proÐles were then calculated to Ðt both ISI mea-surements and also previous observations of spectral linedepths and ratios. Lines of various excitation energies wereused (when available) in order to probe the abundance,temperature, and turbulent structure of the gas. This level ofanalysis relied heavily on the careful modeling preexistingin the astrophysics literature.

3. Theoretical visibilities on and o† the spectral line werecalculated and compared to the observed visibility ratios.The radius of molecular formation set in step 2 was varieduntil all available data were satisfactorily Ðtted.

This method allows one to distinguish between gasmodels with high molecular abundance far from the starand those with lower molecular abundance close to the starin two di†erent ways. While the line depth of a given tran-sition can always be Ðtted by varying the abundance andmean gas temperature, the relative line depths of transitionswith di†erent excitation energies cannot. This probe of theaverage excitation temperature, when coupled with esti-mates of the radial temperature proÐle and assumption ofuniform outÑow, can be used to infer the location of molec-

ular formation (e.g., KR93). In this work, we also apply asecond, more direct, approach by using an interferometer.With suitable spectral and spatial resolution, one candirectly detect the absorption pattern when the moleculesare sufficient close to the star. This is the main thrust of thispaper, in which we show that molecules within would40R

*signiÐcantly modify the emission pattern in the line core,providing a method independent of the line ratio argumentfor detecting the presence of molecules close to the star.

2.5. Comparing Model Quantities to ObservationsAfter fully specifying the dust and gas characteristics, the

Keady code returns a spectral line proÐle and monochro-matic radial emission proÐles. This section discusses someof the details regarding comparison of the modeling resultswith ISI Ðlter-bank data.

2.5.1. Spectral L ine ProÐles

Because of the heterodyne detection scheme, mid-IR radi-ation arriving outside the primary beam of the interferome-ter was not seen. This had a small e†ect on the depth of thespectral line, since only a fraction of the molecular absorp-tion occurs in the outer envelope. The e†ect was compen-sated for by multiplying the angular distribution resultingfrom monochromatic radial emission calculations by thee†ective primary beam of FWHM 3A (see Paper II for morediscussion) and then adjusting the Ñux level accordingly. Allspectral proÐles shown in the next sections have had thiscorrection applied.

Next, the Ðnite bandwidth of the Ðlter-bank observationsand the double-sideband (DSB) nature of the detection wereaccounted for. The bandpass center frequency and widthwere used to determine the average depth of the calculatedspectral line for a corresponding single-sideband (SSB)observation. The dilution of the line depth due to the com-bination of the ““ uninteresting ÏÏ additional continuum side-band encountered in practical observation was accountedfor by dividing the SSB line depth by 2. This resulting DSB(diluted) line depth was then compared to observations withthe Ðlter bank.

Figure 1 shows one of the output Ðgures from the model-ing analysis suite. The bandwidth of the observation ismarked o† by vertical dashed lines, and line diagnosticshave been calculated. The line width and average DSB linedepth were also calculated for comparison with spectral lineobservations. Other quantities were also determined, suchas the equivalent width, which were useful when comparingwith lower spectral resolution data.

2.5.2. V isibility Ratios

The basic observable of the Ðlter-bank experiment is thevisibility ratio on the spectral line compared to the dustcontinuum. Monochromatic radial emission proÐles werecalculated at 10 speciÐc frequencies across the spectral line,sampling the stellar continuum as well as the entire absorp-tion region. The double-sideband, radial-emission proÐlefor the Ðnite bandwidth selected by the Ðlter bank wasdetermined by a Ñux-weighted average of the emission pro-Ðles inside the observation bandwidth and an equal band-width of continuum. The resulting proÐle was multiplied bythe e†ective primary beam and the visibility then calculated.The visibility curve of the continuum emission was calcu-lated as well, and the visibility ratio (on the line comparedto the continuum) as a function of baseline was then deter-mined.


FIG. 2.ÈExample of the mid-IR emission as a function of radius fromthe star for one particular gas model, normalized to unity at radius 0. Solidline shows the radial proÐle for the dust continuum, while the dashed linerepresents the emission at the core of the absorption line. The dot-dashedline represents the emission after accounting for the Ðnite-bandwidth anddouble-sideband detection. The inset image shows a two-dimensional rep-resentation of the absorption region deÐned by the ratio of the absorptioncore to the continuum proÐles.

Figures 1È3 illustrate this entire process, showingexample output at every stage of the analysis process for asilane line around IRC ]10216. All subsequent model visi-bility ratios have been processed in an identical fashion, butthese diagnostic plots are not presented, for brevity. Theparticular gas model shown in Figures 1È3 has a silaneformation radius of only small enough to produce a10R

*,

large change in the visibility on and o† the spectral line.Since the Ðlter-bank system measures a visibility ratio, theradial emission proÐles were usually of only secondaryinterest, and more emphasis was placed on interpretationsof ratios.

FIG. 3.ÈVisibility curves on and o† a spectral feature. The dashed andsolid lines represent the visibility curves on and o† the absorption core,respectively ; the dotted line shows the ratio. The dot-dashed line shows thevisibility ratio after accounting for Ðnite-bandwidth and double-sideband(DSB) detection. Deviations from unity are multiplied, or zoomed in, by afactor of 10, and shown by a triple-dot-dashed line ; the zoom means that,for example, 0.6 now corresponds to 0.96 in the original units. The datapoints on this plot represent coeval visibility measurements of the dustcontinuum reported in Paper II.

To facilitate a better understanding of the visibility data,example brightness proÐles appear in Figure 2. The brightspike at the origin is from stellar photospheric emissionseen through the dust and gas, while the secondary peak at150 mas reveals the location of the dust shell inner radius. Itis important to note that while the star itself clearly shinesthrough the dust envelope (it is the highest surface bright-ness feature of the nebula), it contributes a tiny percentageof the total mid-IR emission, because of the large emissionfrom the dust shell. The inset image is a two-dimensionalrepresentation of the absorption region deÐned by the ratioof the absorption core to the continuum proÐles. One cansee that absorption for this model is indeed highest near thecenter of the dust shell. The basic point of the Ðlter-bankexperiment was to measure the size of this absorptionregion.

Figure 3 shows the visibility curves corresponding to theemission proÐles of Figure 2. The various curves aredescribed in the Ðgure caption, and show the e†ects ofapplying the instrumental corrections discussed in thissection. In this case, a visibility ratio of about 0.92 would beexpected for the range of baselines observed (2È4 m).

The analysis process discussed above took into accountall the practical details of the experiment : Ðnite bandwidth,primary beam, double-sideband detection. The next sec-tions present the data from the Ðlter-bank experiment anddetail the modeling results.

3. INTERFEROMETRY ON SPECTRAL LINES : RESULTS

Spectral line observations were carried out for two targetsources, the carbon star IRC ]10216 and the red super-giant VY CMa. General introductions to both of thesestars, including discussions of previous continuum obser-vations, can be found in Paper II. A summary of all theÐlter-bank data can be found in Figure 4 ; details will bediscussed in subsequent sections. Recall from Paper I thatthe ratio of the visibility on the line compared to that o† theline is made by dividing the fringe amplitude ratio by the

FIG. 4.ÈSummary of all the Ðlter-bank data on spectral lines presentedin this paper, from 22 full nights of observing in the fall of 1998. Each datapoint represents the average of multiple nights of observing at baselinesbetween 2 and 4 m, with the molecular transition and target source indi-cated below each set of symbols. Observing details can be found in Tables2 and 4. The triangles show the ratio of the fringe amplitude on and o† theline, while the star symbols show the ratio of the total infrared (IR) signalon and o† the line. The normalized visibility ratio on and o† the spectralline results from dividing the fringe ratio into the IR power ratio, andappear in the Ðgure as Ðlled circles.


FIG. 5.ÈComparison of the observed line depths of transitionsobserved by G88 and this work. The overall agreement is good, althoughthere is clear evidence of a systematic di†erence. See ° 3.1 for a discussion.

infrared power ratio. Hence, in Figure 4, the visibility ratioswere derived from the fringe (amplitude) ratios and the IRpower ratios, and do not represent an independent set ofmeasurements. See tables of line frequencies in Monnier(1999, Tables C.4 and C.5) for more information regardingspeciÐc molecular transitions.

3.1. Comparison with Previous Spectroscopic ResultsWhile the interferometric data presented here are the Ðrst

of their kind, the depths of the spectral lines have beenobserved before. Figure 5 shows a comparison of all thelines observed with the double-sideband line depthsobserved by G88. While the agreement is good in general,there is a clear signal that the line depths measured in 1998were slightly deeper around IRC ]10216 than the mid-1980s observations of Goldhaber. There are many possibleexplanations for this. Changes in the dust shell geometry,molecular abundance, and di†erent seeing conditionsduring the observations themselves can cause small changesin the line depth. However, the good overall agreement isconÐrmation that the circumstellar environments impor-tant for forming these spectral lines around both VY CMaand IRC ]10216 have not changed radically in the lastdecade, justifying the use of previous modeling e†orts (G88 ;KR93) in developing molecular gas models (see modelingstep 2 in ° 2.4).

4. IRC ]10216

A journal of spectral line observations for IRC ]10216can be found in Table 2, while a full and concise summary ofthe data appears in Table 3. Separate modeling for bothmolecules, and is presented below.SiH4 NH3,

4.1. Silane in IRC ]102164.1.1. Previous Work

The mid-IR transitions of silane around IRC ]10216have been observed by Goldhaber & Betz (1984), G88,KR93, and Holler (1999). Goldhaber and colleagues used aheterodyne spectrometer, which produced the highest spec-tral resolution data, fully resolving the absorption line cores(spectral resolution D0.2 km s~1). KR93 employed aFourier transform spectrometer at Kitt Peak with some-what lower spectral resolution, about 3 km s~1, sufficient todetermine the spectral line strengths but insufficient to fullyresolve the cores. Holler used a broadband radio frequency(RF) spectrometer coupled to the heterodyne detectionsystem of the ISI, resulting in subÈkm s~1 spectralresolution (also see Isaak, Harris, & Zmuidzinas 1999).Because the line depths have remained largely unchangedover the last 15 yr, the modeling results of these workerswas assumed to hold true today. The most detailed analysiscan be found in KR93, and their gas model parameters werea starting point for the analysis that follows.

KR93 found a relative abundance of silane compared tomolecular hydrogen of 2.2] 10~7 with a rotational tem-perature law, (where r is expressed inTrot \ 2000r~0.525units of stellar radii), which falls o† slightly faster than thedust temperature. The calculated column density was2.2] 1015 cm~2. In addition, was taken to be aboutTvib85% of the to match the weak emission observed in theTrot,higher J lines. These results assumed spherical symmetry, auniform outÑow of 14 km s~1 outside and a micro-20R

*,

turbulent velocity of 1 km s~1. It was found that the lineratios were much better Ðtted by truncating the silane dis-tribution inside and KR93 concluded that silane40R

*,

must be forming in the outÑow at about this radius. Withthese assumptions, KR93 were able to satisfactorily matchthe line strengths of seven silane transitions and the spectralproÐle of one of GoldhaberÏs high spectral resolution pro-Ðles. Holler (1999) estimated the column density of SiH4from data taken in 1999 May using one ISI telescope andfound it consistent with previous measurements(D2.7] 1015 cm~2).

4.1.2. V isibility Observations

Table 3 reports the visibility ratios on and o† varioussilane absorption features in fall 1998. A stellar recessionalvelocity of km s~1 has been used to convertVLSR \[26.0

to expansion velocity, based on G88. In all cases, theVLSRTABLE 2

JOURNAL OF IRC ]10216 SPECTRAL LINE OBSERVATIONS

LOTarget Target LO LO Wavelength Dates

Molecule Transition Molecule Transition (km) (UT 1998)

SiH4 . . . . . . R-(00) A2ÈA1 13C18O2 P(20) 10.945 Nov 5, Nov 6, Nov 13SiH4 . . . . . . R-(03) F2ÈF1 13C16O2 R(10) 10.318 Oct 18, Oct 19, Nov 21SiH4 . . . . . . R-(03) A1ÈA2 13C18O2 P(10) 10.853 Nov 4, Nov 10, Nov 14SiH4 . . . . . . R-(09) A2ÈA1 13C16O2 R(30) 10.694 Oct 27, Oct 28, Nov 27, Dec 3, Dec 11NH3 . . . . . . aQ(3,3) 12C16O2 P(34) 10.741 Oct 20, Oct 21, Oct 22, Nov 20


TABLE 3

SUMMARY OF IRC ]10216 SPECTRAL LINE DATA

BANDWIDTH OF

FILTER BANK

TARGET TARGET FRINGE AMPLITUDE IR POWER VISIBILITY

MOLECULE TRANSITION MHz km s~1 RATIO RATIO RATIO

SiH4 . . . . . . R-(00) A2ÈA1 180 1.97 0.881^ 0.013 0.890 ^ 0.006 0.990 ^ 0.016SiH4 . . . . . . R-(03) F2ÈF1 180 1.86 0.912^ 0.013 0.907 ^ 0.011 1.006 ^ 0.019SiH4 . . . . . . R-(03) A1ÈA2 180 1.95 0.871^ 0.019 0.855 ^ 0.008 1.019 ^ 0.024SiH4 . . . . . . R-(09) A2ÈA1 180 1.93 0.946^ 0.031 0.972 ^ 0.007 0.973 ^ 0.033NH3 . . . . . . aQ(3,3) 180 1.93 0.881^ 0.024 0.881 ^ 0.020 1.000 ^ 0.035

NOTE.È The Ðlter-bank bandpass was centered at km s~1 for all observations. Each ratio representsVLSR\ [40the value of the absorption feature with respect to nearby stellar continuum at baselines between 2 and 4 m.

visibility ratio has been observed to be consistent withunity, and data from all baselines (2È4 m) have been aver-aged together. Qualitatively, this implies that the absorp-tion region is large compared to the spatial resolution of theinterferometer baseline, D0A.4.

The model for the molecular envelope developed inKR93 was combined with the new dust shell model fromPaper II as a starting point for this modeling work. Inparticular, the same power-law relation for the rotationaltemperature was used, and the vibrational temperature wasset equal to 85% of the dust temperature. A microturbulentvelocity of 0.6 km s~1 was used to match the line widthsobserved by G88. Next, a series of gas models was calcu-lated using di†erent silane formation radii : and10R

*, 40R

*,

The silane abundances were then scaled to match the80R*.

average line depths of the observed transitions. For each ofthese three gas models and for all four observed lines, thevisibility ratios of the line compared to the continuum werecalculated and compared to observations.

The results of these models appear in Figure 6. Indeed,gas models with the largest formation radii Ðt the linedepths of the four lines the best, as found by KR93, imply-

FIG. 6.ÈResults of modeling the IR power and visibility data for silanearound IRC ]10216 using the temperature laws derived in KR93. Filter-bank data appear as points with error bars, while model results are rep-resented by small triangles connected by lines corresponding to di†erentmolecular density distributions, as marked. The transitions are presented,from left to right, in order of increasing excitation energy. The top pointsand lines correspond to the visibility ratios of the absorption line withrespect to the continuum, while the bottom data points and lines corre-spond to the observed and modeled line depths. The solid line shows amodel with silane forming at The dotted and dashed lines show10R

*.

molecular formation radii of and respectively.40R*

80R*,

ing a relatively low overall rotational temperature of theabsorbing molecules. In addition, the importance of thevisibility ratio observations made with the ISI and Ðlterbank can be seen. For formation radii less than about 40R

*,

the predicted visibility ratios are signiÐcantly below unity.Even for a formation radius of (the choice preferred40R

*by KR93 based on spectroscopy alone), the visibilities in thespectral lines are too small to be consistent with obser-vations (although not strongly ruled out). The columndensity for the most favored model was found to be80R

*1.3] 1015 cm~2 (2.0] 1015 cm~2 for the case).40R*Since we have measurements of four lines of di†ering

rotational excitation energies, the sensitivity of the visibilityratios to the rotational temperature law can be investigated.Models with identical gas density distributions were runusing and the results for these calcu-Trot\ Tvib \Tdust,lations can be found in Figure 7. This temperature law doesnot Ðt the line depths as well as the Ðrst set of models,supporting the adoption of the empirical temperature fall-o† of KR93. Alternatively, the population of low-lying Jtransitions could be enhanced if the mass-loss rate washigher in the past ; this would have the e†ect of increasingthe density of cold silane, increasing the molecular absorp-tion from the ground state. The visibility ratios are similarto those found in the KR93-based models above, and theearlier conclusion of a large molecular formation radius issupported and now shown to be insensitive to choice oftemperature proÐle.

4.1.3. Conclusions

In short, the Ðlter-bank observations largely conÐrm theconclusions of KR93 ; namely, that silane must be forming

FIG. 7.ÈSame as Fig. 6, but assuming Trot\ Tdust

0 20 40 60 80 100Distance from Star ( R_star )

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Rel

ativ

e D

ensi

ty o

f NH

3


at a large distance from the star. The visibility data directlymeasure the size of the absorption region to be larger than

and favor a formation radius even larger than thatD0A.4proposed by KR93. The combination of spectroscopy andinterferometry convincingly demonstrates that silane isforming at a radius of The visibility data are onlyZ80R

*.

able to set a lower limit on the formation radius, since novisibility di†erence on and o† the line was detected withinthe experimental uncertainty.

For the stellar radius of 22 mas used in the model and adistance of 135 pc, corresponds to about 240 AU from80R

*the star. It is not clear why silane would begin to form at soremote a location in the outÑow. The densities of the atomicconstituents of silane are proportional to r~2 for a uni-formly expanding envelope and would act to shut o† chemi-cal reactions that are density dependent. If silane is formedon the surfaces of grains, then the gas-phase density ofsilicon (and its compounds) may not be as important as theamount of gas-phase silicon and adsorbed onto grains.H2Adsorption of on the grain surfaces would probably beH2small at the higher temperatures (1000È1400 K) where dustforms, and be more pronounced at larger distances from thestar (see, e.g., the calculations of Leitch-Devlin & Williams1985). In these models, the temperatures of the gas and dustare about D290 K at and 200 K at40R

*80R

*.

Gas-phase SiS, which forms in abundant quantities in thephotosphere, has been predicted to be depleted signiÐcantlyby adsorption onto grains (Glassgold & Mamon 1992). Infact, depletion of SiS within has already been100R

*observed in both mid-IR (Boyle et al. 1994) and millimeter-wave transitions (Bieging & Nguyen-Quang-Rieu 1989 ;Bieging & Tafalla 1993). We hypothesize that the largeradius of creation is related to the timescale for thisSiH4depletion process and/or the adsorption of onto grains.H2It is hoped that the introduction of these new observationswill stimulate renewed theoretical interest in understandingboth the chemical origins and lineage behind the high abun-dance of silane around IRC ]10216.

4.2. Ammonia in IRC ]102164.2.1. Previous Work

The mid-IR rovibrational transitions of ammonia aroundIRC ]10216 have been observed by B79, G88, KR93, andHoller (1999). Some details regarding the spectrometersemployed have already been summarized in ° 4.1.1. Becausethe line depths have remained essentially unchanged overthe last 15 yr, the modeling results of these workers areagain assumed to be valid today. As in the case for silane,the most detailed analysis can be found in KR93, and theirgas model parameters acted as a starting point for theanalysis that follows.

KR93 found a relative abundance of ammonia comparedto molecular hydrogen of 1.7] 10~7 with a rotational tem-perature proÐle (where r is expressed inTrot \ 2000r~0.60units of stellar radii), a faster fall-o† than the proÐle used forsilane. Even with this steeper fall-o†, the predicted depth ofthe lowest lying aR(0, 0) line was much weaker than thatobserved, requiring either much colder or more dense gas inthe outer envelope The calculated column(Z400R

*).

density was 2] 1015 cm~2, very similar to recent resultsfrom Holler (1999 ; D2.2] 1015 cm~2). These resultsassumed spherical symmetry, a uniform outÑow of 14 kms~1 outside and a microturbulent velocity of 1 km20R

*,

s~1. Since a Ðt of the larger width of the high-excitation

aQ(6, 6) line with a constant velocity Ñow was not possible,a more complicated velocity model was used, which had thegas accelerating to terminal velocity at radii between 5R

*and (see Figs. 3a and 11 in KR93 for the velocity and20R*density laws adopted).

Although unable to reproduce the line shapes in precisedetail, the KR93 models were successful at qualitativelyexplaining the bulk of the spectroscopic observations avail-able by placing the ammonia density peak around 12R

*.

Importantly, these models represent ideal test cases for theÐlter-bank experiment, because the presence of ammoniaabsorption inside of is expected to be clearly indicated20R

*by its visibility.

4.2.2. Results

Table 3 shows the ratio of the visibilities observed in andout of the aQ(3, 3) absorption feature in the fall ofNH31998. A stellar recessional velocity of km s~1VLSR \[26.0has been used to convert to expansion velocity, basedVLSRon G88. The Ðlter-bank bandpass selected (D1.9 km s~1)was somewhat smaller than the full-width half-depth(FWHD) observed by G88, about 5 km s~1, and centeredon the absorption core, corresponding to an outÑow veloc-ity of 14 km s~1. In this case, as for the silane observations,the visibility ratio was observed to be consistent with unity.

The modeling process began with the dust shell modelfrom Paper II and the gas model developed in KR93. Thesame power-law relation for the rotational temperature anda 1.0 km s~1 microturbulent velocity were initially used. Anammonia density and velocity distribution similar to KR93were used, although simpliÐed. SpeciÐcally, the velocity wasincreased linearly from 0.1 to 14 km s~1 between 3 and 20

The ammonia density proÐle used started atR*. 5R

*,

peaked at and decreased outside consistentD10R*, 20R

*,

with a uniform outÑow (o P r~2). This corresponded to alinearly increasing ammonia shell mass until where20R

*,

uniform outÑow was assumed to begin. See Figure 8 for aplot of the density proÐle used.

As was shown for silane in the last section, signiÐcantmolecular absorption inside about necessarily results20R

*

FIG. 8.ÈRelative density of ammonia as a function of radius for theIRC ]10216 gas model (based on KR93). The outÑow velocity wasincreased linearly between 0.1 and 14 km s~1 between and3R

*20R

*.

Using this velocity law and the density of ammonia shown by the solid line,the ammonia shell mass increases linearly with radius from until5R

*at which point it becomes constant, consistent with uniform outÑow.20R*,

The visibility data reported in this paper rule out this model.


in substantial di†erences in interferometric visibilities onand o† the spectral line. Figure 9 shows the spectral proÐleand visibility ratio for the above model of ammonia aroundIRC ]10216, based on KR93, and also the spectral linedata taken from G88. KR93 did not model this speciÐctransition, so the agreement cannot be expected to beprecise ; indeed, the line prediction is narrower than theproÐles observed by Goldhaber. The density of ammoniahas been adjusted to match the line depth observed in fall1998 within the bandpass of the ISI Ðlter bank, resulting ina column density of 8.4] 1015 cm~2 for this model.

The model visibility ratio at a spatial frequency of3 ] 105 rad~1 is 0.926, compared to the observed ratio of1.000^ 0.035. This model is thus ruled out at a 2 p level.This reinforces a conclusion from the modeling of silane :signiÐcant molecular absorption occurring within about

for IRC ]10216 results in a strong on-line and o†-20R*line di†erence in the interferometric visibilities, a signal not

seen with the ISI Ðlter-bank experiment. The conclusionthat ammonia forms at a distance of from the starZ20R

*indicates that, as in the case of silane, ammonia moleculesdo not form near where the dust condenses, but rather atlower temperatures and probably through surface adsorp-tion. The dust grain temperature at is D400 K in20R

*these models.

4.2.3. Discussion

There are other, purely spectroscopic, observations thatalso suggest that the explanation put forth by KR93 for thebroad aQ(6, 6) line, bulk acceleration of gas within 20R

*,

may not be fully correct. KR93 did not attempt to Ðt thehigh spectral resolution proÐles published in G88, whichrevealed details concerning the ammonia around IRC]10216 not reproduced by models relying on acceleratinggas to broaden the absorption lines.

FIG. 9.ÈResults of modeling the IR power and visibility data forammonia aQ(3, 3) transition around IRC ]10216, based on parametersderived in KR93. Top : Model spectral line proÐle convolved with theinstrument response along with the observations of G88. Bottom : Modelvisibility curves on and o† the spectral feature ; can be compared to theobserved dust continuum data (open circles ; see Paper II). The dashed andsolid lines show the visibility curves on and o† the absorption core (deÐnedby the vertical dashed lines in the top panel) respectively ; the dotted lineshows the ratio. The dot-dashed line shows the visibility ratio afteraccounting for Ðnite-bandwidth and double-sideband (DSB) detection.Deviations from unity are multiplied, or zoomed in, by a factor of 10, andshown by a triple-dot-dashed line ; the zoom means that, for example, 0.6now corresponds to 0.96 in the original units.

KR93 Ðtted the aQ(6, 6) line data originally published inB79, which was cut o† at [17 km s~1 relative to the stellarvelocity. Features broadened due to absorption by gas inthe acceleration region would be asymmetric, with a sharpblue edge and signiÐcant redshifted absorption by hot gas.Indeed, the model proÐles of KR93 show this telltale char-acteristic (see Fig. 13 of KR93), but were unconstrained bythe incomplete B79 published proÐle. Complete line pro-Ðles, including the full blue wing of the absorption feature,were published in G88, revealing a rather symmetriclineÈat odds with KR93 model results.

Thus far, the line-width data from G88 cannot be repro-duced in detail with this class of models, independent of thevisibility data. The line widths were observed to increasewith the energy of the rotational level. The 1 p widths weremeasured to be 0.8, 1.7, and 3.1 km s~1 for the aR(0, 0),aQ(2, 2), and aQ(6, 6) transitions, respectively, while therelative velocity of the core remained constant to within D1km s~1. While a near-star acceleration law and suitablypeaked ammonia distribution can be adjusted to reason-ably Ðt the line width of any single transition (e.g., Fig. 9),the large increase between the aQ(2, 2) and aQ(6, 6) lines isnot reproduced. Furthermore, lines broadened by acceler-ating gas should show signiÐcant shifts in the location of thecore as a function of excitation energy.

The presence of decaying gas turbulence outside theacceleration region may qualitatively explain the line-widthbehavior and the lack of a signiÐcant di†erence in the visi-bilities. The inner dust shell of IRC ]10216 is alreadyknown to be quite clumpy in near-IR images (Weigelt et al.1998 ; Hani† & Buscher 1998 ; Tuthill, Monnier, & Danchi1998 ; Monnier 1999 ; Tuthill et al. 2000). Furthermore,dynamical models of dust shell production in carbon starslead to large velocity dispersion as the individual shells ofdust are accelerated (Winters et al. 1995, 1998 ; Weigelt et al.1998). Both turbulence and velocity gradients across indi-vidual dust shells (clumps) will cause signiÐcant broadeningof lines formed in these regions. Under these conditions, onewould also expect the Doppler velocity of the core to benearly constant, consistent with observations, but the linewidths would naturally decrease for lines forming further inthe outÑow as sound waves (or weak shocks) bring theoutÑow into hydrostatic equilibrium. The dynamical dustshell models of Winters et al. could be coupled with theradiative transfer code of Keady to quantitatively test thesesuppositions (as for CO in Winters et al. 1998).

There are other potential explanations for why absorp-tion lines by high-J states are much broader than for lowerexcitation states. For instance, if the high-J states are popu-lated by shock heating, one would expect a higher velocitydispersion due the turbulence and velocity shifts accom-panying shocks. This class of explanation, whereby the exci-tation mechanism (and possibly even the formationmechanism) is directly related to peculiar local conditions(e.g., shocks, high velocity dispersion), needs further con-sideration.

4.3. Summary for IRC ]10216The narrow line widths of all the silane lines and the lack

of an interferometric signal place the location of silane for-mation at or beyond outside the turbulent innerD80R

*envelope. In addition, the lack of interferometric signal andthe broad (symmetric) lines of ammonia place their forma-tion outside beyond the gas acceleration region,D20R

*,


FIG. 10.ÈLikely sites of silane and ammonia formation around IRC]10216, based on the results of this paper and previous spectral line work.Importantly, the data suggest that the outÑow remains quite turbulentand/or clumpy signiÐcantly beyond the acceleration region. The obser-vations undergirding each major element of this schematic are listed inbrackets (Keck : near-IR speckle work [Tuthill et al. 2000] ; ISI : ISI contin-uum data [Paper II] ; ISI-FB: ISI Ðlter-bank data [this work]).

but in a turbulent (or clumpy) Ñow. These ideas are illus-trated schematically in Figure 10 and represent a signiÐcantimprovement in our knowledge of the molecular stratiÐ-cation around IRC ]10216.

5. VY CMa

While no silane has been observed in the oxygen-richstellar wind of the red supergiant VY CMa, many absorp-tion lines of ammonia have been. A journal of these spectralline observations made with the ISI Ðlter bank can be foundin Table 4.

5.1. Previous WorkThe mid-IR transitions of ammonia around VY CMa

were Ðrst observed by McLaren & Betz (1980). However, alarger set of data with better frequency coverage waspublished by G88, and these data have been used for sub-sequent consideration. Details regarding the capabilities ofthe heterodyne spectrometer employed can be found in° 4.1.1. While McLaren & Betz reported a signiÐcantchange in the line proÐle of aQ(2, 2) between 1978NH3October and 1979 December, the proÐle reported by G88observed in 1982 September is nearly identical to the 1979December data. In addition, the G88 line depth is consistentwith the spectral data obtained by the Ðlter bank in thispaper (see Table 5). In light of this consistency, we haveassumed that the G88 line proÐles are still representative ofthe current epoch.

All of the lines, aR(0, 0), aQ(2, 2), aQ(3, 3), and aQ(6, 6),observed by G88 possessed broad absorption features with1 p widths of D3.8 km s~1. The cores of the lines were

centered around km s~1, with the high excita-VLSR D [6tion line cores being slightly less blueshifted. Assuming astellar recessional velocity of km s~1 (based onVLSR \ 22.3maser data), this corresponds to an outÑow rate of D29 kms~1. Using these lines, G88 estimated a column density ofammonia of (6^ 4)] 1015 cm~2 using a simple modelbased on the Sobolev approximation. We have repeatedthese calculations using a similar gas model with the Keadycode.

5.2. Results and ModelsTable 5 shows the visibility ratios observed on and o† a

number of absorption features in the fall of 1998. ANH3stellar recessional velocity of km s~1 has beenVLSR\ 22.3used to convert to expansion velocity, based on G88.VLSRThe Ðlter-bank bandpasses selected were set to equal theFWHD observed by G88, and were centered on the absorp-tion cores. Data in Table 5 represent a nondetection of thesP(4, 3) line, which also had not been detected by any pre-vious measurements. Just as for IRC ]10216 (see Table 3),the visibility ratios were observed to be consistent withunity. In addition to the full aQ(6, 6) absorption line, the redhalf of the line was observed separately in the hopes ofobserving the location of any accelerating gas. However, thesignal-to-noise ratio for this measurement (D10) was nothigh enough to justify further modeling.

A simple gas model based on the line Ðt of the aR(0, 0)line in G88 was developed using the new VY CMa dustshell model of Paper II. Unlike the case for IRC ]10216,the line widths for the lines around VY CMa were allNH3roughly the same. This fact, and the fact that the line corelocations only showed a slight shift with excitation energy,support a model in which the absorption lines all formmostly outside the acceleration region. Therefore, aconstant-outÑow model was adopted, using an expansionvelocity of 29 km s~1, which matched the proÐles of theaQ(2, 2) and aQ(6, 6) lines ; the broad line widths werecreated by model microturbulence of 3.5 km s~1.

The temperature of the J \ K rotational states is con-trolled either by collisions, due to the lack of dipole tran-sitions from these states to lower J, or by IR pumping in the6.1 km band (see ° 2.3.2). During modeling, this temperatureproÐle is normally varied using a power law (as by KR93) toempirically Ðt the line depth ratios. Unfortunately, therewere an insufficient number of lines available in this case toutilize this strategy. An alternative scheme, in which twotemperature proÐles were assumed to represent reasonablelimits, was used here :

1. The rotational temperature was set equal to the dusttemperature, This corresponds to full couplingTrot \ Tdust.of the internal degrees of freedom of the gas molecules tothe radiation Ðeld.

TABLE 4

JOURNAL OF VY CMa SPECTRAL LINE OBSERVATIONS

LOTarget Target LO LO Wavelength Dates

Molecule Transition Molecule Transition (km) (UT 1998)

NH3 . . . . . . aQ(2, 2) 13C16O2 R(24) 10.738 Oct 20, Oct 21, Oct 22, Nov 25NH3 . . . . . . sP(4, 3) 13C16O2 P(30) 11.262 Oct 27NH3 . . . . . . aQ(6, 6) 13C16O2 R(18) 10.784 Oct 18, Oct 19, Oct 28, Nov 5, Nov 24, Dec 11


TABLE 5

SUMMARY OF VY CMa SPECTRAL LINE DATA

BANDWIDTH OF

FILTER BANK FRINGE

TARGET TARGET AMPLITUDE IR POWER VISIBILITY

MOLECULE TRANSITION MHz km s~1 RATIO RATIO RATIO

NH3 . . . . . . aQ(2,2) 540 5.80 0.933^ 0.022 0.932 ^ 0.012 1.001 ^ 0.027NH3 . . . . . . sP(4,3) 420 4.73 N/A 0.983^ 0.026 N/ANH3 . . . . . . aQ(6,6) 540 5.82 0.922^ 0.024 0.950 ^ 0.012 0.971 ^ 0.028NH3 . . . . . . aQ(6, 6)a 180 1.94 0.958^ 0.080 0.956 ^ 0.046 1.002 ^ 0.097

NOTE.ÈThe Ðlter-bank bandpass was centered at km s~1 for all observations, except whenVLSR \[7observing the red half of aQ(6, 6) km s~1). Each ratio represents the value of the absorption(VLSR\[6feature with respect to the nearby stellar continuum at baselines between 2 and 4 m.

a Red half.

where r is expressed in units of stellar2. Trot \T*

r~0.60,radii. This choice is similar to that found empirically forammonia around IRC ]10216 by KR93. While VY CMaand IRC ]10216 do have similar mass-loss rates (within afactor of D10), the di†ering chemistry (O-rich versusC-rich) may a†ect the cooling rates, and this ad hoc tem-perature proÐle is clearly rather speculative.

Because G88 in most cases did not publish the emissioncomponents of the transitions, we were not able toNH3model this aspect of the line proÐle. Instead we followedKR93 (for IRC ]10216) and suppressed emission in ourmodel proÐles by assuming that the vibrational tem-perature was 85% of the dust temperature.

Figure 11 shows the results assuming TheTrot \Tdust.high optical depth at 11 km (qD 2.4 ; see Paper II) e†ec-tively shields the inner dust and molecular envelope fromview. The surface is located at about alongqdust\ 1 12R

*the central impact parameter, and hence most of theobserved continuum emission is occurring outside of this.This explains why none of the models with molecular for-

FIG. 11.ÈResults of modeling the IR power and visibility data forammonia around VY CMa, assuming Filter-bank data appearTrot \Tdust .as points with error bars, while model results are represented by smalltriangles connected by lines corresponding to di†erent molecular densitydistributions, as marked. The top points and lines correspond to the visi-bility ratios of the absorption line with respect to the continuum, while thebottom data points and lines correspond to the observed and modeled linedepths. The solid line shows a model with silane forming at The10R

*.

dotted and dashed lines show molecular formation radii of and40R*respectively.80R

*,

mation radii between 10 and 80 were decisively ruledR*out with the interferometry data of Figure 11. However, one

can see that for this assumed temperature law, the lineratios were best Ðtted by a molecular formation radiusoutside Interestingly, this distance corresponds toD40R

*.

the extent of the acceleration region deduced from proper-motion studies of the masers (Marvel 1996 ; Richards,H2OYates, & Cohen 1998). Figure 12 shows the results for thetemperature proÐle of case 2, assuming theTrot\ T

*r~0.60 ;

same general conclusions still apply, showing that they arenot highly model dependent. It is worth noting that theequivalent widths for models with small molecular forma-tion radii (especially for were systematically higher10R

*)

than those measured by G88. While the line depths in theÐlter-bank bandpass were Ðtted by increasing the ammoniadensity, the line widths themselves were not. Ideally, themicroturbulence parameter should be adjusted for each setof molecular formation radii to compensate for di†eringline-broadening e†ects, such as thermal broadening and theÐnite size of the continuum source. Such adjustments didindeed improve the quality of these Ðts, but signiÐcantlyincreased the complexity of the modeling, while only weaklya†ecting the line and visibility ratios.

5.3. DiscussionWe conclude that probably forms near the termina-NH3tion of the acceleration phase in the circumstellar envelope

FIG. 12.ÈSimilar to Fig. 11, but assuming where r is inTrot \T*

r~0.60,units of stellar radii.


of VY CMa This hypothesis is supported by the(D40R*).

following observations :

1. Weak (but nonnegligible) correlation of absorptioncore velocity with excitation energy suggests that ammoniaexists to a limited degree in the acceleration region.

2. Line ratios of the aQ(2, 2) and aQ(6, 6) transitions werebest Ðtted by molecular formation radii a resultZ40R

*,

found to be insensitive to the rotational temperature proÐle.3. The visibility data for the high-excitation aQ(6, 6) line

marginally supports a large molecular formation radius, butthe high optical depth of the dust shell makes the interfero-metric data relatively insensitive to absorption in the innercircumstellar envelope.

Around IRC ]10216, high-excitation lines wereNH3observed to be signiÐcantly broader than for the low-lying Jstates. Interestingly, this behavior was not duplicated for

around VY CMa. Unlike the case for IRC ]10216, itNH3appears that ammonia is forming at least partly in the accel-eration region around this star, and hence the line forma-tion of all the transitions is more a†ected by largeturbulence in this region. Alternatively, the highly asym-metric inner dust shell seen in the near-IR (Monnier et al.1999) and hinted at by ISI visibility data (Paper II) may beinÑuencing the line formation characteristics. If the outÑowis signiÐcantly asymmetric, line widths will be clearlya†ected by the varying projected outÑow velocities ofabsorbing gas. Continued monitoring of water masers inthe inner dust shell may clarify the gas dynamics and levelof gas turbulence. This information will be critical forfurther progress in understanding the geometry of themolecular envelope around VY CMa.

6. CONCLUSIONS

We have presented the Ðrst interferometric results on

mid-IR spectral lines around evolved stars. SpeciÐc resultsfor the carbon star IRC ]10216 and the red supergiant VYCMa have been summarized in previous sections. In addi-tion, a few general conclusions can be drawn:

1. The formation radii of silane and ammonia are signiÐ-cantly beyond the dust formation zone for both evolvedstars examined here.

2. Since dust formation by itself does not catalyze forma-tion of these molecules, some other physical mechanism(s),still unknown, must be at play. Probably the adsorption ofgas-phase molecules (e.g., SiS or onto grains sets theH2)time/length scale for the important chemical reactionsoccurring on the grain surfaces.

3. When coupled with spectroscopic observations, theseresults indicate that turbulence, or velocity dispersion, isquite high in the inner envelope and is more likely to beresponsible for the broad line widths of high excitation tran-sitions than bulk acceleration.

The authors would like to recognize W. Fitelson, C.Lionberger, and M. Bester for important contributions tothe construction and software development of the Ðlterbank, and K. McElroy for observing assistance. We alsoacknowledge productive discussions with A. Glassgold andA. Betz. J. D. M. also would like to thank J. Keady forkindly allowing his sophisticated radiative transfer code tobe used for this project, and for many stimulating dis-cussions about the molecules of IRC ]10216. This work ispart of a long-standing interferometry program at U.C.Berkeley, supported by the National Science Foundation(grants AST 92-21105, AST 93-21289, and AST 97-31625)and by the Office of Naval Research (OCNR N00014-89-J-1583).

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