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Mon. Not. R. Astron. Soc. 000, 1{14 (2000) Printed 12 February 2001 (MN LATEX style �le v1.4)100-year Mass Loss Modulations on the Asymptotic GiantBranchMassimo Marengo1, �Zeljko Ivezi�c2 and Gillian R. Knapp21Harvard-Smithsonian Center for Astrophysics, Cambridge, MA 02138;International School for Advanced Studies, SISSA/ISAS, Trieste, Italy; mmarengo@cfa.harvard.edu2Princeton University, Department of Astrophysical Sciences, Princeton, NJ 08544; ivezic,gk@astro.Princeton.eduVersion of Sep 21, 2000; submitted to MNRASABSTRACTWe analyze the di�erences in infrared circumstellar dust emission between oxygen richMira and non-Mira stars, and �nd that they are statistically signi�cant. In particular,we �nd that these stars segregate in the K-[12] vs. [12]-[25] color-color diagram, andhave distinct properties of the IRAS LRS spectra, including the peak position of thesilicate emission feature. We show that the infrared emission from the majority of non-Mira stars cannot be explained within the context of standard steady-state out owmodels.The models can be altered to �t the data for non-Mira stars by postulating non-standard optical properties for silicate grains, or by assuming that the dust tempera-ture at the inner envelope radius is signi�cantly lower (300-400 K) than typical silicategrain condensation temperatures (800-1000 K). We argue that the latter is more prob-able and provide detailed model �ts to the IRAS LRS spectra for 342 stars. These �tsimply that 2/3 of non-Mira stars and 1/3 of Mira stars do not have hot dust (> 500K) in their envelopes.The absence of hot dust can be interpreted as a recent (order of 100 yr) de-crease in the mass-loss rate. The distribution of best-�t model parameters agrees withthis interpretation and strongly suggests that the mass loss resumes on similar timescales. Such a possibility appears to be supported by a number of spatially resolvedobservations (e.g. recent HST images of the multiple shells in the Egg Nebula) and isconsistent with new dynamical models for mass loss on the Asymptotic Giant Branch.Key words: stars: asymptotic giant branch | stars: mass-loss | stars: long periodvariables1 INTRODUCTIONAsymptotic Giant Branch (AGB) stars are surrounded bydusty shells which emit copious infrared radiation. Even be-fore the IRAS data became available, it was shown that IRspectra of AGB stars can be reasonably well modeled bythermal emission from dust with radial density distribution/ r�2, and optical properties for either silicate, or carbona-ceous grains (Rowan-Robinson & Harris, 1982, 1983ab). Theavailability of 4 IRAS broad-band uxes and the IRAS LRSdatabase for thousands of objects made possible more de-tailed statistical studies. Van der Veen and Habing (1988)found that AGB stars occupy a well-de�ned region in theIRAS 12-25-60 color-color diagram. They also showed thatthe source distribution depends on the grain chemistry, andis correlated with the LRS spectral classi�cation. Bedijn(1987) showed that in addition to grain chemistry, the mostimportant quantity which determines the position of a par-ticular source in the IRAS 12-25-60 color-color diagram isits mass-loss rate: more dust, more IR emission.A dust density distribution / r�2 is expected for aspherical out ow at constant velocity. Since typical observedvelocities are much larger than the estimated escape veloci-ties, there must be an acceleration mechanism at work. Earlystudies by Gilman (1969) and Salpeter (1974ab), and laterby others (e.g. Netzer & Elitzur, 1993; Habing, Tignon &Tielens, 1994), showed that the luminosity-to-mass ratiosfor AGB stars are su�ciently large to permit out ows drivenby radiation pressure. In this model, hereafter called \stan-dard", the dust acceleration is signi�cant only close to the in-ner envelope edge, and thus the dust density is steeper thanr�2 only at radii smaller than about several r1. Here r1 is theinner envelope radius which corresponds to the dust conden-sation point. At larger radii the dust density closely followsthe r�2 law, in agreement with the observed mid- and far-c 2000 RAS

2 M. Marengo, �Z. Ivezi�c & G. R. KnappIR emission. In particular, Ivezi�c & Elitzur (1995, hereafterIE95) �nd that such steady-state radiation pressure drivenout ow models can explain the IRAS colors for at least 95%of dusty AGB stars. In addition to explaining the IR emis-sion, these models are in good agreement with constraintsimplied by independent out ow velocity and mass-loss ratemeasurements (Ivezi�c, Knapp & Elitzur 1998).AGB stars are long-period variables (LPV) which showa variety of light curves. Based on visual light curves, theGeneral Catalog of Variable Stars (GCVS, Kholopov et al.,1985-88) de�nes regular variables, or Miras, semiregular(SR) variables, and irregular variables (L). The distinctivefeatures are the regularity of the light curves, their ampli-tudes, and their periods. Some types are further subdividedbased on similar criteria (e.g. SRa, SRb, SRc,...).AGB stars of di�erent variability types cannot be distin-guished in IRAS color-color diagrams (Habing 1996, and ref-erences therein). This is easily understood as a consequenceof the scaling properties of dust emission (IE95, Ivezi�c &Elitzur 1997, hereafter IE97). Although steady-state mod-els cannot provide a detailed description of variability, theycan be easily augmented when the variability time scale (�1 year) is shorter than the dust dynamical crossing timethrough the acceleration zone (> 10 years). In this case thedeviations of the dust density pro�le are minor, and themost important e�ect of variability is the change of dust op-tical depth. Optical depth is anticorrelated with luminositybecause of the movement of the dust condensation point:envelopes are bluer (in all colors) during maximum thanminimum light (Le Bertre 1988ab; Ivezi�c & Elitzur 1996,and references therein). Since the change of dust densitypro�le is negligible, a source cannot leave the track in color-color diagrams that corresponds to that density pro�le andgrain chemistry: during its variability cycle the source sim-ply moves along that track due to the change of opticaldepth. Consequently, the overall source distribution is notsigni�cantly a�ected and a random observation cannot re-veal any peculiarities: even if a star is caught during itsmaximum/minimum light, the only change is in its some-what bluer/redder colors (see e.g. the repeated observationsof Mira by Busso et al. 1996). For this reason, systematicdi�erences in IRAS color-color diagrams for AGB stars ofdi�erent variability types are not expected within the frame-work of steady-state models.Kerschbaum, Hron and collaborators (Kerschbaum &Hron 1992, 1994, 1996, Kerschbaum, Olofsson, & Hron 1996,Hron, Aringer, & Kerschbaum, 1997, hereafter we refer tothese papers as KHc) studied IR emission of various types ofLPVs by combining the IRAS broad-band uxes with near-IR observations and the IRAS LRS database. They �nd dif-ferences in observed properties between Miras and SRb/Lbvariables? : SRb/Lb variables have somewhat higher stellartemperatures and smaller optical depths than Miras, andcan be further divided into \blue" and \red" subtypes, theformer showing much less evidence for dust emission thanthe latter. KHc also show that \red" SRb/Lb stars have verysimilar Galactic scale heights and space densities to Miras,? According to KHc, SRa variables appear to be a mixture of twodistinct types: Miras and SRb variables.

and show a similar range of IRAS 25-12 color, possibly im-plying an evolutionary connection.Particularly intriguing are di�erences between the LRSspectra of SRb/Lb variables and Miras with \9.7" �m sil-icate emission (LRS class 2n). Unlike the featureless spec-tra of carbonaceous grains, the silicate dust spectra showrich structure (e.g. Little-Marenin & Little 1988, 1990). Thisstructure may indicate the existence of di�erent dust species,although some of the proposed classi�cation appears to re- ect the radiative transfer e�ects (IE95). The peak positionof the \9.7" �m feature for SRb/Lb sources is shifted long-wards, relative to the peak position for Miras, by 0.2-0.3�m. In addition, the ratio of the streng ths of silicate emis-sion features at 18 �m and 10 �m, F18=F10, is larger forSRb/Lb variables than for Miras. KHc point out that thesedi�erences in LRS features cannot be due to optical depthe�ects because the feature shapes should resemble the grainabsorption e�ciency for the relevant range of optical depths.Such a correlation between the variability type of a star andthe peak position of its grain absorption e�ciency is not ex-pected within the context of standard steady-state out owmodels.Ivezi�c & Knapp (1998, hereafter IK98) compared thedistribution of variable AGB stars in the K-[12] vs. [12]-[25]color-color diagram and found that stars are not distributedrandomly in this diagram, but occupy well de�ned regionsaccording to their chemistry and variability type. While dis-crimination according to the chemical composition is notsurprising, since the optical properties of silicate and car-bon grains are signi�cantly di�erent, the separation of Mirasfrom SRb/Lb variables is unexpected.IK98 also show that, while \standard" steady-statemodels provide excellent �ts to the distributions of Miras ofall chemical types, they are incapable of explaining the dustemission from SRb/Lb stars with silicate dust. They �ndthat the distribution of these stars in the K-[12] vs. [12]-[25]color-color diagram can be explained by models with dusttemperature at the inner envelope radius signi�cantly lower(300-400 K) than typical condensation temperatures (800-1000 K). Such an absence of hot dust for SRb/Lb stars canbe interpreted as a recent (order of 100 yr) decrease in themass-loss rate. Furthermore, the distribution of these starsin the K-[12] vs. [12]-[25] color-color diagram implies thatthe mass-loss rate probably resumes again, on similar timescales.The possibility of mass loss changes with short timescales (on the order of hundred years) seems to be supportedby a number of other observations. Recent HST images ofthe Egg Nebula obtained by Sahai et al. (1997) show concen-tric shells whose spacing corresponds to a dynamical timescale of about 100 years. Although there are various ways tointerpret such shells (e.g. binary companion as proposed byHarpaz, Rappaport & Soker 1997; instabilities in the dust-gas coupling proposed by Deguchi 1997), another possibleexplanation is dust density modulations due to the massloss variations on similar time scales. Time scales of �100years for mass loss variations have also been inferred for RHya by Hashimoto et al. (1998) and for IRC+10216 by Mau-ron & Huggins (1999), and a somewhat longer scale for �Cep by Mauron (1997). The discovery of multiple CO windsreported by Knapp et al. (1998) is also in agreement withthe hypothesis of variable mass-loss.c 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 3Mass-loss rate modulations with time scales of the order100 years are di�cult to explain in terms of the periodici-ties characteristic for AGB stars. Periodic ashes of the Heburning shell in the thermally pulsing AGB phase (knownas \thermal pulses", TP hereafter) occur on timescales of103{104 yr (see e.g. Speck, Meixner & Knapp 2000). On theother end, the typical pulsational periods of AGB stars (50 {500 days) are too short. Various attempts to solve this puz-zle have been proposed, and are well described by Sahai etal. (1998). The basic ideas involve either long period mod-ulations of the luminosity variations, or temperature uc-tuations caused by giant convection cells in the AGB at-mosphere. However, similar mass-loss rate modulations arealso reproduced, without any such additional assumptions,within the framework of time dependent wind models withdriving force varying on time scales of �1 yr (Winters 1998,see also x4).Motivated by these results, we further analyze corre-lations between variability type and IR emission for AGBstars, especially the properties of LRS data, and their im-plications for the models of steady-state radiatively drivenout ows. In addition to the silicate peak position, we also usesynthetic colors calculated from LRS data to study detailedproperties of mid-infrared emission. Earlier �ndings that Mi-ras and SRb/Lb variables exhibit signi�cantly di�erent IRemission properties are con�rmed at statistically signi�cantlevels in x2. We attempt to explain these discrepancies byan interrupted mass loss model, and provide detailed modeltesting in x3. In section x4 we discuss the implications.2 OBSERVED DIFFERENCES IN DUSTEMISSION BETWEEN MIRA AND SRSTARS2.1 Distribution of AGB stars in K-[12] vs.[12]-[25] Color-color DiagramFigure 1 shows the K-[12] vs. [12]-[25] color-color diagramtaken from IK98y (the K data were obtained by Franz Ker-schbaum and collaborators). The thick curved short-dashedand long-dashed lines represent tracks for interrupted mass-loss models which are described in detail in x3. It is as-sumed that mass loss abruptly stops and the envelope freelyexpands thereafter. Due to this expansion the dust temper-ature at the inner envelope radius decreases. Model tracksfor various values ranging from 1200 K to 600 K for car-bon grains (short-dashed lines) and from 700 K to 300 Kfor silicate grains (long-dashed lines) are shown in the �g-ure. These tracks demonstrate that the distribution of starswith silicate dust in K-[12] vs. [12]-[25] color-color diagramcan be reproduced by varying T1 in the range 300{700 K,without any change in the adopted absorption e�ciency forsilicate grains. The distribution of Mira and non-Mira starswith carbon dust is fairly well described by models with T1= 1200 K, and thus the assumption of signi�cantly lower T1is not required by the data. However, note that such modelsy Note that color de�nitions are di�erent than in IK98, here wede�ne all colors as [2]-[1]=-2.5log(F2/F1), where F1 and F2 are uxes in Jy.

are not ruled out by the data since all carbon dust modelsproduce similar tracks.2.2 IRAS LRS Di�erences between Oxygen RichMira and SR StarsThe oxygen rich stars usually show infrared spectra indicat-ing silicate dust. Due to many features in their LRS spectra,such stars are especially well suited for a comparative studyof various subclasses. For this reason, in the rest of this workwe limit our analysis to oxygen rich stars. The stars withoutIRAS LRS data are excluded and the �nal list includes 342sources, consisting of 96 Mira stars, 48 SRa, 140 SRb and58 Lb stars. According to Jura & Kleinmann (1992) andKerschbaum & Hron (1992), the evolutionary state of theSR variables can be determined from their pulsation period,P : stars with P < 100d should be in the Early-AGB phase,while stars with P > 100d are in the TP-AGB phase. It hasbeen suggested that only stars in the TP-AGB phase suf-fer signi�cant mass loss (e.g. Vassiliadis & Wood 1993). Wehave cross-correlated this list with the General Catalogue ofVariable Stars (GCVS, Kholopov et al. 1988) and extractedthe pulsational period for SR stars, when available. We �nd57 stars with P < 100d and 130 with P>�100d.We divide the stars from the list into several subsamplesand analyze the properties of each group separately:� Mira stars� Non-Mira stars, including SRa, SRb and Lb types, here-after NM� SRa stars, in order to test the possibility that SRa area spurious class containing a mixture of Mira and SRb vari-ables.� Short-period (P < 100d) SR stars, hereafter spSR� Long-period (P > 100d) SR stars, hereafter lpSRDue to the heterogeneous nature of the samples fromwhich the KHc list is derived, and to the limitations of theIRAS catalog (e.g. source confusion in the galactic plane),our sample is not statistically complete and may have hid-den biases. However, it is su�ciently large to allow a criticalstudy of the correlation between variability type and proper-ties of infrared emission for oxygen rich galactic AGB stars.2.2.1 Mid-IR colorsThe LRS spectra for a large number of sources can be e�-ciently compared by using synthetic colors based on \ uxes"obtained by convolving LRS spectra with suitably de�nednarrow �lters. We utilize the photometric system developedby Marengo et al. (1999, hereafter M99) as a diagnostic toolfor mid-IR imaging of AGB stars. The system is designedto be sensitive to the strength of the 9.7 �m silicate featureand to the slope of the dust continuum emission in the 7{23�m spectral range. We calculate synthetic uxes from LRSdata by using 10% passband �lters with Gaussian pro�lescentered at 8.5 �m, 12.5 �m, and 18.0 �m. The resulting[8.5]-[12.5] vs. [12.5]-[18.0] color-color diagram for all starsin the sample is shown in Figure 2. Mira stars are shown assolid circles, NM stars as open circles, and SRa stars as graydots. The line shows the locus of black-body colors param-eterized by the temperature, as marked in the �gure.c 2000 RAS, MNRAS 000, 1{14

4 M. Marengo, �Z. Ivezi�c & G. R. Knapp-3 -2 -1 0 1 2

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1200 Figure 1. [12]-[25] vs. K-[12] color-color diagram for a sample of AGB stars discussed in IK98. Oxygen rich Miras and SRb/Lb stars aremarked by open triangles and circles, respectively. Carbon rich stars are analogously marked by �lled symbols. The thin straight solidlines display a scheme which classi�es stars into 4 groups according to their variability type (Miras, m, vs. non-Miras, n) and chemistry(O vs. C). The RJ label marks the locus of dust-free stars. The thick curved short-dashed and long-dashed lines represent tracks forinterrupted mass-loss models which are decribed in detail in x3. It is assumed that mass loss abruptly stops and the envelope freelyexpands thereafter. Note that the models imply a lack of hot dust for oxygen rich SRb/Lb stars.The di�erences between Mira and NM sources are evi-dent. Mira stars are grouped around the black body track,with �0:1 <� [8.5]-[12.5] <� 0:4. This region, as shown byM99, is well described by envelopes with hot dust and in-termediate optical depth 1 <� �V <� 30. All NM stars haveinstead a much larger spread in the [8.5]-[12.5] color, and aredder [12.5]-[18.0] color. The SRa stars have a distributionsimilar to other NM stars, except that their [8.5]-[12.5] coloris on average redder than for the whole sample, and in therange observed for Mira stars.We provide a quantitative test of the Mira/NM sepa-ration in the [12.5]-[18.0] vs. [8.5]-[12.5] color-color diagramin Figure 3, and summarize it in Table 1. The histogramin Figure 3 shows the distributions of the [12.5]-[18.0] colorexcess, de�ned as the di�erence between [12.5]-[18.0] colorand the color of a black body with the same [8.5]-[12.5] colortemperaturez, for Mira, SRa and NM stars. The mean valueof this excess is � 0:11 for Miras, � 0:32 for NM and � 0:33for SRa. The 0.2 magnitude di�erence between the mean val-ues of Mira and NM distributions is slightly larger than thedispersion of the two samples, as measured by the samplevariance (� � 0:18 for both Miras and NM). We tested thisresult with a Student's t-test for the mean values, �ndingthat the di�erence between the two populations is statisti-cally signi�cant (see Table 1 for details). We also performedthe same analysis for the spSR and lpSR subsamples andfound that they have a similar mean color excess (0.36 and0.30 mag); the di�erence of 0.06 mag is not signi�cant.z Note that the black body assumption is not crucial since itsimply provides a reference point.Figure 2. The [12.5]-[18.0] vs. [8.5]-[12.5] color-color diagrambased on synthetic uxes obtained from LRS data (see x2.2.1).Mira stars are shown as solid circles, NM (non-Mira) stars asopen circles, and SRa stars as gray dots. The line is the locus ofblack-body colors parametrized by the temperature, as marked.Note the di�erent distribution of Mira and NM stars.These two statistical tests suggest that, regarding theirmid-IR [8.5]-[12.5] and [12.5]-[18.0] colors, Mira stars andNM stars are di�erent. That is, given the envelope opti-cal depth, as measured by the [8.5]-[12.5] color, NM starsshow more cold emission measured by the [12.5]-[18.0] color.Among the SR sources, the mid-IR colors do not correlatewith the pulsational period. Assuming the validity of theKerschbaum & Hron (1992) correlation between the pulsa-tional period and AGB evolution, this suggests that SR starsc 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 5Figure 3. Distribution of the [12.5]-[18.0] color excess, relativeto a black body with the same [8.5]-[12.5] color temperature, forMira (dashed line), NM (solid line) and SRa (dotted line) stars.Non-Mira stars have�0.2 mag larger color excess than Mira stars(see Table 1).Sample Median Mean � NMira 0.10 0.11 0.18 96NM 0.34 0.32 0.18 246SRa 0.37 0.33 0.19 48spSR (P < 100d) 0.37 0.36 0.17 57lpSR (P >� 100d) 0.32 0.30 0.20 130Sample F-test t-test resultMira vs. NM 0.90 6 � 10�20 Same �, di�. meanSRa vs. Mira 0.70 2 � 10�10 Same �, di�. meanSRa vs. NM 0.60 0.71 Same � and meanspSR vs. lpSR 0.16 0.05 Same � and meanTable 1. Signi�cance of statistical tests for the [12.5]-[18.0] colorexcess. Samples have di�erent � at the 99% con�dence level ifthe variance F-test returns a signi�cance of 0.01 or smaller, anddi�erent mean values if Student's t-test returns a signi�cance of0.01 or smallerform similar circumstellar envelopes in the early and ther-mally pulsing AGB phases. The similarity of SRa with NMin general indicates that the SRa sample is not signi�cantlycontaminated by Mira stars.2.2.2 The peak wavelength of the \9.7 �m" silicate featureFollowing KHc, we also determine the peak wavelength ofthe \9.7 �m"silicate feature for all sources in the sample.Such studies were done �rst by Little-Marenin & Little(1990) who tried to classify LRS spectra for a large sampleof AGB stars. They found that their subsample of SR and Lvariables showed a narrower silicate feature, and shifted tothe red compared to Mira stars. A similar analysis was per-formed by Hron, Aringer & Kerschbaum (1997) for a largernumber of sources, accounting for the dust continuum emis-sion by �tting it with a separate black body. They con�rmed

Figure 4. Distribution of the peak position of the silicate \9.7"�m feature for Mira (dashed line), NM (solid line) and SRa (dot-ted line) stars. The NM stars have the feature shifted for �0.2�m with respect to the Miras.the di�erences between the two classes, �nding a shift ofabout 0.3 �m in the silicate feature peak position.We determine the silicate feature peak position by �t-ting a �fth degree polynomial to each LRS spectrum in the9{11 �m wavelength range. This �tting procedure removesthe e�ect of noise and eventual secondary features, produc-ing \smooth" spectra where the position of the maximumcan be easily recognized. The wavelength of the maximumof the �tting polynomial in the given interval is then as-sumed to be the position of the \true" silicate peak. Withthis technique we measured the position of the silicate peakfor 85 Miras and 162 NM; for the remaining sources (11 Mi-ras and 84 NM) the �tting procedure failed either becauseof the excessive noise in the spectra, or due to the absenceof a signi�cant feature. Many of the sources for which thesilicate feature is too weak to measure the position of itspeak are Lb stars of LRS class 1n.The results for the position of the silicate feature peakare listed in Table 2 and shown as histograms in Figure 4.The mean values for Miras and NM are h�maxiMira ' 9:86�m and h�maxiNM ' 10:01 �m respectively; the mediansare 9.87 and 10.08 �m. Note the di�erent standard devia-tion �� of the two samples, almost twice as large for NM(� 0:42 �m) than for Miras (� 0:28 �m); this di�erence is99.9% statistically signi�cant according to the F-test. TheStudent's t-test for the mean values, performed between thetwo samples (with unequal variances), con�rms the separa-tion of the Mira and NM populations with respect to their�max at a high (99.95%) signi�cance level, in agreement withthe results of Hron, Aringer & Kerschbaum (1997).We performed the same test on the SRa class alone,�nding h�maxiSRa ' 10:08 �m, and �� ' 0:41, consistentwith the results for the whole NM class. This further indi-cates that the SRa subsample does not contain a signi�cantnumber of misclassi�ed Miras. The h�maxi values for theNM subsets with P >� 100 d and P < 100 d are 10.07and 10.09 �m respectively, and the �� are 0.43 and 0.39�m. The di�erence in the �� of the two subsample is notsigni�cant, con�rming that the two subsets are part of thec 2000 RAS, MNRAS 000, 1{14

6 M. Marengo, �Z. Ivezi�c & G. R. KnappSample Median Mean � NMira 9.87 9.86 0.28 85NM 10.07 10.01 0.42 162SRa 10.10 10.08 0.41 37spSR (P < 100d) 10.09 10.04 0.43 31lpSR (P >� 100d) 10.07 10.02 0.38 95Sample F-test t-test resultMira vs. NM 5 � 10�5 5 � 10�4 Di�. � and meanbSRa vs. Mira 6 � 10�3 4 � 10�3 Di�. � and meanbSRa vs. NM 0.82 0.43 Same � and meanspSR vs. lpSR 0.41 0.87 Same � and meanTable 2. Signi�cance of statistical tests for the peak Position ofthe silicate 9.7 �m feature. Samples have di�erent � at the 99%con�dence level if the variance F-test returns a signi�cance of 0.01or smaller, and di�erent mean values if Student's t-test returns asigni�cance of 0.01 or smallersame population, in agreement with the analysis of syntheticmid-IR colors.2.3 Interpretation of the Observed Di�erencesWe have shown that oxygen rich Mira and non-Mira starshave statistically di�erent properties of their infrared emis-sion. In particular, we �nd(i) Di�erent distribution in the K-[12] vs. [12]-[25] color-color diagram.(ii) Di�erent [12.5]-[18.0] excess emission(iii) Di�erent peak position of the silicate featureAs shown by IK98 (c.f. Figure 1), these di�erences arenot in agreement with the \standard" steady-state radia-tively driven wind models: while they can reproduce theproperties of the Mira sample, they cannot explain the in-frared emission from non-Mira stars. There are three waysto augment the \standard" models without abandoning thehypothesis of a radiatively driven out ow: changing the in-put (stellar) spectrum, altering the spectral shape of dustopacity, and employing a di�erent dust density distribution.The star in the \standard" models is assumed to radi-ate as a 2500 K black-body. The observed di�erences in theK-[12] vs. [12]-[25] color-color diagram could imply that typ-ical stellar temperature is signi�cantly di�erent for Mira vs.non-Mira stars, or that black-body spectral shape is not anadequate description of the true stellar spectrum (e.g. dueto an absorption feature in K band like H2O feature seenin IRTS data by Matsuura et al. 1998). A di�erent inputspectrum would a�ect the model K ux, and to some extentthe 12 �m ux in optically thin envelopes. However, sucha change cannot account for the observed di�erences in themid-infrared region (items 2 and 3 above) where the ux isdominated by dust emission.It is possible to produce model spectra in agreementwith data for non-Miras by altering the adopted spectralshape of absorption e�ciency for silicate grains. There aretwo required changes. First, the ratio of silicate featurestrengths at 18 �m and 10 �m has to be increased for a factor

of about 2-3 x. Such a change results in a model track in theK-[12] vs. [12]-[25] diagram which leaves the Rayleigh-Jeanspoint at a larger angle (with respect to K-[12] axis) thanbefore, and passes through the observed source distribution.These models also produce larger [12.5]-[18.0] excess emis-sion in agreement with item 2 above. In order to account foritem 3 above, a second change is required: the peak positionof the \9.7" micron feature has to be shifted longwards forabout 0.2-0.3 �m. For example, the inclusion of Al oxides canshift the peak position to longer wavelengths (Speck et al.2000). We conclude that, although the postulated changesmight seem ad hoc and have little support from model dustoptical properties, the possibility of non-Miras having some-what di�erent grains cannot be ruled out by using near-IRand IRAS data alone{ .The third way to alter the model spectra predicted by\standard" models is to decrease T1, the dust temperatureat the inner envelope edge, which is usually assumed to cor-respond to the dust condensation temperature (�1000 K).The removal of hot dust reduces the ux at 12 �m signi�-cantly more than the uxes in K band and at 25 �m, andproduces model tracks in agreement with the source distri-bution in the K-[12] vs. [12]-[25] color-color diagrams (c.f.Figure 1), and larger [12.5]-[18.0] excess emission. It is re-markable that the models with a low T1 are also capable ofexplaining the di�erences between the peak position of thesilicate feature. The top panel in Figure 5 displays two modelspectra obtained with visual optical depth of 0.6, and T1 =300 K (dashed line) and 700 K (solid line). The dotted lineshows the stellar spectrum. Because the hot dust has beenremoved in the model with T1 = 300 K, both the blue andred edges of the 10 �m silicate emission feature are shiftedlongwards for about 0.2-0.3 �m. While the peak position inthe model spectra is exactly the same in both models, theaddition of noise to the models would make the whole fea-ture for T1 = 300 K model appear shifted longwards. Thus,assuming a lower T1 in models for NM stars can account forall 3 items listed above. Such models are further describedin the next section.We conclude that the two most probable explanationsfor the observed di�erences in infrared emission betweenMira and non-Mira stars are either di�erent grain opticalproperties, or the lack of hot dust in non-Mira stars. Thepossibility that employing di�erent types of grains could re-produce the observed di�erences between Mira and NM starsrequires extensive modeling e�ort and will be analyzed in aseparate publication (Helva�ci et al. 2001). Here we discusslow-T1 models and show that they are consistent with theinfrared emission observed for NM stars. Various observa-tional techniques for distinguishing these two hypothesis arefurther discussed in x4.x This strength ratio is not a very constrained dust property, butthe uncertainty seems to be smaller than a factor of 2 (Draine &Lee, 1984){ Indeed, Sloan et al. (1996) found that the \13 micron" featureoccurs somewhat more frequently in SRb stars (75%-90%) thanin all AGB stars with silicate dust (40%-50%).c 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 78 10 12 14 16 18 20 22 24Figure 5. Model spectra in the LRS region obtained for silicategrains with the visual optical depth of 0.6 and 2 values of thedust temperatures at the inner envelope radius, T1 (solid anddashed lines). Dotted line shows the stellar contribution to thespectra. Note that the silicate \9.7" �m feature appears weakerand is shifted longwards for T1 = 300 K, relative to the positionobtained for T1 = 700 K, although both are calculated with thesame grain optical properties.3 MODELS3.1 Model Assumptions and PredictionsWe calculate model spectra by using the DUSTY code(Ivezi�c, Nenkova & Elitzur, 1997). It is assumed that the starradiates as a 2500 K black-body. Silicate warm dust opac-ity is taken from Ossenkopf et al. (1992), with the standardMRN grain size distribution (Mathis, Rumpl & Nordsiek,1977). Dust density is described by r�2 with an arbitraryinner envelope radius, r1. The outer envelope radius is irrel-evant as long as it is much larger than r1, and we �x it atthe value of 3�1017 cm. In the interrupted mass loss model,the inner envelope radius increases with t, the time elapsedsince the mass loss stopped asr1 = r1(0) + v t = r1(0) + 3:2� 1013 cm v10 tyr (1)where t = tyr years, the expansion velocity v = v10 10 kms�1, and r1(0) is the envelope inner radius at t = 0. Thisradius depends on the grain optical properties and dust con-densation temperature, and the stellar temperature and lu-minosity (IE97). For typical valuesr1(0) = 3� 1014 cm L1=24 ; (2)where the stellar luminosity L = L4104 L�.We specify r1 by the temperature at the inner edge attime t, T1. This temperature decreases with time becausethe distance between the star and the envelope inner edgeincreases. This relationship is approximately given by (IE97,eq. 30)T1T1(0) = �r1(0)r1 � 24+� (3)where � is the power-law index describing the opacity wave-length dependence. This expression is strictly correct only inthe optically thin regime, and furthermore, the silicate dustopacity cannot be described by a simple power law. However,it provides a good description of detailed model results with� = 2=(4+�)�0:40�0:05. Combining the above expressionsgives

T1T1(0) = �1 + 0:1v10tyrL1=24 ��� : (4)As already indicated in x2 (c.f. Figure 1), the distribu-tion of SR stars in the K-[12] vs. [12]-[25] color-color diagramimplies a lower limit on T1 of �300 K. Assuming T1(0) =800 K, v10 = L4 = 1 implies a time scale of 100 yr.The second free parameter is the dust optical depthwhich we specify as the visual optical depth, �V . This param-eter controls the amount of dust and increases with _M, themass-loss rate during the high mass loss phase. The steady-statek radiatively driven wind models give for silicate dust(Elitzur & Ivezi�c 2000)_M = 2� 10�6M� yr�1 �V (0)3=4 L3=44 � rgd200�1=2 (5)where rgd is the gas-to-dust ratio, and �V (0) is the opticaldepth before the mass loss stops. Note that _M / �V 3=4 ratherthan _M / �V due to dust drift e�ects.After the mass loss stops, the optical depth decreaseswith time because it is inversely proportional to r1 due tothe envelope dilution�V�V (0) = �1 + 0:1v10tyrL1=24 ��1 : (6)The models could be parametrized by _M and r1 (or t) in-stead of �V and T1. However, in such a case the parametriza-tion of a model spectrum would involve at least two addi-tional parameters (L and rgd) and would arti�cally intro-duce a four-dimensional �tting problem. As the scaling prop-erties of the radiative transfer imply (IE97), the describedmodel is only a two-dimensional problem fully speci�ed by�V and T1. It is only the correspondence between these twoparameters and other quantities such as _M that involves ad-ditional assumptions about e.g. rgd.In the interrupted mass loss model the changes of T1and �V as the envelope expands are correlated. Combiningeqs. (4) and (6) givesT1T1(0) = � �V�V (0)�� ; (7)and thus during the expansionT1�V �� = C = const: (8)where the value of constant C is determined by _M during thehigh mass loss phase. The model predicts that the distribu-tion of best-�t T1 and �V should resemble a strip in the �V {T1 plane whose width is determined by the intrinsic distri-bution of the mass-loss rates during the high mass-loss ratephase, and with the position along the strip parametrizedby the time since the mass loss stopped.Another model prediction is for the T1 distribution ofsources in an unbiased sample (or equivalently for the �V dis-tribution since �V and T1 are correlated). Eq. (4) shows thatthe �rst derivative of T1 decreases with time and thus thek The steady-state assumptiondoes not strictly apply here. How-ever, the crossing time for the acceleration zone (� 2r1, corre-sponding to �10 yr) is much shorter than the presumed durationof the high mass-loss rate phase, and thus eq.(5) can be used toestimate approximate mass-loss rate.c 2000 RAS, MNRAS 000, 1{14

8 M. Marengo, �Z. Ivezi�c & G. R. Knappnumber of observed sources should increase as T1 decreases.Assuming dN(T1) / dt(T1), where dN is the number ofsources in a given T1 bin, the model impliesdNdT1 / T� 1+��1 / T�3:51 : (9)This prediction applies for sources with T1 smaller than thedust condensation temperature, Tc. The number of sourceswith T1 comparable to Tc depends on the duration of thehigh mass loss phase such that the ratio of the number ofsources with T1 < Tc, to the number of sources with T1�Tc,is equal to the ratio of times spent in the low and high mass-loss phases.To summarize, the interrupted mass loss models assumea sudden drop in the mass-loss rate after which the envelopefreely expands. The infrared spectrum emitted during thisphase depends on only two free parameters, the tempera-ture at the inner envelope edge, T1 and the envelope opticaldepth �V . Both of these quantities decrease with time in acorrelated way described by eq. (8).Note that the two free parameters imply a two-dimensional family of model LRS spectra. It is usually as-sumed that the shape of an LRS spectrum for silicate grainsis fully speci�ed by the 9.7 �m silicate feature strength. How-ever, in this model even for a �xed 9.7 �m silicate featurestrength, there is a family of spectra with di�ering shapesdue to the varying second parameter. We �nd that the ratioof uxes at 18 �m and 10 �m, F18/F10, is a convenient ob-servable, in addition to the 9.7 �m silicate feature strength,which can be used to parametrize the LRS spectra. Thatis, each combination of T1 and �V corresponds to a uniquecombination of the 9.7 �m silicate feature strength and theF18/F10 ratio, and each such LRS spectrum corresponds toa unique pair of T1 and �V . Of course, assuming that allstars have the same L, rgd and v10, a given LRS spectrumcorresponds to a unique combination of _M and r1, and viceversa.This two-dimensionality of LRS spectra is illustrated inFigure 6 which displays a time evolution of model spectraafter the mass loss interruption (for details see the �gurecaption). Each spectrum is fully characterized by �V andT1, which equivalently can be expressed as time t, markedin each panel, and mass-loss rate indicated on top of eachcolumn. The corresponding values of LRS class, which mea-sures the 9.7 �m silicate feature strength, and the F18/F10ratio are also marked in each panel. Note that some spectrahave the same LRS class (e.g. t=0 yr in the �rst column,t=25 yr in the second column, and t=50-75 yr in the thirdcolumn) and yet are clearly distinguishable both by theiroverall shape and the values of the F18/F10 ratio. Anotherimportant detail is that the spectra with comparatively largeF18/F10 ratio are obtained only for comparatively low T1,as discussed earlier.While we assume that the mass loss ceases completely,the data provide only a lower limit on the mass-loss rateratio in the two phases of high and low mass loss. We haveexplored a limited set of models where the mass-loss ratedrops for a factor 3, 5, 10, and 100, and found that with theavailable data we cannot distinguish cases when the mass-loss rate drops by more than a factor of 5. Thus, this is alower limit on the ratio of mass-loss rates in the two phases.

We have computed �2000 model spectra parametrizedon logarithmic grids with 62 �V steps in the range 10�3{350, and 32 T1 steps in the range 100 K { 1400 K. Modelscalculated on a �ner grid in either �V or T1 vary less betweentwo adjacent grid points than typical noise in the data. Asubset of models with T1 restricted to the interval 600{1400K is hereafter called \hot-dust" models. We separately �tthese models to all sources in order to test whether \cold-dust" models (with T1 < 600 K) are necessary to improvethe �ts.3.2 Fitting TechniqueThe best �t model for each source is found by using a �2minimization routine applied to the source and model spec-tra in the IRAS LRS spectral region (8 �m{ 23 �m). The�2 variable is de�ned as�2 = 1N � 2 NXi=1 ��iFO� (�i)� �iFM� (�i)�2�2O + �2M ; (10)where FO� is the observed ux and FM� is the model ux. Theerror �O of the IRAS LRS data was estimated as the root-mean-square (rms) di�erence between the raw and a cubicspline smoothed LRS spectra. The model error �M is takenas the rms di�erence between the two closest models in theparameter space. The �2 variable was then normalized tothe number of wavelengths N , minus the number of �ttingparameters (�V and T1). By comparing each source spectrumwith all spectra in a given model set, we determine the �2and select a model with the lowest �2 as the best-�t model.This procedure is repeated independently for the set of allmodels, and for the \hot dust" subset.As discussed in the previous section, the interruptedmass loss model predicts a particular distribution of sourcesin the �V {T1 plane, which may be a�ected by hidden sys-tematic biases in the �tting procedure. In order to assessthe level of such biasing, we perform a \self-�t" test for allmodels in the sample. We add Gaussian noise similar to thenoise in the LRS data to each of the DUSTY model spectraand then pass such spectra through the �tting algorithm.We consider two noise levels (signal-to-noise ratio, SNR),SNR = 10 typical for the whole sample and SNR = 5 rep-resentative of the stars with the lowest-quality LRS data.The results are shown in Figure 7 where each circle rep-resents a point in the model grid; missing points are modelsfor which the true �V and T1 were not recovered due to noisein the \data". The majority of such \failed" �ts fall on toa neighboring grid point. The �gure shows that increasingnoise can reduce the e�ectiveness of our procedure. How-ever, the T1 distribution of the incorrectly identi�ed modelsis uniform even in the low SNR case, and thus within thelimits of our sample the �tting procedure does not introducesigni�cant biasing in the best-�t parameters.3.3 Best-�t Model ResultsThe quality of a �t is described by the best �t �2 variable.A good �t, in which the details of the source spectra arereproduced by the model (e.g. Figure 8, panel a), gener-ally has �2 <� 5. Fits with 5 <� �2 <� 10 are still acceptable,even though some secondary features in the source spectrumc 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 9

Figure 6. An illustration of the two-dimensionality of LRS spectra. Each column displays a time evolution of model spectra after themass loss interruption, calculated in steps of 25 years. The spectra in 3 columns are displayed for di�erent mass-loss rates before theinterruption, increasing from left to right, and indicated on top of each column. Each spectrum is fully characterized by �V and T1,which equivalently can be expressed as time t, marked in each panel, and mass-loss rate. The corresponding values of LRS class, whichmeasures the 9.7 �m silicate feature strength, and the F18/F10 ratio are also marked in each panel (see text for details).c 2000 RAS, MNRAS 000, 1{14

10 M. Marengo, �Z. Ivezi�c & G. R. Knapp

Figure 7. Test diagram of the �tting procedure. Gaussian noisewith SNR = 10 (top) and 5 (bottom) is added to the full gridof models and the resulting spectra are �tted with the noiselessspectra. Each circle represent a successful recovery of the true�V and T1, while the missing points are incorrectly identi�edmodels. The majority of \failed" models fall on to a neighboringgrid point.cannot be fully reproduced by the model. This seems to bemainly due to the inability of the adopted silicate opacity todescribe all observed spectral features (e.g. the 13 �m fea-ture). A larger �2 (>�10) indicates more serious discrepanciesin the �t, that can range from the convergence errors (e.g.when the �tting routine cannot �nd a well de�ned minimumin the �2 surface) to poor �ts indicating that the adoptedopacity and/or radial dust density law are grossly inade-quate. Such sources represent less than 10% of the sample.3.3.1 The Fit QualityThe statistics of the best-�t �2 values for sources with�2 < 10 are shown in Table 3. The table reports the frac-tion of sources in each subsample (Mira, NM, SRa, spSR,and lpSR) which cannot be �tted with a �2 less than 3 and10 (\excellent" and \acceptable" �ts). The sources are �ttedwith two sets of models: \all temperatures" models whichinclude the full T1 grid, and the \hot dust" models withT1 > 600 K. As evident, a larger fraction of sources in allsubsamples can be �tted within a speci�ed �2 limit with the\all" model set than with the \hot dust" models. This is not

Sample �2<�3 �2<�10 �2<�3 �2<�10all models hot dustMira 35% 3% 42% 12%NM 18% 1% 54% 22%SRa 21% 2% 33% 4%spSR (P < 100d) 18% 0% 67% 21%lpSR (P >� 100d) 21% 2% 48% 6%Table 3. The best �t statistics. The table lists the fraction ofsources in each subsample which cannot be �tted with the speci-�ed �2 criteria. The second and third column correspond to \all"(temperature) models, and the third and fourth column to \hotdust" models (see text).surprising since the former model set includes a greater va-riety of spectra due to the two free parameters, as opposedto the restrictions on one free parameter in the latter set.Nevertheless, the improvement in the best �t quality is moresigni�cant for the NM sample (and all NM subsamples) thanfor Mira stars. For example, more than a half of NM starscannot be �tted with a �2 < 3 by using \hot dust" mod-els, while the inclusion of models with low T1 decreases theirfraction to less than 20%. At the same time, the correspond-ing fractions for Mira stars are 42% and 35% indicating thatlow-T1 models are not necessary to model LRS data of thesestars.An example of the improvement in the �t quality dueto a lower T1 is shown in Figure 8. The model spectra areplotted by dashed dotted lines and the IRAS LRS data bysolid lines. In panel a the SRb star TY Dra is �tted witha cold dust model (T1 ' 370 K), resulting in a very small�2. When the dust temperature is limited to the range 600{1400 K, the �t is unable to reproduce the source spectralenergy distribution, as shown in panel b. The panels c andd show good quality �ts of a Mira star with relatively hotdust (T1 = 825 K) and an SR star with very low inner shelltemperature (T1 = 270 K).3.3.2 Distribution of Best-�t ParametersThe distribution of best-�t �V and T1 is shown in Figure 9.Sources from Mira and NM subsamples are marked by solidand open circles, respectively (since the di�erences in best-�t parameters between the various subsamples of NM starsare not statistically signi�cant, we consider only Mira/NMsubsamples hereafter). A small random o�set (up to 1/3 ofthe parameter grid step) has been added to each T1 and �V ,in order to separate the sources with identical best �t pa-rameters, which would otherwise appear as a single point onthe diagram. The sources are distributed not randomly butrather along a diagonal strip. The density of sources alongthe strip has a local minimum for T1 �500 K (�V�5) sug-gesting a division into four regions as shown by the thin solidlines. The source counts in the quadrants, labeled clockwisefrom I to IV, are given in Table 4. Although both Mira andNM stars are present along the whole strip, Mira tend toaggregate in the upper right quadrant with higher T1 and�V . On the contrary, NM stars aggregate in the lower leftquadrant with T1 < 500 K and �V < 0.5.c 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 11a) b)

c) d)

Figure 8. An example of model �ts (dashed dotted line) to the IRAS LRS data (solid line) for Mira and NM sources. In panel a theSRb star TY Dra is �tted with a cold dust model (T1 ' 370 K), resulting in a very small �2. When the dust temperature is limitedto the range 640{1400 K, the �t is unable to reproduce the source spectral energy distribution, as shown in panel b. The panels c andd show good quality �ts of a Mira star with relatively hot dust (T1 = 825 K) and an SR star with very low inner shell temperature(T1 = 270 K). Sample I II III IVMira 59 1 32 1NM 72 2 169 1SRa 20 1 26 0Table 4. The source distribution in �V vs. T1 diagram (see Figure9). The strong correlation between the best-�t �V and T1seen in Figure 9 is probably not due to hidden biasing ofthe �tting algorithm (c.f x3.2). Indeed, such correlation isexpected in the interrupted mass loss model as discussedin x3.1. Eq.(8) predicts �V / T 1=�1 = T 2:51 shown as a thickdashed line in Figure 9. The close agreement between thesource distribution and predicted correlation is evident. Fit-ting a power law to the source distribution gives a best-�tpower-law index of 2.8 for Mira stars, and 2.5 for NM stars,consistent with the model prediction, given the uncertaintyof � (�0:05).Another model prediction pertains to the distributionof best-�t T1. For sources in the quiescent phase, eq. (9)predicts dN=dT1 / T�3:51 , or equivalently, dN=dlog(T1) /T�2:51 . The histogram of best-�t T1 is shown in Figure 10for Mira stars (dashed line) and NM stars (solid line). Therelation dN=d log(T1) / T�2:51 is shown as a dotted line,normalized to the NM bin with T1 � 200 K. It is evident thatthe T1 distribution is very di�erent for Mira and NM stars.While this distribution is at for Mira stars, with about 2/3of stars having T1 > 500 K, 2/3 of NM stars have T1 < 500K. These stars closely follow the model prediction for starswhose envelopes are freely expanding after their mass losshas stopped.The low-T1 of the NM distribution in Figure 10 abruptlyends at T1 �200 K although the model grid extends to T1= 100 K. As discussed in IK98, this sharp end may indicatethat the mass loss resumes after the quiescent phase becauseotherwise the envelopes with 100 K < T1 < 200 K shouldbe detected. Eq. (4) implies that the time scale for the en-velope expansion until T1 reaches such a low temperature isof the order 100 years. If the mass loss starts again, in lessthan 10 years the new shell would occupy the region wherethe dust temperature is higher than about 600 K, and thusabout 10% of stars could be in this phase. The only di�er-ence between such a double-shell envelope and a steady-stateenvelope with smooth r�2 dust density distribution is thelack of dust with temperatures in the range 200{600 K. De-tailed model spectra in the spectral range 5-35 �m for suchdouble-shell envelopes show that they are practically indis-tinguishable from spectra obtained for envelopes with r�2dust density distribution.The fraction of NM stars with T1 > 500 K is �1/3.This fraction provides an upper limit for the duration ofhigh mass loss phase of �50 years. However, it would notc 2000 RAS, MNRAS 000, 1{14

12 M. Marengo, �Z. Ivezi�c & G. R. Knapp

Figure 9. The distribution of best-�t �V and T1 for Mira stars (solid circles) and non-Mira stars (open circles). A small random o�set (upto 1/3 of the parameter grid step) has been added to each T1 and �V , in order to separate the sources with identical best �t parameters,which would otherwise appear as a single point on the diagram. The plot is divided in four regions, according to the source segregation;the counts in the four quadrants are given in Table 4.Figure 10. Histogram of best-�t T1 for Mira stars (dashedline) and NM stars (solid line). The dashed line shows relationdN/dlog(T1) / T�2:51 , normalized to the NM bin with T1 � 200K.be surprising if this estimate is wrong by perhaps a factorof 2 since the analysis presented here only provides a lowerlimit on the ratio of mass-loss rates in the high and low massloss phases. Thus, the observations do not strongly excludethe possibility that the duration of both phases may be thesame.

3.4 The Distribution of Mass-loss RatesThe width of the strip formed by the source distributionin the �V vs. T1 diagram (Figure 9) is determined by theintrinsic distribution of mass-loss rates. We calculate mass-loss rates from the best-�t �V and T1 by using_M = �V 3=4 �1000KT1 �2:5 10�6M� yr�1 (11)which is derived by combining eqs. (5-7) and assuming(T1(0)=1000K)2:5 L3=44 (rgd=200)1=2 = 0:5. Figure 11 showsthe histograms of calculated mass-loss rates for Mira stars(dashed line) and NM stars (solid line). The histograms arerather narrow, and furthermore, they are the same withinthe uncertainties, according to F-test and t-test analysis.Such a similarity of mass-loss rates between Mira and NMstars is somewhat surprising because a \standard" result isthat NM stars have several times smaller mass-loss ratesthan Mira stars (e.g. Habing 1996). A plausible explana-tion for the smaller mass-loss rates usually derived for NMstars may be the lack of correction for lower T1 (c.f. eq.11) when converting the envelope optical depth to mass-lossrate. The results presented here indicate that the majorityof both Mira and NM stars have mass-loss rates of the order10�5. An alternative explanation is that the KHc sample ofNM stars is biased towards high mass-loss rates, althoughsuch an e�ect is not expected for their selection procedure.Additional selection criteria employed in this work did nota�ect a su�ciently large number of NM sources to result insuch biasing. It is not possible to distinguish between thosetwo possibilites without a large and unbiased sample withc 2000 RAS, MNRAS 000, 1{14

Mass loss modulations on AGB 13Figure 11. Histogram of derived mass-loss rates for Mira stars(dashed line) and NM stars (solid line).uniformly measured mass-loss rates by an IR-independentmethod (e.g. molecular emission).4 DISCUSSIONThe analysis presented here shows that the observed di�er-ences in infrared emission from oxygen rich AGB stars of dif-ferent variability type are statistically signi�cant. Mira starsand NM stars clearly segregate in the K-[12] vs. [12]-[25]color-color diagram, and also have di�erent detailed prop-erties of their IRAS LRS spectra. We �nd no statisticallysigni�cant di�erences between various subsamples of NMstars. The di�erences between Mira and NM stars are hardto interpret in the context of steady state wind models. Inparticular, these models do not provide satisfactory descrip-tion of the infrared emission from the majority of NM stars.Possible ways to augment these models include changing theshape of stellar spectrum, employing grains with altered ab-sorption e�ciency, or assuming that the majority of NMstars have envelopes without hot dust (>� 500 K).We �nd that the absence of hot dust for NMs is themost plausible way to explain the observations, although theavailable data cannot rule out the possibility that the di�er-ences in circumstellar dust chemistry produce the observeddi�erences in infrared emission. For example, Sloan et al.(1996) found that the \13 micron" feature occurs somewhatmore frequently in SRb stars (75%-90%) than in all AGBstars with silicate dust (40%-50%). On the other hand, thisdi�erence could be simply due to di�erent densities in thedust formation region, as pointed out by Speck et al. (2000).We are in the midst of a detailed study exploring the modelspectra obtained for a large sample of di�erent dust typesand grain size distributions (Helva�ci et al. 2001).We provide detailed analysis of models where the ab-sence of hot dust for NM stars is interpreted as an inter-ruption of the mass loss with time scales of the order 100years, and a drop in the mass-loss rate of at least a fac-tor of 5. In such a case, envelope freely expands and thedust temperature decreases with time. This hypothesis pre-dicts a correlation �V/ T 2:51 between the envelope opticaldepth, �V and the dust temperature at the inner envelope

edge, T1, which we �nd consistent with the data. We �ndthat the model prediction for the distribution of best-�t T1also agrees with the data, although this constraint may beplagued by hidden biases in the sample. We interpret thesharp low-T1 end of the source distribution as evidence thatthe mass loss resumes and estimate the duration of highmass loss phase to be of the same order as the duration ofthe low mass loss phase.The number of Mira stars with low T1 is about 1/3 andit is not clear from the present analysis whether this repre-sents evidence for the interrupted mass loss. It was proposedby Kerschbaum et al. (1996), based on similar number den-sities and scale heights, that AGB stars oscillate betweenNM and Mira phases. This idea was further advanced byIK98 based on their analysis of the source distribution inthe K-[12] vs. [12]-[25] diagram. However, recent results byLebtzer & Hron (1999), who compare the abundance of 99Tcin a large sample of SR stars and Mira stars, seem to ruleout this hypothesis. The 99Tc abundance is characterized bya quick increase during the �rst thermal pulse, after whichit presumably stays constant (Busso et al. 1992). Conse-quently, a similar fraction of Tc-rich stars should be foundin the Mira and SR samples, contrary to the observationsby Lebtzer & Hron who �nd that a fraction of stars with de-tectable Tc is lower for SR stars (15%) than for Mira stars(75 %).While the available observations are consistent with theinterrupted mass loss model, the possibility that observeddi�erences between Mira and NM stars are due to di�erentdust optical properties can not be excluded by consideringphotometric data alone. The most obvious and direct testof the interrupted mass loss hypothesis is mid-IR imaging.When T1 decreases by a factor of two, the inner enveloperadius increases by about a factor of four. Such a di�erenceshould be easily discernible for a few dozen candidate starswith largest angular sizes, which are already within the reachof the Keck telescopes (e.g. Monnier et al. 1998). Molecularline observations can also be used to infer the gas radial den-sity distribution because various lines form at di�erent radii.For example, SiO8-7 (347.3 GHz) line is expected to formmuch closer to the star than, say, CO3-2 (345.8 GHz) line.If SRb/Lb stars really lack material in the inner envelope,they should have lower SiO8-7/CO3-2 intensity ratios thanMiras, provided that the excitation mechanisms are similar.Another, indirect, test can be made by employing mass-lossrates determined in molecular, either thermal or maser ob-servations. For a given mass-loss rate, NM stars should havebluer 12-K color because their dust optical depth becomessmaller as the envelope expands. While this e�ect is not verypronounced (di�erence is about 0.2-0.3 magnitudes), a suf-�ciently large sample might provide statistically meaningfulresults.For a few stars there are available spatially resolvedobservations (c.f. x1) and they seem to indicate mass losschanges with short time scales (< several hundred years).If proven correct, the mass-loss variations on time scale ofabout 100 years would signi�cantly change our understand-ing of the stellar evolution on the AGB since the knowntime scales are either much shorter (stellar pulsations, �1year), or much longer (He ashes, �105 years). However, thetime dependent wind models (Winters 1998) seem to pro-duce mass-loss rate variations with time scales much longerc 2000 RAS, MNRAS 000, 1{14

14 M. Marengo, �Z. Ivezi�c & G. R. Knappthat the pulsation period which drives the mass loss (�1year). These longer time scales are not fully understood (seehowever Deguchi 1997) and seem to result from the complexinterplay between the pulsation and dust formation and de-struction mechanisms. While the theoretically obtained timescales (5{10 years) are shorter than those implied by the ob-servations, the recent developments show that it may be pos-sible to increase the model time scale to �100 yr (WintersJ.M., priv. comm.). It is not clear why would Mira and non-Mira stars exhibit di�erent behaviors, unless the couplingmechanisms are very sensitive to the details of the pulsationmechanism (see e.g. Mattei et al. 1997).Another possibility is that the 100-year mass-loss ratemodulations are caused by the luminosity variations on sim-ilar time scales (Sahai et al. 1998). Recent work based on theanalysis of stars observed by both the IRAS and HIPPAR-COS surveys (Knauer, Ivezi�c & Knapp 2000) shows that theextensive mass loss on the AGB seems to require a thresh-old luminosity of �2000 L�. If the luminosity of non-Mirastars oscillates around this value, then the resulting mass-loss rate would be in agreement with the model assumptionsdiscussed here. Within this hypothesis Mira stars could haveslightly larger luminosities (for perhaps a factor of 2) andexhibit a steady mass loss, a possibility that seems to beconsistent with the P-L relation since Mira stars have some-what longer periods that SR stars (Whitelock 1986).ACKNOWLEDGMENTSWe are grateful to Franz Kerschbaum for providing to usJHKLM data without which this work would have not beenpossible. We thank Martin Jan Winters, Mikako Matsuura,Mathias Ste�en, Janet Mattei, John Monnier, Joseph Hron,Moshe Elitzur, Maia Nenkova, Dejan Vinkovi�c and MustafaHelva�ci for illuminating discussions. We also thank the ref-eree, Angela Speck, for comments which helped us improvethe presentation. This work was partially supported by NSFgrant AST96-18503 to Princeton University.REFERENCESBedding, T.R., Zijlstra, A.A., Jones, A., & Foster, G. 1998, MN-RAS, 301, 1073Bedijn, P.J. 1987, A&A, 186, 136Busso, M., Gallino, R., Lambert, D.L., Raiteri, C.M., & Smith,V.V. 1992 ApJ, 399, 218Busso, M., Origlia, L., Marengo, M., Persi, P., Ferrari-Toniolo,M., Silvestro, G., Corcione, L., Tapia, M., Bohigas, J. 1996,A&A, 311, 253Deguchi, S. 1997, in IAU Symp. 180, Planetary Nebulae, ed. H.Lamers & H.J. HabingDraine, B.T., & Lee H.M. 1984, ApJ, 285, 89Elitzur M., & Ivezi�c, �Z. 2000, submitted to MNRASGilman, R.C. 1969, ApJ, 155, L185Habing, H. 1996, A&A Rev., 7, 97Habing, H.J., Tignon, J., & Tielens, A. G. G. M. 1994, A&A, 286,523Harpaz, A., Rappaport, S., & Soker, N. 1997, ApJ, 487, 809Hashimoto, O., Izumiura, H., Kester, D.J.M., & Bontekoe, Tj. R.1998, A&A, 329, 213Helva�ci, M. et al. 2001, in prep.Hron, J., Aringer, B., & Kerschbaum F. 1997, A&A, 322, 280

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