Exploring wind-driving dust species in cool luminous giants II. Constraints from photometry of M-type AGB stars
Sara Bladh, Susanne Höfner, Walter Nowotny, Bernhard Aringer
AAstronomy & Astrophysics manuscript no. Exploring˙wind-driving˙dust˙species˙in˙cool˙luminous˙giants˙II © ESO 2018October 12, 2018
Exploring wind-driving dust species in cool luminous giants
II. Constraints from photometry of M-type AGB stars
S. Bladh , S. H¨ofner , W. Nowotny , B. Aringer , and K. Eriksson Department of Physics and Astronomy, Division of Astronomy and Space Physics, Uppsala University, Box 516, SE-75120,Uppsala, Swedene-mail: [email protected] University of Vienna, Department of Astrophysics, T¨urkenschanzstraße 17, A-1180 Wien, AustriaReceived October 18, 2012; accepted XXXX, 2012
ABSTRACT
Context.
The heavy mass loss observed in evolved asymptotic giant branch (AGB) stars is usually attributed to a two-stage process:atmospheric levitation by pulsation-induced shock waves, followed by radiative acceleration of newly formed dust grains. The dusttransfers momentum to the surrounding gas through collisions and thereby triggers a general outflow. Radiation-hydrodynamicalmodels of M-type AGB stars suggest that these winds can be driven by photon scattering – in contrast to absorption – on Fe-freesilicate grains of sizes 0.1–1 µ m. Aims.
In this paper we study photometric constraints for wind-driving dust species in M-type AGB stars, as part of an ongoing e ff ortto identify likely candidates among the grain materials observed in circumstellar envelopes. Methods.
To investigate the scenario of stellar winds driven by photon scattering on dust, and to explore how di ff erent optical andchemical properties of wind-driving dust species a ff ect photometry we focus on two sets of dynamical models atmospheres: (i)models using a detailed description for the growth of Mg SiO grains, taking into account both scattering and absorption cross-sections when calculating the radiative acceleration, and (ii) models using a parameterized dust description, constructed to representdi ff erent chemical and optical dust properties. By comparing synthetic photometry from these two sets of models to observations ofM-type AGB stars we can provide constraints on the properties of wind-driving dust species. Results.
Photometry from wind models with a detailed description for the growth of Mg SiO grains reproduces well both the valuesand the time-dependent behavior of observations of M-type AGB stars, providing further support for the scenario of winds driven byphoton scattering on dust. The photometry from the models with a parameterized dust description suggests that wind-drivers need tohave a low absorption cross-section in the visual and near-IR to reproduce the time-dependent behavior, i.e. small variations in ( J – K )and spanning a larger range in ( V – K ). This places constraints on the optical and chemical properties of the wind-driving dust species. Conclusions.
To reproduce the observed photometric variations in ( V – K ) and ( J – K ) both detailed and parameterized models suggestthat the wind-driving dust materials have to be quite transparent in the visual and near-IR. Consequently, strong candidates for outflowsdriven by photon scattering on dust grains are Mg SiO , MgSiO , and potentially SiO . Key words.
Stars: late-type Stars: AGB and post-AGB Stars: atmospheres Stars: mass-loss Stars: winds, outflows, circumstellarmatter, dust
1. Introduction
There is a substantial amount of observational evidence for thepresence of dust in the circumstellar environment of asymptoticgiant branch (AGB) stars, and it has long been argued that theslow winds detected in these stars are caused by radiative accel-eration on dust particles (see, e.g., Wickramasinghe et al., 1966;Gehrz & Woolf, 1971; Sedlmayr, 1994; Habing & Olofsson,2004). In fact, for C-type AGB stars (C / O >
1) there is hardlyany doubt that the outflows are driven by radiation pressure oncarbon grains forming in the cool, extended atmospheres cre-ated by pulsation-induced shock waves. Detailed models of thisscenario show good agreement with a range of observations,i.e. high resolution spectroscopy, photometry and interferometry(e.g. Winters et al., 2000; Gautschy-Loidl et al., 2004; Nowotnyet al., 2010, 2011; Sacuto et al., 2011). For M-type AGB stars(C / O < ffi cult (e.g. Jeong et al., 2003) and itis still a matter of debate which grain species are responsible fordriving the outflows (see, e.g., the discussion in H¨ofner, 2009). Characteristic features of various dust species have been ob-served in the mid-IR (see, e.g., Dorschner, 2010; Molster et al.,2010, for an overview) but few of them fulfill the conditionsnecessary for triggering outflows: (i) able to form in the closevicinity of the star, (ii) consisting of abundant materials and (iii)large radiative cross-sections in the near-IR (for a more detaileddiscussion see Bladh & H¨ofner, 2012, hereafter referred to asPaper I).Magnesium-iron silicates, i.e. olivine ([Mg,Fe] SiO ) andpyroxene ([Mg,Fe]SiO ), are commonly considered strong can-didates for wind-drivers in M-type AGB stars. A high abun-dance of silicates in the circumstellar envelopes can be deducedfrom observations of characteristic features at 9.7 µ m and 18 µ m(e.g. Woolf & Ney, 1969; Low & Swamy, 1970; Molster et al.,2002). While such mid-IR features are important for identifyingindividual dust species it is, however, the optical dust propertiesin the near-IR that are critical for the wind mechanism, since The 9.7 µ m band is due to a stretching resonance in Si-O, while the18 µ m band is caused by a bending mode in the SiO tetrahedron. 1 a r X i v : . [ a s t r o - ph . S R ] F e b . Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. most of the stellar radiation is emitted in this region. For silicategrains the absorption e ffi ciency in the near-IR is strongly de-pendent on the Fe-content and silicate materials at the Mg-richend are very transparent to near-IR radiation. Using frequency-dependent wind models with a detailed treatment of dust forma-tion, Woitke (2006) demonstrated that silicate grains have to beessentially Fe-free in the close vicinity of the star; Fe-bearingsilicates heat up when interacting with the radiation field and aretherefore not thermally stable close to the stellar surface. Thelow near-IR absorption cross-sections of Fe-free grains are notsu ffi cient to trigger outflows, which raised doubts about the sce-nario of dust driven winds in M-type AGB stars.In response to the findings by Woitke (2006), H¨ofner (2008)suggested that the outflows in M-type AGB stars may be drivenby photon scattering on Fe-free silicates. This scenario requiresgrains of sizes about 0.1–1 µ m, comparable to the wavelength ofthe stellar flux maximum, in order for scattering to be e ffi cient.Recently, Norris et al. (2012) detected dust particles of sizes ∼ . µ m in the close circumstellar environment of three M-typeAGB stars, using multi-wavelength aperture-masking polarimet-ric interferometry in the near-IR. The dust grains produce a haloof scattered light around the star with a polarization tangentialto the stellar surface, which can be resolved with interferometricmeasurements. Their results provide strong observational sup-port that grains can grow to sizes required for triggering out-flows. Further confirmation of silicate grains in the close stellarenvironment is provided by recent mid-IR interferometric ob-servations of RT Vir (Sacuto et al., 2013). However, measure-ments at such long wavelengths are not sensitive to the grainsize. Stellar winds driven by photon scattering on Fe-free sili-cate grains result in very low circumstellar reddening due to thetransparency of this material in the near-IR wavelength region.The low degree of stellar radiation thermally reprocessed by thedusty envelope could explain why earlier dynamic models with-out wind (e.g. Tej et al., 2003) reproduce observed visual andnear-IR spectra and photometry reasonably well.In order to further test the scenario of stellar winds drivenby photon scattering on silicate grains we here present syntheticphotometry and spectra for the set of models in H¨ofner (2008)and compare them with photometric observations of M-typeAGB stars. Most evolved AGB stars belong to the group of longperiod variables (LPVs) and the photometric magnitudes andcolors change with pulsation phase. A comparison of the lightvariations of observed targets with the corresponding modelingresults can help us test the dynamical models. To understand ifthe photometry resulting from these models is a trivial result, i.e.a generic property of the models, or determined specifically bythe grain properties of Mg SiO , we also consider another set ofmodels that use a parameterized dust description, constructed torepresent di ff erent chemical and optical dust properties. This setof models, first presented in Paper I, allows us to investigate howdi ff erent dust properties will a ff ect the photometry and spectra.In Paper I we focused on dynamical criteria when searchingfor possible wind-driving dust species in M-type AGB stars, i.e.what combination of optical and chemical properties are neces-sary for a dust species to be able to form close enough to the starto initiate mass outflows. Here, on the other hand, we explorethe resulting spectra and photometry of the dynamical models,i.e. what optical properties the wind-driving dust species need topossess to achieve agreement with observations.The paper is organized in the following way: in Sect. 2 weintroduce the atmosphere and wind model and the two di ff erentdescriptions for the dust component. In Sect. 3 we present theparameters used in the models of H¨ofner (2008) and the models included from Paper I, respectively, and also wind properties ofindividual models. A description concerning the details of thespectral synthesis is given in Sect. 4, the observational data setsare presented in Sect. 5 and the photometric results from the dif-ferent model sets are given in Sects. 6–7. We comment on spe-cific dust species in Sect. 8 and in Sect. 9 we provide a summaryof our conclusions.
2. Modeling of atmosphere and wind
The dynamical models cover a spherical shell with an innerboundary situated just below the photosphere and an outerboundary located at the point where the wind velocity hasreached its terminal value, i.e. around 20–30 R ∗ . The variablestructures of the atmospheres are described by the equations ofhydrodynamics (equation of continuity, equation of motion andenergy equation) and the pulsations are simulated by temporalvariation of physical quantities at the inner boundary. The opac-ities of molecules and dust which form in the outer cool layersof the atmospheres dominate the radiation field, and in order toachieve realistic density–temperature structures the models in-clude a frequency-dependent treatment of the radiative transfer(see H¨ofner et al., 2003; H¨ofner, 2008, and Paper I for more de-tails). The models feature two di ff erent descriptions for the dustcomponent: (i) a time-dependent description for the growth ofMg SiO grains with a grain-size dependent treatment of theoptical properties (see Sect. 2.1) or (ii) a parameterized dustdescription based on a simplified treatment of both the graingrowth and the optical properties (see Sect. 2.2). In both casesthe detailed dynamical models produce snapshots of the radialstructure of the atmosphere, and thereby provide informationabout properties such as velocity, temperature, density and de-gree of condensation for the dust component as a function ofradial distance and time. In the models presented by H¨ofner (2008), the growth of pureforsterite particles (Mg SiO ) is modeled according to the netreaction2Mg + SiO + O −→ Mg SiO + , (1)under the assumption that the step determining the total growthrate is the addition of SiO molecules to the grain surface. Theequation describing the growth and decomposition of Mg SiO grains follows Gail & Sedlmayr (1999) and is given by da gr dt = V Mg SiO (cid:104) J grSiO − J decSiO (cid:105) = V Mg SiO α SiO v SiO n SiO − p v , SiO n SiO kT g (cid:115) T g T d , (2)where a gr is the grain radius, assuming spherical grains. J grSiO and J decSiO denote the growth and decomposition rate of SiO moleculesper grain surface area, V Mg SiO is the volume of the monomer In this context the stellar radius is defined by R ∗ = (cid:112) L (cid:63) / πσ T (cid:63) ,where L (cid:63) is the luminosity and T (cid:63) is the e ff ective temperature of thestar. The inner boundary is situated typically a few percent below thispoint. Note that this equation is given here in the co-moving frame, in con-trast to the di ff erential equations of radiation-hydrodynamics in Paper I.2. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. ! [ µ m]0.00.20.40.60.81.0 g s c a a gr = 0.01 µ ma gr = 0.30 µ ma gr = 0.40 µ ma gr = 0.50 µ ma gr = 0.60 µ ma gr = 0.70 µ m1 10 ! [ µ m]10 -10 -8 -6 -4 -2 Q QscaQabs
Fig. 1.
Optical properties of spherical Mg SiO grains as afunction of wavelength, calculated for grain radii varying be-tween 0 . − . µ m, as well as grains in the small particle limit( a gr = . µ m, black curves). These properties were calculatedfrom optical data by J¨ager et al. (2003), using Mie theory. Theshaded area marks the region where most of the stellar flux isemitted. Top panel:
The asymmetry factor g sca . Bottom panel:
The absorption and scattering e ffi ciencies, Q abs and Q sca , heresmoothed to avoid unrealistic resonances inherent to Mie theory.(the basic building block of the grain material), α SiO is a stick-ing coe ffi cient, v SiO is the thermal velocity of the SiO molecules, n SiO is the number density of SiO molecules in the gas and p v , SiO is the hypothetical partial pressure of SiO molecules in chem-ical equilibrium between the gas phase and the solid. For theatmospheres of M-type AGB stars there is currently no well-established nucleation theory. For simplicity we assume the ex-istence of seed particles that start to grow when the atmosphericenvironment favors grain growth. This will result in a uniformgrain size for all dust particles at a given distance from the stel-lar surface.The output of the equation describing the grain growth(Eq. (2)) is the grain radius a gr at a given distance and time. IfMg SiO particles grow to grain radii comparable to the wave-length of the flux maximum, the contribution to the radiative ac-celeration from the scattering cross-section is substantial, dom-inating over true absorption by several orders of magnitude, ascan be seen in the lower panel of Fig. 1. To include the contribu-tion from photon scattering in the radiative acceleration, i.e. inthe opacity entering the equation of motion (see Sect. 3.1 Paper I), we calculate the grain-size dependent dust opacity per massaccordingly κ acc ( λ, a gr ) = A mon ρ gr Q acc ( λ, a gr ) a gr ε Si + ε He f c , (3)see Sect. 2.1 in Paper I for details. Here A mon is the atomic weightof the monomer, ρ gr the bulk density of the grain material, ε Si and ε He the abundances of silicon and helium, respectively, and f c the degree of condensation. The e ffi ciency Q acc ( λ, a gr ), i.e. theradiative cross-section divided by the geometrical cross-sectionof the grain, is defined by Q acc = Q abs + (1 − g sca ) Q sca (4)where Q abs and Q sca are the e ffi ciencies of absorption and scat-tering, respectively, and g sca is the asymmetry factor describingdeviations from isotropic scattering (a value of zero indicatesisotropic scattering and a value of one pure forward scatter-ing). These quantities can be computed from optical data, usingMie theory (program BHMIE from Bohren & Hu ff man, 1983,modified by Draine). Figure 1 shows the absorption and scat-tering e ffi ciencies, as well as the asymmetry factor, as a func-tion of wavelength for forsterite grains of di ff erent sizes. As canbe seen, grains in the size range 0 . − . µ m (relevant for themodels in set D) lead to predominantly forward scattering in thewavelength region where most of the stellar flux is emitted. Thismeans that only a fraction of the scattering events will transfermomentum to the dust particles, which is taken into account bythe factor (1 − g sca ) in Eq. 4, and consequently in the equation ofmotion.The degree of condensation, i.e., the fraction of siliconbound in dust compared to the total amount of silicon, can becomputed from the grain radius a gr (given by (Eq. (2)), the vol-ume of the monomer V Mg SiO , the abundance of seed particles n gr / n H and the elemental abundance of silicon ε Si , f c ( r , t ) = π a ( r , t )3 1 V Mg SiO n gr n H ε Si . (5)The only free input parameter in this model for grain growthis the abundance of seed particles. Generally, within the rangewhere observable wind properties are still reproduced, a lowerabundance of seed particles will result in condensates with largergrain radius, due to less competition in accumulating the sur-rounding material, whereas a higher abundance of seed particleswill produce smaller grains.
In Paper I we introduced a parameterized dust description in or-der to systematically study the e ff ects of a range of optical andchemical dust properties on the dynamics and the spectral energydistribution of the model atmospheres. The formula uses a sim-plified description of grain growth, expressed in terms of f c , incombination with a wavelength-dependent power-law functionˆ κ ( λ ) describing di ff erent optical properties κ acc ( λ ) = ˆ κ ( λ ) · f c ( r , t , T c ) . (6) This quantity is defined here as the number of grains per hydrogennucleus, expressed as the ratio of the number density of grains to thetotal number of hydrogen particles per volume of atmosphere. 3. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. ! [ µ m]10 Q / a [ c m - ] p=2.4p=1.7 p=1.2p=-0.9p=-0.5 amCFeMgFeSiO Mg SiO MgSiO Fig. 2. E ffi ciency per grain radius Q acc / a gr in the small particlelimit, as a function of wavelength, for a selection of dust species.The dashed lines show the power law fit corresponding to Eq. (8)and the shaded area indicates the wavelength region for whichthe optical data is fitted (for references to the sources of opticaldata see Table 3).Our description was inspired by a formula used by Bowen(1988) in his dust driven wind models, but is generalized to allowfor wavelength-dependent optical properties. The degree of con-densation f c describing the grain growth is designed to increasemonotonically with falling grain temperature, approaching unityas the grain temperature T d drops well below the condensationtemperature T c of the condensate. f c ( r , t , T c ) = + e ( T d ( r , t ) − T c ) / ∆ T (7)Given the low density of the circumstellar environment and theproximity to a strong radiation source, the grain temperature isassumed to be determined by radiative equilibrium rather thancollisions with gas particles. Because of the varying radiationfield the grain temperature is a function of both time and distancefrom the star. The parameter ∆ T regulates the width of the dustformation zone (see Fig. 3 of Paper I).The optical properties of the dust material are modeled by apower-law functionˆ κ ( λ ) = κ (cid:32) λλ (cid:33) − p , (8)where p is obtained by fitting a power-law to the e ffi ciency pergrain radius Q acc / a gr , assuming small particles, in the wave-length region where most of the stellar flux is emitted (see theshaded area in Fig. 2). In this expression κ is a scaling factorsuch that ˆ κ ( λ ) = κ .To distinguish between e ff ects of scattering and true absorp-tion of photons on dust grains we further introduce a quantity f abs which sets the percentage of the dust opacity κ acc that is tobe considered as true absorption κ abs ( λ ) = f abs · ˆ κ ( λ ) · f c ( r , t ) where f abs = κ abs κ acc (9)The dust opacity κ acc , which includes contributions from bothtrue absorption and scattering, is used to calculate the radiativeacceleration in the equation of motion, and the true absorptionpart κ abs is used to determine the grain temperature. This allowsus to separate the dynamical and thermal e ff ects of the dust opac-ity, and the parameter f abs can be adjusted to explore the e ff ectsof varying degrees of true absorption. l o g ( d M / d t [ M S u n / y r ]) Observations of M-type AGB stars
Model A2
Model A3Model B1Model B2Model B3Model C1 l o g ( d M / d t [ M S u n / y r ]) fabs=1.0 p=-1.00p=-0.75p=-0.50p=-0.25p=0.00p=0.25p=0.50p=0.75p=1.00p=1.25-1.50 l o g ( d M / d t [ M S u n / y r ]) fabs=0.5 p=-1.00p=-0.75p=-0.50p=-0.25p=0.00p=0.25p=0.50p=0.75p=1.00p=1.25p=1.50-2.50 Fig. 3.
Observed mass-loss rates vs. wind velocities of M-typeAGB stars (Olofsson et al., 2002; Gonz´alez Delgado et al., 2003,plus signs) and the corresponding properties for the dynamicalmodels (filled circles).
Top panel: dynamical properties of themodels in set D.
Middle and bottom panel: dynamical proper-ties of the models in set P, color-coded according to p -value.Generally, within a set of models with same p (e.g. the darkgreen sequence with p = − .
75) the mass-loss rate increaseswith increasing condensation temperature. For a more detaileddiscussion on the dynamical properties of model set P, see PaperI.
3. Dynamical models: parameters and properties D etailed dust description This set of dynamical model atmospheres (DMAs) was first pre-sented in H¨ofner (2008) and is here expanded to include a modelwith more extreme stellar parameters in order to investigate the
4. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II.
Table 1.
Model parameters, dynamical properties and dust characteristics for the models in set D.
DMA M (cid:63) L (cid:63) T (cid:63) P ∆ u p n gr / n H (cid:104) ˙ M (cid:105) (cid:104) u (cid:105) (cid:104) f Si (cid:105) (cid:104) a gr (cid:105) [ M (cid:12) ] [ L (cid:12) ] [K] [d] [km / s] [ M (cid:12) / yr] [km / s] [ µ m]A2 1 5000 2800 310 4.0 1 × − × − × − × −
10 0.22 0.36B1 1 7000 2700 390 4.0 3 × − × − × − × − × − × −
11 0.20 0.34C1 1 10000 2600 525 4.0 3 × − × − Notes.
Columns 2–7 list the input parameters of the models: mass M (cid:63) , luminosity L (cid:63) , e ff ective temperature T (cid:63) , period P and piston velocityamplitude ∆ u p and the assumed seed particle abundance n gr / n H . Columns 8–9 list the resulting wind and dust properties properties: mass-loss rate (cid:104) ˙ M (cid:105) , terminal wind velocity (cid:104) u (cid:105) , degree of condensation (cid:104) f Si (cid:105) of the key element Si and grain radius (cid:104) a gr (cid:105) . Note that the resulting wind and dustproperties are temporal means as indicated by the angular brackets. The optical data ( n , k ) for Mg SiO are taken from J¨ager et al. (2003). the e ff ects of a higher mass-loss rate (model C1 in Tab 1). Themodels include a detailed description for the growth of Mg SiO grains (see Sect. 2.1) and take into account the e ff ects of photonscattering on dust particles when calculating the radiative ac-celeration. The outflows produced in these models are, in fact,driven by scattering of stellar photons on grains with radii be-tween 0.1–1.0 µ m, not by true absorption (which is negligible inthis context).The stellar parameters for the di ff erent models (denoted bythe letters A–C) are listed in columns 2–4 in Table 1. The pe-riod in column 5 follows the period–luminosity relation fromFeast et al. (1989). The piston velocity amplitude (column 6)used to simulate pulsations at the inner boundary was set to4 km / s, a reasonable value when comparing with observationsof molecular lines forming in the inner atmospheric region(Nowotny et al., 2010). The only free input parameter in thedescription for grain growth, the abundance of seed particles n gr / n H (denoted by the number in the model name) is listed incolumn 7. The resulting dynamical properties and dust charac-teristics are listed in columns 8–11.Observed mass-loss rates versus wind velocities of M-typeAGB stars (derived from profiles of CO radio lines, Olofssonet al., 2002; Gonz´alez Delgado et al., 2003) and the correspond-ing properties of the models in set D are shown in the top panelof Fig. 3. Note that the models with stellar parameters accordingto combinations A and B, already presented in H¨ofner (2008),agree reasonably well with observations, whereas model C1,added here for studying the e ff ect of a higher mass-loss rate, isfurther away from the region covered by the observational sam-ple. P arameterized dust description This set of dynamical model atmospheres was first presented inPaper I and is here restricted to models that produce outflows(see the colored area in Fig. 4 and 8 of Paper I). All dynamicalmodels in this set have the same stellar parameters: a stellar massand luminosity of 1 M (cid:12) and 5000 L (cid:12) , respectively, an e ff ectivetemperature of 2800 K and solar abundances (corresponding toModel A in set D). The piston velocity amplitude was set to 4km / s.To investigate the dynamical e ff ects of di ff erent chemical andoptical dust properties we vary the input parameters p and T c inthe formula for the parameterized dust opacity (see Eqs. 7-9). Tocover the most probable combinations we let p vary from -1.0to 2.5 and T c from 700 K up to 1700 K, in increments of 0.25and 100 K respectively, resulting in a total of 165 individual dy- namical models, of which we select a subsample of 85 modelsthat actually produce outflows. The parameter ∆ T that adjuststhe width of the dust formation zone is set to 100 K. This valuewas chosen by comparing with the typical width of the dust for-mation zone for the models A in set D. In addition to p and T c ,we also vary the degree to which the dust opacity is consideredtrue absorption by setting the parameter f abs to 1.0 and 0.5 re-spectively (100% and 50% true absorption).The critical dust opacity, κ crit = π cGM (cid:63) / L (cid:63) , needed for theradiative acceleration to overcome the gravitational accelerationis equal to 2.6 cm / g for the chosen set of stellar parameters.We set κ = . / g when p = p so that the flux-averaged dust opacity (cid:104) κ (cid:105) H remains fixed. By setting κ such that (cid:104) κ (cid:105) H > κ crit an outflowwill be triggered in these dynamical models if the atmosphericenvironment is such that it allows for grain growth close enoughto the stellar surface ( f c ≈ f abs = . f abs = .
5, respectively. The smaller spread inwind velocity noticeable in the models with a smaller fractionof true absorption ( f abs = .
5) is due to a less pronounced red-dening of the radiation field when the dust component absorbsless of the stellar flux (for a detailed discussion on the trends inmass-loss rates and wind velocities for the models in set P, seePaper I).
4. Spectral synthesis and photometry
We calculate spectra and photometry for set D and P, i.e. the dy-namical models that include a detailed description of Mg SiO grains (set D) and the models using a parameterized dust de-scription (set P), by sampling 16 snapshots of the radial structureduring a typical pulsation cycle, equidistant in phase. The a pos-teriori radiative transfer was computed with opacities from theCOMA code (Aringer, 2000) resulting in an opacity samplingspectrum with a resolution of R = . µ m and 25 µ m for each snapshot.Based on these data we compute photometric filter magnitudes,following the Bessell system (described in Bessell & Brett,1988; Bessell, 1990), and low resolution spectra (R =
5. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II.
Table 2.
Dynamical properties of the models in set P with pa-rameterized dust opacity. The table shows mass-loss rate (cid:104) ˙ M (cid:105) and terminal wind velocity (cid:104) u (cid:105) , in addition to the combination of p and T c used in the parameterized dust description. f abs = . f abs = . p T c (cid:104) ˙ M (cid:105) (cid:104) u (cid:105) (cid:104) ˙ M (cid:105) (cid:104) u (cid:105) [K] [ M (cid:12) / yr] [km / s] [ M (cid:12) / yr] [km / s]P01 -1.00 1100 7 × −
13 - -P02 -1.00 1200 2 × −
15 2 × − × −
16 5 × − × −
18 9 × − × −
19 2 × − × −
20 3 × − × −
20 3 × − × −
13 - -P09 -0.75 1300 2 × −
15 3 × − × −
16 7 × − × −
18 1 × − × −
19 2 × − × −
19 3 × − × −
13 2 × − × −
15 5 × − × −
16 1 × − × −
17 2 × − × −
18 3 × − × −
11 - -P20 -0.25 1400 3 × −
13 3 × − × −
14 9 × − × −
16 2 × − × −
16 3 × − × −
11 2 × − × −
13 6 × − × −
14 2 × − × −
15 3 × − × −
11 - -P29 0.25 1500 4 × −
12 4 × − × −
12 1 × − × −
13 2 × − × −
10 2 × − × −
11 9 × − × −
11 2 × − × − × − × −
10 6 × − × −
10 2 × − × − × − × − × − × − × − × − × − × − × − × − × − × − × − × − Notes.
Columns 3–4 lists the dynamical properties for the models with f abs = . f abs = .
5. For the combination of p and T c where nomass loss or wind velocity is listed, the corresponding model failed toproduce an outflow. Note that the resulting wind and dust properties aretemporal means as indicated by the angular brackets. (J- K ) Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)M-type COMARCS models (Aringer)Windless model
Fig. 4.
Color-color diagram containing observational referencedata for comparison with the models, adopted from di ff erentsources: Galactic Bulge Miras (Groenewegen & Blommaert,2005, grey squares), field M-type LPVs (Mendoza, 1967, reddiamonds), and C-rich giants (Bergeat et al., 2001, green tri-angles). Over-plotted are the locations of simulated blackbodyemitters in the range of T (cid:63) = − L (cid:63) = L (cid:12) , T (cid:63) = M = M (cid:12) ,are plotted in blue and the static initial model in orange (dia-mond).In the a posteriori radiative transfer the micro-turbulence pa-rameter was set to ξ = . / s, which is in agreement with thevalue used for the gas opacities in the dynamical models. Thetreatment of the opacities is also consistent with the computationof the atmospheric structures concerning the included atomic,molecular and solid-state sources. For the elemental abundanceswe assume solar values following Grevesse & Anders (1989),except for C, N and O where we took the data from Grevesse &Sauval (1994), and we take into account the depletion in the gasphase caused by dust formation. Information about the speciesincluded in the radiative transfer, and the line lists, can be foundin Aringer et al. (2009). Note that in this work we used only thedata of Barber et al. (2006) for H O.Scattering on dust particles can have a significant e ff ect onthe momentum of individual grains and is therefore taken intoaccount when calculating the wind dynamics (see Sect. 2.1).However, it should be mentioned that we do not consider scat-tering on dust particles when solving the radiative transfer. Forthe models in set D the fraction of light scattered by dust parti-cles is small compared to the radiative flux emitted by the starand the scattered photons will not noticeably change the overallradiation field. In fact, scattering of photons in a spherical andunresolved circumstellar shell does not lead to changes in theobserved colors, regardless of the wavelength-depedence of thescattering opacity. This can be understood most easily by consid-ering total energy conservation for a spherical object observedfrom arbitrary viewing angles.
5. Comparative observational data
To gain insight into how di ff erent dust properties a ff ect the spec-tral energy distribution we compare synthetic colors from thesets D and P to observations, not only in the dust-feature rich
6. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. -1012 KJ (cid:113) v m [ m a g ] V Fig. 5.
Observed photometric variations of the M-type MiraRR Sco in di ff erent filters. Measurements from di ff erent periodsare merged into a combined light cycle and each data point isplotted twice to highlight the periodic variations. Sine fits areover-plotted with dotted lines. For references to the observa-tional data, see Sect. 5.mid-IR region, but also in the visual and the near-IR part of thespectra. The interest in the visual band is motivated by the ob-served di ff erences in spectra between M-type and C-type AGBstars in this wavelength region, but also by how di ff erent theabsorption cross-sections are for the main wind-driving candi-dates in these two types of stars (i.e. amorphous carbon and Fe-free silicates for C-type and M-type AGB stars, respectively; seeFig. 2). Consequently we use the color-color diagram ( J – K ) vs.( V – K ) for a detailed analysis of the modeling results and fortesting against selected reference observations. Since most AGBstars show noticeable photometric variability, simultaneous ob-servation in all three bands would ideally be required for sucha study. However, simultaneous data in the visual and the near-IR are only sparsely available in the literature and we thereforecompile data from various sources to estimate ( V – K ) values forthis color index. Figure 4 shows the resulting compilation.The largest and most important group of targets in this fig-ure consists of M-type Miras identified in the galactic bulgeby Groenewegen & Blommaert (2005) while exploiting thephotometric variations provided by the OGLE survey. The au-thors cross-correlated their list of Miras with the 2MASS cat-alogue and provide the resulting single-epoch JHK photome-try. The latter is used in this work after de-reddening accord-ing to Matsunaga et al. (2005) and converting the magnitudesto the Bessell system following Carpenter (2001). In addition,Groenewegen & Blommaert (priv. comm.) cross-correlated theirtarget list with the OGLE “photometric maps” (Udalski et al.,2002) and provided mean V magnitudes, which we de-reddened according to Sumi (2004). Both kinds of data can subsequentlybe merged to estimate ( V – K ) colors. Note that the flux varia-tions in the K band are much smaller than in the V band (see,e.g., Fig. 5) and the uncertainties of color indices based onsingle-epoch data for the K magnitudes should be within lim-its. A few other data sets are also shown in Fig. 4. Mendoza(1967) presented multi-color photometry for a number of LPVsand we adopted values for the M-type subsample from theirTable 3 and transformed the magnitudes following the relationsgiven in Bessell & Brett (1988). For illustration we also over-plotted the observed photometry compiled by Bergeat et al.(2001), representing C-rich giants with moderate properties con-cerning variability and mass loss (cf. Nowotny et al., 2011).Additionally, we show the evolutionary track of a typical solar-like star (1 M (cid:12) , Z (cid:12) ) based on synthetic evolutionary models(Marigo & Girardi, 2007; Marigo et al., 2008) and hydrostaticCOMARCS model atmospheres (Aringer et al., 2009), using thesame approach to compute synthetic photometry as in this work.Most evolved AGB stars belong to the group of LPVs andthe photometric magnitudes and colors – e.g., the ones in Fig. 4– change with pulsation phase. A comparison of the light varia-tions of observed targets with the corresponding modeling re-sults would be very valuable for constraining the modelingmethod. Unfortunately, no systematic photometric monitoring ofM-type LPVs simultaneously covering visual and near-IR mag-nitudes has been performed so far. We make an attempt to rem-edy this situation by using the same approach as outlined in de-tail in Nowotny et al. (2011) for the C-type Mira RU Vir. In or-der to use this method the targets must have reasonably regularlight-curves (which we checked with the help of data from theAAVSO database ) and time-series photometry in various bandsshould be available. We ended up with a list of seven M-typeMiras (R Car, R Hya, R Oct, R Vir, RR Sco, T Col, and T Hor).For these objects we adopted photometric data in the visual fromEggen (1975) as well as Mendoza (1967), and complementedthose with the near-IR data published by Whitelock et al. (2000).The observed photometric measurements were combined intoone composite light cycle as described in Nowotny et al. (2011),the phase information needed for this merging was again deter-mined on the basis of AAVSO visual light-curves. This resultedin combined light-curves as can be seen in Fig. 5. Based on a sinefit to the latter we can derive characteristic photometric varia-tions, even for filter combinations where no simultaneous obser-vations were obtained, as for example the desired ( V – K ) color.The loops produced by the selected M-type Miras in the color-color diagram chosen for our comparison can be seen in the toppanels of Fig. 6. To illustrate the strong di ff erence in the visualand near-IR colors, we also include the results for the C-typeMira RU Vir from Nowotny et al. (2011).
6. Photometry of the models in set D
Realistic dynamical model atmospheres of M-type AGB starsshould be able to capture the time-dependent photometric vari-ations seen in the top panels of Fig. 6, something hydrostaticmodels are unable to do, even if they might produce similarcolors as a variable object at a given time-instance. In order tocompare photometry from our dynamical models with observedphotometric variations we calculate synthetic spectra, and subse-quently photometric fluxes, for the wind models in set D, cover-ing a full pulsation cycle. The resulting colors can be seen in the http: // / data / lcg 7. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. (J- K ) RR ScoR CarR HyaR OctR VirT ColT HorRU Vir (C-type) (J- K ) (J- K ) Model A2Model A3Model B1Model B2Model B3Model C1 (J- K ) (J- K ) Model A2Model A3Model B1Model B2Model B3Model C1 (J- K ) Fig. 6.
Observed and synthetic photometric variations of M-type Miras (and one C-type Mira RU Vir, which is included for illus-tration purposes).
Top panels:
Photometric variations for the sample of observed targets, derived from sine fits of light-curves (seetext in Sect. 5 for details).
Middle panels:
Photometric variations for the dynamical models in set D.
Bottom panels:
Photometricvariations for the dynamical models in set D, with colors calculated from sine fits of the light-curves, same as for the observationaldata in the top panels. The right panels show the same content, zoomed in and centered on the color loops. For comparison, we alsoshow the observational data of Fig. 4middle panels of Fig. 6. The lower panels of Fig. 6 also show thecolors for the models in set D, but in this case calculated fromsine fits of the synthetic light-curves in the V , J and K bands.This is done in the same way as for the observational data (seeSect. 5 and Fig. 5) in order to facilitate the comparison betweenthe observed and synthetic photometry.As demonstrated by Fig. 6, the models in set D show sim-ilar behavior as the observed targets in the colors ( J – K ) and ( V – K ), with loops occupying e ff ectively the same range in thecolor-color diagram. Most noticeable, both observed and syn-thetic photometry show large variations in ( V – K ) and smallvariations in ( J – K ) during a pulsation cycle. A closer exami-nation of the synthetic photometry reveals that the variations in( V – K ) are largest for the dynamical models with stellar parame-ters according to combination A, followed by B and then C. Thevariations in ( J – K ) are very similar for all models, except for
8. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. ! [ µ m]10 " L " [ e r g / s ] Model A2
V I J H K L M ! [ µ m]10 " L " [ e r g / s ] Model A3
V I J H K L M ! [ µ m]10 " L " [ e r g / s ] Model B1
V I J H K L M ! [ µ m]10 " L " [ e r g / s ] Model B2
V I J H K L M ! [ µ m]10 " L " [ e r g / s ] Model B3
V I J H K L M ! [ µ m]10 " L " [ e r g / s ] Model C1
V I J H K L M
Fig. 7.
Spectra of the DMAs in set D, during a luminosity maximum (upper curve) and a luminosity minimum (lower curve). Foridentification of molecular features, see Fig. 8.the model C1. This is a consequence of the high mass-loss ratecombined with the relatively low wind velocity, resulting in ahigher density in the wind-acceleration zone than for the modelsA and B (since ˙ M ∝ ρ u ). A higher density will cause more of thestellar radiation to be thermally reprocessed by the circumstellarmatter, and consequently, slightly redder values for ( J – K ).To understand what is causing the temporal variations incolor, we plot the spectra of the models in set D during luminos-ity extremes (minimum and maximum, respectively) in Fig. 7.It is clear from these spectra that the flux variations during lu-minosity extremes are larger in the V band than in the J and K band and that the variations in ( V – K ) will be dominated by thechanges in the visual flux. The flux variations in the J and K bands during luminosity extremes are of the same magnitude,leading to small variations in ( J – K ). In the visual wavelength region the molecular features aremostly due to TiO, whereas H O features have a strong impact inthe near-IR wavelength region (see the relevant molecular con-tributions in Fig. 8). However, H O does not produce any deepfeatures in the K and J band since the filters are designed toavoid atmospheric water vapor. The strong influence of TiO onthe V band, on the other hand, is noticeable in the spectra shownin Fig 7. The variations in the visual band are most pronouncedin the models A2 and A3. Figure 9 shows the abundance of TiOas a function of distance from the star, indicating the distancewhere the optical depth τ = / V band with verticallines. It is clear that the abundance of TiO varies strongly at thisdistance during a pulsation cycle in model A3, while no signifi- The distance from the star where τ = / R V ( τ = / = (cid:82) F V ( λ ) R λ ( τ = / d λ/ (cid:82) F V ( λ ) d λ . Here F V
9. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. cant variation occurs in model B3 and C1. The lower concentra-tion of TiO during the luminosity maximum, and consequentlythe larger variations in ( V – K ), is caused by the higher e ff ectivetemperature of model A3 (see Table 1).As mentioned in Sect. 3.1, the outflows of the models inset D are driven by photon scattering on Mg SiO grains witha very low absorption cross-section in the visual and near-IR.The scattering is predominantly forward oriented for the grainsizes produced in these models (see Fig. 1), and the spectral en-ergy distribution will not be a ff ected significantly. As a resultwe see strong molecular features in the visual band and weakcircumstellar reddening, i.e. not much of the stellar radiation isthermally reprocessed by the dust particles. Consequently, thetransparent circumstellar envelope will lead to small variationsin ( J – K ) and large variations in ( V – K ). The striking similaritybetween the observed photometric variations and the syntheticphotometry gives support for stellar winds driven by photon scat-tering on dust grains. The fact that hydrostatic COMARCS mod-els (see Fig 4), as well as dynamical model atmospheres withoutwind (e.g. Tej et al., 2003), produce colors very similar to ob-served M-type AGB stars may be taken as another indicationthat the circumstellar envelopes are quite transparent. This is notthe case for C-type AGB stars, where objects with even moder-ate mass-loss rate show noticeable circumstellar reddening dueto dust absorption (e.g. Nowotny et al., 2011).
7. Photometry of the models in set P
At this point the question arises if the shape, location and tiltof the photometric variations discussed above are generic prop-erties of dynamical models, or to what degree they do giveconstraints on the chemical composition and absorption cross-section of the grain material driving the wind. In order to inves-tigate how photometric data is influenced by di ff erent optical andchemical properties of a hypothetical wind-driving dust species,we calculate photometry and spectra for the dynamical modelsin set P. The resulting colors of the models in set P, averaged over phaseand color-coded according to p -value, are plotted in Fig. 10.The averaged colors for the dynamical models in the grid with f abs = . p (cid:38) .
25, are unlikelywind-drivers for M-type AGB stars. The resulting colors are toored, both in ( V – K ) and ( J – K ), compared to the bulk of the ob-served values and in particular compared to the well-observedset of Miras in the top panel of Fig. 6. Similar criteria are validfor the grid with f abs = . J – K ) forboth grids: the two highest ’arcs’, corresponding to models with T c = − ff erent areas in thecolor-color plots for the two di ff erent values of f abs . This canbe explained by the fact that more of the stellar radiation isthermally reprocessed by dust particles (i.e. absorbed at shorter is the filter function for the V band and R λ is the distance from the starwhere τ = / λ . l o g ( P / P g a s ) model A3 H O (min)H O (max)TiO (min)TiO (max) l o g ( P / P g a s ) model B3 H O (min)H O (max)TiO (min)TiO (max) l o g ( P / P g a s ) model C1 H O (min)H O (max)TiO (min)TiO (max)
Fig. 9.
Abundance of TiO (red) and H O (blue) as a functionof distance from the star for the models A3, B3 and C1, duringminimum (dashed lines) and maximum (solid lines) luminosity.The vertical lines mark the average distance where τ = / V band during minimum (dashed line) and maximum (solidline) luminosity. Since TiO features dominate in the visual wave-length region the black circles mark the abundance of interest forthe V band (note that H O does not contribute to this band).wavelength and emitted at longer wavelengths) when the frac-tion of true absorption f abs is higher, resulting in larger circum-stellar reddening and higher values of ( J – K ). If we take mass-loss rates into account (see Table 2 and the middle and bottompanel of Fig. 3) we see that for a given p , a higher mass-lossrate corresponds to a higher value of ( J – K ), although the trendis much weaker for grains with a lower fraction of true absorp-tion. For ( V – K ), however, there is no such simple correlationbetween color and mass-loss rate. It is also interesting to note
10. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. ! [ µ m]0.20.40.60.81.01.2 . - F / F c o n t TiOVOZrOV I J ! [ µ m]0.20.40.60.81.01.2 . - F / F c o n t COH2OTiOYOJ H K L
Fig. 8.
Important molecular contributions in the spectrum of an M-type AGB star, in the wavelength region 0.3-1.35 µ m (left panel)and 1.0-3.9 µ m (right panel), calculated for a hydrostatic model atmosphere with L = L (cid:12) , T (cid:63) = M = M (cid:12) . Thedi ff erent photometric bands are also marked. (J- K ) fabs=1.0 Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=-1.00, Tc=1100-1700Kp=-0.75, Tc=1200-1700Kp=-0.50, Tc=1300-1700Kp=-0.25, Tc=1300-1700Kp=0.00, Tc=1400-1700Kp=0.25, Tc=1400-1700Kp=0.50, Tc=1500-1700Kp=0.75, Tc=1500-1700Kp=1.00, Tc=1600-1700Kp=1.25-1.50, Tc=1600-1700K (J- K ) fabs=0.5 Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=-1.00, Tc=1200-1700Kp=-0.75, Tc=1300-1700Kp=-0.50, Tc=1300-1700Kp=-0.25, Tc=1400-1700Kp=0.00, Tc=1400-1700Kp=0.25, Tc=1500-1700Kp=0.50, Tc=1500-1700Kp=0.75, Tc=1500-1700Kp=1.00, Tc=1600-1700Kp=1.25, Tc=1600-1700Kp=1.50-2.50, Tc=1600-1700K
Fig. 10.
Phase-averaged photometry color-coded according to p -value for the models in set P. The higher the condensation tem-perature for a given p -value (circles with same color) the furtherthe filled circles are from the bottom right corner. Top panel:
Thefraction of true absorption is set to f abs = . Bottom panel:
Thefraction of true absorption is set to f abs = . f abs = . (J- K ) Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=0, Tc=1400-1700K, fabs=1.0p=0, Tc=1400-1700K, fabs=0.5 (J- K ) Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=-1.0-1.0, Tc=1600K, fabs=1.0p=-1.0-1.0, Tc=1600K, fabs=0.5
Fig. 11.
Photometric variations for models in set P, with f abs = . f abs = . Top panel: models with p = T c = − Bottom panel: models with T c = p varying between [ − . , . p -value thefurther the loops are from the bottom left corner. In contrast to the phase-averaged colors discussed in the pre-vious section, let us now study time-dependent photometry indetail. In the top panel of Fig. 11 we plot the colors ( J – K ) and
11. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. ! [ µ m]10 " L " [ e r g / s ] V I J H K L M
Model P27, fabs=0.5Model P27, fabs=1.0
Fig. 12.
Spectra of the model P27 ( p = T c = f abs = . f abs = . V – K ) as a function of time for grey dust ( p =
0) and di ff er-ent condensation temperatures. The color variations plotted inred show photometric data for models with f abs = . f abs = .
5. For both sets of models, the color ( J – K )increases with increasing condensation temperature. The reasonfor this is that an increased condensation temperature will movethe dust formation zone closer to the stellar surface, where thedensity is higher. This leads to higher mass-loss rates, which willincrease the circumstellar reddening and consequently producehigher ( J – K ) values (see Paper I for further discussion). In thedynamical models with a lower fraction of true absorption, lessradiation is thermally reprocessed. Therefore the color ( J – K )will increase less with increasing mass-loss rate, as can be seenin the top panel of Fig. 11.The understand why the color loops have such di ff erentshapes in models with f abs = . f abs = . ff er the most in the near-IR and visual regions, wherethe model with a lower fraction of true absorption emits signif-icantly more stellar flux compared to the model with a higherfraction of true absorption. Another noticeable di ff erence is thatthe visual magnitude varies more strongly with time when thefraction of true absorption is lower. This change in flux, causedby variations of the molecular features (mainly TiO) in the un-derlying atmosphere, becomes visible when dust is not obscur-ing the stellar radiation. Strong variations in the local gas tem-perature during a pulsation cycle drastically change the molec-ular abundances in these models, and consequently, how muchof the visual flux is absorbed. These di ff erences in the spectraare the reason why ( V – K ) is bluer and spanning a wider rangein the color-color diagram for models with f abs = . f abs = .
0. The circumstellar reddening is alsoless pronounced in the model with f abs = .
5, which results insmaller flux variations in the J band, and consequently, smallervariations in ( J – K ).To systematically study how the photometric variationschange with di ff erent values of p (i.e. di ff erent wavelength de- Note that dust opacity κ acc in the equation of motion is the same forboth grids, resulting in similar mass-loss rates. (J- K ) fabs=1.0 Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=-1, Tc=1200K (P02)p=-1, Tc=1300K (P03)p=-1, Tc=1400K (P04)p=-1, Tc=1500K (P05) (J- K ) fabs=0.5 Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)p=-1, Tc=1200K (P02)p=-1, Tc=1300K (P03)p=-1, Tc=1400K (P04)p=-1, Tc=1500K (P05)
Fig. 13.
Photometry variations for models P02-P05 in set P( p = − T c = − Top panel:
The fraction oftrue absorption is set to f abs = . Bottom panel:
The fractionof true absorption is set to f abs = . J – K ) and ( V – K ) fora set of dynamical models where p is varied between [ − , T c = f abs = . f abs = .
5, on the other hand,have loops very similar to the observed colors when p (cid:46) . J – K ) and a large span in ( V – K ). Forlarger p -values the color ( J – K ) varies too much compared tothe colors fitted from observations in Fig. 6.As mentioned in Sect. 6, the resulting colors from the dy-namical models in set D, using a detailed description of thegrowth of Mg SiO grains, are consistent with the colors fittedfrom observations. This grain material has a very low absorptioncross-section in the visual and near-IR wavelength region and apower law index of p ≈ − J – K ) and ( V – K ) for dynamical models using a parameter-ized dust opacity with p = − T c = − f abs = . f abs = . f abs = .
12. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. and they are situated within the same region of the color-colordiagram (see bottom and middle panel of Fig. 6). However, thespan of ( V – K ) for each model is more restricted. One possibleexplanation for this discrepancy is the question of applicabilityof the power-law fit in the visual region. The real optical data ofMg SiO grains and the power law fit diverge quickly outside thewavelength range used for the fit, as can be seen in Fig. 2. Thiscould a ff ect the magnitude in the visual band. Another possibleexplanation is that the Mg SiO grains have such low absorptioncross-sections that we would need to use a lower value for f abs to reproduce the span of ( V – K ). To sum up the discussion so far, it is evident that the chemi-cal and optical properties of the wind-driving dust species a ff ectthe resulting spectra and photometry strongly and that the real-istic color variations produced by the models in set D are not atrivial result. By comparing observed visual and near-IR colorsfrom M-type AGB stars to photometry from the models in setP, covering a range of chemical and optical dust properties, wecan conclude that in order to produce colors with similar time-dependence as indicated by observations, i.e., small variationsin ( J – K ) and spanning a larger range in ( V – K ), the dust mate-rial needs to be quite transparent in this wavelength region. Thelarge variation in ( V – K ), caused by molecular species such asTiO, can only be seen if the circumstellar envelope is not opti-cally thick. In addition, transparent grain materials will lead toweaker circumstellar reddening, and thereby, smaller variationsin ( J – K ).Furthermore, considering the location of the models in thecolor-color diagram, the absorption coe ffi cient has to be close togrey or increase with increasing wavelength ( p (cid:46) .
25) and thecondensation temperature has to be equal to or below 1500 K,in order not to cause too red values in ( V – K ) and ( J – K ), re-spectively. There is a possibility for a hypothetical dust materialthat has an absorption coe ffi cient that increases steeply with in-creasing wavelength ( p (cid:46) − .
75) and a high condensation tem-perature ( T c > V – K ) or ( J – K ), but among the optical data currently avail-able for dust species which are assumed to exists in M-type AGBstars, no such dust species can be found (see Table 3).
8. Evaluating suggested wind-drivers
In Paper I we looked at dynamical criteria, i.e. what combinationof optical and chemical properties are needed for a dust speciesto form close enough to the star to initiate mass outflows, whenevaluating di ff erent dust materials in search for possible wind-drivers in M-type AGB stars. In this section we evaluate specificdust material from a photometric perspective instead, to gain fur-ther insight into the dust properties that are needed to both trig-ger winds and produce spectra and photometry consistent withobservations.Dust species that include Fe and for which optical data inthe near-IR exist in the literature have p -values outside the pa-rameter space which gives realistic colors (e.g. SiO andMgSiO fulfill the constraints. The chemical and optical proper-ties of TiO and MgAl O also fall within the parameter space,but the constituent elements have too low abundances, leading toinsu ffi cient radiative acceleration. Uncertainties concerning theoptical data for SiO and Al O in the near-IR wavelength re-gion makes them hard to evaluate (a more detailed discussion on Table 3.
Examples of p and T c values for dust species likely toexist in the circumstellar environments of AGB stars. p Ref. T c [K] Ref.1 Fe 2.4 3 1050 12 FeO 1.6 4 900 13 Mg . Fe . O 1.9 4 1000 14 Mg . Fe . SiO SiO − . SiO − . O O − . . Notes.
The dust species above the separating line are likely to exist inthe circumstellar environment of M-type AGB stars, whereas the dustspecies below are found in C-type AGB stars. Note that the p -value forSiO is from interpolated optical data and that the optical data in thenear-IR for Al O is uncertain (see discussion in Sect. 6 of Paper I). References. (1) Gail (2010); (2) Lattimer & Grossman (1978); (3)Ordal et al. (1988); (4) Henning et al. (1995); (5) Zeidler et al. (2011);(6) Dorschner et al. (1995); (7) J¨ager et al. (2003); (8) Palik (1985);(9) Koike et al. (1995); (10) Begemann et al. (1997); (11) Rouleau &Martin (1991); (12) Pegourie (1988). these issues can be found in Paper I) even though Al O is nota probable candidate due to low element abundance of Al. SiO ,on the other hand, consists both of abundant atomic elementsand is very transparent in the near-IR (i.e. thermally stable closeto the star) and could be of interest for AGB stars where theC / O-ratio approaches unity and most of the oxygen is bound inCO-molecules, making it less available for dust formation.
As a consequence of the results by Woitke (2006), which in-dicated problems with the dust-driven wind schemes based onFe-bearing silicates, an alternative scenario for the mass loss ofM-type AGB stars was suggested by H¨ofner & Andersen (2007).They speculated that the outflows from these stars might bedriven by a small amount of carbon grains, with Fe-free silicategrains forming as a by-product in the wind and producing theobserved mid-IR features. In chemical equilibrium, most of thecarbon in an atmosphere with C / O < ff , 2006, 2011). The question remains if carbonaceousgrains can actually form from freed carbon atoms in the wake ofthe shock waves, but nevertheless we here investigate the e ff ecton spectra if outflows in M-type AGB stars indeed were drivenby carbon grains.The absorption coe ffi cient of amorphous carbon can be fittedwell by a power-law function, even quite a bit outside the wave-length range where the star radiates most of its flux (see Fig. 2),with a value of p ≈
1. Given the high absorption cross-section inthe near-IR of amorphous carbon, the momentum transfer fromstellar photons to the carbon grains will be dominated by true ab-sorption and not scattering. To investigate the e ff ects of carbon
13. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. (cid:104) [ µ m]10 (cid:105) L (cid:105) [ e r g / s ] Model P38 (p=1, Tc=1600K, fabs=1.0)Model A3, Mg SiO grains V I J H K L M (J- K ) Bulge Miras (G&B 2005)Field C-type LPVs (Bergeat 2001)Field M-type LPVs (Mendoza 1967)Model P38 & P39 (f abs =1.0)Model A3, Mg SiO grains Fig. 14.
Spectra and photometry for wind models using a param-eterized dust description simulating carbon grains.
Top panel:
Spectra for the model P38 with f abs = . Bottom panel:
Photometric variations for the modelsP38-P39 ( f abs = .
0) and A3. Over-plotted are the locations ofsimulated blackbody emitters in the range of T (cid:63) = − p = T c = f abs = .
0. Forcomparison, we also consider the spectrum of the model A3 inset D. This latter model was chosen since the photometry agreesvery well with the colors fitted from observations (see Fig. 6).The synthetic spectra at luminosity extremes are shown inthe top panel of Fig. 14. It is obvious that a grain material withoptical properties similar to amorphous carbon will greatly sup-press the molecular features in the visual and near-IR, especiallyduring the luminosity minimum, and cause significant circum-stellar reddening. This is something that is not observed in thespectra of M-type AGB stars. In contrast, these stars show strongmolecular features in the visual and less circumstellar reddeningcompared to carbon stars. On the other hand, Fig. 14 also showsthat dynamical models which include a detailed description ofMg SiO grains produce spectra with the strong molecular fea-tures in the visual intact and low circumstellar reddening.In addition to the e ff ect on the spectra in the visual wave-length region, the resulting photometry from model P38 doesnot agree with the observed values for M-type AGB stars, ascan be seen in the bottom panel of Fig. 14. Both ( V – K ) and( J – K ) are too red compared to values by Mendoza (1967) orGroenewegen & Blommaert (2005) and the photometric varia-tions di ff er significantly from the photometric variations derived from observations (see top panel in Fig. 6). Given these results,it is clear that the amount of carbon grains necessary to producean outflow in M-type AGB stars would a ff ect the spectra in waysthat are not compatible with observations and that the scenariopresented in H¨ofner & Andersen (2007) is not viable.
9. Summary and conclusions
It has long been speculated that winds of M-type AGB stars aredriven by radiative acceleration on silicate grains observed inthe circumstellar envelopes of these stars. Recent theoretical re-sults by Woitke (2006), showing that silicate grains have to bevirtually Fe-free in the close vicinity of AGB stars, however,raised doubts about this scenario. The low near-IR absorptioncross-sections of such Fe-free grains are not su ffi cient to trig-ger outflows. As a response to this result H¨ofner (2008) arguedthat wind of M-type AGB stars may be driven by photon scat-tering on Fe-free silicates, provided that the grains grow to sizesof about 0 . − µ m. Strong observational support for this sce-nario was recently given by Norris et al. (2012), who detecteddust particles of sizes ∼ . µ m in the close circumstellar en-vironment of three M-type AGB stars, using multi-wavelengthaperture-masking polarimetric interferometry.In this paper we provide further support for the idea of windsdriven by photon scattering on dust by presenting photometry forthe set of self-consistent wind models in H¨ofner (2008). The re-sulting V , J and K photometry reproduces remarkably well boththe values and the time-dependent behavior, i.e. small variationsin ( J – K ) and spanning a larger range in ( V – K ), of photomet-ric observations of M-type AGB stars. To our knowledge, theseare the first self-consistent wind models for M-type AGB starsthat reproduce well both observed dynamical properties, such aswind velocities and mass-loss rates (see Fig. 3), and photometryin the visual and near-IR wavelength region (see Fig. 6).To determine if the trends in photometry are a generic prop-erty of the dynamical models or if they constrain the optical andchemical properties of the grain material driving the wind, weexplore photometry for a set of models presented in Bladh &H¨ofner (2012). These models use a parameterized dust descrip-tion and span a range of optical and chemical dust properties, in-cluding varying transparency. Looking at the photometry for thisset, it is evident that the chemical and optical properties of thewind-driving dust species a ff ect the resulting spectra and pho-tometry strongly, and that the realistic color variations producedby the models using a detailed dust description for the growthof Mg SiO grains are not a trivial result. The wind-driving dustspecies need to have a low absorption cross-section in the visualand near-IR to reproduce the typical time-dependent behaviorobserved in M-type AGB stars. The large variation in ( V – K ),mainly due to molecular species such as TiO, can only be seen ifthere is no substantial absorption due to dust in the circumstel-lar envelope. In addition, transparent grain materials will leadto less thermal reprocessing of the stellar radiation, resulting insmall variations in ( J – K ). The photometric observations alsoplace constraints on the optical and chemical properties of thewind-driving dust species ( p (cid:46) .
25 and T c (cid:46) V – K ) and ( J – K ). By self-consistent we here mean radiation-hydrodynamical modelsthat include a time-dependent description for the grain growth, grain-size dependent dust opacities and frequency-dependent radiative trans-fer. Note also that the a posteriori radiative transfer is done consistentlywith the dynamical computations, only di ff ering in the number of fre-quency points used.14. Bladh et al.: Exploring wind-driving dust species in cool luminous giants II. Concerning specific grain materials, we conclude that carbongrains (suggested by H¨ofner & Andersen, 2007) are not viableas wind-drivers in M-type AGB stars since they would a ff ectthe spectra in ways that are not compatible with observations.Strong candidates for wind-driving dust species in M-type AGBstars are Fe-free silicates, such as Mg SiO and MgSiO , pro-vided that they reach grain sizes where scattering is e ffi cient.They consist both of abundant materials and are quite transpar-ent in the visual and near-IR. Another possibility could be SiO ,especially for stars with a C / O-ratio close to unity where most ofthe oxygen is bound in CO-molecules, making it less availablefor dust formation.
Acknowledgements.
Sincere thanks are given to M.A.T. Groenewegen andJ.A.D.L. Blommaert who provided mean OGLE- V -magnitudes for the GalacticBulge Miras and to B. Gustafsson for valuable feedback and insights.We acknowledge with thanks the variable star observations from theAAVSO International Database, contributed by observers worldwide and usedin this research. This research has made use of (i) NASA’s Astrophysics DataSystem, and (ii) the NASA / IPAC Infrared Science Archive, which is operatedby the Jet Propulsion Laboratory, California Institute of Technology, under con-tract with the National Aeronautics and Space Administration. The computationswere performed on resources provided by the Swedish National Infrastructurefor Computing (SNIC) at UPPMAX.This work has been funded by the Swedish Research Council(
Vetenskapsrådet ) and the Austrian Science Fund (FWF): P21988-N16. BA ac-knowledges support from Austrian Science Fund (FWF): AP23006 & AP23586and from contract ASI-INAF I / / / References
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