Forsterite Abundance and Mass-Loss of Red

Supergiants

Matthijs MullerDuration: Jan 2009 - Jul 2009

Supervised by: Pr. Dr. L.B.F.M. Waters

Second opinion: Pr. Dr. L. Kaper

July 30, 2009

Figure 1: This is an image of the red supergiant Antares, taken with the UKSchmidt Telescope.

Univerity of AmsterdamFaculty of Science

Astronomical Institute Anton Pannekoek

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Abstract

The behaviour of red supergiant spectra has been studied, focussingon mass-loss and the crystalline silicate forsterite. Also the possible posi-tive relation between red supergiant mass-loss and forsterite abundance inits dust shell have been investigated. Using the recent survey of all RSGwith M < 10−5M�yr−1 by Verhoelst et al. and the detection of crys-talline silicates in the interstellar matter of starburst galaxies by Spoon etal., a case will be presented confirming the suspected relationship. Alsoforsterite hiding contrast effects, due to differences in opacities of the sil-icates, have been investigated and determined to play a crucial role forlow mass-loss red supergiants.

Samenvatting voor 6 VWO:Melkwegstelsels kennen geen lege ruimtes. Naast de logische vulling metsterren en planeten, bevindt zich overal gas en stof, beter bekend als “in-terstelaire materie” (ISM). Het ISM doorgaat een constante cyclus, erworden sterren van gemaakt, maar de levende sterren (en ook de ster-vende: super novae) voegen weer gas en stof toe aan het ISM. Het blijktdat zware sterren de grootste bijdrage doen aan het verrijken van het ISM.Ze verliezen meer massa en eindigen eerder als een super novae. Dit laat-ste klinkt misschien onlogisch, maar er geldt: hoe meer massa, hoe snellerdood. Nou is er in 2006 door Spoon een bepaald soort kristal ontdektin het ISM van een ander melkwegstelsel, tussen de 7 en 13 procent vanhet gewicht van het stof. Het gaat hier om de stof familie van silicaten,een op glas gelijkend stof soort. Rode superreuzen worden aangewezen alsmogelijke fabricanten van die kristal. Een rode superreus is een bepaaldefase uit het leven van een zware ster en wordt gekenmerkt door hoog mas-saverlies en een daarmee geassocieerde stof wolk. In mijn onderzoek hebik de rode superreuzen bekeken met een computer model, waarbij specialeaandacht is uitgegaan naar deze kristallen. Daarbij presenteer ik bewijsdat er mogelijk een relatie bestaat tussen de geproduceerde hoeveelheidkristal en het massaverlies van de rode superreus. Dit heb ik gedaan doorgebruik te maken van een observatie van alle rode superreuzen uit onzemelkweg met een laag massa verlies: kleiner dan 10−5M�yr−1 (zonsmas-sas per jaar). In geen van deze sterren werden de kristallen gedetecteerd.Echter door het bestaan van een detectie limiet is het mogelijk dat dezewel aanwezig zijn. Ik heb aangetoond dat de maximale aanwezige hoeveel-heid 7-8 procent kan zijn, zonder men het kan detecteren. Rode super-reuzen zijn niet de enige die stof aan het ISM toevoegen, dit betekent dathet stof in de wolken van de rode superreuzen zelf een nog veel groterehoeveelheid moeten hebben dan door Spoon. Dit strookt niet met degevonden waardes van maximaal 8 procent, dus waarschijnlijk moeten derode superreuzen met hoger massa verlies een grotere hoeveelheid van de

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kristallen hebben om de aanwezigheid in het ISM van Spoon te kunnenverklaren!

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Contents

1 Introduction 51.1 Red Supergiant Stars . . . . . . . . . . . . . . . . . . . . . . . . . 51.2 Dust . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.3 The Setup and Goal of this Paper . . . . . . . . . . . . . . . . . 10

2 Observations 10

3 Methodology and Theory 143.1 MCMax code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143.2 Central Object Properties . . . . . . . . . . . . . . . . . . . . . . 153.3 Dust Envelope Properties . . . . . . . . . . . . . . . . . . . . . . 153.4 Governing Physics Properties . . . . . . . . . . . . . . . . . . . . 15

3.4.1 Particle Model . . . . . . . . . . . . . . . . . . . . . . . . 153.4.2 Dust: Composition, Condensation and Thermal Contact . 15

3.5 Standard Model and Parameter Space . . . . . . . . . . . . . . . 16

4 Results and Analysis 174.1 Parameter examination . . . . . . . . . . . . . . . . . . . . . . . 17

4.1.1 Mass-loss . . . . . . . . . . . . . . . . . . . . . . . . . . . 174.1.2 Forsterite and Enstatite Abundance . . . . . . . . . . . . 204.1.3 Metallic Iron . . . . . . . . . . . . . . . . . . . . . . . . . 214.1.4 Inner Radius . . . . . . . . . . . . . . . . . . . . . . . . . 224.1.5 Outer Radius . . . . . . . . . . . . . . . . . . . . . . . . . 23

4.2 Equivalent width at 33.6 micron . . . . . . . . . . . . . . . . . . 244.3 EW: Forsterite and Enstatite Abundances . . . . . . . . . . . . . 254.4 EW: Metallic Iron Abundance . . . . . . . . . . . . . . . . . . . . 264.5 EW: Inner Radius . . . . . . . . . . . . . . . . . . . . . . . . . . 274.6 EW: Outer Radius . . . . . . . . . . . . . . . . . . . . . . . . . . 284.7 EW: Post-RSGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Discussion 31

6 Conclusion 33

7 Thanksgiving 34

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1 Introduction

The weight of all stars in a galaxy alone never accumulates to the total mass of agalaxy. This is because a galaxy knows no empty space between the stars, everycubic meter contains dust and gas. This interstellar matter (ISM) undergoes acontinuing cycle: it is enriched by the matter thrown off by stars and by thesupernovae of dying stars, but from the ISM, new stars can be formed again.Though every star contributes to the ISM, the magnitude of contribution isthe highest for the massive stars. Especially in the red supergiant (RSG) andluminous blue variable (LBV) phase of massive stars (both know to have highmass-loss), is the enrichment of the ISM significant.

Recently, Spoon et al. detected a species of dust, the crystalline silicateforsterite with a 7 − 13% mass abundance of the dust, in the ISM of starburstgalaxies. This species does not appear to be present in the ISM of our Milky Way[18]. Starburst galaxies are characterised by their high star forming rate (SFR),up to a few hundred M�yr−1 compared to a SFR of approximately one M�yr−1

for the Milky Way. Massive stars have short life times, which is why few of themare found in the Milky Way, however, because of the high SFR, massive starsare relatively more abundant in starburst galaxies, and must therefore play avital role here. Furthermore, based on observation, a possible relation betweenforsterite and stellar mass-loss of a RSG is suggested by Molster et al. [17].

This study is motivated by the previously mentioned observational findingsand is intended to investigate RSG mass-loss and stellar wind with respect toforsterite. Key to this study is the the monte-carlo radiative transfer softwarecode developed by Min et al. [5], which produces synthetic spectra of RSGs.

1.1 Red Supergiant Stars

Depending on the initial mass, a star undergoes several phases throughout itslife. These phases are most notably characterised by the stellar properties interms of temperature, luminosity and size. This is graphically displayed in figure2 (a Hertzsprung-Russell diagram), which can be divided into several regionscontaining only stars of the same phase. During its life, a star moves from re-gion to region. The RSG phase is believed to be attainable only for stars withmasses ranging from 10 to 45 M�. However, the evolutionary tracks before andafter the RSG phase are different amongst these masses. Stars with an initialmass of 10 to 25 M� will evolve as:

O −→ BSG←→ RSG −→ SN

Here O is the main sequence star of this spectral type. This phase lasts ap-proximately 90% of the stars total life time and is characterised by the fusionof hydrogen in the core. After the main sequence, the star will first evolve to ablue supergiant (BSG). This transformation occurs when core activity decreasesas the hydrogen is exhausted, causing the core of the star to shrink in size andreleasing potential energy. This pushes up the temperature of the core, some-times reaching up to 25000K. The stellar wind in this phase has a very highvelocity, but low density. The further shrinking of the core eventually triggerstemperatures high enough for hydrogen shell burning. The shell expands and

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cools rapidly and the star now enters the RSG phase. The star possibly under-goes several loops as a RSG can also turn into a BSG again. This loop occurswhen the the shell contains less than 30% of the total mass of the star. Even-tually this life cycle ends in a supernova (SN).

Figure 2: This image displays a Hertzsprung-Russell diagram. Because of thecharacteristic luminosities and temperatures of each phase, the diagram is di-vided into multiple regions reserved for a specific phase. The red supergiantphase, subject of this paper, is located in the upper-right corner.

For stars with a mass in the range of 25 to 45 M�, the following cycle isthought to occur.

O −→ Of −→ BSG −→ LBV ←→ RSG −→ (WR) −→ SN

Here Of is a different spectral type. LBV stands for “luminous blue variable”, ahighly unstable phase where stars often dump large amounts of mass due to theproximity of their luminosity to the Eddington limit [10]. This phase is reachedonly by stars with with masses higher that 40M�. Also, with higher masses it isnow possible to reach the “Wolf-Rayet“ (WR) phase, where the star has had allits hydrogen rich layers stripped off, leaving a star with a He rich atmosphere.

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Again this star life cycle will end in a supernova [11].A typical RSG is Antares (HD 148478), shown in the illustration on the

front page. During the RSG phase, stars have temperatures ranging from 3000to 4500K, radii up to several AUs and, compared to the other phases, highmass-loss. It is because of this relatively high mass-loss that RSGs are oftensurrounded by envelopes of this expelled matter. See figure 3, here RSG VYCanis Majoris (HD 58061) and its envelope are shown. It can been seen that thedust shell shows a-symmetric features. Recently, the RSG dust shells have alsoattracted the attention of supernovae specialists, for it has been suggested thatLBVs could also be progenitors of a type II supernovae, thus not necessarily, ashas always been believed, a RSG [12]. The light curve of a SN is affected by thestructure of the stellar ejecta and can therefore provides insight on the phaseof the progenitor. This is an extra reason for further investigation of RSGs andtheir dust shells.

Figure 3: This figure shows VY Canis Majoris and its dust envelope with fourdifferent filters taken with the Hubble Space Telescope [12].

1.2 Dust

The high mass-loss in RSGs is driven by both stellar pulsations and radiationpressure exerted on dust and gas. Because of its high opacity compared to gas,the dust gets accelerated easily by the star light. When moving away from thestar, the dust drags along gas, because of the drag force between the two [19].

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All of this dust and gas gathers around the central object in an envelope, seefigure 3. The variety of dust species is very large. However, it can be split intwo general groups: crystalline dust and amorphous dust. In crystalline dust,molecules have a well ordered lattice structure, whereas in amorphous dust, thegrains only show a lattice structure on a very small scale but show disorder ona long-range scale. Only when the dust reaches high enough densities and coolsvery slowly for a long period of time, will it condense like a crystal. When thecooling process goes too fast, the molecules freeze before being able to positionthemselves in an orderly way, thus forming amorphous dust. The dust speciessubjected to research in this paper are the crystals Forsterite (Mg2SiO4) andEnstatite (MgSiO3), members of the silicate families Olivine and Pyroxene re-spectively. It is the crystalline dust that is of high interest to this research, forthis dust shows very specific and recognisable features in its spectrum (figure4). This is contrary to amorphous dust, which shows no narrow peaks, but justtwo wide bands at 10 and 18 micron, see figure 5. These band are caused bythe bending or stretching of the Si − O connection in the small scale latticestructure of the amorphous silicate. More on this in section 2 and 3.4.2.

Figure 4: This graph shows the opacities of Enstatite and Forsterite at differentwavelengths. It displays many characteristic peaks, most notably the 11.3 and33.6 micron features of forsterite.

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Figure 5: This figure shows the opacities of metallic iron (top panel), amorphoussilicates without metallic iron (mid panel) and amorphous silicates with tenpercent metallic iron (bottom panel). Note that metallic iron is very effectiveat absorbing small wavelengths, an attribute that is adopted by the amorphousdust when mixed with metallic iron. Also, amorphous silicate shows two widebands at 10 and 18 micron.

As a beam of light passes through a dust cloud, a fraction of the energy,depending on the density and opacities, is absorbed. However, assuming thermalequilibrium, the same energy absorbed must also be reradiated by the dust. Theoptical depth (τν), which is the column density times the opacities, indicateshow much light is absorbed and is therefore a measure of how deep the observerlooks into the dust shell. Note that the optical depth is frequency dependant.For an optically thin object, the observer looks straight at the central objectand almost every photon, emitted by both the star and the envelope, escapeswithout absorption. But as the density of the dust shell increases, so does theoptical depth and the observer therefore starts seeing less and less deep intothe shell. Consequently, because the temperature of the dust drops as we moveaway from the star, the observer will start seeing an increasingly colder objectas the optical thickness increases. The behaviour of the spectra can be mademore clear using the equation of radiative transfer [1]:

Iν = Istarν e−τν + Sν(1− e−τν )

Here Iν is the observed spectral intensity, Istarν is the spectral intensity of the

central object and Sν is the intensity radiated by the dust envelope (sourcefunction) which is equal to the Planck function when thermal equilibrium isassumed. τν is the optical depth of the entire envelope. In the range of wave-lengths of interest to this paper, the RSG hardly emits any light, so the firstterm (Istar

ν ) can be neglected. This leaves just the contribution of the envelope.

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There are two cases to be considered: τν << 1 (optically thin) and τν >> 1(optically thick). In the first case, the equation of radiative transfer simplifiesto:

Iν = Sντν

So, in the regime of low optical thickness, a peak in the opacity (and thus alsoin τν) will cause an increase in intensity and thus an emission feature. Whenthermal equilibrium is assumed, Sν is equal to the Planck function. So thetemperature of the dust is also linked to the emission feature. In the case ofoptical thickness, the equation simplifies to:

Iν = Sν

Now consider again the effect of a peak in the opacity of a dust species. Com-pared to its shoulders, the peak has a higher optical depth and therefore, thephotons of this frequency originate from layers closer to the surface of the en-velope. But because the layers closer to the surface are cooler, they radiateless than the deeper layers. Thus opacity peak causes an absorption feature.The shifting of the Planck curve explains why small wavelength features go intoabsorption for lower cloud densities than longer wavelength features. This isbecause an increase in optical thickness and thus a decrease in observed tem-perature, shift the Planck curve to the right, increasing the emphasis on largerwavelengths. In this paper the emphasis will be on the 33.6 micron feature offorsterite. This feature is preferred over the 11.3 micron feature, for it is moredominant in the RSG regime of optical depth. Also the measuring of the 11.3micron feature is more difficult since it is located on the shoulder of the 10micron feature of the amorphous silicate.

1.3 The Setup and Goal of this Paper

This paper is intended to provide insight into the behaviour of red supergiantspectra and to further investigate the suspected relation between crystallineabundances and stellar mass-loss. This relation could either be caused by adifferent temperature of the amorphous and crystalline dust components, ob-scuring the crystals for lower mass-loss, or it could be that only high mass-losscreates circumstances fit crystal formation. The goal of this paper is to deter-mine whether this effect could be responsible for the relation.

In section 2 a closer look will be taken at some spectra acquired by observa-tion, furthermore, insight will be provided on the effects at play when observingdusty objects. In section 3 the methodology will be discussed, also explaininghow MCMax, the radiative transport code developed by M. Min et al., functionsand what assumptions lie at its base. In section 4 the results will be presented,analysed and interpreted. After this, consequences and suggestions for possibleimprovement and future research will be brought forth in section 5. Finally, theimportant findings will be presented and summarised in section 6.

2 Observations

Spoon et al. have found mass abundances from 7− 13% forsterite to be presentin the dust of the ISM in ultra luminous infrared galaxies (ULIRG; a type of

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starburst galaxy) [2]. See figure 6 for a spectrum. ULIRGs are very dusty placesand RSGs are expected to play a key role in the production of forsterite. Thoughthe SNe are also important dust factories, their more hostile environments areexpected to have a negative effect on the production of crystals.

Figure 6: Top panel: the optical depth spectrum of IRAS IRAS 08572+3915(black). The effects of different choices for the local continuum are indicated bythe grey shaded area. The bottom panel is the result of subtracting the fittedcontinuum from the observed spectrum [2].

The recent observing of post-RSGs has provided a case for a theory suspect-ing a possible relationship between forsterite abundance and stellar mass-loss.Ground for this theory is that forsterite is only detected in the spectra of post-RSGs showing high mass-loss histories (M > 10−3M�yr−1) [17]. However, amajor problem, in order to test this theory, is the small number of usable RSGspectra, especially in the high mass-loss regime where forsterite was detectedfor post-RSGs. Only one confirmed current RSG is know to show forsterite:NML Cyg, with a mass-loss M ' 3.3× 10−4M�yr−1 [3], [4]. This low numberis mainly due to the steep initial mass function (for the birth of each 20 M�star, roughly 100000 sunlike stars are born [11]), the short life times of massivestars and the decrease in duration of the RSG phase as mass-loss increases.A recent survey by Verhoelst et al., covering all usable RSGs with mass-losses

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below M < 10−5M�yr−1, provides a lower limit since in none of the spectraforsterite was detected [8]. For an example of observation see figures 7& 8.

Figure 7: This figure shows the Spitzer IRS spectra of (I) R66, a B[e] Supergiant[9], (II) IRAS05402-6956, a RSG or AGB with high mass-loss, (III) HV888: aRSG [13]. (III) clearly shows amorphous silicates, but not forsterite, possiblybecause of the contrast effect. (II) & (I) do show forsterite. (I) is know to havea thick and flat dust disc, this is why formation of crystals is expected to bemore likely here because of the higher densities and temperatures.

Two possible explanations are presented for the absence of crystalline sili-cate features in low mass-loss star spectra: either the suitable environment forcrystalline dust condensation occurs only for higher mass-losses or the fact thatcrystalline silicates are not observed for low mass-loss stars is simply a contrasteffect [15]. This contrast effect is caused by the difference in opacities of crys-talline and amorphous dust. RSGs radiate most of their energy in the shortwavelength range, here amorphous dust is more opaque than crystalline dust,especially when the amorphous dust contains Fe, see figure 5. Therefore, if thedust shell is optically thin and thus every dust particle directly feels the shortwavelength star light, the amorphous silicates heat up more effienctly than thecrystals, see figure 9. This effect may cause one to observe only amorphous sili-cates, since they radiate relatively stronger because of their higher temperature.In other words, due to this contrast effect, eventhough a significant abundanceof crystalline silicates is present one does not necessarily detect it. However,when mass-loss and thus optical depth increases, more and more of the shortwavelength star light is absorbed and reradiated at longer wavelengths. But forlarger wavelengths, the difference in opacity between amorphous and crystallinesilicates decrease. With more similar temperatures (see figure 10), the contrasteffect is reduced for higher mass-loss. This could explain why forsterite couldonly be detected in high mass-loss RSGs.

Note that, technically speaking, it is not correct to refer to an object asbeing ’optically thick’, since one should always mention with respect to what

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Figure 8: This is the ISO spectrum of LMC LBV R71 [14], showing Forsterite(F) and polycyclic aromatic hydrocarbon (PAH) features.

wavelength. Unless mentioned otherwise, optical depth, as used in this paper,refers to the wavelength regime of the central object (3-5 micron).

Figure 9: This image shows the temperature of the Forsterite (red) and theAmorphous silicate (blue) as a function of its distance to the central object. Thisis for an optically thin star (M = 10−6M�yr−1), so every dust particle receivesthe star light without absorption. Note the big difference in temperature.

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Figure 10: This image shows the temperature of Forsterite (red) and Amor-phous Silicate (blue), but now with an optically thick dust shell (M = 3 ×10−4M�yr−1). All the star light is absorbed and reradiated at longer wave-lengths, decreasing the difference in temperature for the two dust species.

Note that in figure 10 the temperature of the dust for the inner regions ishigher than in figure 9. This is because the inner radii receive an approximatelyequal amount of radiation directly from the central object, however, in the op-tically thick case, the dust around the inner radius also receives a significantamount of radiation from the dust behind it. This effect is called ”back warm-ing” and explains the higher temperatures for the inner region. For the outerregions the opposite is true, now the dust of the optical thin case (figure 9) ishotter. This makes sense since in the optically thick case, light is obscured forthe outer regions.

As mentioned before, the lack of forsterite bands in the spectra of low mass-loss stars could also be explained by the dust formation circumstances. There isreason to believe these circumstances might be more favourable for crystallinesilicates in high mass-loss dust envelopes. Here the density and temperature arehigher, increasing the probability of gas condensing in a lattice structure.

3 Methodology and Theory

In this section, the MCMax software and further theory will be discussed, ex-plaining the code and the theory.

3.1 MCMax code

MCMax, the monte carlo radiative transport code developed by M. Min etal.[5], lies at the base of this research. Based on given input, it produces the-oretical spectra of stars surrounded by spherically symmetric dust envelopes.The content of this input can roughly be split up in three groups, the first beingthe central object properties (temperature, luminosity, mass-loss), the secondgroup concerns the parameters about the dust envelope (density, expansion ve-locity, size). Finally one needs to provide the model with information aboutthe governing physics that lie at the base of the calculations (particle shapeand interaction). MCMax divides the dust evelope into a grid of cells and emits

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photon packages from the centre of the grid throughout the dust shell. The tem-perature of each cell, used to calculate the spectra, is statistically determinedby the scattering, (re-)emission and absorption properties dust.

3.2 Central Object Properties

The star at the centre of the dust sphere, which is defined by its mass-loss,temperature and radius, is given a range of typical red supergiant properties.The central object was given a black body spectrum. More realistic results couldbe produced by using a real RSG spectrum instead of a black body radiator,this might be a recommendation for future research.

3.3 Dust Envelope Properties

The characteristics of the spherically symmetric dust envelope cover the size interms of inner and outer radius, dust species abundances and expansion velocity.The latter determines the density of the envelope together with the mass-lossof the central object. A constant mass-loss and constant expansion velocity areused, resulting in density inversely proportional to the square of the distance tothe central object.

3.4 Governing Physics Properties

This subject can be divided into two subsections, one concerning the theoreticalassumption about the dust grains and the other concerns assumed propertiesbased on previous research and observation.

3.4.1 Particle Model

Unlike gas, dust clumps together as grains. The input shape of these grains isof high influence when calculating the radiative transport. This is why M. Minet al. investigated the particle shapes extensively. The shapes can be dividedinto two main groups, particles that are homogeneous spheres and particle thatare not. It was found that, in order to get a meaningful representation of dust,homogeneous spherically symmetric particles cannot be used, because they causeunrealistic resonance effects [16]. To break the spherical symmetry, a the particleshape of a Continuous Distribution of Ellipsoids (CDE) was chosen. Thereare of course more candidate non-homogeneous and non-spherically symmetricdistributions, however, CDE is preferred over the other distributions for it isbetter known, widely used and easily reproduced. Also, CDE maximises theopacity of metallic iron, making it possible to pose stronger underlimits, moreon this in section 3.5.

3.4.2 Dust: Composition, Condensation and Thermal Contact

The composition of the amorphous dust is to resemble the results from a studyby M. Min et al. of Mira [5]. Mira is a low mass-loss source so the 10 mi-cron feature of the amorphous dust is in full emission. This makes it rela-tively easy to determine the dust composition since the feature is only pro-portional to the opacities and the source function. The best fit was achievedusing Mg1.36Fe0.64SiO4, which is a mixture of 67.7% MgFeSiO4 and 34.3%

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Mg2SiO4 and for the size distribution of the grains a power law with index−3.5 (the number of grains with given size a: N(a) ∝ a−3.5).Dust grains are formed when molecules condense, for magnesium silicates thisoccurs at temperatures below 1400K. It is currently believed that formationand growth of silicates and metallic iron starts on a seed of TiO2 or Al2O3

(or rutile and corundum respectively). The silicates condense first, for they aremore stable than metallic iron. The metallic iron is included later, either di-rectly in silicate or in inclusions [19]. These grains are simulated by putting themetallic iron and amorphous silicates in thermal contact, meaning they sharethe same temperature.

3.5 Standard Model and Parameter Space

In order to investigate the behaviour of dust enshrouded RSG spectra, a rangeof parameters has been inspected.◦ The mass-loss ranging from 1× 10−6 to 5× 10−3M�yr−1.◦ Forsterite and Enstatite abundances ranging from 0 to 10%.◦ Metallic iron abundance ranging from 0 to 10%.◦ The inner radius of the dust shell is varied from 75 to 450 AU.◦ The outer radius of the dust shell is varied from 2500 to 15000 AU.Evidence suggest that the enstatite abundance always equal or greater than theforsterite abundance [17]. Therefore, keeping this suggestion in mind, forsteriteand enstatite are always equally abundant in each of the models. A forsteriteover enstatite ratio of unity is assumed for simplifying reasons. Also a few pa-rameters have been kept constant in each model:◦ Expansion velocity: 30km/s◦ Effective temperature of star: 4000K◦ Stellar radius: 930R�◦ Luminosity: 198653L�◦ Mass: 25M�◦ No thermal contact is assumed between amorphous and crystalline dust.To bring perspective to the resulting spectra, a standard configuration was de-fined. This standard model has the following properties and is to resemble atypical RSG:◦ Mass-loss: 1× 10−4M�yr−1

◦ Metallic iron abundance: 4%◦ Forsterite abundance: 4%◦ Enstatite abundance: 4%◦ Inner radius of the dust shell: 75AU◦ Outer radius of the dust: 15000AU

Note that, with respect to observing forsterite, this paper investigates theworst case scenario. For the contrast effect is maximised by assuming ther-mal contact between metallic iron and amorphous silicate, but not betweencrystalline and amorphous silicate. The result is a minimal temperature forthe crystalline silicates and maximum temperature for the amorphous silicates.This justifies the posing of very strong limits, if the forsterite can be detectedin the synthetic spectra than it must also be detectable in real spectra withthe same stellar and dust shell configuration, for the circumstances can only be

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more favourable than assumed in this paper.

4 Results and Analysis

In the first part of this section the behaviour of the red supergiant spectra inthe defined parameter space will be analysed. In the second part, the contrasteffect and its possible responsibility for the observed mass-loss forsterite relationwill be analysed and tested.

4.1 Parameter examination

In this section the effects of the varied parameters will be investigated, whichwill be brought to perspective by comparison to the standard model. Figure11 shows the spectrum of the standard model. As explained in section 3.5, ourconfiguration is a worst case scenario, to indicate why, a best case scenario wasadded to this figure. In the best case scenario, forsterite and enstatite share thesame temperature with the other dust species, so no contrast effect hiding thecrystal abundances is present. As can be seen in the figure, absence of thermalcontact smooths the spectrum, thus hiding the crystals.

Figure 11: Standard model with (red) and without (black) thermal contact.The crystal features are better visible with thermal contact.

4.1.1 Mass-loss

In figures 12,13,14 and 15 the stellar mass-loss is varied over a range from1× 10−6 to 5× 10−3M�yr−1. As a frame of reference, the standard model wasadded to each window (the dotted line, though it does not yet show for the low

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mass-loss rates). Note that the previously mentioned observational suspectedtrend is confirmed by the synthetic spectra: only for higher mass-loss does onedetect crystalline spectral peaks. The 33.6 micron forsterite feature only showsfor a stellar mass-loss exceeding 5× 10−5M�yr−1. As explained in section 1.2,the feature starts to overcome the contrast effect. Also note the 10 micronfeature of the amorphous silicates and for higher mass-loss also the 11.3 micronfeature of forsterite, are both going into absoption. Note that it may seem asthough the total flux increases as mass-loss increases. This though is false, forthe flux is defined in term of Jansky [J−1m−2Hz−1]. Here the Hz dependenceexplains the increase of surface underneath the spectra.

Figure 12: This image displays the spectra of different mass-losses in the rangeof 1× 10−6M�yr−1.

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Figure 13: This image displays the spectra of different mass-losses in the rangeof 1× 10−5M�yr−1. With the first clearly visible 33.6 micron feature showingin the bottom right panel. The dotted line is the standard model spectrum.

Figure 14: This image displays the spectra of different mass-losses in the rangeof 1× 10−4M�yr−1. The dotted line is the standard model spectrum.

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Figure 15: This image displays the spectra of different mass-losses in the rangeof 1× 10−3M�yr−1. The dotted line is the standard model spectrum.

4.1.2 Forsterite and Enstatite Abundance

The effect on the spectrum of the standard model caused by different abundancesof forsterite and enstatite is shown in figure 16. The findings are in accordancewith the expectations: the forsterite and enstatite features become stronger astheir abundance increases, while the continuum of the amorphous dust decreasesin flux.

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Figure 16: This images shows the standard model with different abundancesof forsterite and enstatite. The abundances are 0% forsterite and 0% enstatite(black), 2% forsterite and 2% enstatite (red), 4% forsterite and 4% enstatite(green), 6% forsterite and 6% enstatite (blue), 8% forsterite and 8% enstatite(turquoise) and 10% forsterite and 10% enstatite (purple).

4.1.3 Metallic Iron

In our model, the only dust species in thermal contact with metallic iron isamorphous silicate dust. Metallic iron has a high opacity, especially in the lowwavelength range. This is why the flux of the amorphous silicate dust continuumis raised as the Fe abundance increases, see figure 17. Note that variability inspectra, caused by different Fe abundances, is a problem when observing sincethe Fe abundance is hard to determine, due to the absence of specific featuresin its spectrum.

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Figure 17: This images shows the standard model with different abundances ofmetallic iron. The abundances are 2% (black), 4% (red), 6% (green), 8% (blue)and 10% (turquoise).

4.1.4 Inner Radius

The closer to the star, the higher the density and temperature of the dust.Therefore, as the inner radius expands, the amount of hot and dense dust de-creases. It is this dust that adds most significantly to the optical depth. Thiscan be seen in figure 18, where the 10 micron feature goes further into emissionas the inner radius grows larger, a sign of decreasing optical depth. It appearsthat in this range of inner radii, the optical depth does not drop significantlyenough to affect the 33.6 micron feature of forsterite.

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Figure 18: This images shows the standard model with different inner radii.The radii are 75 AU (black), 100 AU (red), 150 AU (green) and 250 AU (blue).

4.1.5 Outer Radius

In this section the effects of the outer radius are examined. As can be seen infigure 19, the increase of outer radius only shows notable effects for the smallerradii. Beyond 10000 AU, the differences disappear. As the outer radius in-creases, dust is added. This dust is increasingly getting colder and will addless and less to the spectrum, until at some point its temperature is no longersignificant. This explains why the spectra converge. Note that, assuming con-stant expansion velocity and mass-loss, the outer radius is proportional to theage of the mass-loss. This means that, as the spectral differences between theincreasing outer radii disappear, so does potential information about the age ofthe mass-loss. This happens after approximately 1600 years.

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Figure 19: This images shows the standard model with different outer radii.The radii are 2500 AU (purple), 5000 AU (black), 10000 AU (red), 15000 AU(green), 20000 AU (blue), 25000 AU (turquoise) and 150000 AU (yellow).

4.2 Equivalent width at 33.6 micron

In this section the spectra will be analysed in a more quantitative fashion, bymeasuring the size of the 33.6 micron feature of forsterite. This is done in termsof equivalent width (EW) of a peak, defined in this paper as the surface betweenthe spectral feature and the continuum. The continuum is represented by thelinear line, drawn between the spectrum at 31.18 micron and 35.53 micron, seefigure 20. A small error is introduced here by using the same boundaries for allmodels.

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Figure 20: This image shows the close-up of 33.6 micron feature and the linearcontinuum. The surface of the yellow area is the equivalent width of the bump.

4.3 EW: Forsterite and Enstatite Abundances

First, the equivalent widths have been examined for different forsterite andenstatite abundances, keeping other parameters constant, see figure 21. As tobe expected, increasing the crystal abundance increases the equivalent width:the 33.6 features of forsterite goes further into emission. The upward slope ofthe overall parabolic shape can be explained by the decreasing presence of thecontrast effect, responsible for the increase in equivalent width. The graph startsout optically thin in both the short and long wavelength. The envelope becomesoptically thick for low wavelengths first. As explained is section 2, this reducesthe contrast effect. Eventually, as the density increases for higher mass-loss, theenvelope also becomes more optically thick for 33.6 micron photons, thus forcingthe feature into absorption as explained in 1.2. For the same reasons, the sameparabolic shape can also be recognised in the other graphs of equivalent widthwith different parameters (22, 23 and 24).

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Figure 21: This figure shows the equivalent width versus mass-loss for differentforsterite and enstatite abundances: 2% forsterite and 2% enstatite (turquoise),4% forsterite and 4% enstatite (straight black), 6% forsterite and 6% enstatite(red), 8% forsterite and 8% enstatite (green) and 10% forsterite and 10% en-statite (blue).

4.4 EW: Metallic Iron Abundance

Next, the effect of metallic iron on the equivalent width for different mass-losseswere investigated, see figure 22. Increasing the Fe abundance decreases theequivalent width and thus detectability of the 33.6 micron feature. A crude es-timate: a 10% Fe abundance decreases the equivalent width with approximately25%. As mentioned before, the problem here is the difficulty in measuring theFe abundance. This inevitably makes it harder to relate the magnitude of theequivalent width to a forsterite abundance.

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Figure 22: This figure shows the effects of metallic iron on the equivalent widthfor different mass-losses: 0% Fe (straight), 10% Fe (dotted), 4% forsterite plus4% enstatite (black) and 10% forsterite plus 10% enstatite (red)

4.5 EW: Inner Radius

Also, the effect of the inner radius of the dust shell on the equivalent widthhas been examined. Again showing the previously seen parabolic shape. It alsoshows another notable feature: the peak shifts. The inner part of the dust shellcontributes most to the optical depth, because of the higher density. So, inorder to maintain the same level of optical depth for attenuation of the contrasteffect, the mass-loss must increase, shifting the graph to the right. Note thatmaximum lies higher, this is explained by the decrease in hottest dust wherethe contrast effect was most strongly present.

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Figure 23: This figure shows the relation between the inner radius of the dustenvelope and the equivalent width: Rin = 75AU (black), Rin = 450AU (red),4% forsterite plus 4% enstatite (straight) and 10% forsterite plus 10% enstatite(dotted)

4.6 EW: Outer Radius

Note that in figure 24, showing the effect of the outer radius of the dust shell onthe equivalent width, the smaller outer radii have not been included. The effectsare small, therefore this graph further illustrates the previously made point: forlarge outer radii the additional contribution is marginal. For smaller outer radii,the effects are expected to be significant since these regions contribute more tothe 33.6 micron feature.

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Figure 24: This figure shows the effects of the outer radius of the dust envelopeon the equivalent width: Rout = 15000AU (black), Rout = 20000AU (red),Rout = 25000AU (blue), 4% forsterite plus 4% enstatite (straight) and 10%forsterite plus 10% enstatite (dotted).

4.7 EW: Post-RSGs

Recall that it was the post-RSG phase that provided a case for a possible relationbetween mass-loss and forsterite abundance. In order to investigate the post-RSG phase, the effects of setting mass-loss to zero are examined. This wassimulated by letting the inner and outer radius expand. Because of the constantexpansion velocity, the expansion is proportional to the time passed since zeromass-loss. This was done for different crystal abundances in the dust shellsof a M = 1 × 10−4M�yr−1 RSG and a M = 3 × 10−3M�yr−1 RSG, seefigures 25 & 26. Note that only for a higher initial mass-loss, a significantincrease in equivalent width is predicted. When the envelope moves outward,both temperature and optical depth decrease. For the initially lower mass-lossRSG, the decrease in optical depth immediately results in the revival of thecontrast effect, decreasing the equivalent width. For the higher mass-loss RSG,the envelope is initially so very dense that only after approximately 500 yearsof decreasing optical thickness, the contrast effect begins to play a part again.The cooling of the dust shifts the Planck curves towards the long wavelengths,increasing the relative emission in this regime and thus pushing up the equivalentwidth.

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Figure 25: This graph shows the evolution in time of the equivalent width of aformer M = 1×10−4M�yr−1 RSG for which mass-loss was set to zero at t = 0.Forsterite abundance: 4%

Figure 26: This graph shows the evolution in time of the equivalent width of aformer M = 3×10−3M�yr−1 RSG for which mass-loss was set to zero at t = 0.Forsterite abundance: 4%

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5 Discussion

To provide a means of further interpreting the previous results, a possible de-tection limit will be considered. Assume a signal-to-noise ratio (SNR) of 40for today’s detection equipment (which is reasonably high in this wavelengthregime) and a 3 sigma detection confidence interval. The spectral resolution(λ/∆λ) will be assumed at 100, resembling the Spitzer Space Telescope. Withλ = 33.6µm −→ ∆λ = 0.336µm. The feature has minimum full width at halfmaximum (FWHM) of 0.51µm and a maximum FWHM of 1.15µm. Thereforethe spectral band contains a minimum of 0.51µm/∆λ = 1.51 (Nmin) and a max-imum of 1.15µm/∆λ = 3.42 (Nmax) resolution elements. σ = 1/(SNR), thus ifthe band consist of only one resolution element, the feature can be detected onlyif the feature is 3 times higher than the signal: Fband/Fcontinuum = 3/(SNR)),with Fband = Fobserved − Fcontinuum. Now using the

√n-law for n resolution

elements gives: Fband/Fcont = 3/(SNR√

n). This tells us that the current de-tection limit is between an equivalent width of 0.04 micron for the maximumFWHM and 0.06 for the minimum FWHM, represented by the purple and greenhorizontal lines respectively, drawn in figure 27. Considering the Verhoelst sur-vey covered all RSGs with a mass-loss below M < 10−5M�yr−1 (representedby the vertical red line) [8], one can conclude that in this range of mass-loss noRSG exist with a forsterite abundance above 8-9%. This is a very strong limit,for the circumstances with respect to the detection of forsterite could only bemore favourable than was assumed in this paper. Recall that that Spoon et al.found an abundance of 7 − 13% mass of dust in the ISM of starburst galaxies,most likely produced by RSG. Note that the abundance in the ISM is diluted byother dust factories, and that therefore, the abundance in the dust shells of theRSGs itself must be even higher. Since no such abundances have been detectedfor the low mass-loss RSGs, the high mass-loss RSG must be responsible for themajority of the forsterite production. This provides evidence that indeed thesuspected relation between forsterite abundance and mass-loss of a RSG is bereal. It does, however, not exclude the possible presence of the contrast effect.

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Figure 27: This graph shows the equivalent widths for different forsterite andenstatite abundances: 2% forsterite and 2% enstatite (dotted black line), 4%forsterite and 4% enstatite (straight black), 6% forsterite and 6% enstatite (red),8% forsterite and 8% enstatite (green) and 10% forsterite and 10% enstatite(blue). It also contains two possible detection limits, represented by the hori-zontal green and purple lines. The yellow marked area contains all usable RSGsthat have been investigated so far by Verhoelst et al., no forsterite was detected.

As can be seen in figures 25 & 26, the equivalent width temporarily increasesafter the mass-loss stops only for high mass-loss RSGs. However, the timescales of this increase are relatively very short (around 1000 years) comparedto the total life time scale (a few million years), which makes the probability ofdetecting the RSG in the phase very hard. Note that an important lesson canbe learned from these two images, though the compositions of the dust shells areidentical, their spectra are very different, making it very hard to determine anabundance with observations. As example, see figure 28 with the spectra of twopost-RSGs, the left and right panel could very well have the same abundance.

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Figure 28: This image shows two dust enshrouded post-RSG. Left panel: AFGL2298, showing no forsterite. Right panel: HD 179821, showing both forsteriteand water

6 Conclusion

Forsterite has been detected in the dust shells of post-RSGs showing very highmass-loss histories (M > 10−3M�yr−1) [17], but not for any of the know cur-rent RSGs, except one. None of the low mass-loss RSGs (M < 10−5M�yr−1)from the Verhoelst et al. survey show forsterite, so there is reason to suspecta relation between forsterite and mass-loss. In this paper two explanations arebrought forth: i) either the dust is not present in the low mass-loss so circum-stances fit for forming forsterite are only created by high mass-loss RSGs or ii)a contrast effect hides the forsterite for the observer. This latter effect is causedby the lower opacity of forsterite compared to the amorphous dust in the wave-length range where the RSG emits most of its energy, making the amorphousdust relatively hotter and radiate stronger. In this paper the effects of parameterchanges have been investigated for a stereotypical red supergiant with a spher-ically symmetric dust shell. This was done using a radiative transport code [5].With respect to the detectability of the crystalline silicate forsterite, the mass-loss (history) of the RSG appears to be the most important parameter, asidefrom the actual silicate abundances. The forsterite hiding effects of the contrasteffect have been made apparent. A current detection limit for the equivalentwidth between 0.04 and 0.06 micron has been considered, resulting in the con-clusion that in the survey of all RSGs by Verhoelst et al., with mass-losses belowM < 10−5M�yr−1 [8], no RSG are present with a forsterite abundance > 8%.The detection of 7− 13% mass in the dust of the ISM in starburst galaxies bySpoon et al. [18] cannot be explained by the production of forsterite in lowmass-loss RSGs. This is evidence that the forsterite in the ISM, for which pro-duction RSGs are the most suitable candidates, is most likely produced by highmass-loss stars, confirming the suspected relation. It is, however, not possibleto exclude the presence of the contrast effect. Future research would requirea more accurate detection limit and the including of higher mass-loss to thesurveys in order to further strengthen this evidence.

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7 Thanksgiving

I would like to express my gratitude towards Rens Waters, for his supervisingeye in the past few months. Also, Michiel Min and Ben de Vries have been veryhelping, them I also wish to thank.

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