PULSATION-TRIGGERED MASS LOSS FROM AGB STARS: THE 60 DAY CRITICAL PERIOD

The mechanisms triggering mass loss during the red and asymptotic giant branch (RGB/AGB) phases of stellar evolution remain unclear. Canonical theory states that stars on the RGB, and those early in their AGB evolution, have winds driven by surface magnetic fields (Dupree et al. 1984). Later, pulsations levitate material from the stellar surface, where it can cool and condense into dust. Radiation pressure on that dust forces it from the star, and collisional coupling with the surrounding gas means the entire circumstellar envelope can be ejected (e.g., Winters et al. 2000). The dust reprocesses some of the radiation from the star into the mid-infrared ($\lambda \gtrsim 10$ μm), therefore the mass-loss rate can be linked to the infrared color of the star (e.g., K–[25]). Winds driven by this combination of pulsation and radiation pressure are expected to end the evolution of all low- and intermediate-mass stars (0.8–8 ${M}_{\odot }$). But what initiates this final mass loss?

A number of studies have linked both mass-loss rate and wind velocity to stellar luminosity, suggesting that dust driving dominates the kinetics of the wind. Woitke (2006) showed that momentum transferred from absorbed stellar radiation is insufficient to drive winds in oxygen-rich stars, and scattering by large dust grains is now thought to be the dominant momentum input (Höfner 2008; Norris et al. 2012). This has profound implications for the early enrichment of galaxies by AGB stars: metal-poor stars cannot easily lose mass if an optically thick layer of large dust grains is required to trigger strong mass loss ($\dot{M}\gtrsim {10}^{-8}$ ${M}_{\odot }$ yr⁻¹). Contrary to this expectation, prodigious dust production is seen in even the most metal-poor stars (e.g., Sloan et al. 2010; McDonald et al. 2011b; Sloan et al. 2012).

However, the above works focus on luminous stars which are established mass losers. The inability to drive reasonable winds for metal-poor and less-evolved stars with dust-driven winds suggest that strong mass loss may be initially triggered by pulsation, rather than dust nucleation (McDonald et al. 2011a, 2011b, 2014, 2016). AGB stars increase in both pulsation period and amplitude as they evolve, expand, and lose mass. A correlation between this increasing pulsation period and increasing mass-loss rate was shown by Vassiliadis & Wood (1993). Further observations and theoretical calculations have shown that a fully developed, pulsation-enhanced, dust-driven wind probably requires a star pulsating with period $P\gt 300$ days (Groenewegen et al. 1998, 2009; Winters et al. 2000; Uttenthaler 2013); hence, most studies have concentrated on the most-evolved stars in this regime. However, substantial dust production is also seen at shorter periods. Glass et al. (2009) note a systematic increase in dust production at P = 60 days for Galactic stars in Baade's Window. Beyond this period, the IR excess flattens off at ${K}_{{\rm{s}}}-[24]\approx 1.5$ mag until $P\approx 300$ days, when there is another sharp increase (see also Boyer et al. 2015). These sharp jumps in ${K}_{{\rm{s}}}-[24]$ (and their proxies, K_s–[22] and ${K}_{{\rm{s}}}-[25]$) indicate that pulsation period also has a strong impact on the amount of dust stars produce at $P\lt 300$ days.

In this Letter, we examine nearby, short-period AGB stars with distances from the Hipparcos sample (van Leeuwen 2007). We study the relation between period and mass loss, and identify pulsation as a potentially important trigger of strong stellar winds.

Our data set comprises a sample of nearby giant stars. Initially, 560 stars with parallax distances of $d\lt 300$ pc were selected from the Hipparcos catalog (van Leeuwen 2007). Most of these stars have luminosities (L) and temperatures (${T}_{{\rm{eff}}}$) determined by McDonald et al. (2012), and a cut was made to only include giant stars with $L\gt 680$ ${L}_{\odot }$ and ${T}_{{\rm{eff}}}\lt 5000$ K. $L\gt 680$ ${L}_{\odot }$ represents the luminosity where substantial infrared excess due to circumstellar dust production is first seen. Some bright stars lacked unsaturated photometry in the surveys used in McDonald et al. (2012), so were not included in this initial list. We have manually added missing bright (${M}_{{\rm{Ks,2MASS}}}\lt 0;$ Cutri et al. 2003) stars from the Hipparcos catalog. This cutoff approximates our criteria of $L\gt 680$ ${L}_{\odot }$ and ${T}_{{\rm{eff}}}\lt 5000$ K, but may also lead to the inclusion of some fainter stars. The only star likely to meet the selection criteria and be within 300 pc, but not included in Hipparcos, is the optically enshrouded star CW Leo. With its addition, we obtain a near-complete sample of giant stars with $L\gt 680$ ${L}_{\odot }$ within 300 pc. Some stars may still be erroneously included or excluded depending on their ${K}_{{\rm{s}}}$-band bolometric corrections and parallax uncertainties, which affect their derived distances and luminosities.

Infrared photometry for each star has been drawn from the 2MASS and WISE surveys (Cutri et al. 2013), allowing us to construct K_s–[22] colors that are representative of the dust column density in front of the star. For bright stars, the WISE photometry displays inaccuracies. Sources with 25 μm IRAS fluxes (Beichmann et al. 1988) of ${F}_{25}\gt 115$ Jy were found to strongly disagree with WISE results. For these stars, we have interpolated between the 12 and 25 μm IRAS fluxes in log(F)–log(λ) to provide a 22 μm flux. For HIP 113249, IRAS12 μm photometry was unavailable. For this star we simply use the 25 μm flux to represent the 22 μm flux.

Pulsation data have been obtained from three sources. Most optically bright stars have V-band Fourier-decomposed periods and amplitudes listed in Tabur et al. (2009). The period with the highest amplitude was chosen as representative for the star. Stars in the Tabur et al. (2009) sample are limited to $V\lesssim 8$ mag and periods of $P\lt 300$ days, thus miss the reddened, longer-period pulsators. Additional V-band periods and peak-to-peak amplitudes from VSX (Watson 2006) and periods from GCVS (Samus et al. 2006) were adopted. The VSX amplitudes are generally much larger than those of Tabur et al. (2009) due to the addition of harmonics and variability on timescales of $P\gt 300$ days. VSX and GCVS light curves also extend to redder objects with higher amplitude variations, as they are sensitive to optically fainter stars.

The final sample contains 519 stars with an Hipparcos distance, at least one measure of variability and a K_s–[22] color. We also retain separately a list of stars in the GCVS without Hipparcos distances, but with K_s–[22] colors. We limit these to stars with ${K}_{{\rm{s}}}\lt 9$ mag, to avoid sensitivity limits in the [22] data.

Most stars should be within a factor of two of the solar metallicity (Taylor & Croxall 2005). Because of this, the sample is almost entirely oxygen-rich. There are only two known carbon stars in the sample: U Hya and RT Cap. No known S stars are included.

In order to approximately convert K_s–[22] color to mass-loss rate, we use the Siebenmorgen et al. (1994) version of the Siebenmorgen & Kruegel (1992) dust model, assuming efficient condensation into silicate dust and a silicon fraction of 10 per million atoms. Effective dust-to-gas collisional coupling and a 10 km s⁻¹ outflow velocity were assumed. This K_s–[22] color to mass-loss rate conversion compares well to the ${K}_{{\rm{s}}}$–[25] relation seen in nearby stars (e.g., van Loon et al. 2007). However, uncertainties and differences in stellar luminosity, grain properties, condensation efficiency, and outflow velocity limit the accuracy of this conversion to a factor of a few.

Figure 1 shows that dust-production rate clearly increases sharply as soon as stars reach the critical 60 day period identified by Glass et al. (2009). After this initial jump, the amount of dust excess and the fraction of stars with dust excess both continue to increase to $P\approx 120$ days. Following this, dust excess may plateau between $120\lesssim P\lesssim 300$ days, before increasing again at longer periods. In the Hipparcos 519-star sample, stars with $P\gt 500$ days or K_s–[22] > 4 mag are supergiants (α Ori) or known binary stars. At high mass-loss rates, the K_s–[22] color will saturate as the SED peak becomes longer than 22 μm. However, only the most extreme stars listed here (K_s–[22] ≫ 4) should fall into that high-mass-loss-rate regime.

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A significant number of stars retain colors K_s–[22] < 0.85 mag but have periods $P\gg 60$ days. The period–luminosity diagram (Figure 2(b)) shows that these stars are found predominantly below the RGB tip, while stars with infrared excess are distributed nearly evenly across the RGB tip. Above the RGB tip, 93% of stars have excess. The remaining 7% mostly have $P\lt 60$ days and are probably RGB stars with uncertain distances. This suggests that the dust-producing stars are mostly or entirely AGB stars, and that the RGB stars produce little or no dust.

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The relation between pulsation amplitude and K_s–[22] color is clearer (Figures 2(c) and (d)). The pulsation amplitudes of both the Tabur et al. (2009) and VSX samples correlate very strongly with K_s–[22] color for low-amplitude variables. However, in the VSX data, this relationship breaks down at $\delta V\approx 1$ mag. This is a smaller amplitude than the classical Mira–semi-regular-variable split at $\delta V=2.5$ mag. Stars in the region of $\delta V=1$–2.5 mag (named in Figure 2(d)) still tend to have very regular variability, hence belonging to the paradoxically termed SRa class of "regular semi-regular" variables. The correlation between amplitude and K_s–[22] color picks up again at $\delta V\approx 3.5$ mag.

This gap between $\delta V\approx 1$ and 3.5 mag where the amplitude–color relation breaks down can be explained by examining the period–amplitude diagrams (Figures 2(e) and (f)). These diagrams show a correlation between period and amplitude up to $P\approx 100$ days and. In the VSX data, stars with $P\approx$ 100 days typically have $\delta V\sim 1$ mag. In the regime $100\lesssim P\lesssim 300$ days, the correlation breaks down: few stars are found with $\delta V\gt 1$ mag. The same is true of the Tabur et al. (2009) data, although the Fourier-based amplitude is correspondingly lower ($\delta V\sim 0.3$ mag). In the VSX data, the correlation restarts at $P\sim 300$ days and $\delta V\sim 3$ mag. This hiatus between 100 and 300 days is commensurate with the rapid transition of many stars from being semi-regular variables on the first overtone sequence of the period–luminosity diagram to being "Mira" variables on the fundamental pulsation sequence (e.g., Boyer et al. 2015; Wood 2015).

For stars that do produce dust (K_s–[22] > 0.85 mag), one would expect a dust-driven wind to produce a correlation between dust-mass-loss rate and luminosity, but none is seen. Figure 2(a) shows a large amount of scatter among the dust-producing stars on both sides of the RGB tip. These stars are not expected to differ widely in metallicity (95% of stars should be within –0.3 ≲ [Fe/H] ≲ +0.3 dex; Taylor & Croxall 2005). Nor should they vary much in C/O (C/O ≈ 0.4 for most stars, up to ≈0.9 for a few of the most-evolved stars currently experiencing dredge-up, plus the two carbon stars). The primary difference among stars at given luminosity is therefore expected to be (current) mass. This may vary by an order of magnitude (0.53–8 ${M}_{\odot }$). However, the initial mass function of stars, the relatively low star formation rate of the solar neighborhood in recent cosmological times, and the rapid increase in mass-loss rate toward the end of a star's life should dramatically bias the mass distribution to the range of ∼0.7–1.4 ${M}_{\odot }$ (e.g., Basu & Rana 1992; Aumer & Binney 2009). The dust-producing stars shown in Figure 2(a) cover a factor of ∼10 in luminosity, yet, despite the expected homogeneity of the stellar parameters, no correlation is seen between luminosity and infrared dust excess.

The various plots in Figure 2 show that both bright and faint stars produce dust, therefore luminosity is not the primary driver of dust production in most local AGB stars, and stellar mass-loss rate cannot be easily defined in terms of luminosity. Pulsation amplitude and dust production are correlated, but both the small- and large-amplitude pulsators still produce dust. Of all the related parameters (luminosity, period and amplitude), the clearest onset of dust production comes with the change in pulsation period (Figure 1).

The onset of strong dust production at a 60 day pulsation period in AGB stars, already found in Baade's Window and (tentatively) toward the LMC, also exists in local stars. These three very different populations have different star formation histories (i.e., different stellar masses) and different metallicities, and the consistency of this 60 day period among them strongly suggests that it is the trigger of stellar dust production. The question remains as to whether this is a true step function in stellar mass-loss rate, or whether it is simply that dust begins to condense in an already-established wind.

Few homogeneously derived gas mass-loss rates exist for stars with such short periods. Some constraint comes from Groenewegen (2012) and McDonald et al. (2016), which examine two very similar stars close to the 60 day boundary: VY Leo and EU Del, respectively. Both are barely producing dust (K_s–[22] = 0.465 and 0.729 mag, respectively). Their gas mass-loss rates are a few ×10⁻⁹ and a few ×10⁻⁸ ${M}_{\odot }$ yr⁻¹, respectively. Both dust and gas mass-loss rates are difficult to determine with absolute accuracy, but the similarities in their outflow velocities indicate that they should have good relative accuracy. Accounting for the likely metal-paucity of EU Del ([Fe/H] ≈ –0.27 dex), these are commensurate with our adopted mass-loss rate to K_s–[22] color conversion, and indicate that the dust:gas ratio does not change appreciably as one approaches the 60 day transition. This suggests dust condensation is roughly as efficient for stars below and above our K_s–[22] = 0.85 mag cutoff, although further data for stars across the 60 day transition will be needed to show this conclusively.

The significance of the 60 day period remains undetermined. Mosser et al. (2013) fit a relationship between pulsation period and amplitude. For this relationship, pulsation acceleration approaches the surface gravity of the star at a period of ∼60 days. This would allow the ballistic motion of the pulsation to eject the outer envelope of the star, with the mass-loss rate being set by the density of the unbound region. The sharp increase at 60 days would therefore correspond to the unbound region migrating inward to reach a density jump in the stellar atmosphere. However, we note that the Mosser et al. (2013) analysis ignores stellar temperature variations, whereas we know that the spectral types of these stars change considerably (Samus et al. 2006).

We have shown that stars can start to produce dust at 60 days, but not all do. Their distribution across the RGB tip indicates the dusty stars are AGB stars. However, the surface properties of AGB and RGB stars are very similar at this point. Observations in the Magellanic Clouds show that RGB stars typically populate the second and third overtone pulsations, but not the first, which is apparently exclusively reserved for AGB stars (Soszyński 2009). As noted above, the vast majority of evolved stars in the solar neighborhood have present-day masses in the range ∼0.7–1.4 ${M}_{\odot }$, hence initial masses in the range ∼0.8–1.4 ${M}_{\odot }$. Periods of 50–80 days represent the evolutionary phase where AGB stars of 0.8–1.4 ${M}_{\odot }$ will transition onto the first overtone period (sequence ${C}^{\prime }$ in Wood 2015, Figure 10). It may be that pulsation on this sequence is required to initiate dust production, as noted by Boyer et al. (2015).

The slightly lower mean metallicity of the Magellanic Clouds (canonically [Fe/H] = −0.3 dex) results in a slightly different timing of the transition between pulsation modes. For a star of given mass and given luminosity (near the RGB tip), stellar radius of a star at [Fe/H] = 0 dex will be ≈15% larger than one at [Fe/H] = −0.3 dex due to the increased atmospheric metal-line and molecular opacity (e.g., Dotter et al. 2008). This implies a density (ρ) decrease of ∼44%. Since $P\propto \sqrt{\rho }$ (e.g., Catelan & Smith 2015), the pulsation period should be ≈22% or ∼13 days longer for the [Fe/H] = 0 dex star compared to the [Fe/H] = −0.3 dex star. While pulsation period clearly appears to be a major factor in driving strong stellar mass loss, other factors (radius, temperature, etc.) may also be important. These may be traced by repeating our present study in environments of differing metallicity.

The correlations we identify with pulsation period, amplitude, and sequence indicate that pulsation triggers the dusty wind of evolved AGB stars. The lack of correlation between dust excess and luminosity shows that dust driving is not an important factor at this stage, although it may become important later. We therefore reach the following conclusions:

• 1.  
  Strong mass loss does not normally begin until the pulsation period exceeds ∼60 days.
• 2.  
  Most AGB stars with $P\gtrsim 120$ days produce copious dust.
• 3.  
  Strong mass loss starts here for AGB stars, but not typically for RGB stars.
• 4.  
  Observations of VY Leo and EU Del indicate that this appears to be an increase in mass-loss rate, not just dust-production rate. While not conclusively shown, it may be linked to pulsations providing a ballistic trajectory to the outermost atmosphere that allows it to escape from the star without substantial radiation pressure on dust.
• 5.  
  Pulsation period and amplitude may together define the mass-loss rate during this early dust-producing phase. A survey of circumstellar CO lines for stars in this regime is suggested, in order that a relation can be defined between pulsation properties and both stellar mass-loss rates and terminal wind velocities.
• 6.  
  The data are still consistent with the previously published increase in mass-loss rate at $P\sim 300$ days. This would correspond to the stars moving from the first overtone to the fundamental mode. However, relating pulsation period to mass-loss rate likely requires a step function to accommodate this transition.

This work was supported by the UK Science and Technology Research Council, under grant number ST/L000768/1.