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Astron. Astrophys. 319, 578-588 (1997)

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1. Introduction

Over the past decade some circumstantial evidence has been obtained that cool dwarf stars may be loosing mass at considerably higher rates than the Sun. The first evidence was found in a UV spectrum of the detached binary V471 Tau (Mullan et al., 1989). This system consists of a white dwarf and a K2V star. Discrete absorption features in the UV continuum of the dwarf could be identified as mass ejections from the K2V star. The temperature of the ejecta was [FORMULA] and the total mass loss rate caused by the ejecta was estimated to be a few times [FORMULA]. Houdebine et al. (1990) obtained optical spectra during a flare event on the dMe star AD Leo. It was found that a coronal mass ejection took place during the flare. Based on the flare frequency and depending on the temperature of the ejecta these authors argued that the total flare-related mass loss is the range [FORMULA].

Doyle and Mathioudakis (1991) published the first tentative ([FORMULA]) detections of two dMe stars at wavelengths of 1.1 and 2 mm obtained with the JCMT. The authors pointed out that the observed fluxes indicate the presence of excess emission at these wavelengths above the black-body emission from the star.

Mullan et al. (1992, hereafter MDRM) pointed out that the combination of radio, JCMT and IRAS data is indicative of the presence of a power-law flux distribution [FORMULA] with [FORMULA] in the radio - IR range. In Fig. 1 we have reproduced the data on which MDRM based their conclusions. Such power-law distributions are commonly found in the spectra of early type stars undergoing mass loss at rates of [FORMULA] (Wright and Barlow, 1975, Lamers and Waters, 1984). By applying the expressions for the expected flux from a mass loosing star, as derived for winds from hot stars, MDRM concluded that certain dMe stars undergo mass loss of rates of a few times [FORMULA]. This would have profound implications for the mass balance in the interstellar medium. MDRM estimate the total number of M dwarfs in the galactic disk to exceed [FORMULA]. The total mass supply to the interstellar medium from the winds of M dwarfs could then amount to [FORMULA]. This value is twenty times higher than the mass supply from the `normal' donors: OB stars, planetary nebula etc.. In this way M stars could play an important role in the enrichment of the interstellar medium.

[FIGURE] Fig. 1a-c. Reproduction of the data on which MDRM based their estimates for the mass loss rates for dMe stars. The power-law approximations run between the radio data and the IRAS data. The data near [FORMULA] are from the JCMT. The objects shown are a Gliese 285 = YZ CMi, b Gliese 644 = Wolf 630 and c Gliese 873 = EV Lac.

There are two important assumptions in the work by MDRM. Firstly, it is assumed that the radio, mm and infrared fluxes are caused by the presence of a stellar wind. Secondly, it is assumed that mass loss rates of [FORMULA] do result in a power-law flux distribution. The first assumption has important consequences for the interpretation of ISO data. The evidence for a wind emission is however scant if one looks at the data. The IRAS fluxes at [FORMULA] m and [FORMULA] m are in reasonable agreement with what is expected from the stellar Planck function. The excess emission is only present at [FORMULA] m and [FORMULA] m but these data points are very uncertain due to cirrus or extended source sizes. The JCMT data points are near the detection thresh-hold of the bolometric instrument used on the JCMT at that time, resulting in less than [FORMULA] detections. The radio emission from dMe stars is commonly interpreted as gyro-synchrotron emission from non-thermal particles or coherent emission and not as free-free emission. The observed variability, the polarization and the required emission measure argue against a wind interpretation. Concerning the second assumption it must be noted that the derived mass loss rates for the dMe stars are factors [FORMULA] smaller than those of hot stars. This leads to a decrease of the optical depth in the wind and, as we will show, a modification of the spectrum. A second important difference is that for the winds from hot stars the temperature of the wind is in general lower than the temperature of the star while for cool M dwarfs the reverse holds. This leads to a substantial modification of the flux distribution compared to the distributions found for hot stars.

Because of the importance of mass loss from M dwarfs for the mass balance in the interstellar medium, and because of the importance for the interpretation of ISO data we have re-analyzed the data presented by MDRM. Instead of applying the expressions for winds from hot stars we have solved the radiative transfer problem for winds near cool stars. We show that winds from cool stars do not result in a power-law distribution in the radio - IR frequency range. Furthermore we show, by using observational constraints, that the mass loss from the dMe stars cannot be higher than a few times [FORMULA].

When this work was completed Lim and White (1996) published independently similar constraints for the mass loss from dMe stars. These authors report an upper limit of 10 mJy at 3.5 mm for YZ CMi obtained with the BIMA array. The detection by MDRM of a flux of [FORMULA] at 1.1 mm can be reconciled with the BIMA result by noting that the detection at 1.1 mm was only at a [FORMULA] level. Lim and White base their constraints on the fact that the nonthermal radio emission from dMe stars must not be absorbed by a stellar wind, a point we also address in this paper. In this paper we take however into account the ionization state of the wind which permits us to pose constraints on the mass loss rate for a range of wind temperatures. Also we show that the expressions for the flux from a wind, as derived by e.g. Wright and Barlow (1975), cannot be applied directly when the mass loss rate is low and the wind temperature exceeds the temperature of the star.

The outline of the paper is as follows. In Sect.  2 we derived the basic expressions for the free-free emission from a wind taking the ionization balance into account. Also we present effective gaunt factors as follow from a self-consistent treatment of the ionization balance. In Sect.  3 we apply the resulting expressions to the flux distributions discussed by MDRM. Additional observational constraints for the mass loss from dMe stars are discussed in Sect.  4. Our conclusions are presented in Sect.  5.

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© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998