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A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
08(08.12.1;08.13.2;09.07.1;13.09.6;13.18.5;13.21.5)
ASTRONOMY
AND
ASTROPHYSICS
4.9.1996
Constraints on mass loss from dMe stars: theory and observations
G.H.J. van den Oord 1 and J.G. Doyle 2
1 Sterrenkundig Instituut, p.o. box 80.000, 3508 TA Utrecht, The Netherlands
2 Armagh Observatory, Armagh BT61 9DG, N. Ireland
Received ;accepted
Abstract. We show that the flux distribution of a wind from a
cool star differs considerably from what is predicted by the the­
ory for mass loss from hot stars. The differences are caused by
the facts that 1) the mass loss rates are lower, resulting in smaller
optical depths in the wind, and 2) for winds from cool stars the
temperature of the wind is higher than the temperature of the star
while for winds from hot stars the reverse holds. These differ­
ences result in substantial modifications of the flux distribution
and imply that care must be exercised when applying the flux
predictions by e.g. Wright and Barlow (1975) to winds from
cool stars. By using observational constraints we show that the
mass loss from cool dwarf stars equals at most 10 \Gamma12 M fi =yr.
This is a factor hundred lower than previous estimates. At this
rate the mass loss from dMe stars is of little importance for
the enrichment of the interstellar medium. By solving the ra­
diative transfer equations for stellar winds from dMe stars, we
show that the inferred power­law flux distributions, based on
radio, JCMT and IRAS data, cannot be reconciled with the
flux distributions from a stellar wind of 10 \Gamma10 M fi =yr as was
previously assumed. The maximum allowable mass loss rate is
at most a few times 10 \Gamma12 M fi =yr which implies that the fluxes
observed with JCMT, IRAS, and in the future with ISO, re­
quire a different interpretation than free­free emission from a
stellar wind.
Key words: Stars:late­type -- Stars:mass­loss --ISM:general --
Infrared:stars -- Radio continuum:stars -- Ultraviolet:stars
1. Introduction
Over the past decade some circumstantial evidence has been
obtained that cool dwarf stars may be loosing mass at consid­
erably 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 ! ¸ 2 10 4 K and the total mass
loss rate caused by the ejecta was estimated to be a few times
10 \Gamma11 M fi =yr. 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 flare­related mass loss is the
range 2:7 10 \Gamma13 \Gamma 4:4 10 \Gamma10 M fi =yr.
Doyle and Mathioudakis (1991) published the first tentative
(2oe) 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 black­body 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 power­law flux distribution F š ¸ š ff with
ff ú 0:7\Gamma1 in the radio -- IR range. In Fig. 1we 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 10 \Gamma5 \Gamma 10 \Gamma8 M fi =yr
(Wright and Barlow, 1975, Lamers and Waters, 1984). By ap­
plying the expressions for the expected flux from a mass loos­
ing star, as derived for winds from hot stars, MDRM concluded
that certain dMe stars undergo mass loss of rates of a few times
10 \Gamma10 M fi =yr. 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 10 11 . The
total mass supply to the interstellar medium from the winds of
M dwarfs could then amount to 10 M fi =yr. 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.
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 10 \Gamma10 M fi =yr do result in a
power­law 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 12¯m and 25¯m are in reasonable agreement
with what is expected from the stellar Planck function. The ex­
cess emission is only present at 60¯m and 100¯m but these data

2 G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations
Fig. 1. Reproductionof the data on whichMDRM basedtheir estimates
for the mass loss rates for dMe stars. The power­law approximations
run between the radio data and the IRAS data. The data near log š = 11
are from the JCMT. The objects shown are (a) Gliese 285 = YZ CMi,
(b) Gliese 644 = Wolf 630 and (c) Gliese 873 = EV Lac.
points are very uncertain due to cirrus or extended source sizes.
The JCMT data points are near the detection thresh­hold of the
bolometric instrument used on the JCMT at that time, resulting
in less than 3oe detections. The radio emission from dMe stars
is commonly interpreted as gyro­synchrotron emission from
non­thermal particles or coherent emission and not as free­free
emission. The observed variability, the polarization and the re­
quired 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 10 2 \Gamma 10 5
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
re­analyzed 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 power­law distribu­
tion 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 10 \Gamma12 M fi =yr.
When this work was completed Lim and White (1996) pub­
lished 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 13:2 \Sigma 6 mJy at 1.1 mm can be reconciled
with the BIMA result by noting that the detection at 1.1 mm
was only at a 2oe 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 free­free emission from a wind
taking the ionization balance into account. Also we present ef­
fective gaunt factors as follow from a self­consistent treatment
of the ionization balance. In Sect. 3 we apply the resulting
expressions to the flux distributions discussed by MDRM. Ad­
ditional observational constraints for the mass loss from dMe
stars are discussed in Sect. 4. Our conclusions are presented in
Sect. 5.

G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations 3
2. Free­free emission from a wind
For a spherically symmetric wind the equation for mass con­
servation reads
_
M = 4úr 2 ae(r)v(r) = 4úr 2 v(r)¯mH n i (r) (1)
where _
M is the mass loss rate, ae is the mass density, v is the
wind velocity, mH is the hydrogen mass, n i is the ion density
and ¯ is the mean atomic weight per ion. Because the observed
emission originates from the ionized gas component in the wind
it is necessary to consider the ionization balance in the wind.
Let n e be the electron density, n Z;z the ion density of the ions
from the element with atomic number Z and with a charge z, n Z
the total density of neutrals and ions of the elements with atomic
number Z and A Z = n Z =nH the element abundance. Note that
nH = n(H I) + n(H II). The electron density is given by
n e =
X
Z;z
n Z;z z = nH
X
Z;z
A Z
n Z;z
n Z
z j nHS e (2)
while the ion density is given by
n i =
X
Z;z
n Z;z = nH
X
Z;z
A Z
n Z;z
n Z
j nHS i . (3)
The average number of electrons per ion is given by n e =n i =
S e =S i j fl and the mean atomic mass per ion is given by
¯ = ae
mHn i
= 1
S i
X
Z
A Z
m Z
mH . (4)
The fraction of neutral hydrogen is given by i j n(H I)=n H .
Since there is no information available from observations
concerning the ionization balance in the wind, the most plau­
sible assumption one can make is that, after an initial accel­
eration of the wind, the ionization balance is frozen­in due to
the rapid decrease of the density. The ionization balance in the
wind then reflects the ionization balance at the base of the wind
which is determined by collisional ionization equilibrium. We
determined the values of S e , S i , fl, ¯ and i using the ioniza­
tion balance by Arnaud and Raymond (1992) for iron and by
Arnaud and Rothenflug (1985) for the other elements. Solar
photospheric abundances were assumed (Anders and Grevesse,
1989). The results are presented in Table 1 for a number of wind
temperatures in the range 8000 \Gamma 10 6 K.
The linear free­free absorption coefficient is given by
(Allen, 1973)
Ÿ(š; T ) = 3:692 10 8
ae
1 \Gamma exp
`
\Gammahš
kT
'oe
T \Gamma1=2 š \Gamma2
\Thetan e
X
Z;z
n Z;z z 2 g ff (Z; z; š; T ) . (5)
The second part of this expression can be written as
fln 2
i G ff (š; T ) with
G ff (š; T ) =
P
Z;z n Z;z z 2 g ff (Z; z; š; T )
P
Z;z n Z;z
. (6)
Fig. 2. Gaunt factors, as follow from Eq. (6), as a function of the
frequency and for fifteen values of the temperature. Higher curves
correspond to higher temperatures.
Table 1. Values for S e = n e =nH , S = n i =nH , ¯ = ae=(mHn i ) and
i = n(H I)=nH as follow from collisional ionization equilibrium for a
number of temperatures. G ff;R is the gaunt factor at frequency 10 9:7 Hz.
T(K) S e S ¯ i G ff;R
8000 4 10 \Gamma7 4 10 \Gamma7 3:528 10 6 1 4.9986
10000 3 10 \Gamma3 3 10 \Gamma3 466.3 0.997 5.1827
15000 0.419 0.419 3.369 0.582 5.5173
20000 0.935 0.935 1.508 6:66 10 \Gamma2 5.7644
25000 1.004 1.004 1.405 1:09 10 \Gamma2 5.9574
30000 1.053 1.053 1.340 3:09 10 \Gamma3 6.1103
35000 1.085 1.085 1.300 1:23 10 \Gamma3 6.2415
40000 1.094 1.094 1.289 5:98 10 \Gamma4 6.3592
45000 1.097 1.097 1.286 3:36 10 \Gamma4 6.4662
50000 1.099 1.098 1.285 2:08 10 \Gamma4 6.5693
60000 1.105 1.099 1.284 9:81 10 \Gamma5 6.8255
80000 1.155 1.099 1.283 3:50 10 \Gamma5 7.9481
10 5 1.181 1.099 1.283 2:17 10 \Gamma5 8.6460
5 10 5 1.203 1.099 1.283 6:50 10 \Gamma7 10.923
10 6 1.203 1.099 1.283 2:53 10 \Gamma7 11.6569
For calculating the gaunt factors we followed the procedure
outlined by Waters and Lamers (1984) with the exception that
Lamers and Waters write G ff = z 2 g(š; T ) with z 2 the mean
value of the squared atomic charge. In our case separating out
z 2 would be impractical given the form of Eq. (6). For low
values of hš=kT we use the expression for the gaunt factor
given by Allen (1973) but with the correction discussed by
Leitherer and Robert (1991). For high values of hš=kT we use
the expression by Mewe et al. (1986) (see also Gronenschild
and Mewe, 1978). In practice we took the maximum value for

4 G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations
G ff , at a given temperature and frequency, which resulted from
these approximations. The results are shown in Fig. 2.
By introducing the dimensionless parameters x = r=R \Lambda and
w(x) = v(r)=v 1 , the absorption coefficient can be written as
Ÿ(š; x) = X \Lambda X š
\Phi
R \Lambda w 2 (x)x 4
\Psi \Gamma1
(7)
with
X \Lambda = 3:692 10 8 h
k
` _
M
4úmH v1
' 2
T \Gamma3=2 R \Gamma3
\Lambda
fl
¯ 2 (8)
and
X š = 1 \Gamma exp(\Gammahš=kT )
hš=kT
š \Gamma2 G ff . (9)
The constant X \Lambda is independent of the frequency.
The total flux emitted by the star and the wind is easily
calculated following the standard procedure outlined by Wright
and Barlow (1975), Panagia and Felli (1975) and Lamers and
Waters (1984). The total flux F š = 4úd 2 f š is given by
F š = 8ú 2 R 2
\Lambda
Z 1
0
B \Lambda e \GammaÜ max (q) qdq
+8ú 2 R 2
\Lambda
Z 1
0
Bw
\Gamma 1 \Gamma e \GammaÜ max (q)
\Delta qdq (10)
where B \Lambda = B(š; T \Lambda ), Bw = B(š; Tw ), B(š; T ) is the Planck
function, T \Lambda is the black­body temperature of the star, Tw is the
wind temperature and q is the impact parameter of the line of
sight (see e.g. Fig. 1 in Lamers and Waters, 1984). The optical
depth at impact parameter q is given by
q ? 1 : Ü max (q) = 2
Z 1
q
X \Lambda X š
w 2 x 3
p
x 2 \Gamma q 2
dx
q Ÿ 1 : Ü max (q) =
Z 1
1
X \Lambda X š
w 2 x 3
p
x 2 \Gamma q 2
dx
The optical depth depends of course on the assumed velocity
law of the wind for which no information is available from
observations. Therefore we use in this paper a velocity law for
a wind which is accelerating up to some distance R 1 and then
obtains its final velocity v 1
v(r) = v 0 (r=R \Lambda ) fi for r ! R 1 ; v(r) = v1 for r – R 1 .
The acceleration of the wind is determined by the value of fi.
The dimensionless velocity is given by w = (x=x 1 ) fi for x ! x 1
and w = 1 for x – 1.
Given a velocity law for the wind, the run of the ion density
in the wind n i (r) can be determined from Eq. (1). In Table 2 the
related expressions for Ü max (q) are listed. Also listed in Table 2
are the expressions for the emission measure EM of the wind
and the neutral hydrogen column density NH along the line of
sight at the centre of the star. For the emission measure we took
into account that part of the wind does not contribute since it is
obscured by the star.
With the expressions for Ü max (q), as given in Table 2, part
of Eq. (10) can be evaluated analytically resulting in
F š
8ú 2 R 2
\Lambda
=
Z 1
0
B \Lambda e \GammaÜ max (q) qdq +
Z 1
0
Bw
\Gamma 1 \Gamma e \GammaÜ max (q)
\Delta
qdq
+
Z x 1
1
Bw
\Gamma
1 \Gamma e \GammaÜ max (q)
\Delta
qdq
+ Bw
1
2 x 2
1
ae
e \GammaV \Gamma 1 + V 2=3 fl(
1
3 ; V )
oe
(11)
with V = (ú=2)X \Lambda X š =x 3
1 and fl(a; x) the incomplete Gamma
function (Abramowitz and Stegun, 1968). The first term on
the right accounts for the emission by the star, which can be
attenuated by absorption due to the wind. The second term
accounts for the emission from the cone in front of the star
while the third term accounts for the emission from the wind
acceleration region outside the previously mentioned cone. The
fourth term described the emission from the volume (outside
the cone) where the wind has reached its terminal velocity. Note
that for a wind with constant velocity (x 1 = 1) the third term
does not contribute. At low frequencies, at which Ü is large,
only the last term effectively contributes to the flux resulting in
F š = 4ú 2 R 2
\Lambda Bw \Gamma(
1
3 )
` 1
2 úX \Lambda X š
' 2=3
= 5:14 10 \Gamma6
` fl
¯ 2
' 2=3 ` _
M
v1
' 4=3
(G ff š) 2=3 (12)
which is identical to the expression found by Wrightand Barlow
(1975). At higher frequencies, at which Ü becomes small, we
can make the approximation 1 \Gamma exp(\GammaÜ max (q)) ú Ü max (q) in
Eqs. (10) and (11). Evaluation of the resulting integrals shows
that, at frequencies at which the emission is optically thin, the
flux is given by
F š = 4ú 2 R 2
\Lambda B \Lambda + 8ú 2 R 2
\Lambda BwX \Lambda X š P (x 1 ; fi)
= 4ú 2 R 2
\Lambda B \Lambda + EM ffl(š; T ) (13)
with P (x 1 ; fi) given in Table 2 and ffl(š; T ) the free­free emis­
sivity (e.g. Rybicki and Lightman, 1979)
ffl(š; T ) = 6:8 10 \Gamma38
T 1=2 exp
` \Gammahš
kT
'
G ff erg s \Gamma1 cm 3 Hz \Gamma1 . (14)
The last identity in Eq. (13) results from applying Kirchhoff's
law. As could be anticipated, in the optically thin part of the
spectrum the flux is composed of the contributionby the star and
the free­free emission from a wind with an emission measure
EM .
For completeness we present in Table 2 also the effective
radius r eff and the effective optical depth Ü eff (see Wright and
Barlow, 1975). The effective radius is defined by assuming that
the emission at a given frequency originates from the volume
at r ? r eff
F š =
Z 1
r eff
(4ú) 2 Bw (š; Tw )Ÿ(š; Tw )r 2 dr
with F š given by Eq. (10). The effective optical depth is then
defined by Ü eff =
R 1
r eff
Ÿ(š; Tw )dr.

G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations 5
Table 2. Expressions for: the optical depth at impact parameter q (see Eqs. (10) and (11)), the emission measure EM of the visible part of a
isothermal stellar wind, the neutral hydrogen column density NH , the effective radius r eff and the effective optical depth Ü eff .
Optical depths as function of impact parameter q:
q = 0 Ümax (q) = 1
3 X \Lambda Xš
\Theta 3
2fi+3 x 2fi
1
\Gamma
1 \Gamma x \Gamma2fi\Gamma3
1
\Delta
+ x \Gamma3
1
\Lambda
j 1
3 X \Lambda XšH(x 1 ; fi)
0 ! q Ÿ 1 Ümax (q) = X \Lambda Xš
h 1
2
\Gamma x 1
q
\Delta 2fi
q \Gamma3
n
B q 2 (fi + 3
2 ; 1
2 ) \Gamma B q 2 =x 2
1
(fi + 3
2 ; 1
2 )
o
+ 1
2 q \Gamma3 B q 2 =x 2
1
( 3
2 ; 1
2 )
i
1 ! q ! x 1 Ümax (q) = X \Lambda Xš
h \Gamma x 1
q
\Delta 2fi
q \Gamma3
n
B(fi + 3
2 ; 1
2 ) \Gamma B q 2 =x 2
1
(fi + 3
2 ; 1
2 )
o
+ q \Gamma3 B q 2 =x 2
1
( 3
2 ; 1
2 )
i
q – x 1 Ümax (q) = 1
2 úX \Lambda Xš q \Gamma3
H(1; fi) = 1; for x 1 – 2: H(x 1 ; fi) ú 3
2fi+3 x 2fi
1
Emission measure visible part isothermal wind (without contribution from cone obscured by the star):
EM =
R
V vis
n e n i d 3 r = fl
R
V vis
n 2
i d 3 r j EM 0 P (x 1 ; fi)
EM 0 = 2úflR 3
\Lambda
i _
M
4úR 2 \Lambda v1¯m H
j 2
= 1:1 10 53 F 3=2
R;13
1
G ff;R
i
R \Lambda
R fi
j \Gamma1
= 8:1 10 52
i _
M \Gamma10
v 1;7
j 2
i
R \Lambda
R fi
j \Gamma1 fl
¯ 2 cm \Gamma3
P (x 1 ; fi) j x 2fi
1
2fi+1
\Gamma 1 \Gamma x \Gamma2fi\Gamma1
1
\Delta + 1
x 1
1
2 x 2fi
1
i
B(fi + 1
2 ; 3
2 ) \Gamma B 1=x 2
1
(fi + 1
2 ; 3
2 )
j
+ 1
2 B 1=x 2
1
( 1
2 ; 3
2 )
P (1; fi) = 1 + ú=4; for x 1 – 2: P (x 1 ; fi) ú x 2fi
1
\Gamma 1
2fi+1 + 1
2 B(fi + 1
2 ; 3
2 )
\Delta
Neutral hydrogen column density:
NH =
R 1
R \Lambda n(H I)dr = i
R 1
R \Lambda nHdr = i
S i
R 1
R \Lambda n i dr j N 0
ae
1
x 1
+ x fi
1
fi+1
\Gamma 1 \Gamma x \Gammafi\Gamma1
1
\Delta oe
N 0 = R \Lambda
i _
M
4úR 2 \Lambda v1¯m H
j
i
S = 4:3 10 20
i
R \Lambda
R fi
j \Gamma1 _
M \Gamma10
v 1;7
i
¯S i
= 5 10 20
i
R \Lambda
R fi
j \Gamma1
F 3=4
R;13 (G ff;R fl) \Gamma1=2 i
S i
cm \Gamma2
Effective radius x eff = r eff =R \Lambda :
x eff ? x 1 x eff = X \Lambda XšBw (4úR \Lambda ) 2 =Fš
x eff ! x 1 Fš = X \Lambda XšBw(4úR \Lambda ) 2
ae
1
x 1
+ x 2fi
1
2fi+1
\Gamma x \Gamma2fi\Gamma1
eff \Gamma x \Gamma2fi\Gamma1
1
\Delta oe
at radio frequencies x eff AE x 1 : x eff = 4(X \Lambda Xš ) 1=3 (ú=2) \Gamma2=3 =\Gamma( 1
3 )
Effective optical depth Ü eff :
x eff ? x 1 Ü eff = 1
3 X \Lambda Xšx \Gamma3
eff
x eff ! x 1 Ü eff = X \Lambda Xš
2fi+3 x 2fi
1
\Phi x \Gamma2fi\Gamma3
eff \Gamma x \Gamma2fi\Gamma3
1
\Psi
at radio frequencies x eff AE x 1 : Ü eff = 1
3 X \Lambda Xšx \Gamma3
eff = 0:2471

6 G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations
Fig. 3. Flux distributions for constant velocity winds with temperatures of (a) Tw = 4 10 4 K and (b) Tw = 10 6 K. The dots are the observed
fluxes for YZ CMi (Fig. 1a). The thick solid line is the resulting distribution from the wind and the star (Eq. (11)). The thin solid line is the
contribution by the wind which dominates at low frequencies. The dashed­triple dot line is the contribution by the star (first term in Eq. (11)).
The dashed line is the black­body curve for the star and the dotted line that for the wind. For these curves the area is taken equal to the stellar
disk. The dashed­dotted line is the optically thin approximation (Eq. (13)) which is very accurate at frequencies above the frequency š t .
3. Applications to observations
Fig. 1 shows that the flux distributions of the three objects
are very similar. Therefore we start with a discussion of the
flux distributions in general terms before turning to the specific
objects. From the observed flux at radio frequencies (Eq. (12))
it follows that
_
M \Gamma10
v1;7
= 1:17¯F 3=4
R;13 (G ff;R fl) \Gamma1=2 (15)
where _
M \Gamma10 is the mass loss rate in units of 10 \Gamma10 M fi =yr, v1;7
is the terminal wind velocity in units of 100 km/s, F R;13 is the
observed flux at 6cm (log š = 9:7) in units of 10 13 erg s \Gamma1 Hz \Gamma1 .
G ff;R is the gaunt factor at log š = 9:7 as given in Table 1.
Because for all objects F R;13 is of the order unity, Eq. (15)
shows that the radio fluxes imply mass loss rates of the order
of 10 \Gamma10 M fi =yr as was inferred by MDRM who took v 1;7 ú
3. Also it follows that the wind temperature has to be higher
than 10 4 K because otherwise ¯ is so large (see Table 1) that
unrealistic mass loss rates (? 10 \Gamma8 M fi =yr) result.
An important assumption made by MDRM is that the ob­
served power­law distribution F š ¸ š ff in the radio -- IR fre­
quency range is indicative of a stellar wind. This assumption
is based on the fact that similar power­laws are observed for
early type stars loosing mass. There is however an important
difference between the above inferred mass loss rate for dMe
stars and that of early type stars. The latter have mass loss rates
in the range 10 \Gamma5 \Gamma 10 \Gamma8 M fi =yr which is a factor 10 2 \Gamma 10 5
larger than the data for dMe stars suggest. This has important
consequences for the flux distribution because the lower mass
loss rates of dMe stars will result in smaller optical depths. This
leads to a modification of the spectrum and in the following we
show that, if dMe stars loose mass at a rate of 10 \Gamma10 M fi =yr,
the resulting flux distribution is not a power­law in the radio
-- IR range. Apart from the fact that the optical depths in the
winds differ, there is a second difference between early and late
type stars: for early type stars T \Lambda ? Tw while for dMe stars the
reverse holds.
Because hš=kT = 1 occurs at frequency š = 2 10 14 T 4 Hz
we can use for Bw and B \Lambda the Rayleigh­Jeans approximation
while in Eq. (9) X š ú š \Gamma2 G ff;R . From Eqs. (8) and (15) it
follows that
X \Lambda = 6:4 10 22 F 3=2
R;13 T \Gamma3=2
4
` R \Lambda
R fi
' \Gamma3 1
G ff;R
= 4:7 10 22
` _
M \Gamma10
v 1;7
' 2
T \Gamma3=2
4
` R \Lambda
R fi
' \Gamma3 fl
¯ 2 (16)
In order to discuss the flux distribution it is useful to consider
the optical depth along the line of sight passing through the
center of the star Ü max (0). Cassineli et al. (1977) have argued
that the emission originates from Ü = 1=3. It is convenient
to introduce the optical depth Ü 0 = X \Lambda X š H(x 1 ; fi) with H
defined in Table 2. At some frequency š t , Ü 0 will become unity.
Because Ü 0 ¸ X š ¸ š \Gamma2 , the transition between optically thick
and optically thin will occur rapidly near this frequency. Unit
optical depth corresponds to X \Lambda X š H = 1 or
š t = 2:54 10 11
p
H
/
F R;13 R 2
fi
T 4 R 2
\Lambda
! 3=4 ` G ff (š t ; T )
G ff;R
'1=2
Hz. (17)
For x 1 = 1 (constant velocity wind) H = 1. At frequencies
below š t the wind is optically thick and has a F š ¸ (G ff š) 2=3
spectral distribution while at higher frequencies the optically

G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations 7
Fig. 4. (a) Flux distributions for six combinations of x 1 and fi and a wind temperature of Tw = 4 10 4 K. The data points are those for YZ CMi.
Case 1 corresponds to Fig. 3a. (b) Contributions to the total wind emission for case 6 in panel (a). The solid curve is the total emission from the
wind. The curves labeled 2, 3 and 4 correspond to the second, third and fourth term on the left hand side of Eq. (11). Curve B 2 is the flux from
a black­body with a area equal to the stellar disk. Curve B 3 is the flux from a black­body with a area equal to the acceleration region minus the
stellar disk area. At frequency šx 1 the effective radius equals the size of acceleration region. At frequency š the emission becomes optically
thin and at frequency š 1 the effective radius equals the stellar radius.
thin approximation Eq. (13) applies. Eq. (13) shows that, in the
optically thin part of the spectrum, the contribution by the wind
is almost independent of frequency, at frequencies hš ! kTw ,
apart from a small variation caused by the frequency depen­
dence of the gaunt factor. We define š th j kTw=h. At š ? š th
the wind emission drops rapidly as exp(\Gammahš=kT w ).
Table 3. The values for šx 1 , š t and š 1 for the models shown in Fig. 4.
no. x 1 fi š 11 (x eff = x 1 ) š t;11 š 12 (x eff = 1)
1 1 0 19.9 7.9 1.99
2 2 0.5 3.4 9.6 2.43
3 2 1 3.4 10.3 3.04
4 2 5 3.3 98.5 27.66
5 5 0.5 0.9 14.5 3.68
6 5 1 0.9 27.7 7.05
In Fig. 3 we show the calculated emission from the star and
the wind (for x 1 = 1) as follows from numerical integration of
Eq. (11) for Tw = 4 10 4 K and Tw = 10 6 K (thick solid lines).
Also indicated are the black­body distributions from the star
and the wind, the separate contributions by the star and the
wind to the observed flux and the optically thin approximation
(Eq. 13). The data points for YZ CMi are also plotted. The fig­
ures clearly show that up to frequency š t the flux distribution
is that of a mass loosing star, as assumed by MDRM, but at
frequency š t the wind contribution becomes relatively flat. At
higher frequencies the contribution by the star starts to dom­
inate the spectrum. In the range š t ! š ! š th the variation
of the wind contribution is only caused by the gaunt factor. In
Fig. 3a frequency š th corresponds to 8 10 14 Hz above which
frequency the wind contribution drops exponentially. Note that
at frequencies ? š t the optically thin approximation (Eq. 13)
is very accurate. For low temperatures of the wind, like e.g.
4 10 4 K, the black­body emission by the star is slightly reduced
due to wind absorption but at those frequencies the wind emis­
sion dominates anyway. Figs. 3a and 3b show that frequency
š t goes up as the temperature of the wind increases. Because
š t ¸ T \Gamma3=4 , apart from a weak dependence on the Gaunt factor,
reducing the wind temperature to a value lower than 4 10 4 K,
like e.g. 1:5 10 4 K, does not improve the fit to the data points.
The reason is that at frequency š t the black body emission of
the wind varies as Bw ¸ š 2
t Tw ¸ T \Gamma1=2
w and is therefore only
weakly dependent on the wind temperature. At the same time,
for higher values of š t , the effective radius of the source r eff
becomes smaller. Together these effects result in that the flux
distributions of winds with Tw ! 4 10 4 K resemble very much
the flux distribution shown in Fig. 3a. We conclude that the
observed flux distribution cannot be reconciled with that of a
stellar wind because the IRAS­ and, depending on the wind
temperature, also the JCMT­data points are not fitted at all.
A possible way out would be to increase the optical depth so
that š t is found at IR frequencies. This can be accomplished by
allowing the wind to accelerate over some distance (so increas­
ing H in Eq. (17)). Fig. 3 shows that š t has to be increased by at
least a factor 100 in order to have the turn­over frequency near
the IRAS points and that cool winds are preferable. Eq. (17)
and Table 2 show that š t ¸
p
H ¸ x fi
1
p 3=(2fi + 3). There­
fore either x 1 or fi has to be large, or both. This has how­

8 G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations
ever a strong effect on the emission measure which scales as
EM ¸ P ¸ x 2fi
1 (1=(2fi + 1) + 0:5B(fi + 0:5; 1:5)). The strong
increase of the emission measure which occurs when the wind
is allowed to accelerate has a dramatic effect on the flux distri­
bution at high frequencies. To illustrate this we show in Fig. 4a
the flux distributions for six combinations of the parameters x 1
and fi. For each combination we give in Table 3 the values of
the frequencies at which the emission becomes optically thin
(š t ), at which the effective radius equals the acceleration region
(š x 1 at x eff = x 1 ) and at which the effective radius equals the
radius of the star (š 1 at x eff = 1). The combination x 1 = 1, fi = 0
(case 1) corresponds to the example given in Fig. 3a. In cases
2 ­ 4 we have kept the acceleration radius at two stellar radii
and varied fi while for cases 5 and 6 the acceleration radius is
at five stellar radii.
The figure clearly shows that as š t becomes higher the emis­
sion measure increases. This results in a (strong) increase of the
flux at high frequencies. For all combinations of x 1 and fi either
the IR data points are not fitted or there is too much flux at
frequencies above 10 15 Hz. The flux distributions can be ex­
plained by considering the contributions by the different terms
in Eq. (11). Because the IRAS data points are best fitted when
x 1 = 5 and fi = 1 we show in Fig. 4b the contributions by the
different terms in Eq. (11) as an illustration. We start with the
last term in Eq. (11) (curve 4 in Fig. 4b) which dominates at low
frequencies and results in a F š ¸ (G ff š) 2=3 distribution. The
part in the curly brackets can be approximated as \Gamma(1=3)V 2=3
for V ? 5 and as 2V for V ! ¸ 5. This implies that near V = 5
the contribution by this term will change. V = 5 corresponds to
X \Lambda X š = (10=ú)x 3
1 = 3:18x 3
1 . The frequency at which the effec­
tive radius equals the acceleration radius (x eff = x 1 , see Table 2)
corresponds to X \Lambda X šx 1
ú (\Gamma(1=3)=4) 3 (ú=2) 2 x 3
1 = 0:74x 3
1 .
Combining these expressions we see that V = 5 corresponds
to a frequency
p 0:74=3:18š x 1 ú 0:5š x 1 . Above this frequency
the contribution by the last term in Eq. (11) becomes flatter and
becomes proportional to Bwx 2
1 V = (ú=2)Bw X \Lambda X š =x 1 . This
shows that for larger values of x 1 this term becomes relatively
smaller at high frequencies. The flattening of the contribution
above frequency 0:5š x 1 is clearly visible in curve 4 in Fig. 4b.
The second and third term of Eq. (11) are shown as curves
2 and 3 in Fig. 4b. At low frequencies, at which the emission
is optically thick, these terms equal 0:5Bw and 0:5Bw (x 2
1 \Gamma 1)
respectively. Their sum equals the flux from a black­body at
temperature Tw and with a surface area set by the size of the
acceleration region. Above frequency š x 1 the outer parts of the
acceleration region become increasingly optically thin. This has
the effect that towards higher frequencies one observes the flux
from a black­body Bw with a decreasing surface area (curve
3). At frequency š the emission becomes optically thin. This
occurs before frequency š 1 (at which r eff = R \Lambda ) is reached. In
the frequency range š x 1
! ¸ š ! š t the second and third term
in Eq. (11) dominate. Because at these frequencies the flux is
proportional to Bw , with Tw ? T \Lambda , the flux can become rela­
tively strong (cases 4 and 6 in Fig. 4a). Table 3 shows that in
the consecutive cases 2, 3, 5, 6 and 4 the difference between š x 1
and š t becomes larger. Fig. 4a shows that larger differences be­
tween these frequencies are accompanied by stronger emission.
The reason is that we have Tw ? T \Lambda contrary to the situation in
winds near early type stars.
The arguments used by MDRM to explain the power­law
distributionsshown in Fig. 1 were based on the theory for stellar
winds from early type stars. Above we demonstrated that this
theory cannot be applied to the (possible) winds of late type
stars. The two fundamental differences are: 1) the derived mass
loss rates for dMe stars from the radio data are factors 10 2 \Gamma
\Gamma10 5 smaller than for early type stars. This implies that the
frequency at which the emission becomes optically thin (Ü ¸
X \Lambda X š ¸ ( _
M=š) 2 ), and the frequency at which r eff = R 1 , are
found at lower frequencies. This results in a deviation from
the power­law spectrum. MDRM assumed the presence of a
power­law distribution between the radio and IR data points. 2)
the winds in dMe stars are characterized by Tw ? T \Lambda . This has
the consequence that at IR frequencies the emission can become
very strong. Evenmore important is the fact that Tw ? T \Lambda results
in strong emission from the wind in the Wien part of the stellar
black­body distribution. Although the flux distributions in the
radio ­ IR range can be fitted by assuming the presence of a
wind acceleration region, these models predict too much flux at
frequencies š ? ¸ 10 15 Hz.
4. Alternative constraints
From the discussion in the previous section it must be con­
cluded that it is unlikely that dMe stars loose mass at rates of
10 \Gamma10 M fi =yr. If the mass loss rate is in reality lower, then
the radio, JCMT and IRAS data points require alternative ex­
planations. For the radio data these are readily available. The
common interpretation of radio emission from dMe stars is
gyro­synchrotron emission from non­thermal particles (or co­
herent emission). This interpretation is supported by the results
of Benz and Alef (1991) who discuss intercontinental VLBI ob­
servations of YZ CMi at 1.7 GHz. They found that the source
was not resolved at this frequency and found a radio diameter
of 1:0 \Sigma 0:5 mas or 1:7R \Lambda . The derived brightness temperature
was 1:7 10 9 K with a lower limit of 4 10 8 K. This brightness
temperature already rules out the possibility that the radio emis­
sion is caused by a stellar wind. If YZ CMi would be loosing
mass at a rate of ¸ 10 \Gamma10 M fi =yr, as suggested by MDRM,
then the effective radius at 1.7 GHz would amount to
x eff = r eff
R \Lambda
= 133
` _
M \Gamma10
v1;7
' 2=3
T \Gamma1=2
4
` fl
¯ 2
' 1=3 i g 1:7
5
j 1=3
with g 1:7 the gaunt factor at 1.7 GHz. A source of this size
would certainly have been resolved with intercontinental VLBI.
Alternatively, we can argue that at 1.7 GHz r eff has to be smaller
than the 1:7R \Lambda found by Benz and Alef. This gives an upper
limit for the mass loss rate which is compatible with the VLBI
results
_
M \Gamma10
v 1;7
! 1:4 10 \Gamma3 T 3=4
4
` ¯ 2
fl
' 1=2 i g 1:7
5
j \Gamma1=2
. (18)

G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations 9
This upper limit automatically implies that the wind is optically
thin at radio frequencies. The frequently observed nonthermal
emission from dMe stars implies that this emission is not ab­
sorped by a wind. Requiring that the optical depth of the wind
at e.g. 6 cm is less than unity gives
_
M \Gamma10
v 1;7
! 2:2 10 \Gamma3 T 3=4
4
` ¯ 2
fl
' 1=2 i g 5
5
j \Gamma1=2
. (19)
with g 5 the gaunt factor at 5 GHz. Comparing Eqs. (18) and
(19) shows that they have the same form but that the upper limit
set by the VLBI observations is slightly more restrictive.
Additional constraints on the mass loss rate can be obtained
by considering the observed fluxes at other frequencies. E.g.
from the data presented by Doyle (1989) it follows that the flux
from YZ CMi in the IUE--SWP band­pass (1150 \Gamma 1950 A)
amounts to log F IUE = 28 (in erg s \Gamma1 ). Gudel et al. (1993) give
for the flux in the ROSAT--PSPC band­pass (0:1 \Gamma 2:4 keV) a
flux of log F Rosat = 28:47. We have calculated the emissivities
in these band­passes for the temperatures listed in Table 1 us­
ing the Utrecht spectral code SPEX (Kaastra and Mewe, 1993,
Mewe and Kaastra, 1994). From the fact that any emission from
a stellar wind must not exceed the observed fluxes, a maximum
value for the permitted emission measure can be derived. By
using the expression for EM , as given in Table 2, this can be
translated into an upper limit for _
M=v1 . Another constraint
follows from the fact that the wind must not contribute sub­
stantially to the interstellar absorption between the star and the
observer. There have been no reports that spectral fits of EUV
and X­ray data from dMe stars require abnormal column den­
sities. Interstellar absorption is caused by photo­ionization. In
the expression for the neutral hydrogen column density given
in Table 2 we have only considered the presence of hydrogen.
In that way the expression for NH yields only an lower limit to
the absorption by a wind. By assuming that the absorption by
the wind must not exceed the canonical value NH = 10 18 cm \Gamma2
an additional constraint for _
M=v1 follows.
In Fig. 5we show the upper limits for _
M=v1 as followfrom
1) VLBI (Eq. (18)), 2) the neutral hydrogen absorption NH , 3)
the observed flux in the IUE -- SWP band­pass and 4) the ob­
served flux in the ROSAT -- PSPC band­pass. It is important
to emphasize that each curve, related to a specific instrument,
provides the best constraint in a specific temperature range, e.g.
for a hot stellar wind (¸ 10 6 K) the neutral hydrogen column
density would be a rather poor constraint; in this case it is better
to use the radio and/or X­ray data. At 10 5 K IUE and VLBI
provide good constraints. The figure shows that, as expected, at
low temperatures (! 17:000 K) the neutral hydrogen absorp­
tion provides the most stringent constraint. The upper limit for
the VLBI source size gives the most important constraint while
IUE and ROSAT also provide reasonably useful constraints.
Note that the latter constraints were derived assuming that the
emission by the wind equals at most the observed flux. If one
were to use as a constraint that the allowable wind emission is
only a fraction f of the observed flux (in order not to mask the
coronal emission), then the IUE and ROSAT curves in Fig. 5
must be multiplied by a factor p
f .
Fig. 5. Constraints on the mass loss rate of YZ CMi as follow from the
maximum source size set by VLBI observations, the observed fluxes
in the IUE -- SWP and the ROSAT -- PSPC, and the constraint
that the neutral hydrogen column density in the wind must be smaller
than 10 18 cm \Gamma2 . The horizontal axis corresponds to the temperature of
the wind. Each curve corresponds to the upper limit for _
M \Gamma10 =v1;7
as follows from a specific instrument or constraint. All curves are for
winds with constant velocities (x 1 = 1). At each temperature the lowest
curve presents the relevant constraint.
All curves in Fig 5 are calculated for winds without an
acceleration region (x 1 = 1). The constraints set by the IUE
and ROSAT fluxes are proportional 1= p
P (x 1 ; fi) ¸ 1=x fi
1 so
that the presence of an acceleration region near the star can
considerably reduce the upper limits for the mass loss shown
in the figure. The same applies for the constraint set by the
neutral hydrogen column density which (roughly) scales with
(fi + 1)=x fi
1 . Furthermore, all curves are for a terminal wind
velocity of 100 km/s. Higher velocities of the wind lead to a
proportionally higher vlaue for the allowable mass loss rate.
At low temperatures a large number of atoms in the wind
is not fully ionized. Therefore the permitted value for the mass
loss rate at temperatures ! ¸ 3 10 4 K is likely to be at least a
factor two lower than indicated in the figure because we did
not consider the presence of He, C, N and O in the expression
for NH . In­between the IUE and ROSAT curves, data from
the Extreme Ultraviolet Explorer EUVE can probably result in
additional constraints given the wavelength range covered by
the EUVE.ForYZCMinoEUVE data are however available to
us. Also more refined constraints can be obtained by considering
the observed fluxes from individual lines in e.g. IUE spectra.
For the moment we conclude that if the wind temperature is
in the range 2 10 4 Ÿ Tw Ÿ 10 5 K, the mass loss rates of dMe
stars must be ! ¸ 10 \Gamma12 M fi =yr. At higher temperatures a safe
upper limit is 2 10 \Gamma12 M fi =yr. At these rates the winds will not
result in an observable signal in the radio -- IR range. Because
the frequency at which the spectrum becomes optically thin is
proportional to the mass loss rate, š t will be at least a factor 100

10 G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations
lower than the values given in Table 3. At radio frequencies the
flux by the wind is reduced by at least a factor 10 8=3 = 464
(Eq. (12)).
The only way to infer the presence of such tenuous winds
is by considering the effect the wind has on the strength of
strong spectral lines at EUV wavelengths. Schrijver et al. (1994)
pointed out that strong lines can be subject to resonant scatter­
ing. Although scattering does not result in photon destruction,
except in the case of branching, these authors demonstrated
that, if an asymmetry is introduced between the emitting vol­
ume and the scattering volume, the photon flux towards the
star can be increased. The photons can then be destroyed at the
stellar surface. In the case of a chromosphere/corona embed­
ded in a stellar wind the required asymmetry follows naturally.
The photons emitted in the chromosphere or corona are then
scattered in the tenuous wind and a fraction is subsequently
destroyed upon impact at the stellar surface. Weak lines are
not affected by scattering and therefore this effect can lead to
a detectable difference between the ratio of line intensities of
weak and strong lines and the expected ratio. The optical depth
(at the line centre) for scattering is given by
Ü = 10 \Gamma19 C d
` A Z
A Z;fi
' n e `
p
T 6
.
The constants C d can be found in Schrijver et al. for a number
of strong lines. In general their values are in the range 0:5 ! ¸
C d ! ¸ 2. The electron column density of the scattering medium
is given by n e `. In the case of a stellar wind we have
n e ` = 4:3 10 18 fl
¯
` R \Lambda
R fi
' \Gamma1 _
M \Gamma12
v1;7 = 1:2 10 19 fl
¯
_
M \Gamma12
v1;7
where the last step applies to YZ CMi. These expressions show
that for mass loss rates of the order of 10 \Gamma12 M fi =yr the optical
depth for scattering can become unity leading to a detectable
effect. On the other hand it can be argued that if the mass loss
rate would be of the order of 10 \Gamma10 M fi =yr, the optical depth
for resonant scattering would be ¸ 100. This would have a
dramatic effect on the strong lines in EUV and X­ray spectra
which would be strongly attenuated. There is no observational
evidence that this occurs. An illustration of the effect of photon
scattering, for inferring the presence of a tenuous wind from
Procyon, can be found in Schrijver et al. (1996).
Finally we note that Fig. 5 is compiled under the assump­
tion that the wind is isothermal and that the ionization balance
reflects the kinetic temperature in the wind. If the temperature of
the wind would drop with radial distance, while the ionization
balance would be determined by a much higher freezing­in tem­
perature, a different situation arises. In that case we would be
dealing with a cool wind which is still e.g. fully ionized (`over­
ionized'). This results in a modification of the VLBI constraint.
The reason why the VLBI curve turns upward near 10 4 K is
that at low temperatures the plasma contains many neutrals and
¯ becomes large in Eq. (18). If we would be dealing with a cool
wind, which is over­ionized because of freezing­in at the base,
then ¯ and fl in Eq. (18) must be evaluated at the much higher
ionization temperature. Taking ¯ ú 1:283 and fl ú 1:09 (see
Table 1) changes the VLBI constraint to
_
M \Gamma10
v1;7 ! 1:7 10 \Gamma3 T 3=4
4
i g 1:7
5
j \Gamma1=2
(20)
with T now the kinetic temperature of the wind. This shows
that for cool over­ionized winds the VLBI constraint almost
coincides with the NH curve at T Ÿ 17:000 K. Of course, when
over­ionization due to a frozen­in ionization balance occurs the
NH curve is not relevant anymore because there are no neutrals.
But at the same time the VLBI constraint becomes as restrictive
as the original NH constraint at low temperatures.
5. Conclusions
In this paper we have demonstrated that the observed power­
law flux distributions of a number of dMe stars in the radio --
IR frequency range cannot be reconciled with that of a stellar
wind. Although the radio data suggest mass loss rates of the
order of 10 \Gamma10 M fi =yr, the resulting flux distribution is not a
power­law. The reason is that this mass loss rate is much lower
than the rates of hot stars leading to a reduction of the optical
depths in the wind and a corresponding modification of the
spectrum. A second difference is caused by the fact that for dMe
stars the temperatures of the winds are higher than the effective
temperatures of the stars. If the radio, JCMT and IRAS are to
be fitted simultaneously, it is necessary to invoke the presence of
a wind acceleration region. This increases the emission measure
of the wind so strongly that at high frequencies ? 10 15 Hz a
strong excess is present which has not been observed. This
excess is caused by the fact that the required emission measure
is so high and that Tw ? T \Lambda .
Reliable upper limits for the mass loss rate from dMe stars
can be obtained by considering the fact that the flux by the
wind must not exceed the observed fluxes by instruments like
IUE and ROSAT. Also, at radio wavelengths the size of the
wind region cannot exceed the upper limits for the radio source
size as follow from intercontinental VLBI. Furthermore, if the
winds are cool ( ! ¸ 4 10 4 K), the contribution to the interstellar
absorption must not be larger than ¸ 10 18 cm \Gamma2 . By applying
these constraints we arrive at an upper limit for the mass loss
rate of 10 \Gamma12 M fi =yr. At higher temperatures, e.g. 10 6 K a safe
upper limit is 2 10 \Gamma12 M fi =yr. Additional support for this upper
limit comes from the fact that at higher mass loss rates EUV and
X­ray line photons would be subject to considerable scattering
in the wind (and possibly subsequent photon destruction). This
has not been observed.
Even if the mass loss from dMe stars would amount to
10 \Gamma12 M fi =yr the observed excess fluxes at mm wavelengths
and in the IR cannot be explained by a stellar wind. This implies
that if instruments like ISO and SCUBA would find evidence
of excess emission, alternative explanations, like e.g. emission
from circumstellar dust, are required.
If the mass loss is to proceed in a clumpy way, in the form of
coronal mass ejections, then our arguments still apply. If there
are only a few remnants of ejecta around the star the approach

G.H.J. van den Oord et al.: Constraints on mass loss from dMe stars: theory and observations 11
we followed in this paper is not valid but then the contribution to
a possible stellar wind is small anyway. If there are many ejecta
near the star, then one has to consider the way this affects the
optical depth Ü max (q). In general if will be reduced compared to
a homogeneous wind. This will cause the turn­over frequency
š t to shift to lower frequencies resulting in lower fluxes at mm
and infrared wavelength. If the number of ejecta becomes very
high then one approaches the situation of a homogeneous wind
as we considered in this paper.
Given the reduction of the maximum allowable mass loss
rate from dMe stars by a factor 100, when compared to the
estimates by MDRM, the winds from dMe stars become less
important a mass donors for the interstellar medium. At most
they contribute 0:1 M fi =yr but it is likely that as additional
constraints from EUVE data and VLBI observations become
available, this number will be reduced. Finally we note that
our derived upper limits for the mass loss rate are in agreement
with the (independently) derived upper limits by Lim and White
(1996).
Acknowledgements. G.H.J. van den Oord acknowledges financial
support from the Netherlands Organization for Scientific Research
(NWO). Research at Armagh Observatory is grant­aided by the Dept.
of Education for N. Ireland. We thank the referee for carefully reading
the manuscript and for pointing out the necessity to consider over­
ionized winds.
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