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% 
\newcommand{\kms}{~km~s$^{-1}$}
\newcommand{\Mdot}{\mbox{$\dot M$}}                       % M. perte de masse
\newcommand{\Msolyr}{~M$_{\odot}$\,yr$^{-1~}$}             %  masse sol/yr
\newcommand{\Lsol}{\mbox{L$_{\odot}$}}                    % L solaire
\newcommand{\Msol}{\mbox{M$_{\odot}$}}                    % M solaire
\newcommand{\Rsol}{\mbox{R$_{\odot}$}}                    % R solaire
\newcommand{\GE}{\mbox{$G_{\oplus~}$}}                    % KI photoinis. at Earth
%
\begin{document}
\section{Appendix}
 This appendix  fully explains  our evaluation of
the parameters listed in Table 3. 
\subsection{Distances, mass-loss rates and fractional ionization}
\subsubsection{Massive supergiants}

The mass loss rate of $\alpha$ Ori for $d$=200~pc is presently
rather well determined at
$2.0~10^{-6}$~\Msolyr by recent CI radio
emission (Huggins et al. 1994), in agreement with the value based on HI~21~cm
by Bowers and Knapp (1987). A number of observations suggest that  CO and dust
are underabundant in the shell which is mainly atomic 
(see discussion in Haas and Glassgold 1993), so we choose
 $x_{e}$=3~10$^{-4}$.\\

The M supergiant $\mu$~Cep is at $\sim$830 pc and is
 a member of Cep OB2 (Humphreys 1978;
 see also Le Borgne and Mauron (1989) for a discussion of
 its distance, luminosity
and  discrete  absorption lines).
Bujarrabal (private communication) has kindly provided us with
CO J=1-0 and J=2-1 IRAM-30m profiles which supersedes the J=2-1
profile of Le Borgne and Mauron (1989). These profiles  (Figure 2)
 suggest an expansion velocity
of $\sim$20\kms, which is in agreement with one of the CO infrared
 circumstellar
lines detected by Bernat~(1981). The 30-m antenna temperatures,
$T_{MB}$(1-0)$\sim$0.035~K 
and $T_{MB}$(2-1)$\sim$0.1~K, allow us to infer a mass loss rate by 
adopting the method of Loup et al. (1993): with $v$=20\kms, $d$=830~pc and
$f$=CO/H$_{2}$=5~10$^{-4}$, we obtain \Mdot=1.1~10$^{-6}$\Msolyr. 
Considering mass loss rates deduced from dust, Jura and Kleinmann (1990)
derive from the IRAS 60~$\mu$m flux a rate of 0.9~10$^{-6}$\Msolyr 
with  $v$=10\kms. Skinner and Whitmore (1988)
found from  LRS and PSC2 data a value of \Mdot=2.1~10$^{-6}$\Msolyr, with
a modelisation which takes into account free-free chromospheric
 emission, adopts the values
$d$=600~pc and $v$=15\kms and assumes a gas to dust mass ratio of 500, about 
two times larger than the standard $\sim$ 200. 
Le Borgne and Mauron (1989), who investigated the dust scattered halo
around the star, showed the existence of 2 shells, inside and outside
$\sim$17 arcsec, a geometry which is  supported by KAO scans at 50 
and 100~$\mu$m reported by Hawkins et al. (1993). 
For the inner shell which is relevant here, Le Borgne and Mauron (1989) 
have inferred a mass loss rate of 1.6~10$^{-7}$ \Msolyr if
the dust condensation is complete, that is if their f, which is
the fraction of Si atoms locked in dust, is set to 1 (although they
argue with considerable uncertainty for f$\sim$0.2).
 In view of these various determinations, 
a first choice is  \Mdot=10$^{-6}$\Msolyr, together with
a normal dust/gas ratio leading to take $x_{e}$=2~10$^{-5}$.\\


According to Sanner (1976), the star CE Tau (119 Tau) is at 400 pc, with
a wind velocity of 8\kms, and  \Mdot=2.4~10$^{-7}$\Msolyr.
Heske~(1990) reports a non-detection of the CO J=1-0 line with 
$T_{rms}$=0.18~K
at the IRAM 30-m antenna. With Loup's formulae, $T_{MB}$$<$0.18~K and 
$f$=5~10$^{-4}$ , one
obtains \Mdot$_{CO}$$<$3.3~10$^{-7}$\Msolyr. In terms of dust,
the PSC2 fluxes are 145~Jy, 46~Jy and 7~Jy at 12, 25 and 60$\mu$m respectively.
The ratio F$_{12}$/F$_{60}$=20.6 is identical to that (21.6) of M stars 
without infrared
excess  (Stencel and Backmann  1991). Also, considering the K-band
flux as free from dust emission, the ratio F$_{60}$/F$_{K}$  can be
compared to similar dust-poor stars in the list of Jura and Kleinmann (1990),
revealing no infrared excess. Its  LRS spectrum is flat. An interesting
feature of CE Tau  however is
the presence of an extended emission seen at 60$\mu$m
(Stencel et al. 1988), but it is not clear to us whether this shell
is really due to past mass loss or rather illuminated interstellar dust. CE Tau
was not examined by Young et al. (1993a,b) in their survey of IRAS resolved
 shells. In summary, we think that compared to $\alpha$~Ori  and with an almost
identical spectral classification, CE Tau displays even less CO and dust in
its envelope, which is probably mainly atomic,  so that we infer
 $x_{e}$=3~10$^{-4}$, with an uncertain \Mdot=2~10$^{-7}$\Msolyr.\\

 
For  $\alpha$ Sco, we have adopted $d$=180~pc, $v$=17\kms~
 and \Mdot=1.0~10$^{-6}$~\Msolyr from the
studies of Kudritzki \& Reimers (1978), and Hagen et al. (1987), which
are based on optical and ultraviolet lines in the spectra of the M-giant and
its B2V companion. Depending on \Mdot~ and the uncertain
amount of Lyman continuum photons emitted 
by the hot star, the HII region may or may not be extended around it.
Our observations were done $\sim$4" West of the M-giant, that is on the side of 
the B companion located  at $\rho$=2.9" with a  
position angle from North to East PA=274$^{o}$ (Proust et al. 1981). 
Although the cool wind might be
significantly ionized in the B-star surroundings, we shall assume
for homogeneity with other objects an $x_{e}$$\geq$3~10$^{-4}$ corresponding
to complete (single) ionization of C.

Sanner (1976) attributes to BU Gem a mass loss rate of 2~10$^{-6}$\Msolyr,
with $v$=10\kms and a distance of 1300~pc based on its membership to Gem OB1.
Heske's (1990) non-detection of CO J=1-0 with $T_{rms}$=0.11~K at the 30-m 
leads, with $f$=5~10$^{-4}$, $T_{MB}$$<$0.11 and the above distance and velocity, to
 \Mdot$_{CO}$$<$1.2~10$^{-6}$\Msolyr
(Loup's formulae). Infrared data clearly show dust emission, and  Skinner
and Whitmore (1988) give 2.7~10$^{-6}$\Msolyr for $d$=1700~pc. In their
study of nearby massive red supergiants, Jura and 
Kleinmann (1990) rejected BU Gem because of insufficient luminosity
($L$$<$10$^{5}$~\Lsol ). If  we apply their formula (2) with
F$_{60}$=10.5~Jy, $\lambda_{10}$=0.2 and taking $L$$<$10$^{5}$ from $M_{bol}$=-7.9
of Sanner (1978), we obtain \Mdot$>$2.8~10$^{-7}$\Msolyr. We have adopted
\Mdot=1~10$^{-6}$\Msolyr, and since dust appears abundant,
 $x_{e}$=2~10$^{-5}$.\\

\subsubsection{Irregular Giants}

The characteristics of $\alpha$ Her, detailed in MC92,
are in essential agreement with the results of
Thiering and Reimers (1993): we take $d$=70~pc,
\Mdot=1~10$^{-7}$\Msolyr, $v$=8\kms and  $x_{e}$=3~10$^{-4}$.\\

 Those of
$\beta$ Peg are $d$$\sim$60~pc from its parallax of
 0.015$\pm$0.05~arcsec,
 $v$=5\kms; the only available  \Mdot~
  is from Sanner (1978) at 1~10$^{-9}$\Msolyr; no evidence for
circumstellar dust exists, and this star is even 
considered as a standard case
of photospheric 2-60$\mu$m continua by Engelke (1992), again
supporting no dust, so that
we shall adopt  $x_{e}$=3~10$^{-4}$ as a first approximation.\\

 For $\rho$ Per, one has  d$\sim$95 pc, 
 $v$=7\kms~  from Sanner (1978) who obtains 
\Mdot=1.2~10$^{-8}$ \Msolyr, and his estimations of circumstellar
column densities are about 3 times those of $\beta$ Peg.
The IRAS or LRS data do not indicate  any dust infrared emission.
From the absence of 10~$\mu$m silicate bump, we can derive
with the method of MC92 (appendix B) an upper limit  to the dust loss
rate: by taking
$\tau_{10\mu}$$<$0.01, $T_{eff}$=3450~K and $\phi_{*}$=0.0155 arcsec  from
di Benedetto (1993), R$_{\*}$$\sim$160 \Rsol, we find an inner shell radius
 $r_{i}$=26R$_{*}$ and
\Mdot$_{dust}$$<$1~10$^{-10}$~\Msolyr, which implies that, if we keep
the assumption of normal gas/dust mass ratio ($\sim$200), we find
\Mdot$<$2~10$^{-8}$\Msolyr in compatibility with Sanner's rate.
 The only attempt to detect CO radio emission on $\rho$~Per is
that of Wannier and Sahai (1986) who did not find any J=2-1 signal
at $T_{rms}$=0.26~K with the 12-m NRAO antenna. With Loup's formulae
and taking  $T_{MB}$(2-1)/$T_{MB}$(1-0)$\sim$3, one obtains an upper limit
of \Mdot$_{CO}$$<$1~10$^{-7}$~\Msolyr. We therefore consider 
\Mdot$=$1.~10$^{-8}$\Msolyr and  $x_{e}$=3~10$^{-4}$ as plausible
values.\\

The star g Her is included in the recent study of semi-regulars
  by Kahane \& Jura (1994), based on very good 
IRAM-30m CO 1-0 and 2-1 observations and careful modelisation. From
that work, we adopt $d$=130~pc, $v$=8\kms
and \Mdot=1.1~10$^{-7}$\Msolyr. Exactly the same rate would be
found from Loup's formula with the observed $T_{MB}$(1-0)=0.20~K and
above parameters.
 The mass-loss rate that Kahane and Jura derive from the 60$\mu$m flux
is about 3 times smaller, but a number of uncertainties
are recognized, including the unknown CO and dust to H$_{2}$ 
ratios, the  rather poor fit of the CO profiles and the important asymmetry
of the shell shown by Plez and Lambert (1994). 
We shall adopt the above \Mdot~   based on CO, 
with $x_{e}$=2~10$^{-5}$ since dust
and CO are certainly present in the envelope.\\
\subsubsection {Oxygen-rich miras}

The case of o Cet has already been discussed in MC92, who adopted
$d$=77~pc (parallax 0.013~$\pm$0.005"), $v$=4\kms, \Mdot=1~10$^{-7}$\Msolyr
from HI, CO and dust data. Concerning the distance,  we might
also follow Jura and Kleinmann (1992) and apply their  $M_{K}$-log$P$ relation
to obtain $d$=100~pc. More recent observations or analysis include:
 i/the one of Young (1995) from detections of CO J=3-2 and
J=4-3 submillimeter lines which lead to \Mdot=2-3.6~10$^{-7}$\Msolyr for
$d$=100~pc; ii/ the CO J=3-2 maps of Stanek et al. (1995) giving
\Mdot=2-3.6~10$^{-7}$\Msolyr for 80~pc; iii/ the one of Ivezic \& Elitzur (1995)
 based on a new physical model of
infrared data, who derive a value of 4~10$^{-7}$\Msolyr
for a distance of 110~pc.
  We  shall adopt \Mdot=2~10$^{-7}$\Msolyr and $x_{e}$=2~10$^{-5}$ since dust
and molecules appear abundant compared to HI.\\

The star W Hya is classified SRa in the General Catalog of Variable Stars
but is considered as  Mira-type  by Jura and Kleinmann (1992) whom we
follow. It is
 unusual because of its huge
envelope (Hawkins 1990). Its period is $P$=361 days, putting it at 80~pc
with the  $M_{K}$-log$P$ relation.  The wind velocity is 8\kms~ from CO
observations. Bujarrabal et al. (1986) reports $T_{MB}$(1-0)=0.17~K with the
IRAM 30m, which gives with Loup's formula 0.6~10$^{-7}$\Msolyr. A 3-times
larger rate would be derived from the $T_{MB}$(2-1)=0.63~K seen by Wannier
\& Sahai (1986) with the NRAO 12m. With the
CO J=3-2 and 4-3 lines,  Young (1995) finds 1.8 \& 2.1 10$^{-7}$\Msolyr for
80~pc. With CO 3-2 maps,  Stanek et al. give 0.8~10$^{-7}$\Msolyr for 90~pc.
From data concerning dust, Jura and Kleinmann (1992) estimate that
\Mdot= 1.0~10$^{-7}$\Msolyr whereas Ivezic \& Elitzur find 
3~10$^{-7}$\Msolyr for 120 pc. Appropriate  scaling on $d$ and $f$ leads us to
finally
adopt  \Mdot= 1.0~10$^{-7}$\Msolyr. It is interesting to note that the ratio
SiO/CO is especially large for W Hya according to Bujarrabal et al. (1994),
 suggesting at first glance either incomplete CO formation or incomplete
 inclusion of Si in dust. The HCN molecule has also been detected on this 
object, by Lindqvist et al. (1992). We have adopted
  $x_{e}$=2~10$^{-5}$ because the abundances of dust and
 molecules seem quite significant.\\ 

 The object R Hya is an ordinary Mira-type variable with a period of
388 days, and  a distance of 110~pc through the  $M_{K}$-log$P$
relation. Like many other objects, its dust shell has been
angularly resolved by IRAS at 60~$\mu$m, with
an external radius   of $\sim$6' (Young et al. 1993a,b).
  From CO J=2-1 data, Loup et al. (1993) give  
 \Mdot= 1.4~10$^{-7}$\Msolyr for 130~pc and $v$=8\kms, while Young (1995)
derive 4$\pm$0.2~10$^{-7}$\Msolyr at 110~pc from CO J=3-2
 and 4-3 lines. Ivezic and Elitzur (1995) give \Mdot= 2~10$^{-7}$\Msolyr
for 130~pc. We adopt $d$=110~pc,  $v$=8\kms, \Mdot= 2.5~10$^{-7}$\Msolyr and
$x_{e}$=2~10$^{-5}$.\\


\subsubsection{Carbon stars}
For the carbon stars TX Psc, Y CVn and U Hya, our distances  are taken
from Olofsson et al.  (1993), and are based on an assumed  absolute magnitude
$M_{K}$=-8.1~ which is the mean $M_{K}$ of LMC optical carbon stars.
Mass loss rates of these stars have been determined  among others, by
Claussen et al. (1987), Groenewegen et al. (1992), Olofsson et al. (1993a) from
which we consider their \Mdot$_{g,CO}$ and their  \Mdot$_{{\Delta}IRe}$,
Loup et al. (1993) and Kastner (1990).
 The last two authors put the stars at somewhat larger distances, giving
larger values of \Mdot. Our compilation yields the following values,
 in units of 10$^{-7}$\Msolyr:
TX Psc 0.7, 1.0, 0.91, 0.29, 5.6, 4.7; Y CVn 1.1, 0.36, 0.49, 1.2, 4.2, 1.2;
U Hya 1.2, 2.7, 1.2, 1.4, 5.0, 2.8. We finally adopted as reasonable
estimates 
1.5~10$^{-7}$, 1.5~10$^{-7}$ and 2~10$^{-7}$ \Msolyr for TX Psc, Y CVn and U Hya
respectively. Dust and molecules (CO, HCN, CN, CS) being usually well observed 
(see Olofsson et al. 1993b), we take $x_{e}$=2~10$^{-5}$.\\


\subsection{ Chromospheric ultraviolet and KI photoionizing rates}

 The goal of this section is to estimate \GE which is 
 the KI stellar photoionization rate in Equ. (1) , i.e.
convolution of the KI ionization cross-section with the
ultraviolet stellar flux. This flux
is taken as  observed at Earth, but should be corrected up
in case of significant interstellar extinction. The uncertainty
on \GE~ is mainly dependent on the knowledge of UV fluxes
of red giants below the KI ionization threshold
($\lambda$$<$2856~\AA). This knowledge is usually
rather poor and best estimates of \GE for $\alpha$~Ori,
$\alpha$ Her,  $\beta$ Peg, o Cet  and TX Psc were
obtained by MC92 from IUE or other UV data.  
When the recent data from Hubble Space Telescope are considered for
$\alpha$~Ori (Carpenter et al. 1994), one finds 
\GE=3.7~10$^{-18}$~s$^{-1}$,
or almost half the rate given by MC92, but we keep the MC92 rate to
account for a plausible interstellar extinction (A$_{v}$$\sim$0.5mag).
As for $\alpha$ Her, adopting an A9 type (Thiering and Reimers 1993)
for its companion, instead
of the average on F2-F8 types as in MC92, increases  \GE by a factor
 of $\sim$3, giving \GE=19~10$^{-18}$ s$^{-1}$.\\

The determination of \GE for the other objects was essentially
based on the assumption that similar spectral types (see
Table 3) should
correspond to identical UV fluxes normalized to luminosity.
The results are given in Table 3, and details are given
below.\\

For $\mu$ Cep for which IUE spectrophotometry
 indicates a strong interstellar
absorption A$_{v}$$\sim$2.0 mag., making IUE data
useless for $\lambda$$<$2600~\AA~ (Rodgers et al. 1983),
  we scaled the $\alpha$~Ori rate with the
mean difference on I, K and L  magnitudes of these
similar objects, giving $\Delta$$m$=2.54$\pm$0.2 mag. or
a factor of $\sim$10 on the \GE's. These passbands are chosen because
they contain the bulk of luminosity and
are not strongly sensitive to both possible dust infrared
excess and interstellar absorption. Scaling on commonly
adopted distances would have given a factor 17. 
For CE Tau, similar scaling on $\alpha$~Ori and I, K and L yields
$\Delta$$m$=3.3$\pm$0.2 mag. (factor 20); alternatively scaling on
$\beta$ Peg gives the same \GE. The  BU Gem ultraviolet flux
 was also obtained by scaling on
$\alpha$~Ori with IJKL bands, yielding $\Delta$$m$=5.2$\pm$0.2
mag.\\

The UV radiation of $\alpha$~Sco is dominated by its B2.5V V=5.17
companion and suffers an interstellar A$_{v}$=0.6 (Kudritzki and
Reimers 1978). Because the B-star IUE spectrum is not
given by these authors nor by Hagen et al. 1987, we
considered the IUE spectrophotometry of HD~61831 (B2.5V)
 in the atlas of Wu et al. (1983) with appropriate
correction for extinction, and we obtained
a very strong \GE=25000~10$^{-18}$~s$^{-1}$. As in the
case of $\alpha$~Her, this value must be considered
as only  indicative because of the off-center position
of the UV source relative to the M giant wind, but
it provides an order of magnitude which is good enough for
discussion.\\

For $\rho$ Per, we adopted the IUE spectrophotometry
from Wu et al (1983) which is useful down to 2400~\AA. Below this limit,
extrapolation was achieved with the slope observed
between 3000~\AA~ and 2500~\AA, that is
 d(log~F$_{\lambda}$)/d(log$\lambda$)=7. About 80 percent of
the resulting \GE value  unfortunately comes from this
 extrapolated region.\\

For g Her which is a semi-regular clearly cooler than
$\rho$ Per, IUE only provided a few emission line fluxes
as listed  by Eaton and Johnson (1988, Table 3).
The ratios of these line fluxes in the sense
 F$_{\rho~Per}$/F$_{g~Her}$ have an average of 4$\pm$2, so that
we adopted \GE(g~Her)$\sim$0.25~\GE($\rho$~Per) with a large
uncertainty. A scaling between these two stars based
on JKL photometry would have attributed about the same UV flux
as for g~Her than for $\rho$ Per, but this procedure
does not take into account the cooler spectral type of the former
and is a priori worse.\\


Whereas the UV radiation which is present in the circumstellar
shell of o Cet is mainly due to its hot companion (see MC92), and
at least is observable and measurable with however some uncertainty,
the case of R Hya and W Hya, which are not known as binaries, is
quite different.  The chromospheres and transition regions
of such stars are poorly known. Radio emission detected at 250GHz by
 Altenhoff et al. (1994) is a source of information
in the general case of giants and supergiants, but in the case of 
cool Mira stars, it is  satisfactorily explained by warm dust, without need
to invoke a chromosphere. The MgII lines nearly constitute the only 
observable diagnostic.\\

 IUE spectra of W Hya were reported by Kafatos et al.
(1980) who did not find any MgII doublet emission, nor any
continuum which could be convincingly attributed to
a chromosphere, one observational problem being scattered 
light contamination. However, these lines are variable, and
a non-detection does not mean a constant absence of emission. Indeed,
the lines of MgII have been detected on two Mira stars: S Car and R Car
(Bookbinder et al. 1989). The case of S Car ($P$=149~days, $d$=460~pc from
Jura 1994) is interesting because
its strong velocity shift (v$_{helio}$=+284~\kms) prevents mutilation by
interstellar MgII atoms. Its MgII lines are variable both in intensity and
profile and are attributed to a post-shock cooling region.
Because S Car (M2.5IIIe) is notably warmer than W Hya and R Hya,
it seems plausible that for these two objects, any ultraviolet emitted
by shocks will suffer a substantially larger circumstellar 
absorption than for S Car. The S Car apparent total MgII flux being
in the range 0.2 to 2~10$^{-12}$ ergs~cm$^{-2}$~s$^{-1}$ for a distance
of 460~pc, we may first estimate that MgII fluxes for W Hya and R Hya
(at $\sim$ 100~pc) should be at most (460/100)$^2$$\sim$20 times that
 level, i.e. $<4~$to$~40$ 10$^{-12}$ ergs~cm$^{-2}$~s$^{-1}$.\\

The other star R Car (M6.5IIIe, $P$=308 days) is more similar to W Hya 
(M8IIIe, $P$=361 days) and R Hya (M7IIIe, $P$=389 days). It
has K=-0.99 (Fouque et al. 1992) yielding a distance of
185~pc with the $M_{K}$--Log~$P$~ relation. Considering Table 2 of
Bookbinder et al. (1989), the MgII fluxes of R Car are
of the order of 2 to 7~10$^{-12}$ ergs~cm$^{-2}$~s$^{-1}$, but
probably suffer interstellar extinction.
Taking into account the distances, a second estimation of the total MgII
fluxes for W Hya and R Hya might be around
 $\sim$ 7 to 25~10$^{-12}$ ergs~cm$^{_2}$~s$^{-1}$. Consequently,
we have adopted as a plausible estimate for W Hya and R Hya a 
MgII flux  F$_{MgII}$=10~10$^{-12}$ ergs~cm$^{_2}$~s$^{-1}$.\\

In order to  assess  the  KI photoionization rate due to this
stellar MgII flux  at $r$=$\theta$$d$, noted  G$_{MgII,\theta}$~, with
 $\theta$$\sim$5" in the shell, we compare
 it to the interstellar rate G$_{IS}$: we have
  G$_{MgII,\theta}$=$\sigma$$_{2800}$.(F$_{MgII}$/h$\nu$)./$\theta$$^{2}$
where the KI cross-section at 2800~A  is
 $\sigma$$_{2800}$$\sim$ 0.004~10$^{-18}$~cm$^{2}$. One
 obtains  G$_{MgII,5"}$$\sim$0.095~10$^{-10}$~s$^{-1}$ which is
6 times lower than  G$_{IS}$=0.6~10$^{-10}$~s$^{-1}$ 
(for the stars studied here, the interstellar field and  G$_{IS}$ are not
 expected to be significantly reduced by circumstellar extinction 
for the outer layers of interest, i.e. at $r$=$\theta$$d$).
The importance of other possible emission lines and a continuum
has also to be adressed, but proves relatively uncertain since no observation
is available. For example,
let us  consider CII]~$\lambda$2325.
According to Judge (1989), and Judge and Stencel (1991), 
if this line and the MgII ones are emitted by a chromosphere, the flux
ratio F(MgII~$\lambda$2800)/F(CII]~$\lambda$2325) is about
16 and  11 for M and C giants, respectively. Adopting a value of 16 and
since $\sigma$$_{2325}$$\sim$0.052~10$^{-18}$~cm$^{2}$, one
 obtains G$_{CII,5"}$$\sim$0.064~10$^{-10}$~s$^{-1}$, which
is comparable to the MgII rate. Again, we do not
 really know whether this chromospheric
MgII/CII] line ratio is really applicable in the present case.
 The continuum, especially between $\sim$2400~\AA~
and the KI threshold at 2856~\AA, may on its side contribute
significantly to \GE. For example, consideration of the IUE
spectrum of Mira A at maximum but excluding the Mira B emission
lines (Fig.1 bottom, in  Reimers and Cassatella 1985) allowed us
to find that the MgII contribution is rougly 1/5 of that
from the 2300-2860~\AA~ region. Applying this ratio for R Hya and W Hya
gives G$_{5"}$$\sim$G$_{IS}$, equivalent to \GE=0.035~10$^{-18}$~s$^{-1}$,
which we take as our best estimate. There is of course a large
uncertainty on this value \GE. The factor $I_{r}$ in equation (1) 
is correspondingly set at 0.4~.\\

For the carbon stars U Hya  and Y CVn, we have adopted the same 
estimation as for TX Psc: \GE=0.02~10$^{-18}$~s$^{-1}$.
 IUE observations of U Hya (Johnson
and Luttermoser 1987) show no significant flux difference compared
to TX Psc, and the fact that we ignore the region $\lambda$$<$2300~\AA~ is the
main source of uncertainty. Because again the stellar photoionization
is comparable with interstellar rate, $I_{r}$ is set to 0.4~.\\

\end{document}
