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A&A manuscript no.
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ASTRONOMY
AND
ASTROPHYSICS
1.4.1996
Estimating the total radiative power output from the hot
outer layers of late­type stellar atmospheres: How many
lines are required?
J.G. Doyle
Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
email: jgd@star.arm.ac.uk
Received date, accepted date
Abstract. The total radiative power output from the hot
outer layers of six late­type stars (of different spectral
types and luminosity class) is derived via an emission mea­
sure technique. This analysis was based on observational
data from the spectral range 100 š A to 3000 š A obtained
as a result of three separate satellite missions, i.e. Hub­
ble Space Telescope, International Ultraviolet Explorer
and the Extreme Ultraviolet Explorer. Solar observational
data of active regions, coronal holes, sunspots, `quiescent'
regions and flares were also used. Based on the derived
total power output from all of these different plasma, it
is shown that a linear relationship involving a single tran­
sition region line can be used to provide an accurate es­
timate of the total power output as previously shown for
the Sun. The derived relationship does not include losses
due to hydrogen, nor the UV continuum which can be a
large contributor, particularly for very active stars.
Key words: hot outer layers -- magnetic activity -- emis­
sion measure -- radiative loss function
1. Introduction
Modern ultraviolet/extreme ultraviolet spectroscopic ob­
servations, see for example the extreme ultraviolet data
for Procyon given by Drake et al. (1995), provide an
idea on both the complexity and number of spectral lines
in the hot outer layers of late­type stellar atmospheres
(by hot outer layers we refer to the upper chromosphere,
the corona and the intermediate transition zone). These
strong emission lines are generally considered to be the
main contributors to the radiative cooling at those atmo­
spheric heights. Studies based on single spectral lines has
Send offprint requests to: J.G. Doyle
however lead a number of authors to propose that mag­
netic activity levels saturate and yield the so­called `sat­
urated atmospheres' (e.g. Vilhu 1987; Linsky 1991). This
conclusion has been based mostly on chromospheric lines,
e.g. Mg II h&k (Doyle 1987; Mathioudakis & Doyle 1992),
Ca II H&K (Schrijver 1987) and H ff (Herbst & Miller
1989). There is however no convincing evidence that a sat­
uration exists at X­ray wavelengths. Generally, for tran­
sition region lines and broad­band X­rays fluxes, there is
a poorly defined upper envelope separately for main se­
quence stars and other more active stars such as contact
binaries (e.g. Vilhu 1987).
Whether this saturation really corresponds to a satu­
ration in surface magnetic fields is not clear and leads us
to ask the question: how many lines are required in or­
der to estimate the total radiative power output from the
hot outer layers of late­type stars? You may be tempted
to give values ranging from several hundred to thousands
of lines. For example, taking data in the ultraviolet &
extreme ultraviolet down to the X­ray region, will cover
plasma temperatures ranging from 10 4 to 10 7 K, i.e. from
the chromosphere to the corona. Then, addition of these
individual lines fluxes gives the total radiative output.
This would be a rather time­consuming method to employ
and is currently impossible for targets other than the Sun,
since even using IUE (International Ultraviolet Explorer),
EUVE (Extreme Ultraviolet Explorer) & HST (Hubble
Space Telescope), still leaves spectral regions unobserved.
However, are there alternative methods?
2. Methods used & sources of observational data
Ultraviolet data has been available for several years (as a
result of IUE) for many late­type stars. However, it is only
very recently that objects other than the Sun have been
observed with sufficient sensitivity to resolve spectral lines
in the EUV region. The Extreme Ultraviolet Explorer has

2 J.G. Doyle : Radiative power output
Fig. 1. (a) The derived emission measure curve for ff Cen (solid line) with that derived from the EUVE data alone from
Schrijver et al. 1995 (dashed line), (b) the observed over predicted line ratio and (c) the total power output (in erg s \Gamma1 ) as a
function of temperature
Fig. 2. (a) An emission measure curve for the `average' quiet Sun, (b) the observed to predicted line ratio and (c) the resulting
surface radiative power output (in erg cm \Gamma2 s \Gamma1 ) as a function of temperature
now provided data for a range of late­type stars, including
M dwarfs, RS CVn binaries and solar­type stars.
In order to estimate the total radiative losses, we will
use `the emission measure technique'. This is a quantity
(N 2
e dV ) which is related to the line power via
P (–) = hš
Z
N j A ji N i A
N (H)
N e
N 2
e dV erg s \Gamma1 (1)
where N j is the population of the upper level j normalized
to the total population of all levels in the ion, A ji the tran­
sition probability from level j to level i, N i the ionization
fraction of the ion, A the element abundance relative to
hydrogen and N (H) the abundance of hydrogen relative
to the electron density.
In order to aid in the construction of these emission
measure curves, Raymond & Doyle (1981a) presented a
table of UV & EUV line emissivities, which were updated
by Doyle & Keenan (1992). The emission measure is de­
rived via the simple relation
N 2
e dV = P ob (–)
P pr (–) 10 26:00 cm \Gamma3 (2)
where P ob (–) is the observed power in ergs s \Gamma1 of a line
at wavelength – and I pr (–) is given by Doyle & Keenan
(1992). Note that the above definition of the emission
measure is slightly different from that used by Jordan et
al. (1987), since we integrate in temperature intervals of
log T e = 0:1 compared to log T e = 0:3 used by Jor­
dan et al. Using a sequence of suitable lines (based on
the availability of suitable observational data and on the
accuracy of the existing atomic data) from species of dif­
ferent excitation (i.e. temperature of formation ranging
from chromospheric lines to coronal lines), a trial volume
emission measure ( R
N 2
e dV ) versus temperature may be
derived. We then integrated the intensities of all our lines

J.G. Doyle : Radiative power output 3
over the trail curve, adjusting the curve each time to im­
prove the fit. Further details on the technique is given in
Raymond & Doyle (1981b), while the atomic data sources
are given in Doyle & Keenan (1992).
The biggest source of error in the derived EM curves is
the abundances. Throughout, we used the coronal abun­
dances as given by Meyer (1985), i.e. C, N, O & Ne differ
by factors of 2 to 3 from the solar photospheric abun­
dances. The coronal abundances given by Feldman et al.
(1992) are different from those given here and are closer
to the photospheric abundance of Meyer (1985).
Here, we consider observational data from the above
three missions (i.e. IUE, HST & EUVE) for six different
late­type objects: AU Mic (an active dMe star), ff Cen and
ü Ori (G2 & G0 solar­type stars), Capella and oe Gem (G6
& K1 giants) and Procyon (an F5 IV­V) plus the Sun.
The ultraviolet data for these targets was from: ff Cen
(Ayres et al. 1983), ü Ori (Ayres et al. 1983, 1988), Pro­
cyon (Ayres, 1991), Capella (Ayres, 1984), oe Gem (Ayres
et al. 1984), AU Mic (Quin et al. 1993, Maran et al. 1994).
Radii and distances used were those given by the above
authors.
The above data enables us to produce an EM curve
over the temperature range 10 4 to 2 10 5 K. For the tem­
perature range up to 10 7 K we simply took the EM curves
constructed by Schrijver et al. (1995) and Brickhouse et al.
(1995) based on EUVE data. As a check on the agreement
between the atomic data used here and those of the above
authors, we de­archived the EUVE data for ff Cen. As can
be seen from Fig. 1a the agreement between this analysis
and that of Schrijver et al. is well within probable errors
in the atomic data. Note, we do not include the high tem­
perature (? 10 7 K) tail as derived by Schrijver et al. as it
is not yet clear whether this is real or due to errors in the
background correction. For the average `quiet' Sun, the
derived EM curve is similar to that of Raymond & Doyle
(1981b), who used the observational data of Vernazza &
Reeves (1978), see Fig. 2. In the construction of these EM
curves, an electron pressure of 10 15 cm \Gamma3 K was used for
ff Cen, Procyon and Capella, 2 10 15 cm \Gamma3 K for ü Ori,
4 10 15 cm \Gamma3 K for AU Mic, 9 10 14 cm \Gamma3 K for oe Gem and
5 10 14 cm \Gamma3 K for the Sun.
3. Results and Discussion
As can be seen from an inspection of Figs. 1&2 there are
differences in the solar EM curve and that for ff Cen. It
is however likely that errors in the abundances are the
cause of the discontinuities in the resulting ff Cen EM
curve compared to the smoother solar EM curve. These
probable errors are however not a major problem since we
are interested in the resulting radiative power output of
the star. To derive the power output we fold in the ra­
diative loss function (i.e. the sum of the emitted radiation
from bound­bound, bound­free and free­free transitions at
a particular temperature into the emission measure curve,
Table 1. Total radiative power output from the hot outer lay­
ers for our six late­type stars plus the Sun
Star log P (erg s \Gamma1 )
ff Cen 29.15
AU Mic 30.16
Capella 32.11
Procyon 30.50
oe Gem 32.37
ü Ori 30.29
Sun 28.93
see for example Doyle et al. 1989). This has the effect of di­
minishing errors in abundances as the radiative loss func­
tion is `almost' the inverse of the EM curve. Throughout,
we used the radiative loss function of Cook et al. (1990)
which was derived using the same solar abundance as used
here. A summary of the derived radiative power output is
given in Table 1. However, we did check what changes
different abundance can make to the total radiative out­
put by deriving the EM curves assuming the photospheric
abundances of Meyer (1985). This produced ¸30% varia­
tion in the final figure, these errors been similar to that of
the atomic excitation rates coefficients.
However, even the above emission measure technique
is time consuming and requires a good selection of spectral
lines, which can only be provided by a variety of different
instruments on different satellites, not to mention a good
knowledge of atomic physics. In looking into this problem
for the Sun, Bruner & McWhirter (1988) showed that,
for a variety of different solar plasma, the total radiated
power output, exclusive of hydrogen line radiation, may
be estimated even if one knows the intensity of only one
spectral line (either a line formed in the transition region
or corona). For example, the above authors produced a
relationship between the radiative output from the CIV
1548 š A line (PCIV ) and the total radiative output (P total )
of the form logP total = 2:17 + 1:08 \Lambda logPCIV (both
quantities in erg cm \Gamma2 s \Gamma1 ).
This then takes us back to our original question; would
this approximation operate for stars other than the Sun
as has been suggested by Doyle (1989)? In Fig. 3 we
plot the radiative output based on the emission curves
derived from the IUE/HST/EUVE data and that from
the C IV 1548 š A line for the average surface losses and
for the whole star. As is obvious from the figure, excel­
lent agreement exists; thus, surprising as it may seem,
the answer may be that one transition region line is suf­
ficient. Furthermore, there is no evidence of a saturation
effect, although we should note that this approximation
does not include losses due to hydrogen which Houdebine
et al. (1995a) have shown to be significant. Also, Houde­

4 J.G. Doyle : Radiative power output
Fig. 3. (a) The radiative output at the stellar surface (in erg cm \Gamma2 s \Gamma1 ) versus the C IV 1548 š A flux for six bright UV/EUV
objects (asterisks) plus a selection of different solar features including flares, active regions, sunspots, etc. (open circles) given
by Bruner & McWhirter (1988) and (b) the total radiative power (in erg s \Gamma1 ) versus the radiative output from the CIV 1548 š A
line for our six stellar sources plus the average `quiet' Sun
bine et al. (1995b) have shown that in order to estimate
the total radiated output, the UV continuum is important,
particularly for the very active stars.
However, it is clear from Fig. 3 that use of the C
IV 1550 multiplet is a valuable tool in estimating the
losses from the upper chromosphere, transition region and
corona and therefore can be used to infer information on
the magnetic heating requirements of these regions. This
relationship is valid for the less active stars such as the Sun
where the chromospheric lines are a significant fraction of
the radiative output to the active stars such as AU Mic
where the coronal region is the dominant source. It is not
the intention here to indicate that C IV 1550 š A is the only
line that can be used as an indicator of the radiative power
output. This line is formed near 10 5 K which in energetic
terms is relatively unimportant compared to ¸ 10 4 K or
¸ 10 6 K as the emission measure in the region is low. As
Rutten et al. (1991) showed in their study of flux­flux re­
lations involving Si IV 1396 š A, C IV 1550 š A, C II 1335 š A
and broad­band X­ray fluxes, these are all close to linear,
thus there are several lines which could be used in this
type of analysis. In­fact, Bruner & McWhirter (1988) did
consider several other lines. The main reason for using C
IV 1550 š A is that this is the strongest line observable in the
short wavelength camera onboard IUE, and thus observa­
tional data exits for a large selection of late­type objects.
Further work is however required on obtaining additional
EUVE spectroscopic data for a larger selection of objects.
Acknowledgments Research at Armagh Observatory is
grant­aided by the Dept. of Education for N. Ireland. We
also acknowledge the support provided in terms of both
software and hardware by the STARLINK Project which
is funded by the UK PPARC. JGD wishes to thank the
Center for EUV Astrophysics for funding which enabled
a short­term visit. I would also like to express my thanks
to Drs. M. Mathioudakis & J. Drake for their hospitality
during my stay in Berkeley.
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