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Atmospheric activity in red dwarf stars
Vistas in Astronomy. Vol. 30, 41-51, 1987 Printed in Great Britain. All rights reserved.
ATMOSPHERIC
0083-6656/87 $0.00 + .50 Copyright © 1987 Pergamon Journals Ltd.
ACTIVITY STARS
IN
RED
DWARF
B j c r n R. P e t t e r s e n Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, Oslo 3, Norway
ABSTRACT
Radiation losses from quiescent and flaring regions of red dwarf atmospheres are compared and found to be equally important. The flare emission on all wavelengths approaches 1% of the stellar bolometric luminosity for active dMe stars, but is 100 times less for some dM stars. The discriminating parameter is flare frequency, which may vary with stellar mass, age, rotation rate or other quantities. Radiation losses from chromospheric emission lines are larger than losses from transition region lines. H I is the most important element in late dMe stars, while Ca II dominates the chromospheric radiation loss from early dMe and dKe stars. The corona is less significant in dKe stars, but dominates over chromospheric radiation losses in dMe stars. A sharp drop in coronal importance is seen near dM5e, where stars become fully convective. All forms of radiation losses have a common cause, probably to be found in the convection zone. The magnetic field may be the instrument that brings mechanical energy into the outer atmosphere, where it is radiated into space.
INTRODUCTION
In the Hertzsprung-Russel diagram, flare stars occupy a region along the main sequence, which includes bright stars like the Sun, as well as low luminosity dwarfs with less than 1/1000 of the solar luminosity. Stellar temperatures change about a factor of two over this range of stars, while the mass range is more than a factor of ten. For masses between 1 dr® and 0.3 ,~®, the stars develop radiative cores well before they reach the main sequence (Grossman, Hays, and Graboske 1974), but in the outer envelope, the energy is transported to the photosphere by convection. Stars between 0.3 ag® and about 0.1 ,ago are completely convective, both during their contraction phase, and on the main sequence. Since stars of lower masses are not expected to start nuclear reactions in their interior (except for the burning of small quantities of primordial deuterium at ages 106 - 107 years), the lower mass limit for main sequence stars is accepted to be near 0.1 d~®. However, observations show that stars of lower luminosity do exist (brown dwarfs). Some of these have been reported to flare, and more brown dwarf flare stars will be discovered in the next few years. These stars are completely convective when they contract, but since they do not achieve thermal equilibrium through hydrogen burning, they will cool indefinitely towards a completely degenerate configuration. The interior is characterized by an equation of state for degenerate gas, so their evolutionary tracks are quite different from those of the higher mass stars. Nelson, Rappaport, and Joss (1985) computed models that evolve along or parallel to the lower main sequence (see Figure 1). Compared to the main sequence stars, the brown At
42
r
B.R. Pettersen
dwarfs are up to two orders of magnitude younger when they enter the region of the lowest luminosity red dwarfs in the H-R diagram. All models with d t < 0.08 ag® accelerate their luminosity losses after they have reached the end of the main sequence (below log L / L ® = -3.2). The luminosity drops 30 to 50 times during the next dex in log age, whereas previous dex-steps had factors of 1 to 10. It is, therefore, 3 to 50 times less likely that we will encounter stars in this extremely low luminosity region of the H-R diagram since the luminosity drops so fast. It is during this phase that the effective temperature drops dramatically alSO, by at least a factor two.
-1.0 [_ \ \.
,~r~0t~..
::
"~ii~;i
log L/L,
//
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!./
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i
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-3.0
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i
I
I
i
3.6
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31.
3.3
tog Teff Figure 1. Hertzsprung-Russell diagram for solar neighborhood flare stars. Duplicity effects have been taken out. Evolutionary tracks ( . . . . . . . . ) from Gossman et al. (1974) are shown for red dwarf masses between 0.085 ~ ® and 0.5 d t . Inverted triangles (V) indicate where higher mass models develop radiative cores. The main sequence ( - - ) an~3108 years isochrone ( . . . . . ) are close together and nearly parallel. The 0.1 - 0.75 ./RO main sequence from VandenBerg et al. (1983) is included for comparison. Also shown are evolutionary tracks for two brown dwarf masses ( . . . . ) from Nelson et al. (1985). Markers show log age in years, and demonstrate large age differences with mass for locations near the lower end of the main sequence. The ages of stars as they reach the main sequence are summarized in Table 1.
Table 1 Ages on ZAMS ...~/./~®
0.5
0.3
Age (yrs)
2.108
3.108
0.1
0.08
0.04
0.01
1-109
1.109
108
107
Atmospheric Activity in Red Dwarfs
43
Despite major differences in interior structure, there are objects in all three categories of stars (radiative core with convective envelope; completely convective; partially degenerate interior with convective envelope) which show stellar flares and chromospheric emission lines. Many also show high temperature transition region emission lines and coronal x-rays, but some of these very dimmest of stars are still outside the reach of satellite instruments. The evidence as it stands nevertheless points to considerable atmospheric activity in stars of all categories, and they must therefore possess magnetic fields. Saar and Linsky (1986) have begun to detect and measure fields in the brightest red dwarfs.
RADIATION LOSSES FROM QUIESCENT ATMOSPHERES
The spectra of late type dwarfs are characterized by numerous, and often strong, emission lines at optical and ultraviolet wavelengths. Most of them are formed at chromospheric temperatures (5,000-30,000 K), including H I Balmer lines, Ca II H and K resonance lines and infrared triplet lines, and Mg II h and k. Lines formed at higher temperatures (30,000-300,000 K) are often referred to as transition region lines and include multiply-ionized species like Si IV, O IV, C IV, and N V. The radiation losses in chromospheric lines are much larger than the observed radiation losses from transition region lines.
Table 2 Relative distribution of radiation loss in emission lines.
Spectral
Sample
Class
Stars
dM6e
UV Cet
dM5e
YZ CMi AT Mic
Percentage of total loss in emission lines H I Balmer
77%
Ca II HK+IR
5%
Mg II hk
7%
Other
11%
60
10
15
15
53
21
11
15
YY Gem
43
29
14
13
dM0e
V1005 Ori
30
36
25
9
dK5e(7e)
EQ Vir BY Dra
20
40
20
20
Sun
13
64
23
--
dM4e
EV Lac EQ Peg
dMle
G2
AU Mic
When chromospheric radiation losses are considered individually for various elements, their relative importance is found to vary with spectral class along the main sequence (see Table 2). In late riMe stars, the H I Balmer lines are responsible for more than half of the chromospheric emission line losses. Proceeding to the mid and early dMe stars, we find that both Mg II and Ca II become more important, with the latter increasing more rapidly. Near dM0-1e, Ca II matches the importance of the H I Balmer lines with Mg II being third. The Ca II lines continue to gain importance in the K-dwarfs, and appear to be the dominant source in the Sun at G2. At the same time, the H I
44
B.R. Pettersen
Balmer lines become less significant to the atmospheric energy budget. The present data indicate that Mg II maintains a nearly constant contribution of 25% in the bright stars. The radiation loss from quiescent flare star coronae may be measured by the x-ray flux in a 3 - 60 A continuum plus emission-line bandpass as recorded by the Einstein satellite. In Figure 2, we show the size of coronal radiation loss relative to the chromospheric radiation losses for stars of various spectral types. The upper panel applies the H a luminosity as a measure of chromospheric losses, while in the lower panel, Lchr+tr is obtained by adding up the radiation losses in all detectable optical and ultraviolet emission lines. Values for the Sun were taken from Table 4 in Linsky e t a l . (1982), and the solar x-ray luminosity was taken to be log L x = 27,3 (Lx in ergs/s). Since Htx is a good measure of the chromospheric losses only for the later spectral types, the two panels show very similar behavior for M V > 11'. For the brighter stars, the lower panel gives the appropriate behavior since there H a plays only a minor role in the chromospheric energy budget. A decaying coronal-to-chromospheric ratio starts near d M l e (M V = 9) and continues to G2 (the Sun). We note that all stars in this region have radiative cores with an outer convective envelope that becomes progressively thinner with increasing stellar luminosity. This may affect the efficiency of the stellar dynamo that produces the magnetic fields on these stars. Figure 2 shows that the coronal luminosity drops off faster than the chromospheric luminosity for bright dwarf stars.
I
Lx
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.
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.." ..."
I
8
i
I
10
I
,
12
P
I
f
lt~
I 16
Mv
Figure 2. The ratio of coronal to chromospheric radiation losses as a function of stellar luminosity. See text for details.
Near M V = 12, there is a sharp drop in the coronal-to-chromospheric ratio amounting to about one order of magnitude. Only a couple of datapoints are available for the faintest stars and more observations are needed to confirm if these stars are really low luminosity x-ray sources. We note, however, that the sharp drop seems to occur for luminosities where red dwarfs become completely convective. It is possible that this affects the stellar dynamo,
Atmospheric Activity in Red Dwarfs
45
perhaps changing the mode from a "shell" dynamo in radiative core stars to a "distributed" dynamo in fully convective stars 0tosner 1980). Various arguments have been put forward to corroborate that the magnetic field is generated near the bottom of the convection zone. In the "shell" dynamo, the c0-effect (the generator of toroidal magnetic flux through interaction of poloidal field fines with azimuthal flows during conditions of radial differential rotation) functions primarily near the interface between the radiative core and the convection zone. Since magntic buoyancy is inhibited by Coriofis forces in rotating stars, the c0-effect will operate on a timescale controlled by the stellar rotation rate, the magnetic field strength in the co-layer, and the structure of the convection zone. Different behavior is therefore expected for different masses along the main sequence, along with individual effects related to rotation. In completely convective stars, there is no interface at the bottom of the convection zone. The "distributed" dynamo model assumes that the entire convection zone participates in the dynamo process. Magnetic buoyancy may now transport toroidal flux rapidly through the convection zone. Interaction with turbulence may lead to a complex shredding pattern of small flux bundles, and the co-effect may operate on various timescales over the full depth of the convection zone. Completely convective stars may, therefore, have a different magnetic appearance than the atmospheres of larger stars.
RADIATION LOSSES FROM FLARES
Since radiation from stellar flares escapes from the stars, they constitute a source of radiation loss both in continuum and emission fines. Flares are transient phenomena that affect all layers of the atmosphere, and are seen at x-ray, ultraviolet, optical, infrared and radio wavelengths. Low energy events are very frequent (several per hour at the 1028 ergs level), while gigantic flares (energy in excess of 1034 ergs) have been seen only once or twice in the most extensively observed stars. The smallest flares can only be detected in the intrinsically faintest stars because the photospheres of larger stars are too bright. Flares down to 1026 ergs have been detected, so the total range of flare energy produced by red dwarfs is almost ten orders of magnitude. Flares are best detected in the U-filter when observing from the ground, since the stars are cool and red and the flare event is hot and blue. Most photometric data on stellar flares have been collected in this filter, and we shall use the flare frequency and the amount of energy emitted per unit time in the U-filter to measure activity on these stars. Lj(U) is determined by adding up the U-filter energy (in ergs) emitted in flares over the observing interval (in seconds) for each star.
In Figure 3, this quantity is plotted versus the coronal luminosity L x, the H a
(chromospheric) luminosity LHa, and the U-filter quiescent (mainly photospheric) luminosity L U, repectively. These parameters are all correlated with the flaring quantity L/(U) such that L x O~Lj(U) 5/4
(1)
Lna a/~o3 /.• aL¢o) 3/2
(2) (3)
Since the scatter is large in all diagrams, the numerical values of the egponents should be taken as no more than suggestive. Observations show that both L x a n d L H a are variable for some stars, both on short and long timescales. Lf(U) may also vary with time for some stars. It is, therefore, not surprising that a certain scatter is observed since observations to determine the various parameters were not simultaneous. It is seen from Figure 3 that the coronal x-ray luminosity determined by the Einstein satellite is 5 - 10 times larger than the flare luminosity in the U-ffiter. We show later that the bolometric flare luminosity is one order of magnitude larger than the U-filter flare luminosity, so it follows that the quiescent coronal x-ray emission is approximately matched by the total electromagnetic radiation emitted by flare activity.
46
B.R. Pettersen
30
32
29
31 tog L~O
log Lx
./
28 27 26
29 log LH~
7'. I
29
18 I
io
j'"
28 oe
27
28 •
27
!
•
26
25 25
241 2;
I
I
27
28
29
25
tog Lf(U)
tog Lf(U)
Figure 3. - Relations between quiescent radiation losses from the corona (Lx), chromosphere (LHa), and photosphere L(U), with theflaring radiation loss Lf(U). The lines are given in equations (1) - (3). The relation for the outer atmosphere holds for both dM and dMe stars. At the photospheric level, dM stars are clearly separated from the more active dMe stars. Figure 3 also shows that the H a luminosity is in perfect accord with the U-filter flare luminosity for all stars between M V = 7 and 17. Also, the faintest stars have quiescent U-filter luminosities that are about 5 times larger than the U-filter flare luminosity. This ratio increases steadily for the active stars on the empirical L U aL](U) 3/2 - relation to reach a factor of 100 in the brightest stars.
Four stars are clearly off the relation for active stars in the L U vs. L](U) diagram in Figure 3. They produce significantly less flare luminosity than other flare stars of comparable luminosity. They also show the H I Balmer lines in absorption and only weak Ca II HK emission. They are classified as dM stars rather than dMe. Flare activity, measured in terms of U-filter flare luminosity, is, therefore, not only a function of the mass of the star, since stars of equal luminosity may show up to 100 times less activity. Other parameters of importance may be the stellar rotation rate or evolutionary age. For single stars, there may be a direct correlation between age and stellar rotation since the presence of a magnetic field would lead to rotational braking through interaction with the surrounding interstellar medium and with stellar winds. Members of binary systems may be kept at an artificially high rotation rate through synchronization of the angular rotation velocity with the orbital angular velocity for circularized systems, and with the periastron angular velocity for elliptical systems. Binaries, therefore, have a different functional relationship between age and rotation than single stars. This complicates interpretations, and has, so far, hindered the identification of additional parameters of importance to the flare activity level. In Figure 4, we have drawn more physically meaningful relations than the empirical one of Figure 3. The straight lines are those of constant fractions of the bolometric luminosity of the stars. They are described by L U aLl(U) 2
(4)
Atmospheric Activity in Red Dwarfs
47
The rightmost line shows the location where the U-filter flare luminosity is 0.1% of the bolometric luminosity of the star. The most active dMe flare stars approach this level of activity, but the four dM stars are as low as 10-6 Lbo1.
i
i
i
i
10-6 10-5 lO-~'Lbo[ tog Lu
31
31
30
3C
29
2~
/ /'/
• o
27
2~
26
2~
/
30 -2
-1
28
6
25
i
2E
~
27
log Lf(U)
i
29
i
•
i
i
0
1
log N/T(Eu-lO3Oergs)
Figure 4. - Flare activity for stars of different luminosities. The left-hand panel shows that active dMe stars (.) produce the same fraction of their bolometric luminosity as flare radiation, irrespective of mass. dM stars (o) are 100 times less active. The right-hand panel shows the same functional relationship for flare frequency. See text for discussion.
An important question to consider is whether dM stars in general produce less energetic flares than dMe stars. Alternatively, both classes of stars may be capable of producing large flares, but dM stars produce fewer per unit time at each energy level compared to dMe stars. To investigate this, we have plotted the frequency of flares of different energy ranges versus the quiescent stellar luminosity. We obtain the same functional relationships for the various flare energies considered, namely
L U a (N/T)2
(5)
and in the right hand panel of Figure 4, we show the frequency of flares with U-filter energy in excess of 1030 ergs for stars of different luminosities. Since L U aLj(U) 2 a(N/T) 2, then L f a N/T. The discriminating parameter in
flare activity is the flare frequency. For very low luminosity stars in the lower left of the diagrams, this means that if their flare frequencies were increased by a chosen factor, then their flare luminosity would increase by the same amount. For dM stars, it follows from Figure 4 that if their flare frequencies were increased to bring them onto the dMe relationship, they would also move to the right to relocate near the 10-4 Lbol-line in the left hand panel. The drop in flare frequency from riMe to dM stars fully explains the corresponding drop in flare luminosity. Contrary to an observer's first impression at the telescope, that the intrinsically faintest flare stars are the most active ones, it is seen from Figure 4 that the intrinsically bright dMe flare stars emit more flare energy than faint dMe flare stars, and also flare more often at a given flare energy level. Active flare stars are characterized by
JPVA
30=].-D
48
B; R. Pettersen
their ability to produce about 0.1% OfLbo1 in the form of U,filter flare energy. As we shall see later, this implies that about one percent of the bolometric luminosity appears as flare radiation when all wavelengths are considered. FLARE ENERGETICS AND ATMOSPHERIC HEATING
We demonstrated in Figure 3 that quiescent values of Lx, LHa andL U and theflaring value of L/(U) are all interrelated for active stars. Could one form of activity be the consequence of another? For instance, Cram (1982) has considered if the chromosphere can exist due to the above-lying corona, since both thermal conduction and intense XUV radiation constantly direct energy into the chromosphere. Also, Doyle and Butler (1985), Skumanich (1986), and Whitehouse (1985) have considered that coronae may be heated by flares. Given the correlations between flares and all levels of the atmosphere, it is only appropriate to ask if the entire outer atmosphere is heated by flares. This question cannot be answered directly from existing data, but it is possible to consider the energy involved, as based on available observations. We define the atmospheric luminosity as
Lat m = L x + Lehr+tr
(6)
and determine the following examples (see Table 3) for active flare stars.
Table 3 Comparison of Flaring and Quiescent Luminosities
Lj( U)
Lat m
(ergs/s)
(ergs/s)
Laf~n/Lj( U)
1026
8.0. 1026
8
1027
1.5- 1028
15
1028
2.5- 1029
25
1029
4.0- 1030
40
We must now determine the bolometric flare luminosity in order to estimate the total radiation losses from flares. UBV observations by Moffett (1974)and UBVR! by this author imply that
Lf(optical) = 4 Lj(U)
(7)
Time resolved ultraviolet data of stellar flares have not yet been obtained simultaneously with optical observations. However, a giant flare on AD Leo was observed in ultraviolet and optical fight by Pettersen, Hawley, and Andersen (1986). Near this flare maximum, we find for the continuum that
L/(optical) = L/(uv)
(8)
This is illustrated in Figure 5, which shows the continuum distribution of the flare during a 15-minute interval around the AU ffi 4.5 magnitude maximum. The flux emitted in the 1000-3500/~ uv bandpass is a close match to that of the 3500-9000 ,~ optical bandpass. Assuming that the uv and optical continua vary in unison during the flare decay, we adopt the flux equality of the two bandpasses to be valid throughout the flare.
Atmospheric Activity in Red Dwarfs
I
]
'Eu 10-J;
l
!
I
I
I
49
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f-f
+
B
14. |0 -12 n¢ llJ (ID o
UT 0 / * : 4 0 - 5 5
10~ b-b 10- ~3
I
2000
I
I
I
1
4000 6000 WAVELENGTH (,~)
1
--
!
8000
Figure 5. - The continuum energy distribution 1000-71300 ~ during the maximum phase of a giant flare on AD Leo, as observed with IUE and from McDonald Observatory.
Simultaneous optical and x-ray observations of stellar flares have been obtained in a few instances. Einstein data for a flare on YZ CMi (Kahler et al. 1982) and EXOSAT data for two razes on EV Lac (Ambruster et
al. 1987) imply that Lx = 3
(9)
The x-ray events last much longer than the optical flares. Recent observations with EXOSAT and telescopes at McDonald Observatory (Ambruster et al. 1987) detected x-ray events of a few tL,nes 1032 ergs that lasted for several hours. Several optical flare-ups were noted in the course of these events, and some show no clear response in the xray light curve (see Figure 6). It is, therefore, difficult to identify the optical counterpart. We have added up the Ufilter energy of all flares occurring over the duration of the x-ray flare. Integrating the flare flux over time and over all wavelengths where observations have been made, we find that Lflbol) = 11 LflU).
Since we have not observed flares that occur on the other side of the star, the total
bolometrie flare luminosity is obtained by multiplying with a factor of two, i.e.,
Lfltot, bol) = 22 LflU)
(10)
Referring back to Table 3, we see that for stars of the same luminosity as used in our estimate of the bolometric flare luminosity (EV Lac, AD Leo; LflU) = a few times 1027 ergs/s), the atmospheric luminosity is approximately equal to the bolometric flare luminosity. If, during flares, equal amounts of energy were radiated away as were depos-
50
B.R. Pettersen
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l
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oo
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TIME{UT) Figure 6. - Simultaneous x-ray and optical observations of stellar flares on EV Lac, obtained on 15 October 1985 with EXOSAT and from McDonald Observatory.
ited in the stellar atmosphere, then flare activity would sufficiently heat the outer atmospheres to meet the observed values. This is purely speculative, of course, since we do not know anything about the size of the mechanical energy budget in flares. It is also uncertain whether our numbers apply to fainter or brighter stars on either side of those observed. Taken at face value, the brightest flare stars emit more flux in emission lines than they do in flares, whereas the opposite seems to be the case for the intrinsicallyfaintest stars. It seems indisputable, however, that the interrelations between flares and quiescent atmospheres suggest a common cause for all forms of observable radiation losses. Since all phenomena are so closely connected to the magnetic fields, it is tempting to suggest that the common cause is to be found in the interior of the star. Indirect support for this is provided by the relationship between flare luminosity and stellar luminosity, given in Figure 3 with L U. It is equally valid for Lbo1. In this scenario, the magnetic fields provide communication links to the outer atmosphere, where the radiation loss occurs in several observable ways. We believe the convection zone plays a crucial role in this picture. It generates both the magnetic fields and various kinds of MHD waves that eventually heat the atmosphere and drive a stellar wind.
SUMMARY We started this review by pointing out that the interior structure of flare stars fall in three categories according to the mass of the star. They may have a radiative core surrounded by a deep convection zone, or be completely convective, or have a degenerate core surrounded by a convection zone. The flare activity and presence of emission lines suggest that all stars have surface magnetic fields.
Atmospheric Activity in Red Dwarfs
51
We determined radiation losses from the "quiescent" atmosphere and from flare activity, based on observations from ground-based telescopes and satellites. They are found to have equal importance. Among the "quiescent" components, we find the losses from chromospheric emission lines to be larger than the losses from transition region lines. Both of these are surpassed by coronal radiation losses for dMe stars. In earlier spectral types, the corona is less significant, but it gains importance from spectral type G2 to dM3e, relative to the chromosphere. A sharp drop in coronal-to-chromosphere flux is seen near dM5e, where stars become fully convective. In the chromosphere, the relative importance of H I and Ca II for the energy budget varies with spectral type. Late dMe stars are dominated by H I Balmer line radiation losses, while early dMe and dKe stars are dominated by Ca II HK and IR.
Quiescent values of radiation losses from corona, chromosphere, and photosphere are correlated with the radiation losses inflares. The relationships are valid for outer atmospheres also for less active dM stars, but fail at the photospheric level where dM and dMe stars are clearly distinguished. Radiation losses from flares at all wavelengths are about 1% of the stellar bolometric luminosity for active dMe stars. Radiation losses may be 100 times less in dM stars. The discriminating parameter is flare frequency, which may vary with stellar mass, age, rotation rate, or other quantities. All forms of radiation losses must have a common cause, probably to be found in the convection zone of the star. We speculate that the magnetic field acts as an instrument to bring mechanical energy into the outer atmosphere, where various forms of radiation losses get rid of it. Acknowledgements: I thank my collaborators on recent multi-instrument observing projects for allowing me to show and quote unpublished results, notably Drs. Carol Armbruster, Lawrence A. Coleman, and Suzanne L. Hawley. REFERENCES Armbruster, C. W., Pettersen, B. R., Hawley, S. L., Coleman, L. A., Skiff, B., Melikian, N. D., Melkonian, A. C., and Sandmann, W. H., 1987, in preparation. Cram, L. E., 1982, Ap. J., 253, 768. Doyle, J. C., and Butler, C. J., 1985, Nature, 313, 378. Grossman, A. S., Hays, D., and Graboske, H. C., 1974, Astr. Ap., 30, 95. Kahler, S., et al. 1982, Ap. J., 252, 239. Linsky, J. L., Bornmann, P. L., Carpenter, K. G., Wing, R. F., Giampapa, M. S., Worden, S. P., and Hege, E. K., 1982, Ap. J., 260, 670. Moffett, T. J., 1975, Ap. J. Suppl., 29, 1. Nelson, L. A., Rappaport, S. A., and Joss, P. C., 1985, Nature, 316, 42. Pettersen, B. R., Hawley, S. L., and Andersen, B. N., 1986, in New Insights in Astrophysics, (ESA SP-263), p. 157. Rosner, R., 1980, Smithsonian Astr. Obs. Special Rep. 389, p. 79. Saar, S. H., and Linsky, J. L., 1985, Ap. J. Letters, 299, IA7. Skumanich, A., 1986, preprint. VandenBerg, D. A., Hartwick, F. D. A., Dawson, P., and Alexander, D. R., 1983, Ap. J., 266, 747. Whitehouse, D. R., 1985, Astr. Ap., 145, 449.
ATMOSPHERIC
0083-6656/87 $0.00 + .50 Copyright © 1987 Pergamon Journals Ltd.
ACTIVITY STARS
IN
RED
DWARF
B j c r n R. P e t t e r s e n Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, Oslo 3, Norway
ABSTRACT
Radiation losses from quiescent and flaring regions of red dwarf atmospheres are compared and found to be equally important. The flare emission on all wavelengths approaches 1% of the stellar bolometric luminosity for active dMe stars, but is 100 times less for some dM stars. The discriminating parameter is flare frequency, which may vary with stellar mass, age, rotation rate or other quantities. Radiation losses from chromospheric emission lines are larger than losses from transition region lines. H I is the most important element in late dMe stars, while Ca II dominates the chromospheric radiation loss from early dMe and dKe stars. The corona is less significant in dKe stars, but dominates over chromospheric radiation losses in dMe stars. A sharp drop in coronal importance is seen near dM5e, where stars become fully convective. All forms of radiation losses have a common cause, probably to be found in the convection zone. The magnetic field may be the instrument that brings mechanical energy into the outer atmosphere, where it is radiated into space.
INTRODUCTION
In the Hertzsprung-Russel diagram, flare stars occupy a region along the main sequence, which includes bright stars like the Sun, as well as low luminosity dwarfs with less than 1/1000 of the solar luminosity. Stellar temperatures change about a factor of two over this range of stars, while the mass range is more than a factor of ten. For masses between 1 dr® and 0.3 ,~®, the stars develop radiative cores well before they reach the main sequence (Grossman, Hays, and Graboske 1974), but in the outer envelope, the energy is transported to the photosphere by convection. Stars between 0.3 ag® and about 0.1 ,ago are completely convective, both during their contraction phase, and on the main sequence. Since stars of lower masses are not expected to start nuclear reactions in their interior (except for the burning of small quantities of primordial deuterium at ages 106 - 107 years), the lower mass limit for main sequence stars is accepted to be near 0.1 d~®. However, observations show that stars of lower luminosity do exist (brown dwarfs). Some of these have been reported to flare, and more brown dwarf flare stars will be discovered in the next few years. These stars are completely convective when they contract, but since they do not achieve thermal equilibrium through hydrogen burning, they will cool indefinitely towards a completely degenerate configuration. The interior is characterized by an equation of state for degenerate gas, so their evolutionary tracks are quite different from those of the higher mass stars. Nelson, Rappaport, and Joss (1985) computed models that evolve along or parallel to the lower main sequence (see Figure 1). Compared to the main sequence stars, the brown At
42
r
B.R. Pettersen
dwarfs are up to two orders of magnitude younger when they enter the region of the lowest luminosity red dwarfs in the H-R diagram. All models with d t < 0.08 ag® accelerate their luminosity losses after they have reached the end of the main sequence (below log L / L ® = -3.2). The luminosity drops 30 to 50 times during the next dex in log age, whereas previous dex-steps had factors of 1 to 10. It is, therefore, 3 to 50 times less likely that we will encounter stars in this extremely low luminosity region of the H-R diagram since the luminosity drops so fast. It is during this phase that the effective temperature drops dramatically alSO, by at least a factor two.
-1.0 [_ \ \.
,~r~0t~..
::
"~ii~;i
log L/L,
//
1- A :: ::
!./
\s6.~'.-i// -7 •
i
ki!"
i/
-2.0!
e~t~t~'ii~\,L/""
-3.0
-/~.0
i
I
I
i
3.6
3.5
31.
3.3
tog Teff Figure 1. Hertzsprung-Russell diagram for solar neighborhood flare stars. Duplicity effects have been taken out. Evolutionary tracks ( . . . . . . . . ) from Gossman et al. (1974) are shown for red dwarf masses between 0.085 ~ ® and 0.5 d t . Inverted triangles (V) indicate where higher mass models develop radiative cores. The main sequence ( - - ) an~3108 years isochrone ( . . . . . ) are close together and nearly parallel. The 0.1 - 0.75 ./RO main sequence from VandenBerg et al. (1983) is included for comparison. Also shown are evolutionary tracks for two brown dwarf masses ( . . . . ) from Nelson et al. (1985). Markers show log age in years, and demonstrate large age differences with mass for locations near the lower end of the main sequence. The ages of stars as they reach the main sequence are summarized in Table 1.
Table 1 Ages on ZAMS ...~/./~®
0.5
0.3
Age (yrs)
2.108
3.108
0.1
0.08
0.04
0.01
1-109
1.109
108
107
Atmospheric Activity in Red Dwarfs
43
Despite major differences in interior structure, there are objects in all three categories of stars (radiative core with convective envelope; completely convective; partially degenerate interior with convective envelope) which show stellar flares and chromospheric emission lines. Many also show high temperature transition region emission lines and coronal x-rays, but some of these very dimmest of stars are still outside the reach of satellite instruments. The evidence as it stands nevertheless points to considerable atmospheric activity in stars of all categories, and they must therefore possess magnetic fields. Saar and Linsky (1986) have begun to detect and measure fields in the brightest red dwarfs.
RADIATION LOSSES FROM QUIESCENT ATMOSPHERES
The spectra of late type dwarfs are characterized by numerous, and often strong, emission lines at optical and ultraviolet wavelengths. Most of them are formed at chromospheric temperatures (5,000-30,000 K), including H I Balmer lines, Ca II H and K resonance lines and infrared triplet lines, and Mg II h and k. Lines formed at higher temperatures (30,000-300,000 K) are often referred to as transition region lines and include multiply-ionized species like Si IV, O IV, C IV, and N V. The radiation losses in chromospheric lines are much larger than the observed radiation losses from transition region lines.
Table 2 Relative distribution of radiation loss in emission lines.
Spectral
Sample
Class
Stars
dM6e
UV Cet
dM5e
YZ CMi AT Mic
Percentage of total loss in emission lines H I Balmer
77%
Ca II HK+IR
5%
Mg II hk
7%
Other
11%
60
10
15
15
53
21
11
15
YY Gem
43
29
14
13
dM0e
V1005 Ori
30
36
25
9
dK5e(7e)
EQ Vir BY Dra
20
40
20
20
Sun
13
64
23
--
dM4e
EV Lac EQ Peg
dMle
G2
AU Mic
When chromospheric radiation losses are considered individually for various elements, their relative importance is found to vary with spectral class along the main sequence (see Table 2). In late riMe stars, the H I Balmer lines are responsible for more than half of the chromospheric emission line losses. Proceeding to the mid and early dMe stars, we find that both Mg II and Ca II become more important, with the latter increasing more rapidly. Near dM0-1e, Ca II matches the importance of the H I Balmer lines with Mg II being third. The Ca II lines continue to gain importance in the K-dwarfs, and appear to be the dominant source in the Sun at G2. At the same time, the H I
44
B.R. Pettersen
Balmer lines become less significant to the atmospheric energy budget. The present data indicate that Mg II maintains a nearly constant contribution of 25% in the bright stars. The radiation loss from quiescent flare star coronae may be measured by the x-ray flux in a 3 - 60 A continuum plus emission-line bandpass as recorded by the Einstein satellite. In Figure 2, we show the size of coronal radiation loss relative to the chromospheric radiation losses for stars of various spectral types. The upper panel applies the H a luminosity as a measure of chromospheric losses, while in the lower panel, Lchr+tr is obtained by adding up the radiation losses in all detectable optical and ultraviolet emission lines. Values for the Sun were taken from Table 4 in Linsky e t a l . (1982), and the solar x-ray luminosity was taken to be log L x = 27,3 (Lx in ergs/s). Since Htx is a good measure of the chromospheric losses only for the later spectral types, the two panels show very similar behavior for M V > 11'. For the brighter stars, the lower panel gives the appropriate behavior since there H a plays only a minor role in the chromospheric energy budget. A decaying coronal-to-chromospheric ratio starts near d M l e (M V = 9) and continues to G2 (the Sun). We note that all stars in this region have radiative cores with an outer convective envelope that becomes progressively thinner with increasing stellar luminosity. This may affect the efficiency of the stellar dynamo that produces the magnetic fields on these stars. Figure 2 shows that the coronal luminosity drops off faster than the chromospheric luminosity for bright dwarf stars.
I
Lx
I
I
I
I
I
I
I
i
I
I
I
I
I
I
1.0
tog
LH¢~ 0.5
0.0
O I
I
8
Lx
t
I
10 I
I
0"5 /
.
12 I
I
I
lt~ I
I
16 I
I
•
Lchr+fr / 0.0 - 0.5 ..'
.." ..."
I
8
i
I
10
I
,
12
P
I
f
lt~
I 16
Mv
Figure 2. The ratio of coronal to chromospheric radiation losses as a function of stellar luminosity. See text for details.
Near M V = 12, there is a sharp drop in the coronal-to-chromospheric ratio amounting to about one order of magnitude. Only a couple of datapoints are available for the faintest stars and more observations are needed to confirm if these stars are really low luminosity x-ray sources. We note, however, that the sharp drop seems to occur for luminosities where red dwarfs become completely convective. It is possible that this affects the stellar dynamo,
Atmospheric Activity in Red Dwarfs
45
perhaps changing the mode from a "shell" dynamo in radiative core stars to a "distributed" dynamo in fully convective stars 0tosner 1980). Various arguments have been put forward to corroborate that the magnetic field is generated near the bottom of the convection zone. In the "shell" dynamo, the c0-effect (the generator of toroidal magnetic flux through interaction of poloidal field fines with azimuthal flows during conditions of radial differential rotation) functions primarily near the interface between the radiative core and the convection zone. Since magntic buoyancy is inhibited by Coriofis forces in rotating stars, the c0-effect will operate on a timescale controlled by the stellar rotation rate, the magnetic field strength in the co-layer, and the structure of the convection zone. Different behavior is therefore expected for different masses along the main sequence, along with individual effects related to rotation. In completely convective stars, there is no interface at the bottom of the convection zone. The "distributed" dynamo model assumes that the entire convection zone participates in the dynamo process. Magnetic buoyancy may now transport toroidal flux rapidly through the convection zone. Interaction with turbulence may lead to a complex shredding pattern of small flux bundles, and the co-effect may operate on various timescales over the full depth of the convection zone. Completely convective stars may, therefore, have a different magnetic appearance than the atmospheres of larger stars.
RADIATION LOSSES FROM FLARES
Since radiation from stellar flares escapes from the stars, they constitute a source of radiation loss both in continuum and emission fines. Flares are transient phenomena that affect all layers of the atmosphere, and are seen at x-ray, ultraviolet, optical, infrared and radio wavelengths. Low energy events are very frequent (several per hour at the 1028 ergs level), while gigantic flares (energy in excess of 1034 ergs) have been seen only once or twice in the most extensively observed stars. The smallest flares can only be detected in the intrinsically faintest stars because the photospheres of larger stars are too bright. Flares down to 1026 ergs have been detected, so the total range of flare energy produced by red dwarfs is almost ten orders of magnitude. Flares are best detected in the U-filter when observing from the ground, since the stars are cool and red and the flare event is hot and blue. Most photometric data on stellar flares have been collected in this filter, and we shall use the flare frequency and the amount of energy emitted per unit time in the U-filter to measure activity on these stars. Lj(U) is determined by adding up the U-filter energy (in ergs) emitted in flares over the observing interval (in seconds) for each star.
In Figure 3, this quantity is plotted versus the coronal luminosity L x, the H a
(chromospheric) luminosity LHa, and the U-filter quiescent (mainly photospheric) luminosity L U, repectively. These parameters are all correlated with the flaring quantity L/(U) such that L x O~Lj(U) 5/4
(1)
Lna a/~o3 /.• aL¢o) 3/2
(2) (3)
Since the scatter is large in all diagrams, the numerical values of the egponents should be taken as no more than suggestive. Observations show that both L x a n d L H a are variable for some stars, both on short and long timescales. Lf(U) may also vary with time for some stars. It is, therefore, not surprising that a certain scatter is observed since observations to determine the various parameters were not simultaneous. It is seen from Figure 3 that the coronal x-ray luminosity determined by the Einstein satellite is 5 - 10 times larger than the flare luminosity in the U-ffiter. We show later that the bolometric flare luminosity is one order of magnitude larger than the U-filter flare luminosity, so it follows that the quiescent coronal x-ray emission is approximately matched by the total electromagnetic radiation emitted by flare activity.
46
B.R. Pettersen
30
32
29
31 tog L~O
log Lx
./
28 27 26
29 log LH~
7'. I
29
18 I
io
j'"
28 oe
27
28 •
27
!
•
26
25 25
241 2;
I
I
27
28
29
25
tog Lf(U)
tog Lf(U)
Figure 3. - Relations between quiescent radiation losses from the corona (Lx), chromosphere (LHa), and photosphere L(U), with theflaring radiation loss Lf(U). The lines are given in equations (1) - (3). The relation for the outer atmosphere holds for both dM and dMe stars. At the photospheric level, dM stars are clearly separated from the more active dMe stars. Figure 3 also shows that the H a luminosity is in perfect accord with the U-filter flare luminosity for all stars between M V = 7 and 17. Also, the faintest stars have quiescent U-filter luminosities that are about 5 times larger than the U-filter flare luminosity. This ratio increases steadily for the active stars on the empirical L U aL](U) 3/2 - relation to reach a factor of 100 in the brightest stars.
Four stars are clearly off the relation for active stars in the L U vs. L](U) diagram in Figure 3. They produce significantly less flare luminosity than other flare stars of comparable luminosity. They also show the H I Balmer lines in absorption and only weak Ca II HK emission. They are classified as dM stars rather than dMe. Flare activity, measured in terms of U-filter flare luminosity, is, therefore, not only a function of the mass of the star, since stars of equal luminosity may show up to 100 times less activity. Other parameters of importance may be the stellar rotation rate or evolutionary age. For single stars, there may be a direct correlation between age and stellar rotation since the presence of a magnetic field would lead to rotational braking through interaction with the surrounding interstellar medium and with stellar winds. Members of binary systems may be kept at an artificially high rotation rate through synchronization of the angular rotation velocity with the orbital angular velocity for circularized systems, and with the periastron angular velocity for elliptical systems. Binaries, therefore, have a different functional relationship between age and rotation than single stars. This complicates interpretations, and has, so far, hindered the identification of additional parameters of importance to the flare activity level. In Figure 4, we have drawn more physically meaningful relations than the empirical one of Figure 3. The straight lines are those of constant fractions of the bolometric luminosity of the stars. They are described by L U aLl(U) 2
(4)
Atmospheric Activity in Red Dwarfs
47
The rightmost line shows the location where the U-filter flare luminosity is 0.1% of the bolometric luminosity of the star. The most active dMe flare stars approach this level of activity, but the four dM stars are as low as 10-6 Lbo1.
i
i
i
i
10-6 10-5 lO-~'Lbo[ tog Lu
31
31
30
3C
29
2~
/ /'/
• o
27
2~
26
2~
/
30 -2
-1
28
6
25
i
2E
~
27
log Lf(U)
i
29
i
•
i
i
0
1
log N/T(Eu-lO3Oergs)
Figure 4. - Flare activity for stars of different luminosities. The left-hand panel shows that active dMe stars (.) produce the same fraction of their bolometric luminosity as flare radiation, irrespective of mass. dM stars (o) are 100 times less active. The right-hand panel shows the same functional relationship for flare frequency. See text for discussion.
An important question to consider is whether dM stars in general produce less energetic flares than dMe stars. Alternatively, both classes of stars may be capable of producing large flares, but dM stars produce fewer per unit time at each energy level compared to dMe stars. To investigate this, we have plotted the frequency of flares of different energy ranges versus the quiescent stellar luminosity. We obtain the same functional relationships for the various flare energies considered, namely
L U a (N/T)2
(5)
and in the right hand panel of Figure 4, we show the frequency of flares with U-filter energy in excess of 1030 ergs for stars of different luminosities. Since L U aLj(U) 2 a(N/T) 2, then L f a N/T. The discriminating parameter in
flare activity is the flare frequency. For very low luminosity stars in the lower left of the diagrams, this means that if their flare frequencies were increased by a chosen factor, then their flare luminosity would increase by the same amount. For dM stars, it follows from Figure 4 that if their flare frequencies were increased to bring them onto the dMe relationship, they would also move to the right to relocate near the 10-4 Lbol-line in the left hand panel. The drop in flare frequency from riMe to dM stars fully explains the corresponding drop in flare luminosity. Contrary to an observer's first impression at the telescope, that the intrinsically faintest flare stars are the most active ones, it is seen from Figure 4 that the intrinsically bright dMe flare stars emit more flare energy than faint dMe flare stars, and also flare more often at a given flare energy level. Active flare stars are characterized by
JPVA
30=].-D
48
B; R. Pettersen
their ability to produce about 0.1% OfLbo1 in the form of U,filter flare energy. As we shall see later, this implies that about one percent of the bolometric luminosity appears as flare radiation when all wavelengths are considered. FLARE ENERGETICS AND ATMOSPHERIC HEATING
We demonstrated in Figure 3 that quiescent values of Lx, LHa andL U and theflaring value of L/(U) are all interrelated for active stars. Could one form of activity be the consequence of another? For instance, Cram (1982) has considered if the chromosphere can exist due to the above-lying corona, since both thermal conduction and intense XUV radiation constantly direct energy into the chromosphere. Also, Doyle and Butler (1985), Skumanich (1986), and Whitehouse (1985) have considered that coronae may be heated by flares. Given the correlations between flares and all levels of the atmosphere, it is only appropriate to ask if the entire outer atmosphere is heated by flares. This question cannot be answered directly from existing data, but it is possible to consider the energy involved, as based on available observations. We define the atmospheric luminosity as
Lat m = L x + Lehr+tr
(6)
and determine the following examples (see Table 3) for active flare stars.
Table 3 Comparison of Flaring and Quiescent Luminosities
Lj( U)
Lat m
(ergs/s)
(ergs/s)
Laf~n/Lj( U)
1026
8.0. 1026
8
1027
1.5- 1028
15
1028
2.5- 1029
25
1029
4.0- 1030
40
We must now determine the bolometric flare luminosity in order to estimate the total radiation losses from flares. UBV observations by Moffett (1974)and UBVR! by this author imply that
Lf(optical) = 4 Lj(U)
(7)
Time resolved ultraviolet data of stellar flares have not yet been obtained simultaneously with optical observations. However, a giant flare on AD Leo was observed in ultraviolet and optical fight by Pettersen, Hawley, and Andersen (1986). Near this flare maximum, we find for the continuum that
L/(optical) = L/(uv)
(8)
This is illustrated in Figure 5, which shows the continuum distribution of the flare during a 15-minute interval around the AU ffi 4.5 magnitude maximum. The flux emitted in the 1000-3500/~ uv bandpass is a close match to that of the 3500-9000 ,~ optical bandpass. Assuming that the uv and optical continua vary in unison during the flare decay, we adopt the flux equality of the two bandpasses to be valid throughout the flare.
Atmospheric Activity in Red Dwarfs
I
]
'Eu 10-J;
l
!
I
I
I
49
I
I
f-f
+
B
14. |0 -12 n¢ llJ (ID o
UT 0 / * : 4 0 - 5 5
10~ b-b 10- ~3
I
2000
I
I
I
1
4000 6000 WAVELENGTH (,~)
1
--
!
8000
Figure 5. - The continuum energy distribution 1000-71300 ~ during the maximum phase of a giant flare on AD Leo, as observed with IUE and from McDonald Observatory.
Simultaneous optical and x-ray observations of stellar flares have been obtained in a few instances. Einstein data for a flare on YZ CMi (Kahler et al. 1982) and EXOSAT data for two razes on EV Lac (Ambruster et
al. 1987) imply that Lx = 3
(9)
The x-ray events last much longer than the optical flares. Recent observations with EXOSAT and telescopes at McDonald Observatory (Ambruster et al. 1987) detected x-ray events of a few tL,nes 1032 ergs that lasted for several hours. Several optical flare-ups were noted in the course of these events, and some show no clear response in the xray light curve (see Figure 6). It is, therefore, difficult to identify the optical counterpart. We have added up the Ufilter energy of all flares occurring over the duration of the x-ray flare. Integrating the flare flux over time and over all wavelengths where observations have been made, we find that Lflbol) = 11 LflU).
Since we have not observed flares that occur on the other side of the star, the total
bolometrie flare luminosity is obtained by multiplying with a factor of two, i.e.,
Lfltot, bol) = 22 LflU)
(10)
Referring back to Table 3, we see that for stars of the same luminosity as used in our estimate of the bolometric flare luminosity (EV Lac, AD Leo; LflU) = a few times 1027 ergs/s), the atmospheric luminosity is approximately equal to the bolometric flare luminosity. If, during flares, equal amounts of energy were radiated away as were depos-
50
B.R. Pettersen
~,
0"3I
"~ 0.2 0
l
I
./:
~'0.I
I
I
I
loo
,,,
oo
",,,,',...
..
X
oo
• o
0.0
i
4. .
I
i
i
I
I
i
,
8
6 l
,
10
I
I
I
I
I
t-
._m 2(,o oJ
I 0 -
i
"."."~'
" Ct.oVoa
I
t~
I
6
I
8
I
10
TIME{UT) Figure 6. - Simultaneous x-ray and optical observations of stellar flares on EV Lac, obtained on 15 October 1985 with EXOSAT and from McDonald Observatory.
ited in the stellar atmosphere, then flare activity would sufficiently heat the outer atmospheres to meet the observed values. This is purely speculative, of course, since we do not know anything about the size of the mechanical energy budget in flares. It is also uncertain whether our numbers apply to fainter or brighter stars on either side of those observed. Taken at face value, the brightest flare stars emit more flux in emission lines than they do in flares, whereas the opposite seems to be the case for the intrinsicallyfaintest stars. It seems indisputable, however, that the interrelations between flares and quiescent atmospheres suggest a common cause for all forms of observable radiation losses. Since all phenomena are so closely connected to the magnetic fields, it is tempting to suggest that the common cause is to be found in the interior of the star. Indirect support for this is provided by the relationship between flare luminosity and stellar luminosity, given in Figure 3 with L U. It is equally valid for Lbo1. In this scenario, the magnetic fields provide communication links to the outer atmosphere, where the radiation loss occurs in several observable ways. We believe the convection zone plays a crucial role in this picture. It generates both the magnetic fields and various kinds of MHD waves that eventually heat the atmosphere and drive a stellar wind.
SUMMARY We started this review by pointing out that the interior structure of flare stars fall in three categories according to the mass of the star. They may have a radiative core surrounded by a deep convection zone, or be completely convective, or have a degenerate core surrounded by a convection zone. The flare activity and presence of emission lines suggest that all stars have surface magnetic fields.
Atmospheric Activity in Red Dwarfs
51
We determined radiation losses from the "quiescent" atmosphere and from flare activity, based on observations from ground-based telescopes and satellites. They are found to have equal importance. Among the "quiescent" components, we find the losses from chromospheric emission lines to be larger than the losses from transition region lines. Both of these are surpassed by coronal radiation losses for dMe stars. In earlier spectral types, the corona is less significant, but it gains importance from spectral type G2 to dM3e, relative to the chromosphere. A sharp drop in coronal-to-chromosphere flux is seen near dM5e, where stars become fully convective. In the chromosphere, the relative importance of H I and Ca II for the energy budget varies with spectral type. Late dMe stars are dominated by H I Balmer line radiation losses, while early dMe and dKe stars are dominated by Ca II HK and IR.
Quiescent values of radiation losses from corona, chromosphere, and photosphere are correlated with the radiation losses inflares. The relationships are valid for outer atmospheres also for less active dM stars, but fail at the photospheric level where dM and dMe stars are clearly distinguished. Radiation losses from flares at all wavelengths are about 1% of the stellar bolometric luminosity for active dMe stars. Radiation losses may be 100 times less in dM stars. The discriminating parameter is flare frequency, which may vary with stellar mass, age, rotation rate, or other quantities. All forms of radiation losses must have a common cause, probably to be found in the convection zone of the star. We speculate that the magnetic field acts as an instrument to bring mechanical energy into the outer atmosphere, where various forms of radiation losses get rid of it. Acknowledgements: I thank my collaborators on recent multi-instrument observing projects for allowing me to show and quote unpublished results, notably Drs. Carol Armbruster, Lawrence A. Coleman, and Suzanne L. Hawley. REFERENCES Armbruster, C. W., Pettersen, B. R., Hawley, S. L., Coleman, L. A., Skiff, B., Melikian, N. D., Melkonian, A. C., and Sandmann, W. H., 1987, in preparation. Cram, L. E., 1982, Ap. J., 253, 768. Doyle, J. C., and Butler, C. J., 1985, Nature, 313, 378. Grossman, A. S., Hays, D., and Graboske, H. C., 1974, Astr. Ap., 30, 95. Kahler, S., et al. 1982, Ap. J., 252, 239. Linsky, J. L., Bornmann, P. L., Carpenter, K. G., Wing, R. F., Giampapa, M. S., Worden, S. P., and Hege, E. K., 1982, Ap. J., 260, 670. Moffett, T. J., 1975, Ap. J. Suppl., 29, 1. Nelson, L. A., Rappaport, S. A., and Joss, P. C., 1985, Nature, 316, 42. Pettersen, B. R., Hawley, S. L., and Andersen, B. N., 1986, in New Insights in Astrophysics, (ESA SP-263), p. 157. Rosner, R., 1980, Smithsonian Astr. Obs. Special Rep. 389, p. 79. Saar, S. H., and Linsky, J. L., 1985, Ap. J. Letters, 299, IA7. Skumanich, A., 1986, preprint. VandenBerg, D. A., Hartwick, F. D. A., Dawson, P., and Alexander, D. R., 1983, Ap. J., 266, 747. Whitehouse, D. R., 1985, Astr. Ap., 145, 449.