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A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
07 (08.01.2; 08.01.3; 08.06.1; 08.12.1; 08.09.2 YZ CMi)
ASTRONOMY
AND
ASTROPHYSICS
6.11.1995
Flare energetics: Analysis of a large flare on YZ CMi observed
simultaneously in the ultraviolet, optical and radio ?
G.H.J. van den Oord 1 , J.G. Doyle 2 , M. Rodono 3 , D.E. Gary 4 , G.W. Henry 5 , P.B. Byrne 2 , J.L. Linsky 6 ,
B.M. Haisch 7 , I. Pagano 3 , and G. Leto 8
1 Sterrekundig Instituut Utrecht, Postbus 80.000, NL­3508 TA Utrecht, The Netherlands
2 Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
3 Istituto di Astronomia, Universita di Catania, and Osservatorio Astrofisico di Catania, Viale A. Doria 6, I­95125 Catania, Italy
4 California Institute of Technology, Solar Astronomy 264­33, Pasadena, CA 91125, USA
5 Center of Excellence in Information Systems, Tennessee State University, Nashville, TN 37203, U.S.A.
6 JILA, University of Colorado, and National Institute of Standards and Technology, Boulder CO­80309­0440, U.S.A.
7 Lockheed Palo Alto Research Co., Palo Alto, CA 94304, U.S.A.
8 Istituto di Radioastronomia C.N.R., Stazione VLBI, I­96017 Noto (SR), Italy
Received date 1995, accepted date
Abstract. The results of coordinated observations of the dMe
star YZ CMi at optical, UV and radio wavelengths during 3 ­ 7
February 1983 are presented. YZ CMi showed repeated optical
flaring with the largest flare having a magnitude of 3.8 in the U­
band. This flare coincided with an IUE exposure which permits
a comparison of the emission measure curves of YZ CMi in its
flaring and quiescent state. During the flare a downward shift
of the transition zone is observed while the radiative losses
in the range 10 4 \Gamma 10 7 K strongly increase. The optical flare
is accompanied with a radio flare at 6 cm, while at 20 cm
no emission is detected. The flare is interpreted in terms of
optically thick synchrotron emission. We present a combined
interpretation of the optical/radio flare and show that the flare
can be interpreted within the context of solar two­ribbon/white­
light flares. Special attention is paid to the bombardment of dMe
atmospheres by particle beams. We show that the characteristic
temperature of the heated atmosphere is almost independent of
the beam flux and lies within the range of solar white­light flare
temperatures. We also show that it is unlikely that stellar flares
emit black­body spectra. The fraction of accelerated particles,
as follows from our combined optical/radio interpretation is in
good agreement with the fraction determined by two­ribbon
flare reconnection models.
Key words: UV Cet­type flare stars -- YZ CMi -- flare activity
-- multiwavelength data -- emission measure -- particle acceler­
ation -- two­ribbon flare
Send offprint requests to: G.H.J. van den Oord
? Based on observations collected with the International Ultraviolet
Explorer (IUE) satellite at the ESA­Villafranca and NASA­Goddard
Satellite Tracking Stations and the Very Large Array (VLA)
1. Introduction
Stars of different spectral type and luminosity class, e.g. Be­
type giants, RS CVn sub­giants, T Tauri stars and M dwarfs,
have been observed to flare at all wavelengths. The basic char­
acteristic shared by most of these flares is a rapid increase in
emitted flux followed by a more gradual emission during the
decay phase. In order to study the response of different atmo­
spheric layers to the energy release during a flare, simultaneous
observations covering as large a frequency range as possible are
required. This calls for orchestrated campaigns during which the
observing programs of various observatories are coordinated.
Since flare activity is unpredictable such observing campaigns
are not always successful. The multi--wavelength observations
we analyse in this paper were obtained during a coordinated
programme of simultaneous ultraviolet, optical and radio ob­
servations of late--type single and binary active stars, which
successfully resulted in the detection of flares in all three wave­
length bands on YZ CMi, AD Leo, V 1005 Ori (= Gliese 182)
and AR Lac (Rodono et al. 1984).
There have been several successful multi--wavelength cam­
paigns for dMe stars involving YZ CMi (Kahler et al. 1982,
Doyle et al. 1988), Prox Cen (Haisch et al. 1983), UV Ceti, AU
Mic and BY Dra ( Butler et al. 1986, 1987; De Jager et al. 1988),
AD Leo (Rodono et al. 1989) and EQ Peg (Haisch et al. 1987).
Interesting physics can also be derived from single telescope
observations, however, especially from optical (e.g. Houdebine
et al. 1993a,b) or ultraviolet (Doyle et al. 1989, Linsky et al.
1989) spectroscopic data.

2 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Fig. 1. The complete U­band light curve of YZ CMi on 3 and 6 February 1983, with numbered vertical bars identifying flare events. Horizontal
lines indicate the time intervals of IUE exposures. Capital letters identify secondary peaks. On Feb. 3 frequent flaring activity is seen before
the large flare (no. 11) occurred. The optical and simultaneous microwave light curves of this flare are shown on an enlarged scale in Fig. 2.
Note that, after the rather faint and slow flare no. 6, YZ CMi remained about 10% brigther than pre­flare level. The large flare no. 11 was
accompagnied by a precursor event (no. 10) which had not completely decayed when the large flare occured.

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 3
A widely accepted scenario for solar flares is that during the
impulsive phase, beams of energetic electrons and/or protons
are accelerated in the corona. When the fast electrons/protons
are stopped in the high density chromosphere their energy is
transferred to the ambient medium which is thereby heated.
This interaction produces large pressure gradients which drive
the heated material into the corona (commonly called evapora­
tion) where it cools by radiation and conduction. The radiation
from the `evaporating' material then gives rise to the gradual
phase of the flare with emission at soft X­ray, EUV and UV
wavelengths. If the particle beams deposit their energy deep
enough in the atmosphere a white­light flare may be observed.
An alternative scenario for compact flares is one in which the
energy release results in hot plasma confined between down­
ward traveling conduction fronts. The fast electrons in the tail
of the distribution cross the fronts and bombard the denser at­
mospheric layers, just as in the first scenario.
One should question whether these basic elements of so­
lar flares can explain flares on dMe stars. This fundamental
question was extensively addressed at IAU Colloquium No.
104 on Solar and Stellar Flares (Haisch and Rodono 1989),
where current models and interpretations of flare events are
presented. For a discussion of the physical insight obtained
from multi­wavelength flare observations we refer the reader to
Stellar Flares (Pettersen 1991) and the Annual Review article
by Haisch et al. (1991).
In this paper we present optical, UV and radio observations
of YZ CMi in its quiescent and flaring state during 3 ­ 7 Febru­
ary 1983. We will concentrate on a large flare which we will
compare with solar white­light flares. YZ CMi (Gl 285) is a
dM4.5e star (Gliese 1969) with its Balmer lines in emission.
It is a member of both the UV Ceti class of flare stars and
the group of BY Draconis­variables whose lightcurves show
quasi­sinusoidal photometric variations.
The contents of this paper is as follows: in Sect. 2 we discuss
the observations and the data reduction. In Sect. 3 the energetics
are discussed in terms of the radiative losses in the optical and
the UV, and for the observed radio­flare the source parameters
are derived. A combined interpretation of the optical and the
radio flare­data is presented in Sect. 4. Our conclusions are
presented in Sect. 5.
2. Observational data & its reduction
2.1. Optical data
Several optical telescopes in Australia, Europe and U.S.A. were
involved in the observation campaign during February 1983.
The most successful flare monitoring was carried out at Mc­
Donald Observatory in the Johnson U­band with the 0.9­m
Cassegrain telescope. No flares were detected at the other ob­
servation sites. The McDonald observations were obtained with
a 10--sec integration time on Feb. 3 (3:00 -- 9:00 UT), Feb. 6
(2:50 -- 5:07 UT), and Feb. 7 (3:00 -- 6:00 UT). The typical
accuracy of the McDonald U--band monitoring was 0 m :003.
YZ CMi was quite active on Feb. 3: ten relatively minor flares
Fig. 2. (a) The U­band light curve of the 3 February1983 YZ CMi flare
(---), plus the VLA 6--cm data (\Gamma \Gamma \Gamma). (b) The RH & LH circular
6--cm polarization data.
Fig. 3. The double peaked YZ CMi flare observed on Feb. 6, 1983.

4 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Table 1. Characteristics of the YZ CMi flares observed at McDonald Observatory in the period 3­7 February 1983.
Date no. (U.T.)max
i I f \GammaI o
Io
j
max
\DeltaU t rise t decay P (Eq. 1) Comments
1983 (h:m:s) (min) (min) (min)
Feb. 3 1 3:19:45 0.77 0.62 0.3 3. -- 1st peak
2 3:27:45 0.26 0.25 1.3 15. 5.92 sec. peak
3 3:50:05 0.15 0.15 0.5 1. 0.12 faint flare
4 4:01:45 0.22 0.21 0.7 2. 0.26 faint flare
5 4:44:45 1.88 1.15 1.3 9. 1.43 faint flare
6 5:11:05 0.28 0.27 1.3 ?30 ( b ) 1st peak, long­duration decay
7 5:14:45 0.25 0.24 1.3 ( a ) 1.05 secondary peak
8 5:25:25 0.14 0.14 0.4 ( a ) 0.09 secondary peak
9 5:28:35 1.46 0.98 0.3 ( a ) 1.62
10 6:08:05 1.05 (0.78) --- 2. ( b ) precursor flare, max lost
11 6:12:35 31.76 3.79 1.8 35. 78.92 multi­peaked, largest flare
Feb. 6 1 3:13:55 8.59 2.20 1.4 12. 16.7 double­peaked
( a ) secondary peak during flare no. 6 decay phase
( b ) P value included in the subsequent secondary peak
were observed before a large \DeltaU ¸ 3:8 flare occurred (see
Fig. 1). This large flare (no. 11) occurred while a precursor
event, possibly double--peaked, was still in its decay phase. The
precursor flare appeared to peak at 06:08:10 UT, but the real
maximum was very likely lost during sky measurements. The
large flare started at about 06:10:45 UT, reached light maximum
at 06:12:35 UT, and then decayed to pre--flare level in about 35
min.
After the relatively small precursor flare, the star remained
about 20% brighter than the pre--flare level. We note, however,
that this pre--flare level was already about 10% brighter than the
supposedly quiescent level at the beginning of the observation
run. In fact, after flare no. 6, which was quite faint and slow,
without any spiky fast phase, YZ CMi did not return to its
quiescent level, while other minor flares (nos. 7 to 9) and the
large flare occurred.
On February 6, YZ CMi was much less active, since only a
moderately intense flare (\DeltaU ¸ 2:2) with double--peaked light
profile was observed (see Fig. 3). On February 7, no flares at
all were detected. The principal characteristics of the observed
flares are given in Table 1. The flare energies were derived
by time integrating their U--band light curves and assuming
U=13.8 for the quiescent U--band magnitude and a distance of
6.2 pc (Gliese 1969). These parameters imply a quiescent U--
band luminosity of 3:23 \Theta 10 28 erg s \Gamma1 according to the flux
calibration of Bessell (1979).
2.2. Radio data
Microwave monitoring was carried out with the VLA in its C
configuration. The 27 antennas of the VLA were divided into
two subarrays, one operating at 6 cm (4.89 GHz), and the other
operating at 20 cm (1.47 GHz). Two of the antennas were not
working, leaving 12 antennas in the 6 cm subarray, and 13
antennas in the 20 cm subarray. The data were calibrated in
absolute flux by reference to 3C 286, and the phase calibrator
was 0742+103. Phase calibrator observations occurred every
30 min. The source signal at 6 cm before the large optical flare
(no. 11) was consistent with YZ CMi's known quiescent upper
limit of a few tenths of a mJy at 6 cm. The 6 cm light curve
during the optical flare is shown in Fig. 2a, and the RH and LH
circular polarization data are presented in Fig. 2b. Observations
of the decay of the radio flare were interrupted by a calibration
observation, which took place from 06:20­06:23 UT, some 8­9
minutes after the peak of the U­band burst. The burst was still
in progress at 6 cm after returning from the calibrator at 06:23
UT. Although the observations were taken with 3 sec time res­
olution, the burst was sufficiently weak that its flux at 6 cm was
measurable only on maps with 1 min or longer integration time.
The 1oe noise level of these 1­min maps, after cleaning, was 0.5­
0.7 mJy in each sense of circular polarization. The burst was not
detected at 20 cm. At 6 cm, the flare reached its peak intensity
about 7 mins. later than the U­band peak. Polarization mea­
surements show a slight RH circular polarization excess during
most of the flare, except just before its peak emission. Given
the noise level, this excess RH polarization is not statistically
significant.
2.3. Ultraviolet Spectroscopy
Table 2 provides a list of SWP and LWR low­dispersion UV
spectra of YZ CMi obtained with the International Ultraviolet
Explorer satellite in February 1983. Here we concentrate mostly
on the two separate spectra obtained sequentially on image
SWP19177: the first spectrum appears rather quiescent, while
the large flare and its precursor strongly affect the second 40--
min exposure. The two exposure time--intervals are shown as
horizontal bars in Fig. 1. During the first 40--min exposure no

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 5
Fig. 4. (a) The IUE SWP flare spectrum for the YZ CMi event of 3 February 1983 starting at 06:06 UT and (b) the mean quiescent spectrum.
strong flare activity was observed in the U­band, where the
second 40­min exposure included the entire duration of flares
no. 10 and no. 11. All of the remaining images listed in Table 2
show no signs of flare activity, most likely because the exposure
times were purposely kept short to avoid saturation due to large
flares. The spectra of the usable images listed in Table 2 were
extracted from the photometrically corrected IUE images using
the IUEDR computer program on the UKSTARLINK computer
network (Giddings 1989). Since the nominal resolution of the
IUE spectrograph in low resolution mode is ¸ 4:2A, the final
extracted spectra were slightly smoothed, using a Gaussian with
a FWHM of 3:5A, in order to reduce the noise.
The extracted spectra were further analyzed using the
STARLINK DIPSO program (Howarth & Murray 1990). Line
fluxes for the prominent SWP emission lines were derived by
least squares Gaussian fits. This procedure gives similar results
to a summation under the line for strong unblended lines, al­
though gaussian fits are considered to be superior. The fitting
procedure was carried out by estimating the width and center of
the line, which were subsequently optimized to produce the best
fit. An estimated continuum contributionwas removed from the
data before the line parameters were measured. The derived line
fluxes at Earth were converted to surface fluxes at the star using
the conversion factor, F=f = 5:75 10 17 from Mathioudakis
& Doyle (1992). The flare spectrum and the mean quiescent
spectrum are shown in Fig. 4, where the quiescent spectrum is
the mean of the three nonflare SWP spectra taken on February
3. The individual line fluxes for the quiescent and flaring states
are presented in Table 3.
Table 2. Log of IUE SWP & LWP low­dispersion spectra of YZ CMi
on multiple--exposure images obtained in February 1983. The start
time (U.T.) of the first exposure on each multiple--exposure image is
listed.
Date Image No. U.T. t exp + Comments
(min)
Feb. 3 LWR15169 04:46 4\Theta 8
SWP19177 05:25 2\Theta40 large flare on 2nd exp.
LWR15170 06:54 4\Theta 8
SWP19178 07:50 2\Theta40 weak spectra
Feb. 6 LWR15198 02:45 4\Theta 6
SWP19210 03:15 2\Theta20 too weak spectra
Feb. 7 LWR15205 03:50 8 weak spectrum
LWR15206 04:34 2\Theta 8
LWR15207 05:25 4\Theta 5
+ t exp = no. of exposures \Theta each segment exp. time
3. Results
In this section we derive various parameters for the large flare
(no. 11) on 3 February 1983.
3.1. Optical flare energy
The flare's equivalent duration P is given by (Gershberg 1972)
P =
X
f
[(I f \Gamma I o )=I o ]\Deltat (1)
where I o is the observed countrate from the star in its quies­
cent state after sky subtraction, I f the countrate due to the star
in its flare state less sky background, and \Deltat is the U­band

6 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Fig. 5. (a) The YZ CMi flare EM curve (note that the flare EM must be multiplied by 1=f = 4úR 2
\Lambda =A flare where f is the flare filling factor in
the UV); (b) the EM curve for YZ CMi in quiescence. The flare EM curve above 3 10 5 K is very uncertain since it is only based on the upper
limit of the Fe XXI line at 1354A.
integration time. Taking the quiescent U­band luminosity of
3:23 10 28 erg s \Gamma1 , as derived in Sect. 2.1, the flare's equiva­
lent duration (P = 4735 sec) implies a flare energy of 1:5 10 32
erg in the U­band. This is a lower limit to the total emitted
optical energy. Although flares are unique events that some­
times show unusual time and colour behaviour, statistical stud­
ies based on large collections of flare data (e.g. Lacy et al. 1976)
indicate that the mean ratio between the total energy emitted
in the optical UBV--bands and the energy emitted in the U--
band is E opt =EU = 2:4. Thus for the YZ CMi flare we derive
E opt = 3:6 10 32 erg.
3.2. Radio flare
It is interesting that during the optial flare a radio burst was
detected at 6 cm while no indications were found for radio
emission at 20 cm. The apparent weak excess of RH circular
polarization during the burst is not a statistically significant
3oe­detection. The gradual time profile of the burst, in com­
bination with the absence of strong circular polarization and
the moderate flux at the maximum of the burst, makes it un­
likely that the observed emission is coherent but one­minute
integrations are not ideal to detect spikes of coherent emission,
if present, since the time profile of a burst depends strongly
on the integration time. An example of this is the observation
by van den Oord and de Bruyn (1994) who detected coherent
emission at 360 MHz from II Peg. In one­minute integrations
a highly variable flux was observed, while with four­minute
integrations the burst showed a very smooth time profile (see
their Figs. 2 and 4). That example demonstrates that the spikey
nature of coherent emission can be completely masked when
integration times longer than the characteristic time scale of the
emission are used. Therefore we looked for variability using
10 sec. maps but no indications for spike emission were found.
The fluxes quoted in this paper are based on one minute maps
which provide a reasonable compromise between S/N and time
resolution.
For the present observation the brightness temperature at 6
cm is
T b = c 2
2kš 2
d 2
ü r úR 2 \Lambda
F = 2:4 10 8 F mJy
ü r
K (2)
with d = 6:2 pc the distance of the star, R \Lambda = 0:37R fi the
radius of the star, F the observed flux (F mJy when expressed in
mJy) and ü r the source area of the radio emission normalized
on the stellar disk area. At the maximum of the flare the bright­
ness temperature was approximately 10 9 K if the source were
the size of the stellar surface. For a smaller radio source the
brightness temperature would even be higher. These values of
the brightness temperature indicate that the emission is neither
thermal nor coherent. A more likely interpretation is that the
observed emission is synchrotron radiation from a non­thermal
particle population as is often thought to be responsible for ra­
dio flares. In the case of optically thick synchrotron emission
by a mono­energetic particle population the observed flux is
(Pacholczyk, 1970)
F = ü r úR 2
\Lambda
d 2
š 5=2
c 2 p
c 1 B sin #
x \Gamma5=2 S(x) , (3)
where B is the magnetic field strength, # the angle between
the field and the ray, c 1 = 6:27 10 18 a constant, S(x) =

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 7
Table 3. UV line fluxes for YZ CMi (10 \Gamma13 erg cm \Gamma2 s \Gamma1 ) on 3 Febru­
ary 1983. The quiescent fluxes are derived from the first exposure of
SWP19177 and the two exposures of SWP19178. For the flare the
fluxes are derived from the second exposure of SWP19177.
Ion (A) Quiescent Flare
C III 1176 + -- 3.21
Si III 1205 -- !2.54
N V 1240 \Lambda 1.18 3.72
C II 1335 + 1.32 4.55
C I/Fe XXI 1354 -- !0.76
Si IV 1393 !0.67 4.55
Si IV 1402 !0.34 3.27
C I 1513 -- 2.35
Si II 1526 -- !1.48
Si II 1533 -- !1.71
C IV 1550 \Lambda 2.83 15.80
C I 1561 -- 0.59
He II 1640 0.67 3.34
C I 1656 -- 1.32
Si II 1809 0.23 1.12
Si II 1818 0.55 1.74
C III 1907 -- !0.28
Fe II 1915 -- 0.24
C I 1933 -- 0.84
Cont. 1160--1960A .... 59.2
(from LWR spectra)
Fe II 2600 + \Lambdao 5.40 --
Mg II 2800 \Lambdao 9.30 --
\Lambda doublet
+ multiplet
o mean from six spectra with 2.0 rms
x
R 1
x K 5=3 (z)dz=K 5=3 (x) with K 5=3 a Bessel function of the
second kind, and x = š=š crit . š crit = c 1 B sin #E 2 is the criti­
cal frequency which appears in the expression for synchrotron
emission. The particle energy is indicated by E. The ob­
served flux of ¸ 5 mJy at 6 cm indicates that the particle
energy is E = 0:9=
p
B 2 sin # MeV when ü r = 1 (x = 4) and
E = 2:4=
p
B 2 sin # MeV when ü r = 0:1 (x = 0:52). Here
B 2 = B=100. The derived particle energies are only weak func­
tions of the assumed field strength and the flare area. We con­
clude that the 6 cm flux is compatible with synchrotron emission
from particles with energies of a few MeV.
Our assumption that the flux at 6 cm is optically thick needs
to be checked by considering the absorption coefficient for
synchrotron radiation (Pacholczyk, 1970),
Ÿ = 4:2 10 7 (B sin #) 3=2 š \Gamma5=2 n f x 5=2 K 5=3 (x) cm \Gamma1
= 2:5 10 \Gamma14 (B 2 sin #) 3=2 n f x 5=2 K 5=3 (x) cm \Gamma1 , (4)
where the last identity applies to 6 cm observations. In this
expression n f is the density of the fast particles emitting the
synchrotron radiation. By writing the optical depth at 6 cm
as Ü 6 = Ÿ`R \Lambda with ` the source size along the line of sight
(expressed in stellar radii), we find that Ü 6 ? 1 when n f ` ? ¸
2 10 3 cm \Gamma2 . This is a rather small number indicating that it is
likely that the source is indeed optically thick.
3.3. Emission Measure Analysis
Emission measure (EM) curves were constructed using the tab­
ulation of flux versus pressure for a constant EM from Doyle &
Keenan (1992) and the corresponding contribution functions,
i.e.
EM = F obs (–)
F pred (–) 10 26 cm \Gamma5 , (5)
where F obs (–) is the observed flux at wavelength – and F pred (–)
is the value given in the tables of Doyle &Keenan. The emission
measure curve for an electron pressure of 10 15 cm \Gamma3 K is shown
in Fig. 5 for both the flare and (mean) quiescent periods. Note
that in the flare, the only electron density sensitive line is the
very weak (hence only an upper limit to the flux can be given)
C III 1908A line. The electron pressure was therefore based on
the C III 1176/C III 1908 ratio. On the other hand if we were
to use the Si IV 1394/C III 1908 ratio, an electron pressure of
a factor of 3 higher than the above would be implied. Density
sensitive lines are not seen in our faint quiescent spectra.
At the formation temperature of C III, this pressure implies
an electron density of ¸ 2 10 10 cm \Gamma3 . This is rather low com­
pared to the derived electron density of some RS CVn flares
(e.g. see Doyle et al. 1989, Linsky et al. 1989), but since the
IUE spectrum was of 40--min duration and the flare was en­
tirely contained within this time interval, it is possible that
much higher densities were present during the rise phase, as
is found in solar flares (Wolfson et al. 1983). The EM curve
for temperatures above 3 10 5 K is very uncertain because the
only data point available is the upper limit to the Fe XXI line at
1354A which could also have a large contribution from C I (cf.
the GHRS spectrum of AU Mic obtained by Maran et al. 1994).
It is important to note that, when deriving the emission mea­
sure curves, solar abundances are usually assumed, but Meyer
(1985) has shown that there is a depletion in the solar coronal
abundances of certain elements relative to the photosphere. In
our emission measure curves such abundance variations would
mainly affect the curves of ions of C and N for which Meyer
finds that the ratio of photospheric to coronal abundances is a
factor of 2 or greater. The present data set does not permit us
to check for abundance variations, but in general the shape of
the EM curve is represented satisfactorily by the assumption
of coronal abundances (Cook et al. 1989) and it is from this
data that the subsequent analysis is carried out. We note that
Linsky et al. (1995) found that coronal abundances lead to a
better fit to the emission measure distribution for the Capella
G1 III component.

8 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Table 4. Surface radiative losses for YZ CMi during the flare and in quiescence. Comparison figures are also given for the Sun as derived by
Quin et al. (1993). Note that the surface area assumed for the flare is that of the whole stellar surface. The radiative losses at log T e ? 5:5 are
very uncertain and should be considered as a rough estimate (see Sect. 3.4 for an estimate of the total flare radiative losses).
Atmospheric region Temperature range Radiative losses (10 6 erg cm \Gamma2 s \Gamma1 )
YZ CMi YZ CMi Sun
(flare + quiescent) (quiescent)
upper chromosphere 4.0Ÿ log T e Ÿ4.5 40.2 11.8 2.2
mid T­R 4.6Ÿ log T e Ÿ5.4 12.5 4.4 0.3
upper T­R/lower corona 5.5Ÿ log T e Ÿ6.0 (32.2) .... 0.2
upper corona 6.0Ÿ log T e Ÿ7.0 (32.1) .... 0.1
Fig. 6. The surface radiative losses for the flare and the quiescent state
of YZ CMi based on the IUE fluxes. For the calculation of the flare
radiative losses the flare area is taken equal to the surface area of the
star. The flare filling factor is given by f = A flare =(4úR 2
\Lambda ).
3.4. Radiative losses
The radiative losses in the part of the atmosphere `covered' by
the EM curve may be estimated by multiplying the EM by the
radiative loss function. The radiative loss function used here is
that due to Cook et al. (1989). The derived values for YZ CMi in
different parts of the atmosphere are given in Table 4. In order
to derive the total radiative losses, the values in Table 4 should
be multiplied by the surface area of the star. This gives for
the quiescent state radiative losses of at least 1:3 10 29 erg s \Gamma1
and for the flare 2:9 10 29 erg s \Gamma1 over the temperature range
4:0 Ÿ log T e Ÿ 5:4. Over the temperature range 5:5 Ÿ
log T e Ÿ 7:0, we have additional flare radiative losses of ¸
5:1 10 29 erg s \Gamma1 . Note that the quiescent value has not being
subtracted from this latter figure. Also none of these figures
include losses due to Ca II H&K, and especially for a dMe
star, the Hydrogen Lyman and Balmer lines. During the flare,
the continuum losses over the wavelength range 1160 -- 1960A
(see Table 3) amount to ¸ 2:7 10 28 erg s \Gamma1 . The U­band data
implies losses of 3:6 10 32 erg in the optical UBV bands, giving
total radiative losses over the flare event of at least 2:3 10 33 erg.
In Fig. 6 we plot the surface radiative losses function of
temperature as derived from the IUE data. Again we note that
at log T e ? 5:5 the radiative losses presented in Fig. 6 and Ta­
ble 4 are subject to considerable uncertainties due to lack of line
diagnostics. During the flare the total radiative losses add up to
1:2 10 8 erg cm \Gamma2 s \Gamma1 in the temperature range 4 Ÿ log T e Ÿ 7
(see Table 4). Bruner and McWhirther (1988) derived an em­
perical relation between the C IV line flux and the total radiative
losses in the range 4 Ÿ log T e Ÿ 8 with an accuracy of a factor
two. Using the observed C IV line flux gives for YZ CMi in
its quiescent state a total radiative loss of 4:1 10 7 erg cm \Gamma2 s \Gamma1
at temperatures above 10 4 K. For the flare + quiescent the ra­
diative losses amount to 2:6 10 8 erg cm \Gamma2 s \Gamma1 which is, despite
the uncertainties, only a factor 2.2 larger than the value which
follows from Table 4.
4. Interpretation
It is interesting to see whether the present data permit the con­
struction of a simple model for the observed flare. For solar
flares the white light emission is caused by the bombardment
of the chromosphere/photosphere by beams of energetic par­
ticles. A second energetic particle population causes the non­
thermal radio emission in the corona. Both energetic particle
populations are thought to be energized during the reconnec­
tion process by direct electric field (run­away) acceleration in
a current sheet. This statement does not relate to the coherent
emission by e.g. shock acceleration. The largest solar flares,
that is, those which show white light emission, are related to a
filament eruption and are called two­ribbon flares. The scenario
for a two­ribbon flare is conceptually simple and may be well
suited for an application to stellar flares: as a filament evolves
it can reach a critical height after which it becomes unstable
(van Tend and Kuperus, 1978). The point of instability is char­
acterized by the occurence above the photosphere of a neutral
line, which is unstable and quickly collapses into a neutral sheet
(Syrovatskii, 1981). As the filament moves upward, magnetic

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 9
field lines from the topologically different regions on both sides
of the sheet move towards the current sheet and reconnect. This
`cutting' of field lines due to reconnection permits the filament
to move upward, since the reconnected field lines are not con­
nected to the photosphere. Below the current sheet a growing
arcade of loops is formed while above the current sheet a plas­
moid surrounding the filament moves upward. In this scenario
the filament is located at an O­type neutral point and the current
sheet at a collapsed X­type neutral point. This model was first
worked out by Kaastra (1985) and later extended by Martens
(1986), Martens and Kuin (1989), Forbes (1990, 1991) and
Forbes and Isenberg (1991).
Since our limited data set does not permit a detailed com­
parison with solar two­ribbon flares we use the basic concepts
of the two­ribbon flare to link the observed optical and radio
emission. For that purpose we assume that the acceleration
process in the current sheet results in a particle population
with a typical energy E. When these particles leave the re­
connection site they emit the observed synchrotron radiation
in the ambient magnetic field. Those particles with sufficiently
small pitch­angles can enter the loss cones of the newly formed
loops below the current sheet and precipitate into the chromo­
sphere/photosphere where they lose their energy by Coulomb
collissions and heat the plasma. This heated plasma lies at the
origin of the optical flare emission. We now make the assump­
tion that the optical emission has a black­body spectrum. The
validity of this assumption is discussed later in this paper.
In Sect. 3.2 we found that, depending on the assumed size
of the radio source, the typical particle energy is about one to
a few MeV. Table 5 lists the exact numbers for the cases that
ü r = 0:1 and ü r = 1, but for the range considered the particle
energy does not depend strongly on the assumed source size.
Let us assume, therefore, that the acceleration process results
in particles with an energy of about one MeV. The particles
which remain in the coronal volume and do not precipitate to
denser layers are responsible for the radio flare. These particles
will predominantly lose their energy by collisions in the corona
which for 0.1 ­ 10 MeV electrons occurs on a characteristic
timescale given by (Benz and Gold, 1971)
t col = 1:59 10 12 En \Gamma1 (6)
with E the particle energy in MeV and n the ambient coro­
nal density. A linear regression fit for an assumed exponential
decay of the 6 cm flux gives a characteristic decay time of
1322 seconds. Equating this decay time to the collisional time
scale results in a coronal density of n ú 10 9 cm \Gamma3 , which
corresponds to a plasma frequency of š p ú 0:3 GHz. The
absence of flare emission at 1.47 GHz is therefore not due
to the observing frequency being below the local plasma fre­
quency. The synchrotron emission at a given frequency can
be strongly depressed because of the reduced phase veloc­
ity in a plasma, the so­called Razin suppresion at frequencies
š ! ¸ 20n=B ú 0:2n 9 =B 2 GHz. This frequency is also below
the observing frequencies, so that the absence of detected 20
cm emission can not be attributed to the Razin effect.
If our assumption that the source is optically thick at 6 cm
is true, then the source must also be optically thick at 20 cm.
Using Eq. (3) we find that at the maximum of the radio flare,
when the 6 cm flux amounts to ¸ 5 mJy, the 20 cm flux equals
F 20 = 1=
p
B 2 sin # mJy for ü r = 1 or F 20 = 0:6=
p
B 2 sin # mJy
for ü r = 0:1. Given the noise levels in the one­minute maps
(¸ 0:5 \Gamma 0:6 mJy), these fluxes will not result in a statistically
significant detection. It is important to note that the absence of
emission at 20 cm is compatible with an interpretation in terms
of optically thick synchrotron emission and does not require a
(narrow bandwidth) coherent mechanism.
Next we turn to the optical emission. Those particles which
precipitate into the loss cone loose their energy over a column
depth (Emslie,1978; van den Oord, 1988)
N = E 2 ¯ 0
6úe 4 \Lambda
= 1:28 10 23
` \Lambda
20
' \Gamma1 ` E
1 MeV
' 2
cm \Gamma2 , (7)
where ¯ 0 is the cosine of the pitch­angle at the moment of in­
jection (here taken unity), E is the energy at the moment of
injection, e is the electron charge, and \Lambda is the Coulomb log­
arithm. This expression shows that MeV particles can traverse
substantial column densities and, as a consequence, deposit en­
ergy at a substantial depth in the atmosphere. The atmospheric
volume where the beam energy is deposited will heat up, but
in the atmosphere of a dMe star a considerable fraction of the
beam energy will go into the ionizationof the (abundant) neutral
hydrogen. The most energetic beam particles are stopped in the
deepest layers where a strong temperature gradient is created
since the beam energy input, and therefore the heating, stops
there. This temperature gradient drives a conductive energy flux
out of the heated plasma column. A simple model for the tem­
perature evolution of the (beam) heated plasma column was
proposed by van den Oord (1988) who considered the energy
balance of the heated volume
3
2 Nk dT
dt = F b \Gamma F sat \Gamma F ion erg cm \Gamma2 s \Gamma1 , (8)
where F b is the beam energy flux, F sat =
\Gamma 2
ú
\Delta 1=2
n e m e
i kT
m e
j
is the saturated heat flux and F ion is the ionization loss. The
temperature gradient at the bottom of the heated volume is so
large that classical heat conduction theory breaks down and the
classical conduction should be replaced by the saturated heat
flux (for a discussion see van den Oord, 1988). The ioniza­
tion equilibrium is determined by an (instantaneous) balance
between collisional ionization and radiative recombination. Di­
rect ionization of hydrogen by the beam particles is neglected
in this model but for the energy balance it is not important
whether the beam energy goes directly into ionization energy
or first into heat and then into ionization energy. The system
quickly evolves towards an equilibrium temperature set by the
balance of beam heating and conductive and ionization losses:
F b \Gamma F sat \Gamma F ion = 0. This equilibrium temperature is com­
pletely determined by the beam parameters: the beam flux F b ,
and the energy of the beam particles E. This energy determines
the column depth over which the beam heating takes place (cf.

10 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Eq. (7)). The equilibrium equation reads (see van den Oord,
1988)
F b \Gamma
` 2
ú
' 1=2
m e
` k
m e
' 3=2
NH
` f
f + 1
'
T 3=2
\GammaffN H Nü
` f
f + 1
' 2
= 0 , (9)
where N is the column density (cm \Gamma2 ), NH is the total (neu­
tral and ionized) hydrogen density (cm \Gamma3 ), ü is the ioniza­
tion potential of hydrogen (13.6 eV), and f = C=ff with
C = 10 \Gamma10 T 1=2 e \Gammay the collisonal ionization coefficient and
ff = 2 10 \Gamma11 T \Gamma1=2 '(y) the radiative recombination coefficient,
y = ü=kT and '(y) is a slowly varying function of the tem­
perature. The expressions for ff and C are taken from Tucker
(1975). The total hydrogen density NH can be related to the
column density using NH ú 2 10 \Gamma7 N which follows from a fit
to a model atmosphere for YZ CMi by Giampapa et al. (1982).
(This relation differs by a factor two with the relation used by
van den Oord, 1988). The above expression can now be written
as
F b;11 \Gamma 8:5 10 \Gamma8 N 21
` f
f + 1
'
T 3=2
\Gamma868N 2
21
` f
f + 1
' 2
T \Gamma1=2 = 0 , (10)
where F b;11 = F b =10 11 and N 21 = N=10 21 . For a given beam
flux and column density (or beam particle energy) this non­
linear equation can be solved for the equilibrium temperature of
the heated atmosphere. Note that the expression is quadratic in
N 21 , so that finding N 21 as a function of F b and T is relatively
simple. In Fig. 7 we show the equilibrium temperature as a
function of F b and N . For a large range of parameter values the
temperature varies between 7000 K and approximately 18000
K. These values are in the correct range to explain optical flares.
The insensitivity of the temperature to the values of F b and N
is caused by the ionization which acts as a thermostat. Only for
small values of N and high values of F b (upper left corner of the
figure) are much higher temperatures found. In that case only a
relatively small fraction of the beam energy goes into ionization
losses and the bulk of the beam energy goes into heating.
The black­body temperature of the optical flare (T bb ) is
related to the flare magnitude (4m) in the U­band according to
10 4m=2:5 = A f B(T bb ) + (A \Lambda \Gamma A f )B(T \Lambda )
A \Lambda B(T \Lambda )
= ü opt
B(T bb )
B(T \Lambda ) + 1 \Gamma ü opt (11)
with A \Lambda the stellar disk area, A f the optical flare area, B(T ) the
Planck function, T \Lambda = 3250 K the effective temperature of the
star, and ü opt = A f =A \Lambda .
Eq. (11) indicates that the black­body temperature of the
flare is a simple function of the dimensionless optical flare area
ü opt . In the two­ribbonflare scenario the optical emission occurs
Fig. 7. Equilibrium temperature reachedby a plasmacolumn subjected
to beam injection as a function of the beam flux F and the column
density N . The labels for the contour levels are in units of 1000 K.
Fig. 8. Particle energy as a function of dimensionless optical flare area
ü opt (solid line). Also indicated are the particle energies as derived
from the radio data (dots).
during the impulsive phase of the flare when the current sheet
is at a relatively low altitude. The particles responsible for the
optical flare hit the atmosphere over an area A f = ü opt A \Lambda and
carry all the energy for the optical emission so that
A f F b t inj = E opt , (12)
where t inj is the duration of the beam bombardment, E opt is the
total flare energy at optical wavelengths and F b = n f ficE is the
beam flux with n f the beam particle density. Taking t inj ú 110 s,
equal to the duration of the rise phase of the optical flare, and

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 11
E opt ú 2 10 32 erg, the total energy losses in the U­band, the
beam flux becomes a simple function of the optical flare area
F b = 4 10 8 ü \Gamma1
opt . (13)
Consider ü opt now as a variable. For a given value of ü opt we
obtain from Eq. (13) the beam flux and from Eq. (11) the black­
body temperature of the flare. Inserting this temperature and the
value for the beam flux into Eq. (10) gives the required column
density N 21 , which is related to the beam particle energy E by
Eq. (7). The result is presented in Fig. 8, where the solid line
indicates the particle energy as a function of ü opt . All the combi­
nations of E and ü opt on this line result in a correct value for the
U­band losses. The range of values that E can take, however, is
limited by the radio data. In Fig. 8 the dots indicate the implied
particle energies for two typical, but assumed, sizes of the radio
source at the maximum of the 6 cm flux. With the assump­
tion that both the optical flare and the radio flare are caused by
particle populations with comparable energies we find that the
optical flare area varies between ü opt ú 1:9 10 \Gamma2 for ü r = 0:1
and ü opt ú 10 \Gamma2 for ü r = 1. The corresponding black­body
temperature varies between approximately 8427 K and 9561 K
(see Table 5). These values compare favourably with previous
(spectroscopic) observations of flares on YZ CMi. Mochnacki
and Zirin (1980) found for a flare that ü opt ! ¸ 10 \Gamma2 with the flare
continuum well fitted with a dominant black­body component
and with a smaller contribution by a hydrogen recombination
component. Kahler et al. (1982) found that at the maximum of
an optical flare the emission could well be fitted with a black­
body spectrum with T bb = 8500 K and ü opt = 5 10 \Gamma3 . Although
for the present observation only the U­band flux is available,
more detailed observations sometimes indicate the presence of
black­body emission that supports this interpretation. It is likely,
however, that a black­body signature only arises when the beam
particles deposit their energy deep enough in the atmosphere
while the beam flux is still large. In the present case the MeV
electrons deposit their energy (up to) close to the temperature
minimum in the atmospheric model for YZ CMi by Giampapa
et al. (1982). The results presented in Fig. 8 show that both
the particle energy and the optical flare area are not extremely
sensitive to the assumed size of the radio source. Because the
beam flux and the energy of the beam particles are known, it
is possible to calculate the density of the energetic particles as­
suming they move with a velocity fi = 1. The derived density is
in the range n f ú 2 \Gamma 9 10 5 cm \Gamma3 (see Table 5). In Sect. 3.2 we
found that if the source is optically thick, n f ` ? ¸ 2 10 3 cm \Gamma2 .
With the given values of n f we find that ` must larger that 0.01,
a condition which is easily met.
The typical size of the optical flare area (¸ 0:01A \Lambda =
2 10 19 cm 2 ) is a factor 33 larger than the area of solar white
light flares at flare maximum (¸ 6 10 17 cm 2 , Neidig and Cliver,
1983). Machado and Rust (1974) observed a solar white light
continuum with temperatures in the range 8,500 ­ 20,000 K,
comparable with the temperature range indicated in Fig. 7. The
white light power amounted to a few times 10 27 erg s \Gamma1 during
the impulsive phase. In our case the U­band peak luminosity
amounts to 10 30 erg s \Gamma1 . Because the solar white light flare and
Table 5. Results for two values of the assumed radio source size (ü r ).
ü r 0:1 1
E (MeV) 2:4= p
B 2 sin # 0:9= p
B 2 sin #
N 21 750 97
ü opt 1:85 10 \Gamma2 1:05 10 \Gamma2
T bb (K) 8427 9561
F b (erg/s/cm 2 ) 2:2 10 10 3:9 10 10
n f (cm \Gamma3 ) 1:9 10 5 9:2 10 5
the present flare have comparable temperatures, the larger lumi­
nosity in the U­band can only be explained if the stellar optical
flare area is considerably larger than the typical value for solar
white light flares, as indeed is found.
The above derived optical flare area of ¸ 2 10 19 cm 2 may be
compared with that based on the UV observations. For example,
taking the radiative power output in the UV lines of C IV 1550A,
Si IV 1396A, C III 1176A, and the line emissivities of Doyle and
Keenan (1992), we derive a mean (volume) emission measure
of 2:5 \Sigma 0:1 10 49 cm \Gamma3 for the flare plasma. Assuming a simple
cube structure, this translates to a flare area of ¸ 1:6 10 19 cm 2
(based on the derived electron density from the C III lines in
Sect. 3.3), which is in good agreement with the above derived
optical flare area.
Although the results present in Table 5 show that a com­
bined interpretation of the optical and the radio data results in
reasonable parameters, especially when compared with other
flare observations, some critical remarks are appropriate. The
first point we would like to address is the use of the U­band.
The flux in this band contains a substantial contribution by
higher members of the Balmer series, the Balmer continuum,
the Balmer jump and Ca II H & K (see discussion by Gi­
ampapa, 1983, and Worden, 1983). Although it may contain a
black­body component, the true spectrum is unlikely to con­
sist only of black­body radiation. The optical flare area ü opt ,
as determined from Eq. (11) must therefore be considered as
an effective area for black­body radiation similar to the proce­
dure followed by Mochnacki and Zirin (1980) and Kahler et al.
(1982).
Unfortunately, since there were no X­ray observations for
this event it is difficult to say anything concerning the thermal
electrons in the corona. It has been suggested by various authors
(based on the results of Hartmann et al., 1979, 1982) that the
UV line of He II 1640A can be used to obtain information
about the X­ray plasma since the Hartmann et al. produced
calculations to show that, with increasing magnetic activity, the
He II 1640A line is dominated by recombination. However, an
analysis by Seely and Feldman (1985) of solar quiet and active
regions and of flaring plasma showed that this is not the case.
This conclusion is at variance with the recent radiative transfer
calculations of Wahlstrom and Carlsson (1994) who showed
that this line is formed by photoionizationfrom the ground state
of He II, mainly by the incident of EUVE radiation. Assuming

12 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
that 60% of the He II 1640A emission is due to recombination
(Hartmann et al. 1982), and using the relation between the X­
ray flux and the He line flux (Hartmann et al. 1979), suggests an
X­ray flux of ¸ 8 10 \Gamma12 erg cm \Gamma2 s \Gamma1 during the 40 min. IUE
exposure and a total X­ray radiative losses of ¸ 10 32 erg. This
flux should be considered as a lower limit as it only refers to the
narrow spectral range as covered by the Einstein IPC. A study
by Pallavicini et al. (1990) using the EXOSAT LE detector,
indicates total X­ray energies in the range 0:66 \Gamma 2:8 10 32 erg
for three flares onYZ CMi. Although in principle the thermal X­
ray flare radiative losses can be comparable to the optical losses
we do not elaborate on this further given the uncertainties in the
formation of the He II 1640A line.
The deceleration of the energetic electrons in the atmo­
sphere results in the emission of non­thermal thick target X­ray
emission (Brown, 1971). The ratio of the total radiative losses
during the braking process E rad and the (initial) kinetic power
is the beam E beam is in the thick target approximation given by
E rad
E beam
= 4
3
ff
ú
E
mc 2
1
\Lambda
ú 1:5 10 \Gamma4
` \Lambda
20
' \Gamma1 E
mc 2
where ff is the fine structure constant and E is the electron's
energy at the moment of injection. This expression shows that
MeV electrons loose a negligible fraction of their energy in the
form of X­ray Bremsstrahlung and that practically all energy is
lost by collisions resulting in heating of the ambient medium.
Our model predicts the creation of a heated plasma column
in the lower chromosphere/photosphere. The column depth over
which the heating occurs lies in the range 23 ! ¸ log N ! ¸ 24,
which is determined by the typical particle energy required by
the observed radio flux. The other input parameter is the beam
flux (Eq. (13)) in which there are two sources of uncertainty:
the total optical energy losses, for which the energy must be
supplied by the beam, and the flare area. Because the flare area
is only an effective area, derived under the assumption of black­
body emission,it may differ from the actual flare area. The total
energy losses are probably larger than the value we used because
we used the total losses in only the U­band. The resulting uncer­
tainty in the beam flux will, however, not considerably change
our results. To demonstrate this we present in Fig. 9a the beam
flux as a function of column density and equilibrium temper­
ature. This figure is another presentation of the data in Fig. 7.
The figure clearly shows that in the range 23 ! ¸ log N ! ¸ 24 the
equilibrium temperature is relatively insensitive to the assumed
beam flux. We calculated, for example, the parameters given in
Table 5 using a ten times higher value for E opt . The resulting
temperatures were only 500 ­ 800 K higher than those listed in
Table 5, while the optical flare area was only 25% smaller. Our
results are, therefore, not very sensitive to our underestimate of
the beam flux.
An indication of how the actual optical spectrum may look
can be obtained from the results of Donati­Falchi et al. (1985),
who calculated the optical spectrum of solar flares in the wave­
length range 3600­4000A. The temperature range considered in
their calculations was 7 \Gamma 12 10 3 K, the electron density range
Fig. 9. Beam flux as a function of column density N and equilibrium
temperature T . The results in the top panel are based on a balance be­
tween beam heating and conductive and ionization losses. The results
in the lower panel follow from the balance between beam heating and
black­body and ionization losses. Note the substantial higher beam
fluxes which are required to obtain a given equilibrium temperature
when black­body losses are important.
13:1 Ÿ log n e Ÿ 13:5, and the hydrogen slab depth 400 and 500
km. These values are considered to be typical for solar flares.
How does this compare with our parameters? The column den­
sities we found correspond to geometrical sizes in the range
420­450 km in the model chromosphere for YZ CMi (see Gi­
ampapa et al., 1982). The electron density can be estimated us­
ing n e = (f=(f + 1))NH ú 2 10 \Gamma7 (f=(f + 1))N (see discussion
below Eq. (9)). For T = 8427 K we find n e = 1:9 10 13 cm \Gamma3
and for T = 9561 K we find n e = 2:6 10 13 cm \Gamma3 . Despite the
simplicity of our model, these parameters fit surprisingly well
within the range of typical solar flares parameters. The models
by Donati­Falchi et al. can, therefore, be used to obtain an im­
pression of how the actual spectrum looks. We refer to Figs. (1)
and (3) by Donati­Falchi et al. which show part of the spectrum

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 13
in the U­band range. The presence of higher members of the
Balmer series dominate these spectra with the highest members
merging into a pseuso­continuum.
The applicability of Eq. (9) is limited by its inclusion of
only bound­free transistions. Because of the assumed equilib­
rium between collisional ionization and radiative recombina­
tions these kind of transitions are automatically included. At
the calculated equilibrium temperatures the number of recom­
binations amounts to 3:8 10 40 s \Gamma1 for the whole optical flare
volume. The losses in the Balmer lines are not included but
will probably not strongly change the results. This can be seen
as follows. The inclusion of bound­bound radiative losses will
on average correspond to a correction factor in Eq. (9) in the
term for the ionization losses. But this corresponds to using
Eq. (9) with a lower beam flux. Above we demonstrated that
the resulting equilibrium temperature is insensitive to changes
of the beam flux by say a factor ten. Therefore the inclusion
of bound­bound transitions will not significantly change our
results.
We would like to add a few remarks concerning the applica­
tion of black­body radiation in stellar flare models. Assume first
that the flaring region actually emits a black­body spectrum. In
that case we should include an extra term \GammaoeT 4 in Eq. (9) with
oe the Stefan­Boltzmann constant. Such a term makes the con­
ductive losses unimportant for the global energy balance. In
Fig. 9b we present the beam flux as a function of the column
density and the equilibrium temperature with the beam fluxes
now calculated using Eq. (9) with the conductive losses re­
placed by black­body losses. There is a striking difference with
the results presented in Fig. 9a. To achieve equilibrium tem­
peratures for the flaring volume near 10,000 K, a much higher
beam flux is required. In an equilibrium situation the beam flux
must at least be larger than or equal to the black­body emittance:
F b ? ¸ oeT 4 = 5:7 10 11 T 4
4 erg cm \Gamma2 s \Gamma1 or T ! ¸ 6480F 1=4
b;11 K.
This shows that only very energetic beams can produce black­
body temperatures of ¸ 8500 K as was oberved by Kahler et
al. (1982). In other words, the model we used will more easily
explain an optical flare than a model with black­body losses.
For dMe­stars, which show frequent optical flare activity, it is
therefore likely that the radiative losses are not similar to a
black­body because each of the observed flares would require
very energetic electron beams. We note that for a black­body
spectrum at most 10% of the black­body emittance is detected
in the U­band. This occurs for 8000 K ! T bb ! 12000 K. At
other temperatures this fraction is much less. This implies that
if a black­body spectrum is observed in the U­band, a large
fraction of the radiative losses are outside of the band.
The radio flux peaks about 7 minutes after the optical max­
imum. During this time interval the flaring structure expands
from an area given by ü opt to ü r . The linear expansion veloc­
ity (proportional to p ü) corresponds to v = 110 km s \Gamma1 for
ü : 1:85 10 \Gamma2 ! 0:1 and v = 550 km s \Gamma1 for ü : 1:05 10 \Gamma2 !
1. From the decay of the radio flare we estimated the coro­
nal density to be n ú 10 9 cm \Gamma3 so that the Alfven velocity
corresponds to vA = 6900B 2 = p
n 9 km s \Gamma1 . These expansion
velocities correspond to 0:016v A and 0:08v A . These numbers
indicate that typical velocities of a few hundred kilometer per
second are involved, which are also typical for erupting solar
filaments. The velocity that the erupting filament can obtain
is set by the rate at which magnetic field lines are transported
into the current sheet, since this is the rate at which the field
lines which hold the filament down are reconnected. Models for
magnetic reconnection predict inflow velocities in the range of
1­10% of the Alfven velocity (Petschek, 1964) consistent with
our estimates.
The sub­Alfvenic velocities imply that the filament evolves
almost force­free. This does not come as a surprise, because the
Lorentz force on a filament is so large that enormous accelera­
tions would occur if the filament were not close to the force­free
state. Another way of putting this is that the filament constitutes
a (O­type) neutral point in the magnetic configuration which by
definition must be (almost) force­free.
The pre­flare evolution of a filament is governed by the
balance of two strong but opposite Lorentz forces (van Tend
and Kuperus, 1978): a downward force by the (background)
active region magnetic field on the filament current, and the
upward force by an induced surface current distribution. The
origin of this surface current results from the inability of the
(frozen­in) coronal magnetic field to re­enter the photosphere
which has a much larger intertia than the plasma in the coronal
magnetic field. The photosphere, therefore, acts as a boundary
(separatrix) between topologically different flux systems along
which currents are induced. The effects on the coronal magnetic
field by these surface currents can be modeled by placing a vir­
tual current below the photosphere which is equal and opposite
to the filament current (Kuperus and Raadu, 1974). The force
balance on the filament is then
I
c
` I
cz \Gamma B(z)
'
= 0
with I the filament current, z the height of the filament and
B(z) the active region magnetic field. At heights where B(z)
drops faster than 1=z, no stable equilibrium is possible and
a flare occurs (see van Tend and Kuperus, 1978). The point of
instabilityis also close to the moment that a neutral line emerges
above the photosphere whose presence allows the magnetic
reconnection process to start.
At the moment that the instability occurs we have from
the above equation I = czB, where all quantities relate now
to the critical values at the moment of instability onset. Let
h s now define the height of the current sheet, h f the height
of the filament, and ` the length of the filament. Numerical
simulations (Kaastra, 1985, Martens and Kuin, 1989) indicate
that h s ú 0:1h f . We write ` = aeh f with ae ú 4 \Gamma 6 for solar
filaments. In the following we apply these relationships, based
on models for solar two­ribbon flares, to obtain information
on the reconnection process during the flare on YZ CMi. We
take for the length over height ratio a canonical value ae = 5
indicated by ae 5 and for the dimensionless optical flare area a
value ü opt = 10 \Gamma2 indicated by ü \Gamma2 .

14 G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi
Below the current sheet a semi­cylindrical arcade of loops
is formed during the flare with a radius h s . The optical flare area
corresponds then to approximately ü opt A \Lambda = 2h s ` from which
we find h f = 45:6
p
ü \Gamma2 =ae 5 Mm and ` = 228 p ae 5 ü \Gamma2 Mm.
The total energy in the system is given by W = L/I 2 =2 with
L/ ú `=c 2 the self­inductance. Taking I = ch f B, we obtain
W = 2:4 10 33 B 2
2 ü 3=2
\Gamma2 ae \Gamma1=2
5 erg. This energy is comparable to
the total radiative losses during the flare, but it must be con­
sidered as a lower limit because, as the reconnection proceeds,
an area larger than ü opt can become involved. It demonstrates,
however, that enough energy is available to power the impulsive
phase of the flare.
We found that the typical velocity with which the system
expands is about one hundred kilometers per second. We denote
this expansion velocity as v 7 . The expansion results in a change
of the self­inductance of the system and as a consequence an
inductive voltage V is present in the current sheet. This voltage
is given by
V = I
dL/
dt
= I
c 2
d`
dt
ú I
c
v
c
= h f B
v
c
= 1:5 10 8 B 2 v 7 ü 1=2
\Gamma2 ae \Gamma1=2
5 statvolt (14)
and the related electric field amounts to E = V=` =
6:7 10 \Gamma3 B 2 v 7 =ae 5 statvolt cm \Gamma1 . This value is comparable to
the value of 1:5 10 \Gamma2 found in the numerical model by Martens
and Kuin (1989) and to the observationally derived value of
8:3 10 \Gamma3 by Kopp and Poletto (1986).
The fraction of particles which experiences run­away acel­
eration in the current sheet can be estimated by comparing the
electric field with the Dreicer field ED . In the current sheet the
resistance will become anomalous and for the effective collision
frequency we take the canonical value š ú 0:01! p (Vlahos and
Papadopoulos, 1979) with ! p = 2úš p . Earlier we found that
š p ú 0:3 GHz. The Dreicer field now follows from
ED = 4úš
! 2
p
nev t = 12:5 10 \Gamma3
` T 6
n 9
' 1=2
statvolt cm \Gamma1 , (15)
with v t the electron thermal velocity, so that E=ED ú 0:54.
For a given value of the ratio E=ED , the fraction of runaway
particles is estimated by Norman and Smith (1978) to be
N r
N = 1
2 exp
0
@ \Gamma 1
2
'' `
ED
E
' 1=2
\Gamma E
ED
# 2
1
A . (16)
For E=ED ú 0:54 this expression gives N r =N ú 0:36, imply­
ing that about one third of the electrons entering the sheet are
accelerated. Is this value consistent with our previous results?
The total number of electrons entering the sheet per second is
approximately given by
2h s `nv = 2:1 10 35 n 9 v 7 electrons s \Gamma1 ,
while the total number of accelerated electrons per second can
be estimated from
ü opt A \Lambda n f c = 1:2 10 35
i n f
2 10 5
j
electrons s \Gamma1 .
These numbers imply that N r =N ú 0:57 which is surprisingly
close, given the uncertainties, to the value of 0.36 which fol­
lowed from the independent estimate of the electric field.
We conclude that the observed flare on YZ CMi shows a
strong similarity with the two­ribbon flares observed on the
Sun.
5. Conclusions
In this paper we have discussed combined observations of YZ
CMi at optical, UV and radio wavelengths. YZ CMi was found
to undergo repeated optical flaring. The most outstanding re­
sult is the 3.8 magnitude flare which occured on 3 February
1983. This flare coincided exactly with an IUE exposure and
showed a clear radio counterpart. As a result we were able to
construct emission measure curves for the temperature range
4:0 Ÿ log T e Ÿ 5:4 during the flare and to compare these with
similar curves for YZ CMi in its quiescent state (Fig. 5). At
those locations in the atmosphere were strong temperature gra­
dients are present, like e.g. the transition region, the emission
measure will have a relatively low value. In Fig. 5 it is clear that
during the flare the position of the transition zone has shifted
from T = 10 5 K in quiescence to T ú 10 4:8 K and that the
overall height of the emission measure curves increased. This
behaviour is consistent with the scenario in which the flare en­
ergy release takes place in the corona. By means of particle
beams or a conductive flux, part of the flare energy is transfered
to the chromosphere which heats up, implying a downward shift
of the transition region. This downward shift, associated with
chromospheric evaporation, implies that at each temperature
the density effectively increases so that the radiative losses at
each temperature increase (Fig. 6).
During the flare the radio flux at 6 cm peaks about seven
minutes after the U­band flux. The absence of radio emission
at 20 cm can be understood if the radio emission mechanism is
optically thick synchrotron emission by MeV electrons in coro­
nal fields of about 100 Gauss. In order to explain the absence
of emission at 20 cm, there is no need to invoke a coherent
emission mechanism or flux reduction by means of Razin sup­
presion. The collisional time scale (Eq. (6)) indicates that the
MeV electrons move in a medium with a typical coronal density
of n ú 10 9 cm \Gamma3 .
The lack of spatial resolution makes it difficult to compare
stellar flares with the better observed solar flares. One can at
most make a comparison between the global characteristics. In
this paper we used the global characteristics of the solar two­
ribbon/white­light flare to model the combined optical/radio
flare. Our basic assumption is that the reconnection process re­
sults in an energetic particle distribution with a typical energy
determined by the reconnection process. These energized par­
ticles are then responsible for both the radio and the optical
flare. From the interpretation of the radio flare we found that
this typical particle energy is a few MeV for typical values of
the source size. The particles trapped in the corona loose their
energy by collisions and give rise to the synchrotron emission
at 6 cm.

G.H.J. van den Oord et al.: Analysis of a large flare on YZ CMi 15
The MeV electrons which precipitate in the loss cone can
cross a substantial column depth before they are stopped. Dur­
ing the braking process their energy is transferred to the ambient
medium which is then ionized and heated. In order to calculate
the physical parameters of the bombarded atmospheric column,
we applied the relatively simple model proposed by van den
Oord (1988) which considers only the global energy balance
of the atmospheric column and does not include any dynamics.
In the bombarded column an equilibrium is established, on a
short time scale, between beam heating, ionization losses and
conductive losses. Although the model is rather crude, it has
some very interesting implications. First of all, the equilibrium
temperature reached in the plasma column is mainly determined
by the energy of the beam particles, and therefore the stopping
depth N , while this temperature is fairly insensitive to the ac­
tual beam flux (see Figs. 7 and 9). Secondly, the equilibrium
temperatures are in the range (7.000 ­ 20.000 K) found for solar
white­light flares. The insensitivity of the equilibrium temper­
ature to the actual value of the beam flux implies that during
both weak and strong flares on YZ CMi, the same atmospheric
conditions are created which favour emission at optical wave­
lengths. The difference between weak and strong flares can then
be related to the typical energy of the particles and hence to the
column depth involved.
To derive the characterictics of the optical flare we assumed
that the emission is black­body. With this assumption an effec­
tive optical flare area is found which is comparable with the
earlier results for YZ CMi by Mochnacki and Zirin (1980) and
Kahler et al. (1982). The results of the combined optical/radio
interpretation, given in Table 5, must be regarded as typical pa­
rameters. Even though the radio source size is unknown, the Ta­
ble shows that there is a surprisinglysmall spread in the derived
parameters. This is caused by the insensitivity of the equilib­
rium temperature to the magnitude of the beam flux. The reason
for this behaviour is that in cool dwarf atmospheres the balance
between ionization and radiative recombination acts as a very
efficient thermostat. Only when the beam energy is deposited at
very small column depths, where the plasma is already ionized,
does this mechanism not work and strong temperature increases
result.
We demonstrated that it unlikely that the actual radiative
losses are truely black­body and we only used an equivalent
black­body radiator to derive an effective flare area. If the ra­
diative losses would in reality be black­body, then high beam
fluxes are required to heat the bombarded plasma column to
typical white­light flare temperatures (Fig. 9, lower panel). The
reason is that a black­body is a very efficient emitter (¸ T 4 ), so
that a large energy deposition is required to increase the temper­
ature. With the frequent optical flaring of YZ CMi it is unlikely
that each of these flares would be characterized by the presence
of beams with F b ? ¸ 10 11 erg cm \Gamma2 s \Gamma1 although detailed spec­
troscopic observations of flares during their impulsive phase are
required to see whether black­body emission can in reality be
ruled out.
The results listed in Table 5 indicate that the derived pa­
rameters fit nicely within the parameter range considered by
Donati­Falchi et al. (1985) for solar white­light flare model­
ing. Their model predicts a strong increase of the Balmer lines
which actually has been observed on YZ CMi during a flare
(Doyle et al. 1988, see their Figs. 2 and 10). In order to arrive at
a quantitative comparison, however, better spectroscopic obser­
vations are required. This point has been extensively discussed
by Houdebine (1992) who also addresses the role of MeV elec­
trons in stellar flares. We note however that Houdebine made
no allowance for changes in the ionization fraction during the
beam bombardment while in our model the ionization acts as a
thermostat in the bombarded plasma column.
In addition to comparing the observed flare with the solar
white­light flare, we also checked whether the observed flare can
be interpreted consistently as a two­ribbon flare. The increase
of the radio flux is then interpreted as due to a growing arcade of
loops, forming below a current sheet, which emit synchrotron
radiation. The typical velocity is of the order of a few hundred
kilometers per second as has been observed for erupting solar
filaments. In the current sheet the value of the electric field is
comparable to the values derived, both theoretically and obser­
vationally, for solar two­ribbon flares. Moreover, the predicted
number of electrons which experience run­away acceleration in
the current sheet is of the same order as is required to power the
optical flare.
We conclude that the observed optical and radio flare can be
interpreted within the (global) framework of solar two­ribbon
flares with the optical flare volume showing strong resem­
blances with the atmospheric conditions created during solar
white­light flares.
Acknowledgements. We like to thank the IUE and VLA Observatory
staff for their help in obtaining this data. Research at Armagh Obser­
vatory is grant­aided by the Dept. of Education for N. Ireland. We also
acknowledge the support provided in terms of both software and hard­
ware by the STARLINK Project which is funded by the UK PPARC.
Research on stellar activity at Catania University and Observatory
is supported by MURST (Ministero dell'Universita e della Ricerca
Scientifica e Tecnologica), CNR--GNA (Consiglio Nazionale delle
Ricerche -- Gruppo Nazionale di Astronomia), and Regione Sicilia.
Computer facilities at Catania are provided within the ASTRONET
network. G.H.J. van den Oord acknowledges financial support from
the Netherlands Organization for Scientific Research (NWO).
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