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oscillations in the solar corona have been observed for many years .
wavelength regimes ranging from hard x - ray right down to radio have been investigated to search for evidence of waves .
periods have been found ranging from 0.02 to 1000 s. table 1 in @xcite provides an excellent summary of the different periods that have been found , and an explanation for their existence .
most of these waves have been explained by mhd oscillations in coronal loops .
@xcite has provided an excellent review of waves and oscillations in the corona .
many of the observations of waves have been determined from variations in intensity brightness .
recently , however , a huge step forward has been achieved in solar coronal physics due to the high spatial resolution available with the transition region and coronal explorer ( trace ) .
the first spatial displacement oscillations have been observed in coronal loops ( @xcite ) .
it was suggested that these oscillations were triggered by a disturbance from the core flare site .
various mhd waves were investigated and it was found that a fast kink mode wave provides the best agreement with the observed period of 280@xmath230s .
one of the most exciting aspects of observing waves in this fashion is that it potentially provides us with the capability of determining the magnetic field in the corona .
it is notoriously difficult to measure the magnetic field in the corona .
techniques using the near - infrared emission lines have been successful , but have poor spatial resolution .
most frequently , indirect methods are used such as the extrapolations of the coronal magnetic field from the photospheric magnetic field that can be measured using zeeman splitting .
@xcite made use of the flare - related spatial oscillations sometimes observed when a flare occurs , to determine the magnetic field .
they assume that the oscillation is due to a global standing kink wave , and hence the magnetic field is related to the period of the oscillation , the density of the loop , and the length of the loop . in the case of @xcite
they found the magnetic field to be 13@xmath29 g .
the errors on this are large due to errors on the determination of density , loop length and period .
@xcite suggest that the oscillations are due to a sudden displacement of the magnetic field at the surface which causes an oscillatory relaxation of the field .
recent work by @xcite suggests that the oscillations are second standing harmonics of acoustic waves tied to the loop length .
the model gives a relationship between the oscillation period , the loop length and the average plasma temperature , all of which can be independently observed on the sun .
waves are observed across the electromagnetic spectrum on the sun .
however , observations on other stars are rare .
one reason for this is that on the sun , we have the spatial resolution to zoom in on small regions .
for example , the transverse trace loops that have been observed are away from the main flare site , and hence have lower emission measure .
analysing an x - ray light - curve , for example , would be unlikely to provide evidence of waves if the emission was averaged over the whole sun .
oscillations have been observed for optical stellar flares ( e.g. , @xcite and @xcite ) .
@xcite found a period of 220  s in the decay phase of a white - light flare on the rs cvn binary . using this they determine a magnetic field of 1200  g. @xcite again found oscillations in x - ray active red dwarfs .
they compared their observations to the possibility that they were observing p - modes . on the sun p -
modes give rise to 5-minute oscillations on the surface .
they concluded that p - modes could not produce the amplitudes they observed and that it must be coronal oscillations , which have , until now , not been observed .    in this work
we observe for the first time an oscillation in the corona of .
we measure the periodicity , and hence determine the magnetic field .
this is the first observation of an x - ray oscillation during a stellar flare .
( ) is an m - type binary dwarf , with both stars of the same spectral type ( dm4.5e+dm4.5e ) .
both components of the binary flare frequently .
the radius of given by @xcite is @xmath3 , using a stellar distance of 8.14  pc ( @xcite ) . correcting for the newer value for the distance from hipparcos ( @xmath4 , @xcite ) , using that the stellar radius is proportional to the stellar distance for a given luminosity and spectral class ,
we obtain a stellar radius of @xmath5 .
the mass of given by @xcite is @xmath6 .
for our analysis we used the _ xmm - newton _ observations of on 16 october 2000 during revolution 156 .
@xcite have analysed this data spectroscopically , obtaining elemental abundances , temperatures , densities and emission measures , while a comparative flare analysis between x - ray and simultaneously observed ultraviolet emissions can be found in @xcite . here , we solely used the 0.212  kev x - ray data from the pn - european photon imaging camera ( epic - pn ) .
figure [ figure ] shows the light curve .
the observation started at 00:42:00 and lasted for 25.1  ks ( @xmath7 7  h ) .
there is one large flare , starting @xmath7 4  h into the observation , increasing the count - rate from flare onset to flare peak by a factor of 1.7 , and lasting for 1  h  25  min .
it shows a steep rise ( rise time @xmath8 ) and decay ( decay time @xmath9 ) .
there is an extended peak to this flare , which shows clear oscillatory behaviour .
the amplitude of the oscillation is around 16% .
applying multi - temperature fitting , @xcite obtain a mean flare temperature @xmath10 and a quiescent temperature @xmath11 , and from the line ratio a flare and quiescent electron density of @xmath12 and @xmath13 , respectively .
the total flare and quiescent emission measures are @xmath14 and @xmath15 .
one of the reasons why we concentrated on this observation is that following the rise phase of the flare there was a period of approximately 40 minutes when the light curve stayed at a high intensity level and showed strong oscillations .
the oscillatory activity can be clearly seen by eye ( see fig .  [ figure ] ) , and shows behaviour suggestive of damping .
this character is much different from solar flares where the flare reaches a peak rapidly , followed by a slow decay .
for example , @xcite shows solar flare light curves and a flat top is not seen .
an alternative to oscillations for this flare is that repeated and rapid flaring is occurring .
we do not consider this option in this paper , and assume for our analysis that we are observing a coronal oscillation .
the purpose of our analysis is to determine through wavelet analysis the period and amplitude of the oscillation .
we determine the magnetic field and loop length of the coronal loop assuming that the oscillation is due to an acoustic wave . as a validity
check the value of loop length was compared to the value determined from a radiative cooling model .
to investigate periodicities during the observation , we applied a continuous wavelet transformation to the 10s - binned - data , using a morlet wavelet ( see , e.g. , @xcite ) .
the wavelet coefficients with the lowest periods are displayed in fig .
[ figure ] .
the flare oscillation is picked up with a 5@xmath16 significance level .
the local maximum with the shortest period and a significance of more than 5@xmath16 is simultaneous with the flare top and identifies the oscillation , which , at the local maximum , has a period of @xmath17 .
the period interval where the wavelet coefficients have a significance of 5@xmath16 or more , is [ 730,920 ]  s.      interpreting these oscillations as the second spatial harmonics of an acoustic wave within the flare ( @xcite ) , we can then determine the flare loop length from @xmath18 \approx \frac{1}{6.7 } \cdot p\ [ { \rm s } ] \cdot \sqrt{t\    [ { \rm mk}]}. \label{ll}\ ] ] inserting the above obtained period @xmath19 and a flare temperature @xmath20 , we obtain a loop length @xmath21 .
note that the temperature carries a @xmath22 error of @xmath23 , therefore the error of @xmath24 is at least 8% ( @xmath25 ) .
it is not straightforward to calculate the corresponding @xmath22 error of @xmath26 . with these numbers ,
the inferred speed of sound is @xmath27 .
the loop length can also ( and independently of any oscillation ) be estimated from rising and cooling times obtained from the temporal shape of the flare , applying a flare heating / cooling model ( see , e.g. , @xcite ) .
we follow the approach by @xcite who investigated a flare on ad leo observed in the extreme ultraviolet .
the shape of this flare is very similar to our flare on , but roughly 10 times larger ( in duration as well as in the increase of the count rate ) .
it also shows a flat top with a possible oscillation .
the flare loop energy equation for the spatial average is given by @xmath28 with @xmath29 the volumetric flare heating rate , @xmath30 the optically thin cooling rate and @xmath31 the time rate change of the loop pressure . during the rise phase ,
strong evaporative heating is dominant ( @xmath32 ) , while the decay phase is dominated by radiative cooling and strong condensation ( @xmath33 ) . at the loop top
, there is an equilibrium ( @xmath34 ) .
the loop length can be derived as @xmath35 where @xmath36 is the rise time , @xmath37 the flare decay time ( indicated in fig .  [ figure ] with the vertical dotted lines ) , @xmath38 the apex flare temperature and @xmath39 , with @xmath40 the peak count rate and @xmath41 the count rate at the end of the flare . inserting these values
, the loop length becomes @xmath42 , which is about a factor of 2 smaller that the loop length inferred from the oscillation .
interpreting the oscillations in terms of global standing kink waves , @xcite derive a relation for the magnetic field @xmath43 with @xmath44 the mass density inside , and @xmath45 the mass density outside the loop .
note that there is a correction factor of 0.64 in the equation as presented by @xcite ( @xcite ) .
we can simplify eq .
( [ mag ] ) by inserting eq .
( [ ll ] ) and using @xmath46 and @xmath47 , with @xmath48 the proton mass .
then , the magnetic field is given by @xmath49 inserting the temperature and densities from the spectroscopy results , we obtain a magnetic field of @xmath50 .
note that the large error is resulting mainly from the density uncertainty . using the loop length from the radiative cooling approach ( sect .
[ radcool ] ) and eq .
[ mag ] , the magnetic field is @xmath51 .      to maintain stable flare loops
, the gas pressure of the evaporated plasma must be smaller than the magnetic pressure @xmath52 knowing the flare density and temperature , we get a lower limit for the magnetic field @xmath53 .
again , there is a large error because of the large uncertainty for the density .
@xcite assume pressure balance and give equations for @xmath54 and @xmath55 ( their eqs  7a , b ) .
using these relations , we obtain a magnetic field of @xmath56 and a loop length of @xmath57 .
we have used three different approaches to determine the loop length of the flare and two different approaches for the magnetic field . the loop length derived in sect .
[ oscill ] from the flare oscillation is the largest with @xmath58 , while the loop length derived from radiative cooling times ( sect .
[ radcool ] ) is somewhat smaller by roughly a factor of 2 , @xmath42 .
the loop length derived from pressure balance ( sect .
[ pressbal ] ) is similar to the latter one , @xmath57 .
the loop length derived by assuming that the variations seen are due to oscillations is a factor of 2 different to the loop length determined by more usual methods . considering the assumptions that have to be made ,
this is good agreement , and gives us confidence that we are , for the first time , observing a stellar coronal loop oscillating .
the magnetic field ranges from 50  g ( radiative cooling ) to 115@xmath256  g ( oscillation ) , with the value from pressure balance in between with 70@xmath240  g. again , these three values are all consistent .
this was the first time that an oscillation during flare peak was observed in x - rays in a stellar flare and flare loop length and magnetic field derived from it .
the values are consistent with other flare models .
we acknowledge financial support from the uk particle physics and astronomy research council ( pparc ) .
umk would also like to thank the european space agency ( esa ) and the university college london ( ucl ) graduate school for financial assistance to attend the cool stars 13 conference .
we analyse oscillations observed in the x - ray light curve of the late - type star . 
 the oscillations occurred during flare maximum . 
 we interpret these oscillations as density perturbations in the flare loop . applying various models derived for the sun , the loop length and the magnetic field of the flare 
 can be estimated . 
 we find a period of 740  s , and that the models give similar results ( within a factor of 2 ) for the loop length ( @xmath0 ) and the magnetic field ( @xmath1 ) . 
 for the first time , an oscillation of a stellar x - ray flare has been observed and results thus obtained for otherwise unobservable physical parameters .