We study the hypothesis that observed X-ray/extreme ultraviolet emission from coronae of magnetically active stars is entirely ( or to a large part ) due to the superposition of flares , using an analytic approach to determine the amplitude distribution of flares in light curves .
The flare-heating hypothesis is motivated by time series that show continuous variability suggesting the presence of a large number of superimposed flares with similar rise and decay time scales .
We rigorously relate the amplitude distribution of stellar flares to the observed histograms of binned counts and photon waiting times , under the assumption that the flares occur at random and have similar shapes .
Our main results are : ( 1 ) The characteristic function ( Fourier transform of the probability density ) of the expected counts in time bins \Delta t is \phi _ { F } ( s, \Delta t ) = \exp \ { - T ^ { -1 } \hskip { -2.845276 pt } \int _ { - \infty } ^ { \infty } \hskip { -5.690551 pt } dt % [ 1 - \phi _ { a } ( s \Xi ( t, \Delta ) ) ] \ } , where T is the mean flaring interval , \phi _ { a } ( s ) is the characteristic function of the flare amplitudes , and \Xi ( t, \Delta t ) is the flare shape convolved with the observational time bin .
( 2 ) The probability of finding n counts in time bins \Delta t is P _ { c } ( n ) = ( 2 \pi ) ^ { -1 } \hskip { -2.845276 pt } \int _ { 0 } ^ { 2 \pi } \hskip { -2.845276 pt } ds e ^ { - ins } % \phi _ { F } ( s, \Delta t ) .
( 3 ) The probability density of photon waiting times x is P _ { \delta } ( x ) = \partial _ { x } ^ { 2 } \phi _ { F } ( i,x ) / \langle r \rangle with \langle r \rangle = \partial _ { x } \phi _ { F } ( i,x ) | _ { x = 0 } 
the mean count rate .
An additive independent background is readily included .
Applying these results to EUVE/DS observations of the flaring star AD Leo , we find that the flare amplitude distribution can be represented by a truncated power law with a power law index of 2.3 \pm 0.1 .
Our analytical results agree with existing Monte Carlo results of ( ) and ( ) .
The method is applicable to a wide range of further stochastically bursting astrophysical sources such as cataclysmic variables , Gamma Ray Burst substructures , X-ray binaries , and spatially resolved observations of solar flares .