Flare Rate Analysis of SDSS M Dwarf Light Curves

1
Flare Rate Analysis of SDSS M Dwarf Light Curves
Adam Kowalski1, Eric Hilton1, Andrew Becker1,
Suzanne Hawley1
1University of Washington
Abstract M dwarfs produce intense flares,
generated by a magnetic dynamo process that is
still poorly understood.  Since M dwarfs comprise
about 80 of thestars in the Galaxy, their
flares will be a significant source of
variability in proposed time domain surveys, such
as LSST.  We seek to characterize the flare
population using a representative sample of gt
7600 M dwarf light curves extracted from
repeat observations of the SDSS Equatorial
Stripe. We describe a variability index used to
identify flares, and present preliminary results
for flaring rate as a function of spectral type
and level of magnetic activity.
Example Flare Spectrum
Equatorial Stripe Population
Light Curves
Figure 1 The central wavelengths and extent of
the SDSS ugriz filters are indicated.  In the
flaring state, the hydrogen lines are strongly in
emission and the blue continuum is greatly
enhanced. Although the u-filter is only partially
shown, it is obvious that the ratio of
flare-to-quiescent flux is greater in the
u-filter than the g-filter.

Light curves with high variability index (gt 400)
Figure 4 Top center - Number of M dwarfs per
spectral class for different magnetic activity
levels active (red), inactive (black), and
weakly active (dashed line). Active stars are
typically later spectral type (Hawley et al.
1996, West et al. 2004). Bottom - The bottom left
plot shows the number of flares with high
variability index, and the bottom right plot
shows the number with intermediate variability
index, both as a function of spectral type.
 Since the sample has many more early type M
dwarfs, it is not surprising that a larger total
number of flares is seen on these relatively less
active stars.
Technique Sample Our sample consists of 7,621 M
dwarf objects (subclassed by magnetic activity
level and spectral type) with an average of 20
epochs/object. Each object has photometric data
in 5 filters u, g, r, i, z. Photometric Tests
We test all of the epochs for good and bad
photometry in the u- and g-filters. Variability
Tests For the epochs in which the u- and
g-filters have good photometry, we calculate a
variability index to determine whether the
epochs flux in both the u- and g-filters
increases significantly enough to be considered a
flare. We use a modified version of the Welch
Stetson (1993) variability index

Light curves with intermediate variability index
(200 to 400)
Flaring Fraction
We use two thresholds to define high and
intermediate variability

• High variability index I gt 400
• Intermediate variability index 200 lt I lt 400

Flux Ratio Test From Figure 1, we expect flares
to increase the flux in the u-filter more than
the g-filter. Therefore, a flare must also
satisfy
Figure 3 The flux ratio (
) vs. epoch number for the u-filter (blue) and
g-filter (red) for a representative sample of
flare candidate light curves. The light curves
are labeled with spectral type and magnetic
activity level. We selected these light curves
as flaring candidates because one or more epochs
have a high (top) or an intermediate (bottom)
variability index. Also, the flux ratio in the
u-filter must be greater than in the g-filter
because we expect flares to produce the largest
flux increase in the u-filter (see Figure 1).
Note that the continuous trends are meant to
guide the eye and that the upward spikes are
defined by a single data point.
Time Sampling
Figure 5 The fraction of observed stars that
flare at each spectraltype is shown for active
(red) and inactive (black) stars, where the
flaring fraction is defined as the number of
flaring epochs observed divided by the total
number of epochs observed for all stars at each
spectral type.  The left and right panels again
show the high and intermediate variability index
results. As expected, the flaring fraction is
much higher for the later type M dwarfs.
References

• Hawley, S.L., Gizis, J.E. and Reid, I.N. 1996 AJ
  112, 2799
• Welch, D. L. and Stetson, P. B. 1993 AJ 105,
  1813
• West, A.A. et al. 2004 AJ 128, 426

Figure 2 We plot the times at which photometry
was taken relative to the time of the first
observation. Every 100th object in our sample is
plotted along the y-axis. There are clusters of
observations separated widely in time over 6
years.
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