|M dwarfs have been the subject of renewed interest as potential habitable planet hosts
and have increasingly become the targets of planet detection surveys. Currently, however,
the number of detections of transiting M dwarf planets remain low. The characterisation
of M dwarf activity is an important consideration for such surveys, and
provides constraints on the modelling of magnetically active low mass stars. Currently
the spottedness of M dwarfs is not well understood owing to their intrinsic faintness
and the lack of diagnostics for assessing starspot morphologies and distributions.
The WFCAM Transit Survey (WTS) contains long term observations of M dwarfs
in the near infra-red and presents an opportunity to study the long term variability
of M dwarfs. The M dwarfs in the WTS are identified by use of colour-spectral type
relations, and the periodically variable M dwarfs in the sample are detected using a
Lomb-Scargle periodogram analysis. A total of 72 periodically variable M dwarfs are
found with periods ranging from 0.16 to 90.33 days. The relations between the spectral
subtypes, amplitudes and periods are studied and comparisons to earlier works studying
M dwarf rotation are made. A number of examples of significant spot evolution are
found, which exhibit complex light curve morphologies that vary in form and amplitude
over periods of months to years. This provides an indication as to the nature of the
spottedness of these stars.
Simulations are performed to probe the connection between spot coverage, temperature
and light curve amplitude. Using the results from these simulations, the spot coverage fractions of the WTS M dwarfs are estimated and they are found to be heavily
spotted. Dynamic models with spots evolving at various average rates are used
to explore how spot evolution can drive increased dispersion in the light curves, and
to what extent this affects the detectability of periodicity by the method used. It is
found that spot evolution can invoke significant noise in an M dwarf light curve, and in
combination with photon noise, can in some instances inhibit the detection of a period.
In reflection of the results, the relation between the light curve dispersion and spot
coverage of the WTS M dwarfs is considered and it is found that more heavily spotted
M dwarfs have intrinsically noisier light curves. The morphologies of the light curves
produced by the simulations, and the manner in which they evolve, are qualitatively
similar to the real M dwarfs in the WTS sample and indicate how models extrapolated
from sunspot distributions can explain behaviour seen in active M dwarf light curves.