Документ взят из кэша поисковой машины. Адрес
оригинального документа
: http://hea-www.harvard.edu/~swolk/thesis/period/node9.html
Дата изменения: Unknown
Дата индексирования: Tue Oct 2 07:13:05 2012
Кодировка:
Поисковые слова: п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п п
|
Next: About this document
Up: Period Analysis
Previous: Starspots
Actual stars are expected to be more complicated than these simulations.
For example, if a
star is inclined and has a nearly polar spot, the variation will be far more
complicated. The spot may be entirely visible most of the time (one
would observe a prolonged flux minimum
low), and then part of it may disappear over the horizon briefly and
then return (slow rise and then fall back to constant level). In this
case, the observed modulation is actually a brightening from the base
signal. Flares on stars are even more troublesome, since they usually
occur near spotted regions. When the photosphere is becoming dimmer,
there can be a very bright group of data points.
In these realistic cases, it would be very difficult to determine the
correct period without high S/N and additional information. With the
set of observations taken here, I have information available from
several comparison stars and color information.
I use four consistency criteria to mitigate against noise, and two
additional criteria to fight aliasing.
- The same period must be found using both period finding
techniques. The rule that was used here was that a peak in the power
distribution of the periodogram had to coincide with a local minimum of the
PDM code.
- The same period must be found using multiple comparison stars.
This is an obvious criterion which is used to remove variable
comparison stars.
- The same period must be found in the V, R and I filters.
If the periodic behavior does not have the same period in the three
filters, it is probably not due to rotation. Five percent deviation is
considered acceptable to allow for measurement errors in the time of
observation and in the sampling grid used by the period search routines.
As is shown in the Figures 3.1, 3.2, 3.3 and 3.5. The full width
half maximum of the peaks in the periodogram functions are quite
wide. This width is caused by the low number of sample used in the
simulation, and the actual data sets.
- The same phase must be found in the three filters.
This criterion is similar to the previous one. Again five percent errors
are considered acceptable.
- The period found must be consistent with the data from any given
night. One way to test whether a true period or an alias has been
found is to compare the fit to the period with the data for a given night.
For example, if the fit to the data predict that on a given night the
target star should be getting fainter, yet the data for that night show
that star is getting significantly brighter, the period is discarded.
- The color changes observed are consistent with the starspot
hypothesis. All the period measurements rest on the initial hypothesis
that the observed modulations are induced by the rotation of spotted
regions of the star onto and off of the side of the star facing the Earth.
This hypothesis has fundamental predictions for the observed color
changes that should be observed. For a star with very cold spots, the
spots appear black relative to the star and the same color variation is
observed in all colors. For a star with warmer spots, 300K cooler
than the photosphere, more flux is removed from the V band
than the I band, therefore the observed variations are greater in
V than in R, and greater in R than in I. If the behavior
differs from this prediction by more than the observed noise in the
signal, the period is discarded.
Before discussing the results, a few cautionary notes should be made
clear. Even with these criteria, there is no method available to completely
prevent false period detections. The statistical FAP calculation should
be looked upon as a relative measure for comparing different results
and not an absolute measure. It is also very difficult to distinguish
between periods that are aliases of each other and are also close to
one day, which is a fairly common occurrence. In the following section, I
present the most probable periods that are consistent with the criteria
that have been discussed. The data are separated into two main sections, those
with FAPs below 1% which are expected to be very secure, and those with FAPs
between 1% and 20% which are far less certain.
Next: About this document
Up: Period Analysis
Previous: Starspots
Scott J. Wolk
Thu Dec 5 11:30:29 EST 1996