Changes
in the Light Curves of Short-Period W Ursae Majoris Binaries: Program Summary
Russell M.
Genet
Orion
Observatory,
Thomas C.
Smith
Dark Ridge
Observatory,
Dirk Terrell
Southwest
Research Institute,
Laurance Doyle
SETI
Institute,
Presented at
the 94th Spring Meeting of the AAVSO,
Abstract We are observing and analyzing changes in
the light curves of a few W Ursae Majoris binaries. This paper summarizes the objectives of our
program and the rationale behind our choice of stars and observational
strategy. It also describes, briefly,
our approach to the seasonal optimization of our reductions, our two primary
analytic approaches (phase-bin and Wilson-Devinney).
1. Program
Objectives
The
The primary science objective of our
program is to characterize the nature and timescales of changes—even very
subtle changes—in the shapes of the light curves of several magnetically-active
stars. Rather than providing a few
disjointed “snapshots” of such systems, it is our intent to provide “movies” of
their behavior over yearly, monthly, weekly, and even daily timescales. Such observations should provide powerful
feedback to theoretical hydrodynamic models of the behavior and evolution of
magnetically active stars.
The secondary science objective of
our program is to search for transits of hot Jupiters across those binaries we
were observing that have high orbital inclinations. If hot Jupiters are orbiting
Our planned multi-year observations
of the same binaries led us to adopt, as a tertiary science objective, the
search for “cold Jupiters” (Jupiter-mass planets in Jupiter-distance orbits), brown dwarfs, or other third bodies
via the light-travel-time effect on eclipse times-of-minima (Deeg et al. 2000). Since Jupiter shifts our own solar system’s
barycenter by five seconds peak-to-peak over the course of six years, one might
be able to detect a similar shift in an eclipsing binary’s barycenter caused by a third,
possibly planetary, body if the precision of the September – December
(2004) seasonal eclipse timing was 1 second or better (3 sigma). Intermittent mass loss, drifting starspots,
and other transient phenomena may mask subtle third-body effects, although
separation may be possible (Kalimeris et
al, 2002).
Supporting our three science
objectives are two technical objectives.
The first is fine tuning our reduction process for each of our major
sets of observations. While such optimization
would not be worthwhile under ordinary circumstances, our large data sets and
the full automation of our reduction and analysis processes allow us to
parametrically explore and optimize such reduction decisions as ensemble star
inclusion, weighting strategies, etc.
Our second technical objective is to
develop our phase-bin analysis process for detecting and evaluating small
changes in light-curve shapes, including those that could be caused by the
transits of hot Jupiters. Our phase-bin
technique has been developed specifically for the analysis of a sizeable number
of complete orbit-in-one-night light curves.
2. Choice of
Stars
To meet our primary science
objective, we needed to select stars that were highly active magnetically. This suggested stars with a high Rossby
number, i.e., stars with rapid rotation and long convective turnover times
(Noyes et al. 1984). Long convective turnover times require deep
convective envelopes, hence late-type stars.
For single stars, the speed of rotation tends to fall off as one goes
from early to late spectral type.
However, as first noted by Eggen (1961), for
To meet our secondary science objective,
we needed to select at least one of our binaries with high enough inclination
angle to allow a hot Jupiter to transit in a close, yet dynamically stable
orbit (Holman and Wiegert 1999). With
an inclination angle of 83.8 degrees, V523 Cas is, at best, a borderline
candidate. We are in the process of
determining, from our photometric observations, the inclination angle of V1191
Cyg. Although a radial velocity curve for
V1191 Cyg is not available, a fairly accurate determination of its inclination
should be possible via photometry alone as both primary and secondary eclipses
are total (Terrell and Wilson 2005).
In addition to the above science
selection criteria, there were a number of practical criteria. The binaries had to be sufficiently bright,
considering our modest-aperture telescopes, to provide a large number of
photometrically-precise observations. A
brightness between 9th to 12th magnitude is optimal for
our systems. Binaries also needed to
have short enough periods to allow complete light curves to be gathered in a
single night for a reasonable time (at least a couple of months). For a given binary, these few months then
become its “observing season” each year.
Those binaries with the shortest periods and most northerly declinations
have the longest observing seasons. Finally,
3.
Observations and Reduction
Observations were obtained at Dark
Ridge Observatory with a 14-inch Meade LX-200
During our first observing season
with (so far) preliminary, non-ensemble reduction, our overall photometric
precision for over 21,000 observations of V523 Cas was slightly better than 5
millimagnitudes. Our O-C residuals, for
V523 Cas were 4.4 seconds (1 sigma) and the error of the seasonal mean (with 32
times of minima) was 0.8 seconds.
Since we observe the same fields all
night long, night after night, we can afford to take somewhat extraordinary
measures to optimize our photometric reduction.
This includes characterization of the 40 or so brighter stars in the
field with respect to standard magnitude and color, spectral type, and
variability. We plan, in essence, to
establish each field as a set of tertiary standards.
There is no uniform agreement among
variable star observers with respect to the optimal choice and weighting of
ensemble comparison stars, nor is it even clear that there is a best
“one-size-fits-all” approach. Some observers
only use ensemble stars which closely match the variable star in color (or
color and magnitude). Proximity of the
ensemble stars to the variable may be a factor.
Surrounding the variable with ensemble stars may improve precision under
cirrus conditions. A number of observers
include all stars without regard to magnitude, color, or proximity; simply
weighting each star by its (estimated) signal-to-noise ratio (Gilliland and
Brown 1988, Honeycutt 1992, Everett and Howell 2001). In any event, care must be taken because differential extinction due to color variations of the
stars can look like transit events and are of similar durations (a few
hours). An entirely different approach,
image subtraction, may be worth considering, although its primary application,
to date, has been in crowded fields (Alard 2000).
While
observers generally agree that variable stars should not be included in
comparison ensembles, at some magnitude level and timescale many stars are
variable (Henry 1999). If one is
employing nightly zeropoint adjustments (renormalization), the use of stars
varying on the timescale of months might be appropriate, particularly if they
are the only bright comparison stars in the field.
To explore and choose between these
alternatives, we are taking an empirical approach, varying the possibilities in
a methodical, parametric manner; noting the effects on “overall performance”
for the entire season. For “classical”
variable / check / comparison (VCK) star photometry, the performance measure
is, typically, the one-sigma standard deviation of the C-K values over the
observational period. Of course there
is no guarantee that the actual V-C performance might not be significantly
different than that of C-K. In ensemble
photometry, where a number of stars form the “C,” and “K” can be variously
defined, one needs to consider different measures of performance. We are employing three.
First, we are choosing, from the
field, a non-variable “stand-in” for the variable, a star as closely matched in
magnitude, color, and position to the real variable as possible. Given the relatively small fields we observe,
this will have to be a significant compromise.
Second, the variable star can, under
appropriate circumstances, be used as its own stand-in. The trick is to make it non variable. In the case of our
Finally, it is known that the
temporal precision with which times-of-minima can be determined are
proportional to photometric precision (Doyle and Deeg 2004). In turn, the standard deviations of the
observed minus calculated (O-C) residuals for best-fit seasonal ephemeredes are
proportional to the times-of-minima precision.
Thus it follows that the standard deviations of the seasonal best-fit
O-C residuals are proportional to photometric precision. Although this measure is computationally
intensive, the full automation of our reduction and analysis processes allows
us to utilize this performance measure in our parametric explorations.
4. Phase-Bin
Analysis
Phase-bin analysis is a
straightforward procedure that is especially applicable to the analysis of a
season of nights where each night has at least one complete orbital cycle. The first step in the analysis is determining
a best-fit seasonal ephemeris. One then
converts, for each night, the observations (HJD) into phase and, after deciding
how many bins per phase cycle to use, assigns each observation a bin number
based on its phase.
The strength of phase-bin analysis
lays in its merger capabilities. All the
observations on one night can be merged into a single phase curve. Similarly, multiple nights can be merged
together. One can even take all the
nights in an entire observing season
and merge them into a single “seasonal master.”
In the case of our V523 Cas seasonal master, the average number of observations
in each of our 100 bins is over 200. In
the final step of any phase-bin analysis, multiple observations within each bin
are simply averaged.
Phase bins averages can be
subtracted from one another to yield phase-bin differences. For instance, one can merge all the nights in
a season together to form a seasonal master, as suggested above, and then, one
night at a time, subtract each night in a season from the seasonal master. The resulting phase-bin difference plots, one
for each night throughout the season, can then be strung together, serially, to
form a “movie” of how each individual night varies from the seasonal
master. This process, in effect, removes
the major underlying variation (the eclipse curve and any non-varying
starspots, etc), leaving just the small differences (changes) within the season
which, with the amplitude scale now greatly magnified, can be readily
seen. In the case of V523 Cas, our
“movie” of four months of observations showed minor variations in the light
curve for the first couple of months, followed by a dramatic change in the
fourth month.
A number of other “experimental
designs” are possible. As both
observatories, on many occasions,
observed the same binary on the same night, we are binning the observations
from each observatory together on those nights and taking the difference to
closely examine any between-observatory differences (i.e. observational
artifacts).
We are using a modified phase-bin
approach to search for transits. Several
nights on either side of the night in question are being binned together to
form a comparison template. The “middle
night”, i.e. the “night in question” is phased and then binned (although not in
the normal way as its temporal sequence must be preserved). A phase-bin difference is then taken over the
“phase” range of the middle night. With
the main eclipse (and starspot) flanking-nights variation removed, any changes
of the middle night with respect to the flanking nights will now stand out,
exposing any hot Jupiter transits. A
much more sophisticated matching filter analysis may eventually be applied
(Deeg et al, 1998). For a discussion of the potential confusion
of planetary transits and starspots, see Queloz et al (2001).
Phase-bin analysis is a method for
removing the average (and hence major) features of light curves so that
non-average, much smaller differences become apparent. Its strength is that it makes no assumptions
about the nature of the average, “comparison” light-curve shape and hence can
be very sensitive to any real differences.
This is also its weakness, however, as it is difficult to interpret the
astrophysical meaning of any differences (with the exception of a transit
event). Used in conjunction with an
astrophysical model, however, the two should provide complimentary insights.
5.
Wilson-Devinney Analysis
The Wilson-Devinney (WD) program
(Wilson and Devinney 1971, Wilson, 1979) is the most widely used program for
analyzing eclipsing binary star data. We
will use WD to analyze our photometric data on both V523 Cas and V1191
Cyg. Radial velocities have been
measured for V523 Cas (Rucinski, et al, 2003) and we will analyze them
simultaneously with our photometry. To
our knowledge, no radial velocities have been measured for V1191 Cyg, but it
has complete eclipses which enables a determination of its inclination (Terrell
and Wilson, 2005). The WD analysis of the binaries will determine basic system
parameters such as the orbital inclination, relative radii of the stars
(absolute radii for systems with radial velocities) and the temperature and
luminosity ratios of the stars.
The WD program models surface
inhomogeneities with circular spots. The spot
parameters that can be specified are the latitude and longitude, spot radius,
and spot temperature factor (the ratio of the spot temperature to the
temperature of the photosphere if the spot were not there). We will use
this capability to model starspots on the binary components and follow them
over time to see if they move in a coherent fashion.
The independent variable can be the
traditional phase quantity, computed with given ephemeris quantities, or the
data can be analyzed with time as the independent variable. In the latter case, the ephemeris parameters
are among the adjusted parameters. Thus,
rather than using times of minimum to estimate the ephemeris parameters, they
are found from the analysis of entire light curves.
We are also working on modifications
to WD that will enable it to model the transits of circumbinary planets. This capability will enable us to explore the
light curve morphology of planetary transits in binary systems and search for
potential transits in our data. It will also enable us to explore morphological differences
between planetary transits and spot phenomena that may mimic transits.
6.
Acknowledgements
Genet
acknowledges a NASA grant via the AAVSO for travel to
References
Alrad, C.
2000, ASP Conf. Series, 203, 50.
Deeg, H.-J.,
Doyle, L.R., Kozhevnikov, V.P., Blue, J.E., Rottler, L., and Schneider, J.
2000, Astron. Astrophys., 358, L5.
Deeg, H.-J.,
Doyle, L.R., Kozhevnikov, V.P., Martin, E., Palaiologou, E., Schneider, J., Afonso,
C., Dunham, E.T., Jenkins, J.M. Ninkov, Z., Stone, R., and Zakharova, P.E.
1998, Astron. Astrophys., 338, 479.
Doyle, L.R.,
Deeg, H.-J., Kozhevnikov, V.P., Blue, J.E., Oetiker, B., Rottler, L., Martin,
E., Ninkov, Z., Stone, R., Jenkins, J.M., Schneider, J., Dunham, E.T., Doyle,
M.F., and Palaiologou, E. 2000, Astron.
J., 535, 338.
Doyle, L.R.,
and Deeg, H.-J. 2004, ASP Conf. Series,
213, 80.
Eggen, O.J.
1961, Royal Obs. Bul., 31, 101.
Gilliland,
R.L, and Brown, T.M. 1988, Publ. Astron.
Soc. Pacific, 100, 754.
Henry, G.W.
1999, Publ. Astron. Soc. Pacific, 111, 845.
Kalimeris, A.,
Rovithis-Levaniou, H., and Rovithis, P. 2002, Astron. Astrophys., 387, 969.
Holman, M.J.,
and Wiegert, P.A. 1999, Astron. J., 117, 621.
Honeycutt,
R.K. 1992, Publ. Astron. Soc. Pacific,
104, 435.
Noyes, R.W.,
Hartmann, L.W., Baliunas, S.L.,
Pribulla, T.,
Kreiner, J.J., and Tremko, J. 2003, Contrib.
Astron. Obs. Skalnate Pleso, 33, 38.
Queloz, D.,
Henry, G.W., Sivan, J.P., Baliunas, S.L., Beuzit, J.L., Donahue, R.A., Mayor,
M., Naef, D., Perrier, C., and Udry, S. 2001, Astron. Astrophys., 379,
279.
Rucinski, S.M.
1992, Astron. J., 103, 960.
Rucinski,
S.M., Capobianco, C.C., Lu, W., DeBond, H., Thomson, J.R., Mochnacki, S.W.,
Blake, R.M., Ogloza, W., Stachowski. G., and Rogoziecki, P. 2003, Astron. J., 125, 3258.
Terrell, D.,
and Wilson, R.E. 2005, Astrophy. Spc.
Sci., 296, 221.
Wilson, R.E.
1979, Astrophys. J., 234, 1054.