One night of photometric observations of a short period eclipsing binary CC Com was carried out with ST8 CCD camera mounted on 0.25 m Great Ohio Telescope. Overall 60 frames in V band and 5 frames in B band were taken during 6 hours, covering one period of the binary system. Reference stars in the fields are used to generate light-curve of a difference in magnitudes as a function of time. A period of 5.1±1.6 hr is found. Calculated color index of (B-V)=0.6 differs from known 1.2 due to the lack of standard stars in the field. Color-period-luminosity relation from Rucinski & Duerbeck 1997 paper is used to estimate distance to CC Com as 83±52 pc and compared to the known value 83±4 pc giving reasonable agreement.
The previous heuristic arguments are the basis of papers written by Rucinski
1967 and revised later by Rucinski & Duerbeck 1997. "(It) ... is a purely geometrical
relation, linking brightness with emitting area and surface brightness," he
says in that article. Using the number of contact binaries with known parameters
the author of the idea derives absolute-magnitude MV
calibration of the form
| Figure 1. The period-color-luminosity relation for contact binaries is shown as an inclined plane. The data of the systems used for the calibration are shown as dots. The rms deviation of the observed values of MV from the plane is 0.17 magnitude. The data are also projected into the horizontal period-color plane, where they exhibit the well known period-colour relation (discovered by Eggen 1961, 1967). Picture is taken from Rucinski & Duerbeck 1997. |
The significance of the above approach is in providing new means of estimating
distances to stellar systems, especially where no other information
(besides period, color and magnitude) is available. The way to do it
is straightforward: once absolute-magnitude is calculated from measured
color and period (which for eclipsing systems can be measured with high
precision), it is used to estimate the distance to the object by a distance
modulus formula
A target chosen for this project is the eclipsing binary CC Com. It has a short period of 5 h 18 min (appropriate for one night observation) and quite large amplitude of variation of visual magnitude (of the order of a unit, which is favorable for small-aperture telescopes in order to resolve variability) around in average value V=11.7 (parameters and light-curves were obtained by Rucinski 1976 and Hong-Nan Zhou 1987). Available for observations in April and relatively bright CC Com is a suitable object for photometric studying on the 0.25 m Great Ohio Telescope (GOT). But the main advantage is in relative photometry, since absolute magnitude value and particular details of the light-curve is not important for period determination.
Rucinski & Whelan 1977 in their spectroscopic study of CC Com found the distance to the object to be 83±4 pc. This distance is comparable to the distance to the cluster Comae Berenices (Melotte 111) which is 89.9±2.1 pc (Casewell 2005), but membership is probably ruled out by proper motion study of Klemola 1977. The main purpose of this work is to estimate distance to CC Com by period-color approach (as discussed above) and compare with known value listed.
Observational procedure was the following: just right after sunset 3 flat-fields
were taken in B filter and 5 flat-fields in V filter, then during set up of
pointing model 9 zero-frames were taken followed by making 3 dark-frames of
70 s, 3 dark-frames of 120 s and 1 dark-frame of 230 s. Next, using finding
chart shown on Figure 2, field was set as shown by solid-line rectangular getting
bright star '4' on guider chip (solid-line square). Started at 2:27:52 UT
(air-mass at that moment was 1.060) 10 frames in V band were exposed for 70 s
each. Later, between 3:04:53 UT and 3:33:47 UT since the target reached the
highest altitudes (for the sake of taking advantage of low air-mass values
of the order of 1.04) 5 frames in B band were taken with 230 s exposure time.
And after, 6 more 70 s frames are taken again in V band. The flip of the
telescope was performed around 3:55 UT changing the orientation and position
of field as shown on Figure 2 by dashed-line, now bright star '1' used for
guiding. Also during the flip procedure 2 dark-frames of 230 s were taken.
Since the camera was in new position after the flip there were dimmer stars in
the field (Figure 2, 'a' and '3' are out of the field) and therefore next
41 frames had longer exposure time of 120 s taken in the same V band. Some
clouds noted on the west in the evening and higher air-mass values (> 2.1)
made stars fainter and the last 3 exposures in V band had 230 s exposure time.
For these reasons around 8:10 UT the object was lost and could be no longer
observed. But using the dark time left 4 dark-frames of 230 s, 3 dark-frames
of 120 s, 6 dark-frames of 70 s and 5 zero-frames were taken. Finally,
4 flat-fields in V and 3 flat-fields in B were made in the morning.
| Figure 2. This is 1x1 degree finding chart with labeled stars (see Table 1) and the target (CC Com) shown by an arrow. Rectangular area is field of view of CCD camera and square region is a guider chip. Solid line refers to the camera position before the flip, and dashed line refers to the camera position after the flip. Picture is generated by The STScI Digitized Sky Survey in quick-V filter. |
| Table 1. Table of properties of the stars which are labeled on the finding chart, Figure 2. |
Conditions during the observational night were quite good as sky was clear and seeing had about 3 arcsec value. Only some clouds were seen on the west and they covered the whole sky in the morning. The Moon disappeared (moon phase was equal to 2) below horizon long before observation of the target. Weak wind was present but didn't affect the data. It was also dry enough during whole night so there was no problem of dew on the correcting lens. Consequently one period of the eclipsing binary was covered with overall 65 frames of fair data.
Task phot were used to find instrumental magnitudes of the stars and to estimate their errors. Each frame was examined by task imexam to find FWHM of PSF of star images (had values from 7 to 12 pixels) and standard deviation of the sky were estimated by imstat applied for rectangular patch of empty sky in the field (varied from 10 to 25 counts per pixel). These two parameters are needed for photometry in task phot. Additionally, size of the sky annulus and aperture size for flux were varied to get converging magnitude, because of avoiding cosmic ray pixels and not crossing an edge of the field (typical values used are 30 pixels for aperture, 30 for inner annulus radius and 3 for width of the sky annulus). Each frame must be evaluated individually with unique parameters for the visually identified star in order to get a trustable data point.
| Figure 3.Calculation of the shift of magnitude difference after the flip with respect to the one before the flip. Data points are chosen around both maxima, and then fitted with linear trend. The shift is calculated as difference between free coefficients yielding value of 1.46±0.03. |
Data obtained in B band still can be used to fill in the gap in
light-curve, which is constructed in V filter. The idea is the
following: data for elapsed time between 0 to 1.4 hr are interpolated
by polynomials of 4th for V and 2nd for B order as it is shown on Figure 4.
Average difference between the functions gives difference of instrumental
color index (b-v)=-0.4±0.1. And it is used to add points to
the V band light-curve.
| Figure 4. Difference of instrumental color index (b-v)=-0.4±0.1 is found from average difference between fitted polynomials in the time gap between 0.5 and 1 hr. |
After all adjustments the resulting light-curve is shown on Figure 5. It has
a shape characteristic for eclipsing binary systems, schematic view of which is
shown on Figure 6. Error bars get bigger as higher values of air-mass were reached
and clouds covered the field of view. At the end statistics got very poor
and the object was finally lost. This part of the light-curve has large error bars
and data points are significantly scattered.
| Figure 5. Light curve as difference of magnitudes between target and comparison star. The flip performed at the first minimum. Before the flip comparison star is 'a', and after the flip it is 'gamma'. Violet dots are the b band values but adjusted to v by shift equal to color index b-v=-0.4±0.1. |
Nightfall is available for free software which models contact
eclipsing binary stars from known light-curve. Considering poor quality
(no details resolved, large error bars, insufficient amount of data for
good statistics ) of the obtained light-curve in this project,
the parameters from Ricinski & Whelan 1977 are used to construct
CC Com geometry shown on Figure 6.
| Figure 6. Geometry of the eclipsing system CC Com modeled by software Nightfall. |
To find the period of the eclipsing system from light-curve in the model
independent fashion the two eclipses are fitted with parabolas
(the reasonable curve for local minimum) and distance between their vertices are
said to be half of the period. It is shown on Figure 7.
The period found this way is equal to 5.1±1.6 hr. Briefly explaining, the fitting of the form of
A x2 + B x + C for the first eclipse gives the coefficients
A=1.28±0.16 , B=-4.45±0.58; for the second eclipse
it gives the coefficients A=1.94±0.23 , B=-16.6±2.0.
Whence the positions of the vertices of the parabolas -B/(2 A)
are 1.74±0.32 hr and 4.28±0.74 hr. Therefore after propagation of the errors
the uncertainty in the period is 1.6 hr.
| Figure 4. Period determination by minima positioning of both eclipses with fitted parabolas, resulting in 5.1±1.6 hr |
The color determination turned out to be the most difficult part of the project.
In order to find it the transformation from instrumental magnitudes to
standard ones must be known. It was done with one standard star 'a'
available in the filed and transformation equation of the form,
Left hand side of the expression is the difference for instrumental color index (for example, -0.4, which was found for the target comparing to the star 'a' ), the right hand side is composed of the difference for standard color index multiplied by transformation coefficient k. Therefore in order to find the standard color for the target one more star with known color has to be known, since it is the only way to calculate unknown value of k. The values of c2 and c5 obtained by task fitparams are meaningless since they strongly depend on initial seed values imposed (this is simply the case of lack of constraints). Due to the fact just discussed (B-V) color value 0.6 is ignored and 1.27±0.05 (Rucinski 1976) is used for distance estimation.
Absolute magnitude MV=7.1±1.3 of CC Com is calculated from
period 5.1±1.6 hr and color index (B-V)0=1.27±0.05 (see
calibration equation in the introduction). Extinction along this line of sight is as small as
0.013 (Casewell 2006) and was ignored. The errors are propagated using the formula
.
Finally, the distance modulus formula yields a value of 83±52 pc for
distance d to the eclipsing contact binary CC Com based on period and color
measurements. The distance uncertainty is calculated by the following expression
for propagation of errors
.
Considering large errors of the measurements and many adjustments made for the light-curve the answer 83±52 pc for distance in a good agreement with 83±4 pc given by Rucinski & Whelan 1977. It supports the period-color-luminosity relation for contact binary systems. Furthermore CC Com can be added to the existing calibration list of contact binaries and used in refining the calibration equation for absolute magnitude. Noticeably enormous uncertainty in the distance is due to the poor statistics and quality of the light-curve, especially in the eclipsing regions. These greatly affect the error in the period especially inferred by minima positioning technique used.
The thousands of contact binary systems were discovered ever since. Mostly it was done in systematic searches of the sky for stellar variability and during the galactic cluster searches. Utilizing ones with known distances from their parallaxes new calibration for luminosity-period-color was calculated and applied to the rest to estimate their distances. In the recent catalog (Gettel et al 2006) 1022 bright contact binary stars were used to calculate their space density. It was found to be uniform up to a distance of 300 pc and has a value of (1.7±0.6) 10-5 bright contact binary systems per cubic parsec. Summarizing, the luminosity-period-color method so far has proved itself to be very powerful and it is waiting when new data on contact binaries with known distances become available to significantly refine the correlation equation.
Improvements to be made if one decides to repeat this project are the following: (1) observe the object in March on photometric night to cover period within smallest values of air-mass (2) lack of standard stars should be treated with additional photometric night observing photometric standard stars for calibration purposes (3) make longer exposures to improve signal to noise ratio that will reduce the error bars (4) switch between the filters while taking the data to avoid large gaps in light-curve.