Despite growing number of large telescopes and fully robotic surveys automatically scanning the heavens, there are still rare objects that remain to be discovered. So there is still room for small telescopes, regardless if operated by amateur or professional astronomers, to discover something new and interesting. CzeV343 is apparently a hierarchical quadruple star system, consisting of two eclipsing binary stars. Only a handful of such systems are known to astronomers and only three of them exhibit eclipses of both double stars — BV Dra and BW Dra, V994 Her and KIC 4247791, the later one discovered using the Kepler planet-hunting space telescope. CzeV343 is apparently a fourth example, unique is several respects. And it was discovered with G4 camera on an affordable 25 cm commercial telescope.
CzeV343 is double eclipsing binary star, probably forming hierarchical quadruple star system. Why we emphasize that both binary systems are eclipsing? Observing of light drops, appearing when the stars eclipse each other, can reveal number of properties about them, especially when combined with other techniques like radial velocity spectroscopy etc. Measuring of orbital time from the observed light curve is obvious and easy, but the actual shape of light curve during eclipses hints other properties like relative sizes, orbital plane inclination etc. Differences in the amount of light drop in different colors indicates mutual relation of star temperatures. Simply put, when a binary star does not exhibit eclipses to observer on Earth, it is difficult or close to impossible even to determine it is a binary star. When both stars pass in front of and behind each other, determining of number of properties of both stars can be done by (relatively) cheap equipment on your backyard. And both binary components of CzeV343 show prominent eclipses, which are easy to observe, because of significant light drop (between 0.25 and 0.1 mag, compared to ~15 mmag drop of KIC 4247791 system B) and very short periods (approx. 1.2 and 0.8 days).
Let us note there is currently no proof that both binary stars of CzeV343 are physically connected (gravitationally bound) and that CzeV343 is a quadruple star. There is still a possibility two independent and completely unrelated binary stars simply project to the same spot on the sky (such situation is called blend). However, such possibility was very carefully examined and despite it cannot be currently ruled out, it is considered very improbable.
CzeV343 is unique in one more way—orbital periods of both binary stars are very close to 3:2 ratio. The relative difference in orbital periods is only around 8.5 × 10-4, which makes CzeV343 a quadruple star with both components orbital periods closest to resonance from all other similar systems. V994 Her component periods 2.08 and 1.42 days are also close to 3:2 ratio, but with relative difference ~10-2 and orbital periods of the KIC 4247791 binaries 4.10 and 4.05 days are close to 1:1 resonance, but again with similar relative difference ~10-2.
Majority of stars in the Galaxy (and I bet in other galaxies, too :-) are not single ones (possibly with a family of planets, e.g. like our Sun), but are gravitationally bound to multiple star systems. While binary stars are simple in principle (both stars orbit their barycenter), systems with three or more stars are stable over long periods of time only if they are hierarchically organized. For instance triple star with similar distances (and thus similar orbital times) among all three stars is inherently unstable, only stable configuration is a double star orbited by a third star pretty far from the binary.
In 1962 Yoshihide Kozai showed in his study that a third star, orbiting a close binary with orbital plane in certain inclinations relative to orbiting plane of central binary, causes periodic increasing of central binary star orbit eccentricity. Such effect is called Kozai cycles now. Increasing eccentricity of binary star orbit cause rapid increase of tidal friction within stars when they pass through periastron. Tidal friction in binary stars orbiting relatively far away (say on close to circular orbit with orbital period tens of days and more) are negligible, they almost do not influence the orbit. But when orbital eccentricity is increased by Kozai cycle, both stars approach closer to each other and tidal friction starts to dissipate significant portion of their orbital (kinetic) energy. Of course tidal friction occurs only when star's orbital period and period of rotation are not equal. When both periods become locked, tidal friction disappears, orbital energy is no longer dissipated by this mechanism and both stars can stay on close orbit for a long time.
Kozai cycles together with increased tidal friction (often referred as KCTF mechanism) is currently considered to be the mechanism explaining existence of very close binaries with orbital periods only days or fractions of a day (every variable star observer already met numerous binary stars with periods shorter than one day, even stars with periods shorter than 10 hours are not that exceptional). Binary stars with such short period could not form that close to each other, because mutual distance of such stars is lower than the sum of radii of respective stars in their early development stages. It is clear such close binary stars had to be born much further away and KCTF is responsible for their current proximity. Of course, a third star is necessary and numerous studies prove a third companion is much more often present around binary star with short period compared to stars with longer orbital periods.
So KCTF is very important mechanism in stellar evolution and numerous studies are focused to its research. Here comes the importance of CzeV343—it is very likely the orbital periods of both components were influenced by mutual KCTF, but no theoretical studies about KCTF in quadruple stars were published yet. And stars like CzeV343, showing eclipses of both components, allowing to study their properties, with orbital periods almost locked, provide material for extending our knowledge about multiple star systems evolution.
CzeV343 was discovered while monitoring of a patch of sky in constellation Auriga around variable star MR Aur, performed between January and April 2012. CzeV343 was among 44 variable stars (and variable star suspects) detected in the field of view, among which only three variable stars were previously known (MR Aur, FV Aur and RZ Aur).
The field was imaged with G4-16000 CCD camera on commercial 25 cm Newtonian telescope with TeleVue Paracorr coma corrector. Because the used optics cannot cover the full 4k × 4k pixels (16 MPx) of the G4 camera, resolution was cropped to only 3k × 3k pixels (9 MPx) by camera driver. Still, even after cropping the setup offers 71 × 71 arc-minutes field of view, despite some vignetting and star image distortions in image corners.
Single 180 s exposure of the target field of view in Auriga, resampled to 1/2 linear dimensions (1/4 area), CzeV343 is marked with red dot (left), G4-16000 camera on the 25 cm Newtonian telescope (right)
The variability of CzeV343 was first detected during the observing run on January 30th, 2012. The star exhibited Algol-type (detached eclipsing binary) variability, showing clearly distinguished minima during occultations. However, measured times of observed minima did not fit into primary/secondary minimum period, typical for Algol-type stars. After first four observing nights, the observed system B minima were considered to be system A secondary minima. But it was not possible to phase these minima with the system A primary minimum. The problem was resolved after acquisition of overlapped system A and system B minima on February 12th, which indicated the assumption the CzeV343 is simple Algol-type binary star is probably wrong. Proper system A secondary minimum was observed on March 3rd, 2012 for the first time.
Light curve of CzeV343 phased with ~1.2 days period of system A (left) and with ~0.8 days period of system B (right)
CzeV343 shows two occultation periods, the system A period was determined to 1.209373 days. The primary minimum is 0.24 mag deep and the secondary one is 0.13 mag deep. The system B period is 0.806931 days, with both primary and secondary minima only around 0.11 mag deep. Both periods are apparently very close to 3:2 ratio, but subsequent observations showed a small difference. This difference can be clearly visible on the light cure phased with system A period as a time drift of system B minima.
Animation showing CzeV343 light curve as a sum of light curves of two eclipsing binaries (click the image to run animation)
As already noted, it is currently not proven that CzeV343 is a real quadruple star. Both binary stars could be physically unrelated and we can only see them on the same position. But number of circumstantial evidences hint CzeV343 is a quadruple system—stars have similar masses, similar temperatures as demonstrated by the acquired photometry in different colors, similar periods very close to 3:2 resonance, ... Still number of attempts to distinguish both stars by various techniques were performed.
The centroid of star image (mean of position of individual pixels comprising star image weighted by particular pixel flux—centroid allows to determine star position with precision significantly surpassing angular size of single pixel) was examined during occultations. We measured CzeV343 image centroid coordinates relative to the close neighboring star in the field of view, determined by the SIPS software astrometry tool. However, relatively low resolution images with 1.39''/pixel sampling, acquired with the photometry telescope, had to be used, because we need to try to detect centroid movement during star occultations. The assumption is weakening of one star contribution to the integrated flux during its occultation would shift image centroid towards the second star. Only images from individual observing runs (single nights), on which both observed star and selected comparison star were placed in the same position relative to the camera field of view, were mutually compared to eliminate influence of telescope (and especially coma-corrector) image distortions.
Images below show our results from January 31st, 2012, when the system A passed through a primary minimum. The top pane on the left image shows CzeV343 light curve during system A occultation, lower two panes show centroid shift during occultation independently in CCD x and y axes in arc-seconds. Right image shows so-called rainfall chart, where centroid shift is displayed on x-axis and star magnitude on y-axis (independent shifts in x and y CCD directions are displayed on two panes). Any shift of image centroid would result into beveled rainfall.
CzeV343 centroid did now show any detectable shifts during occultation, as showed on time-dependent chart (left) and rainfall chart (right)
Same analysis was performed for two more nights—system B minimum (system B primary and secondary minima have almost exactly the same depth) on February 10th, 2012 and partially overlapped system B minimum and system A secondary minimum on February 26th, 2012. None of them showed any significant movement of CzeV343 centroid during occultation. Because the calculated error margins of the determined centroid was unrealistically low, we assume centroid shift method did not reveal any changes up to 0.5 arc-second.
Our telescope/camera used 1.39"/pixel sampling with typical star FWHM around 4". CzeV343 showed no shape distortions on individual frames, but the resolution of photometric telescope is too low. Fortunately CzceV343 can be found in Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) archive. SDSS sampling is only 0.396"/pixel and typical seeing is below 1". Even on SDSS images with significantly better resolution CzeV343 shows no visible image distortions hinting the star image consists of two blended stars.
CzeV343 image from the 0.25 m photometric telescope (left) and z filter image from 2.5 m SDSS telescope (right)
Still the CzeV343 SDSS image was carefully examined. The star shape was enlarged and interpolated to show isophotes and then compared with the similarly processed image of a nearby star from the same SDSS frame. Both shapes are very similar.
Comparison of CzeV343 shape and nearby star shape on SDSS image
The result is CzeV343 cannot be resolved using currently available data. Other observations like hi-res imaging using large telescope with adaptive optics would be beneficial.
Analysis of light curve containing overlapped occultations is quite difficult. Computer modeling of the observed multiple star helps to find best fit for system parameters (orbital periods, orbital plane inclinations, eccentricity, star diameter relations etc.) and to verify the hypothesis about multiple star structure. The best fit than can be used to separate contributions of each binary star to the observed light curve. So the good model of the system allows creating of phased light curves of both binary components as well as to express residuals, revealing data reliability and photometry precision.
We used the cmpfit routine to fit multiple model parameters simultaneously by minimizing χ2 of the model generated with JKTEBOP program written by John Southworth. Resulting χ2 of our model is 1040—very close to the theoretical minimum, which equals to the model's number of degrees of freedom (800 in our case). Such result not only shows the credibility of the model itself, but also demonstrates the quality of the acquired photometry data, obviously not affected by important systematic errors, instrumental errors etc.
Separated light curves of CzeV343 system A (top pane) and system B (bottom pane) together with residuals
The red lines on the above image show the best-fit light curves of both CzeV343 components. Resulting orbital eccentricity of the system A is 0.18, as shown by the solid red line. Model with system A eccentricity set to 0 (dashed red line) showed significantly worse fit. System B orbit eccentricity was set to 0, the observed light curve does not exhibit any significant phase shift of system B secondary minima.
|Parameter||System A||System B|
|e cos ω||0.0147||= 0|
|e sin ω||0.178||= 0|
|r1 + r2||0.4533||0.581|
The presented model very well describes CzeV343 as two eclipsing binaries. The code is made freely available not only to allow analysis of further CzeV343 observations, but also for possible use of the code for modeling of other similar multiple star systems.
Article about CzeV343 discovery and analysis was accepted for publication in the Astronomy & Astrophysics Vol. 544 (August 2012).
J2000 coordinates: R.A. = 5h 48m 24,008s, Dec. = +30º 57' 03,64”
Astronomy & Astrophysics article reference Cagas, P. & Pejcha, O. 2012, A&A, 544, L3
arXiv.org reference http://arxiv.org/abs/1206.4058
O. Pejcha modeling code http://www.astronomy.ohio-state.edu/~pejcha/czev343/
Czech Astronomical Society Variable Star and Exoplanet Section
Sloan Digital Sky Survey SDSS DR7
All images on this page courtesy of O. Pejcha, V. Pribik and P. Cagas.