H How to measure the minima of eclipsing binaries By Laurent Corp Eclipsing binaries are little studied by amateur astronomers: to order to observe them the keen amateur needs to become a photometrist. This chapter sets out to describe the various types of eclipsing binaries, how to predict the times of minima and the means of measurement ? telescope, CCD camera photometric filters and computers ? and finally the way in which the reductions are made. The last part explains light curves obtained in several different observing projects and a criticism of which is also given. 1, What is an eclipsing binary? Variable stars in general can be placed into three categories: the pulsating stars, the cataclysmic systems, and the eclipsing binaries. In the latter case the variation in the light is due to binarity, with mutual eclipses by each component reducing the light of the system as a whole. Eclipsing binaries in turn can be divided into three principle categories: the Algols (to EA), beta Lyrae stars (type EB) and W Ursae Majoris stars (type EW). In addition, there are sub-types which depend on the specification of the Roche Lobe. ? define Roche Lobe. Algol stars (EA) The primary minimum is well marked but the secondary minimum is much less obvious or almost undetectable. There are several thousand stars in this class. Fig 1 ? Light curve of an Algol star Beta Lyrae stars (EB) The primary eclipse is also well marked but in this case the secondary eclipse is almost as important as the primary. The light curve is xx due to the gravitational attraction on each star. This class contains only a few hundred examples. The stars are no longer spherical but deform into ellipsoids due to the intense mutual gravitational attraction. As the stars rotate the shape that they present to the observer varies, and the light from the system is constantly changing. W UMa (EW) Primary minimum is almost identical to secondary minimum (see Figure 4)?? Here also there is an exchange of material between the stars line beta Lyrae. The period of the EW stars is often less than a day and can vary as a consequence of the mass exchange. Fig 3. Light curve of W UMa The orbital period of an eclipsing binary can be calculated by studying the light curve, and the relative ? of each component (?) can be observed by measuring the speed at which the luminosity of the more elongated star fades when the other star passes in front of it. If, in addition, the binary is also a spectroscopic system then the orbital elements can be found and the mass can be deduced relatively easily which means that the density of each of the stars should also be calculable. There is a website at http://cosmion.net/software.ebs which allows you to run a software simulation programme called Eclipsing Binary Simulator. The parameters of the binary system, such as mass, luminosity and distance can all be adjusted to reproduce various types of binary stars. \section*{How is the minimum observed?} From the prediction of the time of minimum to the interpretation of the data, great care must be exercised. It is imperative to have data of the best quality available. A} How to predict the minima Predictions about times of minima are available from Internet sites?. It is important to note that the times furnished by the different sites will be in Universal Time or local time. Certain times are calculated in geocentric time or heliocentric time. Now consider the predictions as an indication of the time of minimum. I strongly suggest using Universal Time from now if you haven?t already done so. The following site http://www.motl.cz/dmotl/predpovedi is managed by David Motl and you can use the predictions on the site the same if you do not have an available Internet connection (see Figure 4). It lists various parameters ? magnitudes, positions etc and different catalogues with lists of star to study. It is often very useful to make your own catalogues. Another telechargeable site is that of Bob Nelson (http:members.shaw.ca/bob.nelson/software1.htm) The site is written by Bob Nelson another enthusiastic observer of these stars. You should note that the time s given by certain programs are deliberately approximate in order not to influence the observer. Internet sites giving predictions of minima http://www/as/up/krakow.pl/epehem - run by J. M. Kreiner of Mount Suhora Astronomical Observatory ? an outstation of Cracow Pedagogical University. This site offers times of primary and secondary minima for stars whose name and constellation are known. http://www.rollinghillsobs.org/perl/calcEBephem.pl Eclipsing binary eclipse generator. This site managed by Shaun Dvorak takes into account a number of catalogues and allows input of the observer?s latitude and longitude, the date and time of observation, maximum and minimum declinations and magnitudes. http://britastro.org/vss This site from the Variable Star Section of the British Astronomical Association also contains lists of stars to observer. The xxx is maintained by Des Loughney with whom I have collaborated on certain precise xxx and who observes with a DSLR in Scotland. b) How to choose a star to measure Choosing a star depends first of all on the amount of time available to the observer. So, if you have an observatory in your garden, setting up time will not be great as in the case where you have a portable telescope where it might take you a couple of hours to reach your observing site and another good hour to prepare for observing. Choice will also depend on local conditions of light pollution, the experience of observation (to begin with it is better to choose stars that are easier to xxx and relatively bright, what sort of equipment is available (CCD, telescope, mounting) and time available. To get the best results I recommend you to start observing 90 minutes before the minimum is predicted to occur and to continue for 90 minutes afterwards. If you have never measured these types of star before I suggest that you choose those objects where the difference between maximum and minimum is more than 0.5 magnitude so that the light curve is easy to make. You can also help yourself by observing the star for a little while before comparing your results with those of others. When eventually you have made your choice of targets you will need the reference card and photometric table which can be obtained from the AAVSO website http://www.aavso.org/observing/charts/vsp The charts show the name of the star, the card number, the field the orientation the magnitudes at maximum and minimum, the type of star and its spectral type. (see Fig 6). 3, What material to choose? 4. Acquisition and xxx of the images On the ground, it is necessary to ensure that the image capture works properly, in other words the star images are not saturated. It is also necessary to obtain a sufficient signal to noise in the signal (SNR) The SNR that you obtain must be at least 50 and your software should be capable of displaying this value instantly. The following table lists some typical SNR values and the associated error in the observed magnitude SNR error 200 0.005 100 0.011 50 0.022 25 0.043 10 0.110 5 0.220 The software should also be able to care of filter changes automatically so that, for instance, V and R can be done alternatively, without manual intervention. If not, then you need to change your software so this can be done. Also, to be useful the PC needs to have an accurate value of UT. The internet contains several sites where this can be obtained. There is also the facility called Expert Mouse Clock. Xxxxx, you can carry out a series of exposures and I recommend say 300 continuous exposures of 30 seconds followed by 150 exposures at 30 seconds each spaced 30 seconds between each. Depending on the season and the target selected, you should be able to make between one and three sets of observations on a single night. The final quality of the data will depend on quality and quantity. Some professional astronomers would like the whole light curve and not just the minimum and so you should have only one aim ? one star each night and on following nights if necessary. It goes without saying that to get precise data, it is necessary to get good calibration frames offset (or bias frames), darks and flats. Preliminary treatment of the raw data conforms to certain rules and ?cosmetic? treatment of the raw data is not done, especially `touching-up? the images to make them flatter ? the final results will be misleading. Calibrations have an effect on the reduced data and it is vital that you are aware of. The page that you can download from the AAVSO site contains comparison star magnitudes which you can use to reduce your variable. You ?before extracting photometric data from your images. Here the method used is the same ? that of differential photometry ? the flux from the variable is compared to that from a nearby comparison star. Here is some advice: Use the comparison stars whose apparent magnitude and colour is nearest to that of the target star. Pick a B-V or V-R colour index which is most suited to the filters being used. Check, using a test star that the reference star magnitudes are stable with time! The light flux from the star in the chosen camera window can be either circular or elliptical. If your camera does not have square pixels, do not transform rectangular pixels into square pixels. Comparing the variable to the nearest neighbouring stars is similar to the technique used by visual observers. The choice of diameters for the circle is very important. In figure x (above) the circles correspond to three objects: Obj1 is the target being observed. Chk1 is the comparison star which has a similar colour index. Ref1; is the reference star. The circle diameters t use for each of these objects is defined as follows. The smallest circle has a diameter 2 X FWHM, the next smallest is 3 x FWHM and the largest circle is 5 x FWHM b) Sending the data The form on which you send the data will depend on the organisation it is being sent to and I cannot advise on this ??..comparison stars which you can use to reduce the data on your variable. If you want to use the best data then use the photometric table. c) Determination of the time of minimum 5. Some light curves Use reference stars whose magnitudes and colour index are close to that of the variable Choose an almost identical B-V or V-R colour index depending on the filters used. Be certain to check that your reference stars are stable with time by checking with a test star. 6. Conclusion This is an ? which demands a lot of time and practice before you can expect to get data which can be taken seriously. Good luck in your observations and clear skies. Logiciels pour l?interpr‚tation des mesures MINIMA 2.5 (gratuit) de Bob Nelson disponible sur http://members.shaw.ca/bob.nelson/software1.htm vous permettra de d‚terminer le minimum en utilisant 6 m‚thodes. TOMCAT (gratuit)de Bob Nelson disponible sur http://members.shaw.ca/bob.nelson/software1.htm permet quand … lui de trouver la p‚riode par rapport au minima calcul‚ PERIOD SEARCH (gratuit) de Bob Nelson disponible sur http://members.shaw.ca/bob.nelson/software1.htm permet quant … lui de trouver la p‚riode par rapport … une portion de courbe de lumiŠre. PHOEBE(PHysics Of Eclipsing BinariEs), gratuit et disponible sur http://phoebe.fiz.unilj. si/?q=node/21 donne une mod‚lisation 3D du systŠme mesur‚. PERANSO (payant) de Tonny Vanmunster disponible sur http://www.peranso.com/ BINARY MAKER (payant) de Contact Software http://www.binarymaker.com 5 ? Quelques courbes de lumiŠres a) OO Aql RA: 19h 48m 13.0s Dec: 9ø 18? 30?? JD0: 54335.36020 P‚riode: 0.5067885 Minima 75 images ? 14 octobre 2009 ? mise en ‚vidence du d‚calage entre le minimum pr‚vu et le minima observ‚ (trait vertical vert) Diagramme O-C (observ‚-calcul‚) de OO AQL, nous voyons trŠs bien l?augmentation de l? ® OC ¯ d?ann‚es en ann‚es tentant … montrer que le transfert de matiŠre est en train de se modifier entre ses deux ‚toiles. b) AB And RA: 23h 11m 32.1s Dec: 36ø 53? 35?? JD0: 52936.66260 P‚riode : 03318922 Mise en ‚vidence des deux minima (primaire et secondaire) c) Epsilon Aurigae Epsilon Aurigae est une ‚toile trŠs particuliŠre qui peut ˆtre ‚tudi‚e avec de faibles moyens. En voici une description sch‚matique : Pour en savoir plus consultez le site http://www.hposoft.com/Campaign09.html , celui-ci est maintenu par Jeff Hopkins Voici la courbe lumiŠre obtenus par des amateurs dans la bande V : Vous trouverez en utilisant ce lien http://www.hposoft.com/Plots09/VBand.JPG la derniŠre courbe r‚actualis‚e, n?h‚sitez pas … contacter Jeff Hopkins pour participer … la campagne d?observations. RW CMI RA: 7h 19m 60.0s Dec: 2ø 31? 60?? JD0: 50837.61000 P‚riode : 6.0838200 Commentaires: 13.2-14.0 Un d‚calage significatif est visible entre le minimum th‚orique calcul‚ (ligne verticale verte) et le minimum r‚el ? remarquez aussi que le minimum dure plusieurs minutes. Mesures obtenues durant une campagne d?observation en f‚vrier 2009 au t‚lescope de 60 cm de l?Observatoire du Pic du Midi http://astrosurf.com/t60 GU BOO RA: 15h 21m 55.0s Dec: 33ø 56? 6?? JD0: 52723.98100 Periode : 0.4887300 Comments: 13.7-14.4, M-type 0.6 Ms EB Aucun d‚calage n?est visible par rapport aux pr‚visions th‚oriques, remarquez aussi la rapidit‚ du minimum Mesures obtenues durant une campagne d?observation en f‚vrier 2009 au t‚lescope de 60 cm de l?Observatoire du Pic du Midi http://astrosurf.com/t60 NOM DE L?ETOILE DATE NOMBRE D?OBS. HEURES PREDITES HEURES MESUREES ECARTS (minutes) COMMENTAIRES RW CMI 26 f‚vrier 122 22:19 22:33 14 A remesurer GU BOO 26 f‚vrier 120 01:32 01:32 6 ? Conclusion Je viens de vous r‚sum‚ en quelques lignes ce que vous pouvez faire pour aider la communaut‚ astronomique … mieux comprendre ce type d?‚toiles. C?est un domaine passionnant qui demande beaucoup de temps et de mises au points successives afin d?avoir des r‚sultats probants. Bons courages dans vos observations et bons ciels Laurent CORP ? 25 octobre 2010 References Expert mouse clock : http://www.gude.info/index.php?lng=1§ion=products&product=emcusb&PHPSESSID=1301b af6557da4dcf66c2dc8e26d2b95 AAVSO American Association of Variable Star Observers (database of light curves, advice, discussion groups, etc.) http://www.aavso.org (this is the best site in my opinion) CCD Observing Manual http://www.aavso.org/ccd-observing-manual Variable Stars South: http://www.varstars.org/ Check the newsletters of May, August, November 2009, February and May 2010 A Guide to Photometry by W. Romanishin (Oklahoma University.): http://observatory.ou.edu/book2513.html Starizona's Guide to CCD Imaging http://starizona.com/acb/ccd/ccd.aspx CCD : Astuces of observations by Bruce Gary: http://reductionism.net.seanic.net/ObservingTips/ObsgTips.html Astronomical institute, Academy of Sciences of the Czech Republic, Ondrejov http://nyx.asu.cas.cz/dbvar/descr.phtml Howell, Steve B., 2006, Handbook of CCD Astronomy, 2nd Edition (Cambridge University.Press) Berry, Richard and Burnell, James, 2005, The Handbook of Astronomical Image Processing (Richmond, VA: Willman-Bell) Henden, Arne and Kaitchuck, Ronald, 1990, Astronomical Photometry (Richmond, VA: Willman-Bell) Brian D. Warner Lightcurve Photometry and Analysis Livre bien fait, tout pour savoir acqu‚rir,traiter ses images et les analyser. W. Romanishin Universitiy of Oklahoma, An Introduction to Astronomical Photometry Using CCDs Book of 175 pages reprenant un cours universitaire an acceptable level without too much mathematics and easy to read. http://observatory.ou.edu/wrccd22oct06.pdf http://www.astrosurf.com/luxorion/Documents/evolstar-bmauclaire.pdf en Fran‡ais ? 43 pages tout sur la vie des ‚toiles Nelson, R.H. website: http://members.shaw.ca/bob.nelson OEJV: http://var.astro.cz/oejv/ SAS : http://www.socastrosi.org -Rapport des conf‚rences … t‚l‚charger. Databases: ADS: http://adsabs.harvard.edu/article_service.html?nosetcookie=1 BBSAG: http://www.astroinfo.org/calsky/Deep-Sky/index.html/8/3 BAV: http://www.bav-astro.de/LkDB/index.php?lang=en CALEB: http://ebola.eastern.edu/ Crakow Atlas of EBs: http://www.as.ap.krakow.pl/o-c/cont.html EB Minima dB: http://www.oa.uj.edu.pl/ktt/krttk_dn.html GCVS: http://www.sai.msu.su/groups/cluster/gcvs/cgi-bin/search.htm IBVS: http://www.konkoly.hu/IBVS/issues.html SIMBAD (Harvard): http://simbad.harvard.edu/simbad/sim-fid SIMBAD (Strasbourg): http://simbad.u-strasbg.fr/simbad/sim-fid