This is probably the most interesting and weird eclipsing variable I have been able to solve since I started analyzing light curves.
It is PW Gem, a 9.1 Vmag. system consisting of two similar white stars with a long orbital period (196.9158 d.) in an extremely eccentric orbit which causes two eclipses very closely spaced in time and with a very different duration. Firstly, the most luminous star is eclipsed by its companion for almost 11 hs. and the combined brightness drops by 0.40 magnitudes. 3 days and 21 hs. later, the secondary eclipse begins and it is 3 times longer (1 d. 11 h. and 44 m.) with a drop of 0.35 mag. Finally, after these two events are over, the stars move away from each other and we see no changes in the following 191 d. and 3 h.
I never saw a similar eclipsing binary before. I doubt there is another one with such extreme behaviour, maybe I found the EB eccentricity world record. This needs to be checked. Have you ever seen another case like this?
This discovery was possible thanks to the combination of data from several missions and surveys: Hipparcos, NSVS, ASAS-3, KWS, ASAS-SN and Kepler.
I have trouble understanding things here... Why is the eclipse duration so different (0.23% compared to 0.75%) if the two eclipses happen so close in time? Do you know of any EB simulations that you can see for extreme cases like this one?
Is there a chance something is wrong? Data from several surveys seem to indicate that the period is correct. K2 data had problems and the corrected data erased the eclipses, I had to use SAP_FLUX uncorrected data. I think about additional eclipses from a companion but if the two eclipses came from two different periods they wouldn't fit in the same folded light curve...
I was going to say... that is odd: a secondary so far from 0.50 and durations so unequal. Like you, I think, I expect them to be nearly equal. Also, that ratio of 3 days to 191 days is "extremely extreme"...
The most extreme secondary phase in Avvakumova's 2013 list of EBs is at 0.86 (0.14).
Just using your lightcurves, it looks like the really nice data through both eclipses, was from K2, so probably data from just one cycle of the system?
Is the ASAS-SN data (just 3 points) in the narrow eclipse from the same cycle (same event, same day) as the K2 data? In which case it could be two systems in line of sight, and you have lots of data supporting the 197 day cycles of one eclipse, and the other one has limited support as being part of the same system (really, just the one ASAS-3 point). It could be a different systems in the same line of sight, and that second, narrower, eclipse won't occur at the same phase "next time arround".
There are three arguments (at least) against this:
-that narrow eclipse should still occur somewhere in the lightcurve, and we don't see any evidence (not a single point) anywhere else in the ASAS-SN data.
-the ASAS-3 datapoint. Only one datapoint, but it does support the narrow eclipse being at that phase, and part of the same binary system, because it would be a totally different epoch from the K2 and ASAS-SN data
-it would be a remarkable coincidence to have two very long period systems in line of sight...
Another possibility: one system, but N>2, i.e. N=3, or a double binary system (2x2)... but this then raises synchronization questions...
Best... Gary Billings
All bits and pieces of eclipses are from different events. 3 primary eclipses and 5 secondary eclipses.
If they were two different systems with different periods, how can the two eclipses fold well using one and the same period?... I don't think it is possible.
The secondary eclipse is made with points spanning from 1992 to 2019.
The three primary eclipses are from 2009, 2014 and 2015.
It looks like it is the same binary...
Big red star - little blue star? The thing that caught my eye was the slight fading before, slight un-fade after the short eclipse. Meanwhile, the longer eclipse seems to do the opposite. Reminds me of one star reflecting heat from the other the other. Then, I suppose they could precess to account for the 197 days, or go for a wild ride from a third, high-mass, neutron star or BH.
I don't see those features in the light curve. Keep in mind that there is a lot of scatter from the different surveys. So ups and downs are mostly due to that. Only the Kepler light curve (in blue) shows the real light curve shape. And it may show a slight ellipsoidal effect caused by tidal distortion at periastron, it seems there is a slight brightening after Min I. But it is small and the light curve has a gap then. The mean from the other surveys shows that it has an amplitude of only 0.01 or 0.02 mag. if it exists.
Also there is no sign of apsidal motion here, the same period is valid for both eclipses.
I have seen many with fast apsidal motion and if that was the case you shouldn't be able to phase both eclipses with a single period. I have a great example of that as my next object soon :)
About the presence of a red and a blue star here, they should be apparebt in the spectrum. It is a bright system, there is a lot of data and the colours do not suggest anything red here. Spectra in the literature are B9, B7IV, A0 and A2V. There is a F6V that looks inconsistent with the catalogue colours. But no red giant or supergiants.
About CSS_J002509.1+38554, I am glad that you let me know. I was supposed to be subscribed to all posts and I did not receive those ones. Sometimes the notifications end up in my spam folder with no reason.
I see that the periods mentioned in that post are very short and it is an EA with a 2.06 d. period. so I don't see any similarity with PW Gem. Also the period of 10.3 d. mentioned in the same post is actually 5 times the other period. If you look at the light curve it shows 5 minima per cycle...
.. and yes, the two eclipses from Kepler are consecutive events, the only two eclipses recorded. There were some points showing a fading that were considered noise. They were a few points and didn't look consistent. They were also several systematic effects shwoing up as fadings down to 12th mag. or so.
More data needed, yes. And not only at the eclipse predicted times, but at other times to confirm the elements.
About the particular datasets used to get the period of this binary (and other long period binaries too).
It is important to know that the ASAS-SN data at mag. 9.1 suffer from saturation problems sometimes. This is particularly true with the g data. And it depends on the camera. Objects brighter than 10 are difficult but we can get something good anyway.
Some cameras may have different zero points too. In this case I checked the data of each camera and discarded one of them altogether and only kept some points with low errors and consistent magnitudes. Magnitudes around maximum are particularly useful because they are saying that there was no eclipse at those dates even when they show some scatter. Faint outliers may be confused as eclipses. One way to check for their reality is to look at the other datapoints on the same date taken only a couple of minutes apart. If you have one point at maximum like the rest of the data and one point 0.3 mag. faint almost at the same time, the "eclipse" is rejected.
ASAS-SN data error figures are usually rather useful unlike other surveys. I get rid of several false eclipses deleting all points with large errors.
It wouldn't be possible to find periods of these long period objects without cleaning up the data because there are very few eclipses and the software won't find the period if wrong points are kept.
I am using the EA solver utility developed by Patrick Wils when periods can't be found by other software. This relies on the selection of true eclipse dates (and the fact that the dates belong to the same eclipse, Min I or Min II but not mixed) so if I have 4 eclipses and 1 is actually a spurious point, I may not find the period at all.
It is more important to keep only reliable eclipses and all possible points at maximum to discard wrong periods.
A first try may result in a multiple or alias period but the folded data may be enough sometimes to show you there are two eclipses with different depths in the light curve even when the period is wrong. This way you can select only minimum epochs corresponding to the same type of eclipses.
With PW Gem that was impossible because both eclipses have similar depths so I had to get rid of any possible wrong point.
May I have discarded some point showing another eclipse? I can't exclude that 100% but I don't think so because the final period doesn't show any evidence of the two eclipses belonging to different systems: there are no points at maximum at the time of the two eclipses and several points from different surveys over several years match both eclipses.
Originally I did not use SuperWASP data because I saw there was no eclipse and the scatter was rather large. SWASP data usually suffer from some systematics and I didn't want to add noise to my period search. But now that the period is very likely solved, I will add those observations to check that indeed there are no points at maximum at the expected phases.
I also did not use hundreds of observations from the KWS survey because the data are presented as dates and times (hours, minutes) instead of HJD. So I just manually added the dates of the two eclipses plus/less two other observations before and after the eclipses. So the complete dataset should also be used to check that no points at maximum are found on the current eclipse phases. Does anyone know a way to get HJD using the current KWS format?
PS: Two more objects to solve for tonight or tomorrow.
I also have a 70 d. period binocular eccentric binary with fast apsidal motion that I was able to solve with the help of my visual observations years ago and that I will share another time ;)
>>> Does anyone know a way to get HJD using the current KWS format?
In response to your question ... I attached an Excel with JD of the PW Gem object in the KWS survey, maybe it will help the analysis.
yes I see, there are few points and show no eclipse (two observations look fainter but look scattery) but they all add up. I hope the system will deserve more attention from now on :)
My initial "intuition" was wrong. I've just done a little bit of crude "proof of concept" modelling in BinaryMaker3, and I can get a secondary at about 2% phase with quite different primary and secondary eclipse widths. (But the eccentricy is crazy high: 0.95.) So far, I'm getting a reflection effect much greater than the actual data shows, but I think I can probably reduce that with more adjustments (lower eccentricity, lower long. peri.)
Nice paper, but, off-hand, I can't get my head aroud equation (1) let alone visualize it.. Then add the Kozai-Lidov mechanism with all it's chaos and I begin to smell a certain vagueness in their idea that the tertiary body migrates binary populations to circular orbits. I suspect that the Kozai mechanism can also have the opposite effect, and that would randomize the population.
For PW Gem, I like the simple idea of big red star - little blue star and the pair being precessed or perturbed by a high mass tertiary. Thank goodness we don't have to write papers for a living.
It's the reflection data on the light curve, typical of a system with two close stars with different temperatures. Then the big-little size difference might assist the differeng lengths of eclipses.
I don't think that the progession to a stable orbit, that the paper suggests, is inevitable. This system is IMO unstable on the scale of 10 or 20 orbits (a wild guess) of a third member. That, just from my efforts to model these things years ago.
I am not doing any modeling as you are, so I tend to follow your work. I respectfully dissagree that there is not evidence of reflection.
Yes, you are totally correct, Ray. There is a reflection effect, of about 0.01 - 0.02 mags, perhaps a wee bit larger where there is little data in the area of phase 0.015 or so.
I was speaking too approximately. The problem I have is the reflection effect that comes out of my model is much too large (0.08 mag or so) -- and that is with equal-temperature stars. I tried unequal temperatures, but that leads to excessively unequal eclipse depths -- although perhaps I could tune that out with inclination... (cans of worms, rabbit holes...)
In this case of a highly eccentric system, the sizes of stars does have an effect on eclipse durations, but I think it would be fair to call it "second order", after eccentricity and arg. of periastron .
I'm not a point with the paper where I want to comment about "progression to stable orbits" !
Thanks for keeping me on my toes...
So I decided to look at LC again and I don't think I see reflection effect. It's so marginal that I don't think it reaches 0.02 mag. More like 0.005-0.01 or just flat. Can someone confirm that almost-equal stars model would produce that flat curves?
I think we should wait for TESS data which, if lucky, should cover both eclipses. I don't know when TESS will be looking at Gemini region or if it already has, but this should confirm or deny reflection effect theory.
What a curious star system you've spotted, Sebastian! It's definitely worth follow-up observations. The long period means there'll be a long wait for eclipses from any particular site, but at least the eclipses themselves are pretty short. I'm sure some of us could get good coverage of them if you want to give target dates.
It really does look like a very eccentric orbit - I don't know how else you'd get two eclipses so close together, and the data looks pretty convincing. My first thought was a hierarchical triple, somewhat like b Per, but I'd expect there to be some scattering in the folded light curve due to the motion of the inner pair.
If I'm visualizing this correctly, I suppose the difference in the eclipse duration could be due to viewing angle and varying orbital velocity. If the argument of periapsis is, say 20 degrees from our line of sight, one eclipse would happen while one star is heading towards us, and a bit farther from periapsis. Its sky motion would, therefore, be a little slower than the other eclipse, which happens closer to periapsis and with its motion more perpendicular to our line of sight.
Yes, you are visualizing it correctly, Shawn (IMHO!). In fact, in my crude playing with BinaryMaker3, I've been using an eccentricity of 0.90+, and a longitude of periastron of 20-30 degrees. ( And two stars of equal size and temperature.) But I haven't been trying for a true "fit" -- just a model with similar enough characteristics to convince myself that one can get this difference in eclipse widths, with eclipses this close together in phase. (Yes, you can!)
One thing I don't get a match on is the amount of reflection effect. I'm getting way too much (0.05 - 0.1 mag). I need to research whether the approximations used are suitable for such a case (e.g., star rotations probably not matched to the very fast passage of the companions at periastron).
I don't think I get the point regarding reflection effect. Why would there be reflection when the two objects have equal temperatures? I see some distortion in the light curve of stars like this one at periastron between the two eclipses but that is not reflection.
I attach a light curve of NSV 18324 which I solved yesterday (or the day before? I don't know which day I live in anymore) and shows this effect.
Thanks for the question, Sebastian. As I understand it, "reflection effect" is always a misnomer. It would better be called "mutual heating", and "less space to radiate in to".
My crude model does show a brightening between the two eclipses, as you show on the LC you attached (ANOTHER interesting star!!!). I am thinking that is reflection effect: what do you think it is?
Maybe if we were to discover spectral types of both stars, we could make better assumptions. Stars might not be equal sizes and theory with high eccentrity should still apply (I'm glad it worked and my theory made on facebook is probably right!). But for now, I think we should stick with existing theory of almost equal stars and try to squeeze everything from it.
I have one more guess why those stars might display reflection effect on the LC, but I might be totally wrong. Maybe stars are getting so close to each other that it makes them behave almost like contact binary - they elongate to each other, but mass transfer never takes place. I think this would result in slight brightness change. I would be glad if someone could make a simulation of it! What do you think of this concept?
My theory was about high eccentrity and orbital nodes not placed parallel to Earth. With slight deviation transit will still occur and orbital velocities should make eclipses be different durations. As I understand it makes argument of periapsis have bigger/smaller value.