# O-C diagrams for Miras

On the Swedish Variable Observations database, SVO, have I begun a project to publish O-C diagrams for Miras based on data from AAVSO and AFOEV. Togheter with the diagrams is some information about the stars from GCVS4, magnitude at max from the maxima found and the result from a linear and parabolic fit to the O-C diagram. A linear trend suggest that the period is constant, but wrong. A parabolic trend that the period is changing with a constant rate. The statiscally significance of the fit is also presented. You can also get a table of the individual maxima and a O-C diagram of the residuals when the linear or parabolic trend is removed.

The digrams can be found at http://var.astronet.se/mirainfooc.php or by SVO's homepage at http://var.astronet.se end then choosing "Ljuskurvor & Resultat -> O-C diagram för Miror". The O-C diagrams are in english but the rest of the site is in swedish...

Thomas Karlsson

The first phase for the O-C diagrams for Mira stars is now finished. Over 42000 maxima for 488 Miras are in the database and is published on http://var.astronet.se/mirainfooc.php

Beside 33000 maxima that was computed of data from AAVSO, AFOEV and VSOLJ, I have also added some 9000 older published maxima to extend the time-line as long as possible for the stars.

The O-C is now also computed by using the mean period of the time-span that is coverad by each stars data, instead of the period from GCVS.

Many intresting patterns can be seen in the periods and it is intresting to notice similarities and differences between the stars.

Thomas Karlsson

Thomas,

This is a terrific result from an enourmous amount of work. It will take me a few days to soak it all in. One thing that observers can take away from this is the names and number of stars that have sufficient data to do this kind of analysis. In order to preserve and maintain the integrity of this kind of long time period analysis we need to continue cataloging data on these particular stars.

I will check this list against our Legacy list to see if there are perhaps some stars we should add or drop.

Anpother thing that seems to jump from the pages is that there are indeed several LPVs that appear to be changing period on human time scales. The O-C graph for T UMi is striking, but there are several others that have similarities.

Thanks for sharing this.

Thomas,

This is a fantastic job you did. I cannot fathom how much time and effort you put into this. I had the same thought as Mike. I'd love to see what Legacy stars are here and see what's up with them from the O-C diagrams. Mike, if you can get this info, possibly you can add it to your web site on the Legacy stars. This info would give us more of a strong reason to observe these stars, and perhaps emphasize some an deemphasize others.

Chris Stephan SET

Robert Clyde Observatory

Sebring, Florida USA

Thomas, Great work!!! All of the stars with significant period changes are captured: R AQR, R CEN, R HYA, LX CYG, R TAU, T UMI and period decrease of W DRA... Perhaps our academics can comment on the outstanding work... Kevin - PKV

Very interesting and gratifying to an old-timer to browse through these fascinating O-C diagrams. The smooth parabola for R Aql caught my eye on the first page and I was hooked; Looked to see how many more such curves there were in this sample. Not many, as it turns out, but the T UMi curve stands out in two ways, the smoothness of the parabolic change and then the sharp change from apparently parabolic to nearly linear change, or at least a dramatic shift in the rate of change.

Another question stands out to a novice in this type of presentation: How do you account for the fact that the results calculated from observations from other, presumably earlier published observations (the blue maxima) are consistently the most negative, or among the most negative, of the observed maxima in comparison to the GCVS mean? Put another way, why are the blue points nearly all more negative than the red points?

Another thing that stands out is that, at least to the casual examiner of these graphs, the zero point on the abscissa is nearly always high on the scale, that is to say there are a lot more maxima that are later than the mean than earlier? Can either of these points be accounted for methodologically, that is through examination of how the GCVS means were computed, from which samples of maxima, from what sources of observations, etc.

In any event, many thanks to Thomas K. for starting this process of analysis in this systematic fashion. it looks like there are more than a few dissertations for theorists in stellar evolution here!

Tom Williams

Thomas, Mike, or anyone who understands O-C diagrams,

Please, as simple as possible, educate me (us) on O-C diagrams, how do I read them on Thomas' web site, and what do they tell me (us). I have never fully understood how to read an O-C diagram, whether it be for LPVs or eclipsing binaries. I know this may sound dumb for someone like me who has been at this so long, but I also thought there may be several newer folks who might wonder the same thing, but feel intimidated to ask. Thanks.

Chris Stephan SET

Thomas,

What does SVO stand for in the Data Source column?

Chris Stephan SET

I'm no expert, but I'll take a stab a this.

The horizontal axis of the an O-C diagram is time, usually expressed in days, most often the JD of the observation. (It can also be cycles or phase)

The vertical axis is the "O - C" part. For each observed event (maxima in these diagrams, but it could also be minima or times of eclipses) one takes the observed time of the event (that's the "O" part) and subtracts the time predicted from the existing data or model of the star. The difference, Observed minus Calculated or "O - C", is plotted on the vertical axis of the graph. The pattern that shows up in the O - C diagram can tell if your predictions (or model) are valid.

If your model is good and you have determined the right value for the period of the variable star, then the points in the O - C diagram will be a straight and level line across the graph.

If your period is slightly off, then your model will get the event times right for a while, but the discrepancy will accumulate as times goes on. In that case, the O - C diagram will look like a slanted straight line.

If the O-C diagram turns out to be curved, the period of the system is changing slowly. If zero is the middle horizontal line of the graph and positive is up and negative down, then a curve leading downwards indicates a shortening period. The events are happening earlier and earlier than predicted. If it curves upward, the events are happening later and later than expexted, so the period is increasing.

Thanks, Mike, that helped me on why the blue are all on the left, they are all older, duh! Still, I guess i don't understand the time scale, times both positive and negative. Are these referred to the epoch of one particular version of the GCVS? or why would there be both positive and negative "dates?"

Tom Williams

Remember, we are subtracting the predicted date from the observed date.

If the JD of the prediction is 2550 and the observed date is 2560, then there is a positive difference of ten days. The event (maxima here, for Miras) occured 10 days later than predicted. If the predicted date is 2550 and the observed date is 2525 the difference is -25, or 25 days ealier than predicted.

Sorry, I forgot the other half of the question.

On the x-axis, the numbers represent cycles since the date of the epoch listed in the data, __or__ number of cycles *before* the epoch date. So for R AND, zero is the JD epoch date 2453820. The number of cycles before that used to calculate the O-C are in negative numbers heading to the left. Dates after 2453820 head to the right.

Thomas, this is great! I really like your site -- I think it will be a great research as well as education resource. It's nice to be able to scroll through many stars at once and pick out interesting candidates (e.g. parabolic O-C curves).

My eye was caught by SU Vir which was on our list of potential period-changers, but also Z Vir, which was **not** on our list. I'm looking forward to paging through it some more soon!

Thanks for all kind words and Mike for the excellent explanation of the basis of O-C diagrams.

SVO in the source column on the data pages stands for the name of the database, Swedish Variable Observations database, and is those maxima that is calculated from observations. By this one can see how far back a star is covered by observations. Many go back to the foundation of AAVSO and some even before that because pre-AAVSO observations has been put in to AID by Kevin P and others. This is the blue dots, the red ones is usually older maxima that is published in Harvard Annals and some other sources to extend the time line backward.

As Mike pointed out it is cycle number that is on the x-axis in the diagrams, with cycle number zero equal to the epoch of the GCVS catalogue. If you click on a diagram you got a data page where you can see what dates each cycle number represents, both calendar date and JD.

The number after DeltaP is by what the average period differ from the GCVS period. You got the new period by adding "Period" by "DeltaP". For example: R And has the period 409.2 in GCVS. The O-C diagram suggest that this should be increased by 0.51 days (this is where a regression line is horizontal in the diagram) and the new period that better represent the behaviour for R And from 1859 to now should be 409.71 days. If you click on DeltaP you got what the O-C diagram look like with the GCVS period of 409.2 instead of the average period 409.71.

DeltaP/C (delta period per cycle) is a best fit for how much the period is changing in days per cycle on average. In most cases the change is to small to significant or the random period changes Miras have can give a false picture. But for example R Aql the picture is quite clear, the period has decreased on average by 0.425 days/cycle since the 1850:s or for over 180 cycles.

Thomas Karlsson

Thanks, Thomas, for some interesting graphs! A better source for periods is the AAVSO's VSX program (http://www.aavso.org/vsx), as it has the most current period and epoch information that has been published in the literature or derived from AAVSO data.

I notice that you have few published Times of Maxima, and no recent ones. The AAVSO maintains a database of the ToM calculations done here in conjunction with the LPV Bulletin project. You can access it at

It contains thousands of Maxima timings for the stars on our program, and is up to date as of early this year. It contains all of the timings from the AAVSO publications by Campbell, Mattei, etc. It would be *very* interesting to compare your computerized timings with those derived by eye to see how well they match.

Another potential project is to compare timings from CCD observations, such as those by ASAS, with visual observations. My guess is that, like eclipsing binary timings, CCD observations with their inherently higher precision may give better timings, reducing some of the scatter seen in your plots. It would be nice to see if that prediction is true, or if there are any systematic trends between CCD ToM and visual ToM.

Arne

Arne, I'm familiar with AAVSO:s database of maxima and minima, in fact it has been a great source of inspiration for my work. I have done a few comparisons of comparable maxima.

For example R Cam, the difference between AAVSO's date for maximum and mine was on average -2.9 days with a standard deviation of 5.0 and the biggest difference -16 days. For R Tri the average difference was 0.31 days with SD 3.63 and a max diff of 11 days.

I think in general the two sets of data agree relatively well, but the shape of the light curve (sharp or flat maximum), the amplitude, spectral class an number of observations can cause greater or lesser deviations.

Thomas Karlsson

From the O-C diagrams I have also calculated diagrams to show how the stars period has developed over time. For this I have used a smoothened version of the O-C, where each new point is a moving average of 3 points before and 3 points after the orignial point. The change of period is then calculated by the slope in the diagram.

Many intresting features can be seen for many stars besides the known stars with changing periods as R Aql, R Cen, BH Cru, LX Cyg, W Dra, R Hya, Z Tau and T UMi.

The new diagrams can be found at http://var.astronet.se/mirainfoper.php

Thomas Karlsson

My O-C and period diagrams are now updated with all relevant data from BAAVSS which yielded about 400 new maxima and incresead the overall precision for many stars. I have also put in about 400 old published maxima in the database, so that the total now is 42800. For the fast changing star LX Cyg I found som interesting maxima from before the star's period started increasing.

The O-C diagrams is found at http://var.astronet.se/mirainfooc.php and the period diagrams at http://var.astronet.se/mirainfoper.php

Thomas Karlsson

Since the last post I have complemented the database with the AAVSO maxima from __http://www.aavso.org/maxmin__. They appear as light-blue dots in the O-C diagrams. To get the two collections more consistent I calculated a mean offset per star from the maxima that are common between the AAVSO collection and them I have determined and added this offset to the dates for the AAVSO maxima. (The offset value is displayed on the data table when clicking on a graph).

I have also updated the database with new maxima from 2012 and 2013 and also with a lot more older maxima from various sources. In total there are now 57600 maxima for 489 stars.

Some evolution theories for mira stars predict that their period should slowly increase for 50000 to 100000 years until it is reset to a lower level again by a short helium flash. (Percy and Au, 1999) To test if one could see a such tendency I removed the 8 stars that have certain changes and from the rest selected those that have good data at least 100 years back (327 stars). I then counted how many that have a positive or negative parabolic curve in their O-C diagrams. I did the counting four times by first using all data and the removing the last 25, 50 and 75 years of data. In the short perspective random fluctuations should be most prominent and one could expect to get a 50/50 distribution of stars with increasing and decreasing periods. If the prediction is right one would expect that with a increasing baseline even a small, but continuous, underlying change of the periods should break through the random noise in the mira periods. The result was:

Year Increasing Decreasing

1938 51,4% 48,6%

1963 54,4% 45,6%

1988 57,8% 42,2%

2013 59,3% 40,7%

Which I think is most interesting... Percy & Au (1999) found in their investigation of the AAVSO database that 55% of the stars had an increasing period. Are we beginning to see real secular changes of the periods for the miras?

Hi Thomas,

I looked at some of your O-Cs, I did the same thing for about 90 southern variables in the 1990s and the computer epochs were generally a better fit than the manual ones. But I'll look up some of the stars that interest me in your database. You've put a lot of time into this.

I have some reservations about all of the period change data, including the paper by Percy and Au. I do not think anyone has yet come up with a foolproof method of determining Mira periods. P and A attribute the changes about a mean line to a random walk but in most cases two alternate periods can be fitted, with a small percentage of intervals close to the mean period. The problem is your mean periods are affected by the length of the sample and just how far from the mean period individual variations go. They do not always deviate by similar percentages, even for the one star. Thus any period will depend upon the data selected.

The other assumption is that the period change will be smooth, producing a parabola. But many variable stars change their periods in abrupt jumps. Maybe, in more time than we have, these jumps will be seen to fit a parabola. It was suggested to me that local effects, such as the number of massive convection cells, tended to suppress the constant change model until the deviation becomes too large and an abrupt catch up takes place.

But it's good to see that these LPVs are not forgotten

Regards,

Stan Walker

Thanks for your comments. Yes, analysing the periods of mira stars is most frustrating. I think a human life is too short to get the answers. It would have been fun to watch these O-C diagrams 1000 year into the future to see what happens. If they still just alter forth and back in a random way or have secular variations.

I agree that the "true" period can't be given with great certainty because of the random walk behaviour, but should we not get closer to the period determined by the star's mass and radius the longer we look? As you write the problem is the time-scale and size of the random variations. For most stars the 100+ years of data we have seems not long enough to see the patterns of these random variations. But I hoped that using a large sample of stars some conclusions could be made.

I did the same test as above for the stars that have 125+ and 150+ years of data. The number of stars are less but their baseline are longer for the 125+ and 150+ groups. I don't know how significant these figures are but the tendency are the same as for the 100+ years stars. The groups are biased in the way that the 150+ stars are also in the 125+ group and the 125+ group are in the 100+ group.

For the 118 stars with 125+ years of data I got the following percentages with increasing period by only using their data up to the year listed.

1938: 43,2%

1963: 51,7%

1988: 55,9%

2013: 59,3%

And for the 66 stars with 150+ years of data I got the following with increasing periods.

1938: 47,0%

1963: 53,0%

1988: 56,1%

2013: 63,6%

Thomas Karlsson

I have now added the Eddington/Plakidis test on the O-C diagrams. This test should help determine if changes in O-C comes from random cycle-tocycle variations or real changes in the period. I have some trouble to interpret the results tough, too many stars seem to fall outside the test (and is therfore candidates for stars with period change)... One of the problem I think is that I need a better algoritm to decide the time for maximum, to remove some of the scatter that is present in many diagrams. Someone that have any ideas how to tackle these matters?

I have also added some more constellations and stars to the site. The goal is to cover all constellations all Miras that have enough observation data to create a decent O-C diagram.

Thomas Karlsson