Polaris variability

lior · Post by **lior** » Fri Dec 03, 2004 10:25 pm

These files show that Polaris changes its brightness over four days. After two days the brightness of Polaris is reduced by about about 2 percents, and two days after it is increased back by the approximately the same percentage.

http://nightskylive.net/temp/alpumi.xls
http://nightskylive.net/temp/alpcas.xls
http://nightskylive.net/temp/alpumi19.xls
http://nightskylive.net/temp/alpumi19.xls

nbrosch · Post by **nbrosch** » Sat Dec 04, 2004 3:35 pm

lior wrote:These files show that Polaris changes its brightness over four days. After two days the brightness of Polaris is reduced by about about 2 percents, and two days after it is increased back by the approximately the same percentage.

http://nightskylive.net/temp/alpumi.xls
http://nightskylive.net/temp/alpcas.xls
http://nightskylive.net/temp/alpumi19.xls
http://nightskylive.net/temp/alpumi19.xls

I am quoting a bit from an article on Polaris that AAVSO carries. The full article is available at http://www.aavso.org/observing/programs ... main.shtml.

"Polaris is a small-amplitude Cepheid variable, with a period close to four days. In the early 1980's, Armando Arellano Ferro discovered, in the course of his PhD research at the University of Toronto, that the photometric and radial velocity amplitudes of Polaris had decreased significantly. Further studies, especially by Don Fernie and Karl Kamper, confirmed that the amplitude was continuing to decrease, and might well decrease to zero. Was it good-bye to Polaris the Cepheid? And if so, why?

Fernie and Kamper's most recent results were written up by Fernie, shortly before Kamper's death; they allow for two possible interpretations: (i) the pho- tometric amplitude has stabilized at about 0.03 or (ii) if all available data are used, the amplitude will decrease to zero in the next decade.

There was actually an error in the original prediction of the date of demise of Polaris the Cepheid, and it is worth noting the reason. It occurred because of a misunderstanding of the meaning of "amplitude". Is it the peak-to-peak difference in magnitude, or is it the coefficient of the sine curve which fits the data? The latter would be one-half the former. Many of us are guilty of this same ambiguity when we use the term.

Is Polaris evolving out of the Cepheid instability strip in the H-R diagram? Initially, this seemed like a promising explanation. Several years ago, however, Fernie pointed out that Polaris was well inside the instability strip, with similar period and temperature to Cepheids with normal large amplitude. But the Hipparcos satellite has put a new slant on this by showing that Polaris is most likely pulsating in the first overtone mode. Theorist Siobahn Morgan has shown that Polaris may well be at the "red edge" of the instability strip for first overtone pulsation, and may be evolving out of it.

These studies of Polaris - the best known star in the (northern) night sky - illustrate many things: the importance of long-term photometric monitoring of variable stars; the role of photometry of bright stars, using small telescopes; and the new insights which are still to be gained in stellar astronomy. For those of you who have access to the Canadian astronomy magazine "SkyNews", I call your attention to the excellent article on Polaris by Ivan Semeniuk, in the March-April 1998 issue."

If I understood your posting, you are showing that the ratio of Polaris to another star in the vicinity of the Pole is changing with a ~four day period and with a peak-to-peak amplitude of ~0.04 mag. This would be a very inetresting result, because it disproves the claim that the variabilty is decreasing, perhaps vanishing. Before writing this up for Nature, I suggest (a) checking this for another star or couple of stars in the same vicinity, (b) extracting magnitude differentials for a long period, if fact, as long as possible [years?] and doing a proper variabiltiy analysis, and (c) constructing a detailed light curve by phasing properly the magnitude differentials. Using the NSL data you may be the person with the best data set to study this phenomenon!

Congratulations, Lior!

Noah Brosch

RJN · Post by **RJN** » Sat Dec 04, 2004 9:11 pm

Good work, Lior. Polaris has been studied in NSL data before with a perhaps credible report of variability. See: http://nightskylive.net/asterisk/viewtopic.php?t=150

Polaris has also been the topic of several external studies in the past few years. A good way to find many of these is to go to ADS and type "Polaris" as the only title word. Two papers discussing photometry of Polaris were presented at meetings of the American Astronomical Society just in 2004. Both have very interesting abstracts. Here are their ADS links:

http://adsabs.harvard.edu/cgi-bin/nph-b ... .204.0610T
Overlooked Properties of the Cepheid Polaris;
Author: Turner, D. G.;
says that the amplitude of variation in V in 2003 was about dm = 0.024 magnitudes. We are reporting a higher dm, but perhaps this is because NSL CCDs are more red sensitive. Also, NSL measurements are averaged over several hours to get the needed sensitivity, and this likely decreases the measurable dm.

http://adsabs.harvard.edu/cgi-bin/nph-b ... .204.0609E
The North Star Mysteries: The Remarkable Brightness Increase of Polaris from Historical and Modern Observations;
Authors: Engle, S. G.; Guinan, E. F.; Koch, R. H.;
says that the amplitude of variation of Polaris is now increasing and is dm = 0.038 V magnitudes during 2004. This is more in line with what we are measuring. Even more interesting, this article says that the Polaris itself is slowly increasing in brightness, now 0.2 magnitudes brighter than 100 years ago.

It now seems that NSL photometry of Polaris can confirm this trend. It might be interesting to run WOLF on year 2000 Kitt Peak (KP) data and see what Polaris was doing then. It might be that an exhaustive comparison of Polaris to Alpha Cas over many many nights might create enough sensitivity to see if Polaris increased its dm or even its brightness just over the past four years!

- RJN

lior · Post by **lior** » Sat Dec 04, 2004 9:20 pm

Thank you Dr. Brosch,

I didn't realize that there is something with true scientific value here, and the main idea here was only to check the performance of CONCAM.

Examining the Excel files, it is clear that Polaris changes its magnitude over 4 days while Alp Cas doesn't. The changes in the brightness of Polaris is roughly 2 percents, but there is no certainty here that the observation is peak-to-peak, since the nights of October 15th and October 19th are not necessarily the night were Polaris reaches its peak. That means that the difference can be even greater than observed in this experiment. In order to find out, I guess we need to find four consecutive photometric nights and to perform the same thing over these four nights.

Since doing this manually using Excel is a pretty exhaustive task, I intend to write a short computer program that does that so we can easily obtain the required information.

nbrosch · Post by **nbrosch** » Sun Dec 05, 2004 4:09 am

Lior, you might also want to look at the paper by Evans et al. (2002, ApJ 567, 1121) that discusses Polaris from an astrophysically evolutionary point of view and combines optical with data at other wavelengths.
Cheers,
Noah Brosch

lior · Post by **lior** » Wed Dec 08, 2004 6:44 pm

Variablity of Polaris measured at KP gave the following results:

http://nightskylive.net/temp/alpumi_alpcas_kp.xls

The whole period is shown here by using 8 consequent "photometric" nights.

More data from MK and HL that also shows the period are available here:
http://nightskylive.net/temp/alpuni_alpcas.doc

nbrosch · Post by **nbrosch** » Fri Dec 10, 2004 5:54 pm

Lior:

I suggest very strongly to use the following procedure:
a. Start using Julian days and fraction of days for timing the exposures
b. Select the mid-time of observation to assign atime to a magnitude
c. Perform the same type of reductions to all Northern Hemisphere CONCAMs
d. Perform the same type of reduction to another star near Polaris, preferrably of the same magnitude and that would be circumpolar and not too far from the pole, to avoid extinction-related efects
e. Gather all the magnitudes and run a Fourier transform on the data. Check what periods appear. As you are using data from different longitudes, the sampling period of 24 hours should not appear.
f. Phase the magnitude differences according to each of the power spectrum peaks and check whether the light curve that results is significantly different from a constant value (chi-square should do)

Cheers,
Noah

lior · Post by **lior** » Fri Dec 10, 2004 7:36 pm

Thank you Dr. Brosch,

In order to follow the instructions, we first need a set of "photometric" nights. I will soon post a list of all photometric pairs of nights in the northern Hemisphere. One problem that we have here is that it is not easy to find good photometric nights in more than one CONCAM. These nights are pretty rare.

Also, we are still in resolution of days, and not hours, but we will soon go deeper so I can follow the procedure that you suggest.

Thanks,
Lior

lior · Post by **lior** » Thu Dec 16, 2004 9:18 pm

In order to show that Pollaris is a variable star, we first tried to show that it varies more than Alp Cas. The process was to take all photometric nights (where Alp Cas is constant) and to show that Pollaris varies more than Alp Cas in these nights. The excel files here shows that the standard deviation of Pollaris in these nights is almost twice than Alp Cas.

Pollaris: http://www.nightskylive.net/temp/kp_photometry.xls
Alp Cas: http://www.nightskylive.net/temp/kp_phot_hd3712.xls

lior · Post by **lior** » Fri Dec 17, 2004 6:51 pm

Polaris and Alp Cas data:

Standard error < 0.01:

Alp Umi:
http://nightskylive.net/temp/kp_alpumi0_01.xls
Alp Cas:
http://nightskylive.net/temp/kp_alpcas0_01.xls

0.01 < Standard error < 0.05

Alp Umi:
http://nightskylive.net/temp/kp_alpumi0_01to0_05.xls
Alp Cas:
http://nightskylive.net/temp/kp_alpcas0_01to0_05.xls

Pimp daddy · Post by **Pimp daddy** » Sat Dec 18, 2004 4:54 am

The daddy in the haus!!
I may be mistaken, but this appears to be random fluctuations?
The pimp seen it many times before, don't feel bad for your mistake!

lior · Post by **lior** » Sat Dec 18, 2004 6:27 pm

Comparing Alp Cas and Alp Umi in 2004 in kp. Alp Umi varies more nights (comparing to the previous night) than Alp Cas.

http://nightskylive.net/temp/ddf.xls

lior · Post by **lior** » Sat Dec 18, 2004 6:28 pm

Pimp daddy wrote:The daddy in the haus!!
I may be mistaken, but this appears to be random fluctuations?
The pimp seen it many times before, don't feel bad for your mistake!

We show a very low standard error, which is much lower the estimated fluctuations. Why do you think this is random? Please explain.

lior · Post by **lior** » Sat Dec 18, 2004 8:13 pm

More Polaris observations from KP.

http://nightskylive.net/temp/alpumi_alpcas_kp.xls

lior · Post by **lior** » Sun Dec 19, 2004 6:56 pm

Alp Umi and Alp Cas based on the same night (the first "photometric" night).

http://nightskylive.net/temp/alpumi_alpcas_kp.xls

The data of october 3rd until october 10th is not good due to a high standard error and many missing days with not even one good observation (comparing to the baseline night).

The data from december 9th do december 15th shows the period of Polaris nicely. Also the data from september 10th to september 17th. Yet, the data from september has the lowest standard error and seems to be the best to show the variablity of Polaris.

lior · Post by **lior** » Mon Dec 20, 2004 8:21 pm

Alp Umi/Alp Cas over 2004 in kp,hl,mk.

Except for several days, the data is usually not good.

http://nightskylive.net/temp/alpumi_alpcas_kp_2004.xls
http://nightskylive.net/temp/alpumi_alpcas_hl_2004.xls
http://nightskylive.net/temp/alpumi_alpcas_mk_2004.xls

lior · Post by **lior** » Mon Dec 20, 2004 10:51 pm

New data with error bars:

http://nightskylive.net/temp/alpumi_alpcas_kp_2004.xls
http://nightskylive.net/temp/alpumi_alpcas_hl_2004.xls
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lior · Post by **lior** » Tue Dec 21, 2004 7:10 pm

New plot:

http://nightskylive.net/temp/alpumi_alpcas_kp_2004.xls

nbrosch · Post by **nbrosch** » Tue Dec 21, 2004 7:21 pm

Lior, I am not sure what are you trying to do. The new plots show the magnitude difference (count ratio) of Polaris to two ther bright northern stars. I am (almost) sure that many of the readers do not understand the EXCEL tables and the plots. In order to show definitiely that you detected and measured the Cepheid variability, I think you should do a period search. This could be from one station only or from all of them together.

The period search can be done by looking at the peaks of a Fourier transform; using data from different observatories should deal with the "24-hour" period that plagues single-observatory data sets.

When you have a tentative period just seelct an arbitrary time, that for example for the first point , and do a data folding by locating subsequent points at the observation time modulo the period you are currently searching. What you obtain from this is a light curve, and you can decide whether it shows real variability or not through a chi-square test. Plot possible periods vs. the chi-square value and find what period is best.

There are many tests to show the reality of a detection; when the time comes I'll write about some. For now, I think that a light curve that shows the detected period significantly would be a convincing argument.

Cheers,
Noah

lior · Post by **lior** » Tue Dec 21, 2004 8:19 pm

Thank you Dr. Brosch,

I'm clearly not sure myself about what I am trying to do here. You are surely right about finding the peaks. What I understand now (as a matter of fact, I noticed that several weeks ago) is that most of the nights are just not reliable for photometry using CONCAM. What I need to do is first to find several groups of several photometric nights, find the peak of each group and then apply the method you suggested.
Thanks.

lior · Post by **lior** » Tue Dec 21, 2004 8:41 pm

Here is another plot showing that Polaris varies more than Alp Cas:

lior · Post by **lior** » Tue Dec 21, 2004 8:51 pm

Some more data. One is a full Polaris period from Haleakala. The rest are from Kitt Peak.

lior · Post by **lior** » Wed Dec 22, 2004 5:06 pm

Alp Umi, Alp Cas at Haleakala:

lior · Post by **lior** » Wed Dec 22, 2004 5:08 pm

Alp Umi, Alp Cas at Kitt Peak:

lior · Post by **lior** » Wed Dec 22, 2004 5:11 pm

Another observation at Kitt Peak

Starship Asterisk*