Finding RR Lyrae in Globular Cluster - M 13

What is a Globular Cluster?

A globular cluster is a gravitationally bound collection of stars. These generally consist of about 10,000 to 1,000,000 stars and span anywhere from several tens to 200 light years in diameter.

What is M 13?

M 13 is a globular cluster in Hercules, its location in terms of R.A. and Dec being 16 41 41.44 and +36 27 36.9 respectively.  It was first discovered by Edmond Halley in 1714, who on discovering this Globular Cluster said, ¡°It shows itself to the naked eye when the sky is serene and the moon absent.¡± M 13 is estimated to have anywhere from 100,000 to over a million stars. The center of M13 has more than 500 times the stars in the solar neighborhood. Nine of these stars have been identified as variable stars called RR Lyrae. M13 spans about 150 light years across in diameter and is about 20,000 light years away from the Earth. It is over 12 billion years old, which is not surprising as globular clusters are among the oldest objects in the galaxy.

What are Variable Stars?

These are stars that undergo significant variations in Luminosity. There are two main kinds of variable stars ¨C Cepheid and RR Lyrae. Since we are concerned with RR Lyrae here, we will be talking further about these.

What are RR Lyrae?

RR Lyrae stars are pulsating Horizontal Branch stars, that is, they change their brightness with a regular period and are usually found in globular clusters. They were named so after the first star discovered of this kind.

The period of pulsation for these stars is relatively small ¨C from 8 or 9 hours to 1.2 days. This makes it possible for us to observe changes in magnitude over a period of few hours of observing.

 

Why do RR Lyrae pulsate?

The pulsation is caused due to the fact that the star enters a physically unstable state internally causing its surface to move in and out causing it to change in terms of size and brightness. The brightness of a star depends on its temperature and size. As the size contracts, the gas is getting compressed into smaller volume leading to increase in temperature and as the size increases, the pressure is released and temperature falls. In the case of RR Lyrae the rate at which the size is changing is not fast enough for the amount of change in brightness that is observed. It is the effect of change in surface temperature along with changes in size that affects the brightness of RR Lyrae stars. So, when the star is smallest and hottest, it is also the brightest. Converse of this is also true.

So starting with a star that is in compressed or contracted state, the He+ in the atmosphere of the star ionizes into He2+. This leads to the atmosphere being less transparent and more opaque. This traps the energy flux within the envelope and as the gas gets heated the pressure builds up. When this pressure exceeds the internal gravitational force of the star, the star starts expanding. As the envelope expands, the atmosphere begins to cool down and the He2+ gains an electron to become He+ again, leading to increase in the transparency of the atmosphere, thereby allowing for the pressure to decrease and the star to shrink back.

 

Why are RR Lyrae useful?

We can study the distance to the globular clusters by comparing the apparent magnitudes with the absolute magnitudes of RR Lyrae stars residing in them. If we know the period of RR Lyrae stars to go from brightening to dimming, then we can find the absolute luminosity of the star, using the Period ¨C Luminosity relationship. This information then can be put into the Distance Modulus to give us the distance to the RR Lyrae, and hence the distance to M13. Since, the periods of these stars are not very long, these are ideal for our project.

 

Project A

We started off by wanting to pick one RR Lyrae star in M13 and making its light curve, to then calculate the distance to this star and hence to M13. In order to do this, we needed to find good finder charts, so that we could have good check stars and be able to identify our RR Lyrae star, without any error. This took an unexpectedly long amount of time and searching. Unfortunately, we were unable to find a good finder chart for this Globular Cluster. Finally, we did find one. However, it was not a very good one as even though it did show us M13 with RR Lyrae in it, the distance scale was such that we were unable to understand and interpret the chart. Wanting to take advantage of a clear night after a series of cloudy nights, we decided to try and make do with our imperfect finder chart, something we soon learnt one should never do. At about 7:30 PM, we started taking twilight flats. After we were done, unfortunately someone accidentally moved the camera, which rendered our twilight flats useless. We went ahead with the observing anyways, deciding to use dome flats instead. Once we had got a picture of M13 and wanted to identify our RR Lyrae, we realized how useless our finder chart was. This and a series of bad luck with weather brought us to reconsider the project. So we switched to Project B, which was to identify known RR Lyrae in M13.

Project B

Now our project had turned into essentially observing for a series of hours one night to try and get as many pictures of M13 as possible at different times. This would enable us to compare the magnitudes of different stars and determine the ones that showed any changes in magnitude. These would be our RR Lyrae. We by this time had found two great finder charts. So we knew the positions of the RR Lyrae stars and just had to verify that they really were RR Lyrae, by checking for changes in their magnitudes in our images.


One of the Finder Charts


Check stars in our image.

 


RR Lyraes in M 13 on our image. The brightest one at the top is RR Lyr 36, of the couple the one to your left is RR Lyr 9 and the one to the right is RR Lyr 5. (Numbering according to our Finder Chart)

 

Observing

We were able observe and get images of M13 on two nights. The first of these nights enabled us to get an excellent image of M13, which can be seen above. Other than this, the night was futile as we talked about earlier under Project A. The second night we got to observe M13 from about 11:00 PM to 4:30 in the morning. Here are some more details about our experience on these two nights:

 

On the first night, we took 3 sets of twilight flats in the R, V, and B filters. These however were useless as our camera was moved. We decided to go ahead with the observing anyways with the intention of taking dome flats later. We then used Arcturus to focus and sync the telescope. After focusing and synching we pointed the telescope to M13. We took 1 set of 2-minute exposures in the R, B, and B filters. We did not use track and accumulate. Also, during the course of re-focusing and readjusting the telescope after taking the twilight flats, we accidentally moved the camera, rendering our flat fields useless for our images.

 

On the second night, between 7:00pm and 11:00pm, the sky was cloudy. We were unable to take twilight flat fields. At the end of our observation run, we took dome flats instead in each of the R, V, and B filters. After about 11:00pm, the sky began to clear. We pointed the telescope to Arcturus for focusing and synching. After focusing and synching, we pointed the telescope to M13. We then took several 1-minute exposures of M13 to make sure that the telescope is focus. We re-focus the telescope. We started with 5-minutes exposures in the R, V, and B filters, and then took three sets 10-minutes in the R, V, and B filters. Between the last set of 10-minutes, we waited for about 45-minutes to take a set of 6-minute exposure images using track and accumulate.

 

Flat fields are use to reduce unwanted signal effects caused by sensitivities across the CCD surface and by dust on the lens. A speck of dust will show up on a flat field image as a doughnut shaped smudge. By dividing the final astronomical image by the flat field we are able to remove the dust. The ideal flat fields are twilight flats. The ideal time to take twilight flats is during dawn and dusk as the sun is rising or setting. Twilight flats are taken by pointing the telescope at the sky away from the sun as it rises or sets. If twilight flats cannot be taken, dome flats can be use instead. Dome flats are taken by illuminating a screen evenly with light and pointing the telescope to the screen.

 

Photometry

Once we had all our images of M 13 along with flats, our first step was to divide the images with the flats taken in their respective filter. Once, we had the flat fielded images in all the filters, we proceeded to identify our check stars and match their magnitudes with the known magnitudes in each filter. Once, we had the images all standardized, we tried to identify the RR Lyrae stars using a finder chart. This turned out to be a lot more difficult as our finder chart was not drawn at a scale similar to the image we had. Neither was it drawn  to scale as far as star sizes were concerned. So, we spent a lot of hours trying to find another finder chart, with no result. In the end we stuck with the chart we had and tried to approximate the position of RR Lyrae the best we could, with the hope of narrowing down to a few suspect RR Lyrae and then checking for magnitude changes in the different images taken over a period of 6 hours.

Check Stars:

 

Star

B

V

S/N (in V)

RF  (V)

Check A

14.07

12.64

95.84

372.51

Check B

14.66

13.42

88.00

372.51

Check C

14.38

13.22

87.27

372.51

Check D

13.91

12.31

87.23

372.51

Check E

15.52

14.30

80.72

372.51

Check F

14.30

12.94

88.28

372.51

 

 

RR Lyrae Stars:

 

Star

Change in V (Observed)

RF

RR Lyr 5

~ 0.36

372.51

RR Lyr 9

~ 0.37

372.51

RR Lyr 36

~ 0.06

372.51

 

Note: Our Finder Chart for the RR Lyrae can be seen at: http://arxiv.org/PS_cache/astro-ph/pdf/0211/0211042.pdf

 

Another method we used to further verify and check our identifications of these variable stars was to take the different images and subtract them from each other, sticking to the same filter. This way all the stars with approximately same magnitudes will be subtracted and what will remain will be stars that had more of a magnitude change. These can be then checked for changes in magnitude and be labeled RR Lyrae accordingly. Here are some of our images and how we worked through them:

 

          

 

                                                                                                                           

 

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Error Analysis

 

1. Readout Noise and Quantization Noise: These depend on the CCD and cannot be improved by the observer. For our ST-8 CCD, the read noise is 15 e -- per pixel per read. The later kind of noise has to do with Quantum Efficiency of the camera.

 

2. There were small differences in the magnitudes of the stars as compared to the known values. So certain error is introduced in the magnitudes of all our stars. This may be quantified as a function of some property of stars or if some pattern can be discerned. An interesting observation is that the magnitudes in the B filter are higher than the magnitudes mentioned in the finder chart for B filter, while the magnitudes in the V filter are lower than the values given in the finder chart. This is true for each star.

 

3. We were unable to start observing until 11 PM, which is quite late. It would have been better if we could have started observing right after sunset, to get as complete a cycle as possible for the pulsation period of the RR Lyrae in M 13.

 

4. We had to use dome flats. It would have been better to have sky flats.

 

5. Selection of the object can be very important. We should have put more effort into finding a good finder chart or selected an object that we knew to have a great finder chart. This can be really rewarding when it comes to verifying your results.

 

6. Quantitative Error: The idea is to identify the RR Lyrae and then using some distance conversions, try to quantify the displacement of our stars from the finder chart and Java Appalet, thereby determining something like a translation error in our positions of RR Lyrae.

7. We were not very good at refocusing a few times, so a few of our images are out of focus, which leads to elongated stars with fuzzy edges making it difficult to choose the toggle box size while doing photometry. This ends up affecting out magnitude determinations.