Learning Curve: Johnson Filter Measurements of Beta

Andromeda & Alpha Andromeda

Matthew Zerilli

Missouri State University

AST 311-001

Dr. Peter Plavchan

December 11^th, 2015

Abstract

With the SBIG ST-i CCD, and 8 inch telescopes at Baker, I took data in the R, V, and B, Johnson filters in order to determine the spectral type of Beta Andromeda (Mirach), and using a comparison A star (Alpheratz) to finding its apparent magnitude, from the instrumental magnitude. After taking measurements in the R,V, and B bands, I subtracted the comparison star by the literature of Alpheratz, and used that number to determine Mirachs magnitude in those bands, B = 3.4884 , R = 2.5147, V = 0.693. I compared them to the literature, and concluded that there was too much of a difference for the data to actually be usable in any form of research. It is an experience that is noted for future use of the CCD’s, the use of the Johnson filters, and the accuracy of the 8 inch telescopes we were provided. 

Introduction

We were given the task of testing SBIG ST-i monochromatic CCDs.  Being Missouri State’s first semester with them, we were allowed to use them in order to start collecting data with them, which we used 8 inch, CPC700 and NexStar 8SE telescopes at Baker Observatory. Dr. Plavchan gave us the option to decide on what we wanted to use these instruments for, so I personally selected measuring Betelgeuse, though whenever we wanted to observe, the constellation Orion would not appear over the horizon until later at night (~1:00 am) in October, and wouldn’t be up at a proper altitude until mid-November. My task was to read spectrum of Betelgeuse, and see if I could determine the remainder of its lifetime, so Dr. Plavchan tasked me with using a different M star, and instead of the spectrograph, use Johnson filters and determine the current spectral type of the star by using a comparison star to calibrate the instrumental magnitude to apparent magnitude.

My main target was Beta Andromedae (Mirach), and my comparison A type star is Alpha Andromeda (Alpheratz). For the purposes of this class, I did not factor in air mass changes into my calculations as they are in the same constellation, and were not significant enough to factor. We will take the observations made with the CCD, and compare it to the SIMBAD literature in order to determine our difference in accuracy. 

Observations

The first night, 10/12/2015, we went out to Baker, I was charged with using the R Johnson filter for my first night. I was using one of the NexStar 8SE telescopes, however, there was slight overcast, and I had to set the CCD exposure to 40 seconds for Mirach, my main target, and 10 for Alpheratz. It should be noted, that these targets had the longest exposure time, but had the lowest counts for the SNR I had for these frames, since these set stars are magnitude 2.05, and should be much brighter with these exposure times.

On the second night, 10/28/2015, I used the BFilter, at first I used a CPC700, but Josh Kern and Joe Regan were both struggling with their telescope alignment, so I allowed them to use the telescope I had. I was having issues originally trying to align it properly, but Josh and Joe overcame the obstacle. I would then use one of the NexStar, but it’s motor would jam up as it would rotate, almost as if it suffered an impact, and would lock up once it had turned too far. I was struggling to align, obviously, since it would not rotate past a certain point, which I had to wait until someone had a telescope I could operate on. I was allowed access on one of the other CPC700’s, which I then noticed that the BFilter had a crack on it, and would sometimes illuminate most of the filter if the star aligned with it. I had to work around the issue, but once I had properly found my targets, I kept them from directly aligning with the crack in the filter. My exposures of Mirach were 0.6 seconds, and 1 second for Alpheratz.

Third and final night, 11/09/2015, I used the VFilter. This was my best night of observing, since I was able to use the CPC700 that is always mounted and kept under the retractable shed. This is the most accurate of all the 8 inch telescopes we had in the array, and I was able to accomplish retrieving all of my data quickly that night. I ended up finishing early, and assisted some of the other students with their observations.  Mirach’s exposure time was 0.3 seconds, and Alpheratz was 0.007 seconds. 

Procedure

With the measurements of our target and calibration star, we took calibration images, 10 darks, flats, and offset-bias frames. They are used to remove artifacts from our science target images, such as, dust particles, hot and dead pixels, and anything that is on the filters or even the detector, it is to help assist in removing them from the image. Dr. Plavchan instructed we take our .fits files, and transfer them off of the computer we were using, to a server that we share as a class. We used a Unix based terminal, PuTTY, and used procedures from the programming language, IDL, to calibrate and read the data from our .fits files.

Figure 1: Notice that I changed from exo to idl by entering “idl” into the command line, which I would use IDL to run the procedures, like reducesti.pro, to do all the readings and calibrations. This procedure requires takes 1 science image, first dark, last dark, first flat, last flat, first bias, last bias, Dark time, Flat time, Science time. It stacks all the calibration images together to look for artifacts, and piece them onto the science image to remove whatever it can. This is done to every single science image.

Figure 2: An example shown of the photometry code, apphot_STI.pro, used for one image of Mirach in the B-band. This gives us the instrumental magnitude (mag), and the error propagation (err) that we will use for our specific data.

            He personally wrote procedures that would take all of our frames, make master frames (master dark, flats, and bias), and would combine them, and implement them into individual science frames through the terminal. Examples in Figures 1 and 2 show what it looks like in the terminal. There was also the possibility of being able to adjust the procedure to calibrate the individual images, and combining them to make a final science image, but was not attempted. After each individual science frame was calibrated, I took their instrumental magnitudes and errors in order to compare them to the literature. Table 1 has the instrumental magnitudes, and their individual errors per image. 

Target/(Johnson Filter)	Instrumental Magnitude +/- (Error)
Mirach (BFilter)	8.8792 +/-0.00138	8.9063 +/-0.00136	8.9009 +/-0.00134	8.8737 +/-0.00138	8.8649 +/-0.00133	8.9009 +/-0.00132	8.8762 +/-0.00132	8.8744 +/-0.00136	8.8788 +/-0.00136	8.8893 +/-0.00136
Mirach (RFilter)	9.5568 +/-0.00344	9.5652 +/-0.00382	9.5634 +/-0.00375	9.5642 +/-0.00355	9.5542 +/-0.00362	9.5551 +/-0.00361	9.5602 +/-0.00352	9.5631 +/-0.00367	9.5539 +/-0.00376	9.5712 +/-0.00317
Mirach (VFilter)	10.836 +/-0.00308	10.806 +/-0.00308	10.764 +/-0.00331	10.753 +/-0.00310	10.694 +/-0.00305	10.860 +/-0.00388	10.643 +/-0.00277	10.857 +/-0.00336	10.719 +/-0.00292	10.798 +/-0.00377
Alpheratz (BFilter)	7.2782 +/-0.00526	7.3601 +/-0.00552	7.3738 +/-0.00558	7.3822 +/-0.00564	7.3549 +/-0.00554	7.3366 +/-0.00549	7.3498 +/-0.00550	7.3367 +/-0.00547	7.3521 +/-0.00553	7.3312 +/-0.00545
Alpheratz (RFilter)	9.7963 +/-0.00339	9.7905 +/-0.00342	9.7903 +/-0.00331	9.7861 +/-0.00342	9.7847 +/-0.00326	9.7921 +/-0.00336	9.7933 +/-0.00337	9.7988 +/-0.00335	9.8115 +/-0.00331	9.8022 +/-0.00336
Alpheratz (VFilter)	12.320 +/-  0.00654	12.288 +/- 0.00649	12.271 +/-0.00695	12.359 +/- 0.00674	12.318 +/-0.00656	12.346 +/-0.00669	12.407 +/-0.00678	12.260 +/-0.00669	12.243 +/-0.00639	12.350 +/-0.00685

Table 1: All of the instrumental magnitudes from both stars in B,R,V filters, and their individual errors.  

Results and Analysis

            It should be noted, that for my RFilter reduction, I had to use dark frames from my BFilter data, since I forgot to take the images during observation night. With my VFilter frames, they had to use BFilter bias and dark frames, specifically because they formatted in the wrong array (16x16), and would not go into the reduction procedure being a different size. My VFilter frames also were not correctly being detected by the apphot_STI.pro IDL code, so Dr. Plavchan had to rework the procedure to detect 2x2 array, instead of 20x20, which he also again edited since the second procedure would not detect the stars in the reduced images. 

Target Stars	Average V Filter I.M. +/- Average Error	Average R Filter I.M. +/- Average Error	Average B Filter I.M. +/- Average Error
Mirach	10.773 +/-0.002419	9.56073 +/-0.002810	8.88446 +/- 0.001051
Alpheratz	12.3162 +/-0.005190	9.79458 +/-0.002617	7.34554 +/- 0.004257

 With the set data in Table 1, we can combine each star in each frame into an average instrumental magnitude and error. Figure 3 has the equations we used to produce our average instrumental magnitude/error per star, per filter, seen in table 2. 

Table 2: The average values of the instrumental magnitudes
and the propagation error. 

            

However, the data is somehow off by ~2 magnitude difference in both R and V. It is notable, even before we compared it to the literature, that the instrumental magnitude had distinctions. In the literature, Mirach is an M0III, and you would expect the R band have a smaller number, as well as V band. With this, however, we will still attempt to produce a spectral type to our readings, and compare them to the index literature. Table 3 has all of our math, and literature of both stars and all the used Johnson filters.

           

Figure 3: y is the average instrumental magnitude, Sigma_y is the average propagation.
 

Our apparent magnitudes of Mirach are 3.4884 for B, 2.5147 for R, and 0.693 for V. Let’s calibrate them to figure out the spectral type, B-V = 0.9737,V-R=-1.8217, the SIMBAD literature has Mirach at B = 3.62, V = 2.05, and R at 0.81. Which gives the B-V=1.57, and V-R=1.24. The numbers are off by a large degree in the color index.

Figure 4: Ballesteros’ formula for finding T_eff.

	BFilter	RFilter	VFilter
Instrumental Magnitude of Alpheratz = (m_x2)	7.34554 +/- 0.004257	9.79458 +/-0.002617	12.3162 +/-0.005190
Literature (SIMBAD) of Alpheratz = (X_2)	1.95	2.09	2.06
Difference of the Filter (m_X2 - V_2=Delta X)	5.396	7.046	10.08
Instrumental Magnitude of Mirach - Calibrated Difference (x_1 - Delta X)	3.4884	2.5147	0.693
Literature of Mirach (SIMBAD)	3.62	0.81	2.05
Adjusted Mirach/Literature of Mirach (SIMBAD) (AdjX/LitX)x100%	96.36%	310.5%	33.81%

            Table 3: Taking the comparison star, subtracting it from the literature, and getting a difference in each filter. Taking that difference and subtracting it from our target star. Using that, I took the literature of the target star, and looked to see the difference we had from the literature.

With the observed B-V, we use the Ballesteros Formula to gauge an estimated T_eff, figure 6, which gives us 4807 Kelvin. Using the SIMBAD literature produced B-V, 1.57, the surface temperature should be ~3691 Kelvin. It’s not off by a large amount, but our observations would suggest that Mirach is a K3 IV star, but with the V-R being -1.8217, it is lower than the readings of any O star, making it quite literally impossible. SIMBAD suggests that Mirach is an M0 III star, and the B-V/V-R support this.

            Other procedures would be taken in order to test out my data, as in comparing the flux and seeing what else we can determine from this data, but with such a large difference compared to the literature, and faulty data, this is as far as we can go. 

Conclusion

Something must have happened the first night of observations, and several things could be in order that have played into my severely flawed RFilter data.

• I did not inspect the R Johnson filter, to see if there were any artifacts.
• There was partial overcast.
• I may not have been inspecting the telescope well enough to see if it was properly fixated, and could have possibly trailed slightly. Distorting the star, thus spreading the light by several pixels.
• Some of my images seem to be poorly focused in the RFilter, and could have ultimately been the cause of why both stars had much longer exposure times than the other filters. Figure 5 and 6 has both stars in order to assess their appearance.

There are several factors that could have been in play here, or just simply one that was critically why the RFilter was so different. The Visual, however, may be because I actually should have went for longer exposures, and had more of the pixels take in light. The star was only be 2x2 pixels, and the rest was just background, and the photometry could originally struggled to detect them. Perhaps it would have been in my favor to do so; regardless I must come to the conclusion that my data is flawed, and is not usable at this time. However, some of the data I have collected could be used as a foreground for using the filters on the CCD’s and provide further testing in order to fully the instruments.  

Figure 5: Mirach R Filter. 40 second exposure.

Figure 6: Alpheratz RFilter. 10 second exposure.