Calibrating measurements of stars

Today's lab exercise should be carried out in pairs, ideally, but it's okay to do it by yourself or in a group of three.

In order to gain credit for this exercise, you must create a PDF document which provides the answers to all the questions: A, B, C, etc. Submit the PDF to the instructor via the "Assignments" tab in myCourses.

In order to carry out the tasks in this exercise, you will need several tools:

a tool to compute mean and standard deviation of a set of numbers
a tool to create simple X-Y scatter graphs from a datafile
the Aladin program (use the desktop version)
access to SIMBAD

You may use a spreadsheet of some sort, or you may try one of a large number of programs designed for the analysis of datasets. I might suggest this one:

gnuplot

The field and target

This exercise involves measurements of a very peculiar variable star named "V404 Cygni". Your first task is to make a finding chart of the field, so that you will be able to recognize stars and identify them in catalogs.

Use Aladin to create a finding chart for V404 Cygni. I suggest you
- choose the "Server Selector" -> "SkyView" tab
- use a field of size 0.25 degrees
- choose survey "DSS1 Blue
Create a screenshot of this finding chart and insert a copy into your report. Keep a copy for your own use.
See chart below.

I observed this star at the RIT Observatory during the month of June, 2015. One of the images from these nights is shown below.

Can you find the four labelled stars A, B, C, and D, in some standard catalog? It will help if you can. I suggest using the APASS9 catalog for this exercise. You can access it within Aladin by choosing in the left-hand panel

   
     Collections -> 
          Catalog -> 
               Vizier -> 
                    II-Photometric Data ->
                         APASS - AAVSO Photometric All-Sky Survey

Fill in the table below with information on the stars labelled in the chart above. If one of the stars doesn't appear in the catalog, don't worry -- we'll deal with that later.




       
         
          Label        RA          Dec         APASS_recno
        --------------------------------------------------------------
            A    306.077841    +33.886783        13926111

            B    306.073663    +33.987620        13926136 

            C    20:24:03.826  +33:52:01.96        

            D    306.009408    +33.916131        13926129
        --------------------------------------------------------------

The input data

I used the 12-inch telescope at the RIT Observatory to acquire a number of images on one night in June, 2015. All the images were taken through a V-band filter. I then processed the images and measured the intensity of each star in each image. The results are in a simple ASCII text file:

data file "intensity.dat"

The datafile starts like this:


#   Julian_Day          A         B         C         D 
 2457197.70876     4924.9   10064.7    5587.3    7372.2 
 2457197.71115     4897.8    9972.4    5500.5    7358.7 
 2457197.71148     4934.0    9944.9    5495.4    7413.1

Your first job is to use the Julian Date to figure out the exact night during which I made these measurements. I suggest looking for a tool for converting Julian Dates into ordinary dates. The American Association of Variable Star Observers (AAVSO) is a very good place to go for all sorts of information related to variable stars. Why not do a little searching for a tool they might have made?

What ordinary calendar date(s) corresponds to the start and end of the data in this datafile

start: Jun 24, 2015 EDT, end: Jun 24, 2015
What tool did you use to answer this question?

AAVSO Julian Date converter

Take a first look at the data by making a graph of intensity versus Julian Date.

Make a graph showing all four stars at once, with intensity on the y-axis and Julian Date on the x-axis.

Convert intensity to magnitude

In order to convert intensities to magnitudes, and in order to shift the magnitudes to a standard scale, one must choose a reference star. It might help to look at the graph of intensities over time.

Which star will you choose as reference? Why?

Star A, as it is closest in brightness to the target

Using your reference star, convert all intensity measurements to instrumental magnitudes. Save those results -- you'll need them soon. Fill in the first four lines of the table below.

# instrumental magnitudes, relative to ref star # Julian_Day A B C D # ------------------------------------------------------------------ 2457197.70876 0.000 -0.776 -0.137 -0.438 2457197.71115 0.000 -0.772 -0.126 -0.442 2457197.71148 0.000 -0.761 -0.117 -0.442 2457197.71182 0.000 -0.758 -0.104 -0.429 ------------------------------------------------------------------

Make a graph showing instrumental magnitudes as a function of Julian Date.
Verify that most of the stars don't vary with time; that's a good sign that your choice for the reference star was a good one.

Yes, it was a good choice: A, B, D are all constant

Convert instrumental magnitudes to calibrated magnitudes

You can now use the reference star to shift all the instrumental magnitudes to standard V-band magnitudes.

What is the V-band magnitude of your reference star?


         
              star A has V = 11.339 
              star B has V = 10.769 
              star D has V = 11.104

What is the difference between V-band magnitude and instrumental magnitude of your reference star? Call this difference Δ.

for star A, Δ = 11.339 - 0.0 = 11.339
Add Δ to all the instrumental magnitudes, of all the stars. This should convert all those instrumental magnitudes to V-band magnitudes.

Done.

You can check that your calibration process was valid by looking at the calibrated magnitudes of the other comaparison stars (besides the reference star) which you can find in the catalog. If things went well, the average calibrated magnitudes of the stars from our images should be close to the V-band magnitude for each star listed in the catalog.

Compute the average magnitude value for each of the two comparison stars (other than the reference star and the target). Write down the average and standard deviation

       
         
              Now star B has   V =  10.56 +/-  0.01

              Now star D has   V =  10.90 +/-  0.01

Compare these measured V-band magnitudes to the V-band magnitudes in the APASS catalog. Do they agree within the uncertainties?


       
         
           Star            APASS V              my average V
         ----------------------------------------------------
             B          10.77 +/- 0.01        10.56 +/- 0.01

             D          11.10 +/- 0.00        10.89 +/- 0.01
         ----------------------------------------------------

             No, they don't agree within the uncertainties ...
             but the difference between them is 0.33 in catalog,
             and 0.32 in my measurements.  That's encouraging.

A calibrated light curve of the variable star

You are now ready to make a light curve of the target star, V404 Cygni, using your calibrated V-band magnitude measurements.

Make a light curve showing V-band magnitude of the target star on the y-axis, and Julian Date on the x-axis.

Do a little reading in the literature

This light curve should show some pretty crazy changes in brightness over a pretty short period of time. This object, V404 Cygni, is actually not an ordinary star; nor is it a single star. Ordinary stars don't behave like this.

Just what sort of system is V404 Cygni? To find out, look at SIMBAD's entry for this star. Go to the References section and search for all papers published during the period 2016 to 2016 (don't worry, that just means all of the calendar year 2016).

Look for a paper with first author "Kimura". What is the title of this paper?

Repetitive patterns in rapid optical variations in the nearby black-hole binary V404 Cygni
To read a copy of the paper, click on "View the references in ADS", then hover over the icon of a page with folded corner, and click on "arXiv PDF".

Okay.
This paper shows light curves of the system in both optical and X-rays. One of the panels in one of the figures shows the optical light curves, in V-band and I-band, for the same night you analyzed. Which figure and panel is this?

Figure 2 b
How similar to the published V-band light curve is your light curve?

Very similar -- though the entire light curve might be shifted vertically by 0.1 or 0.2 mag.
Just what sort of stars are in the V404 Cygni system?

It's a black-hole binary system, containing a black hole and an "ordinary" star (a cool giant star) orbiting their common center of mass. Some of the material from the ordinary star flows away from its outer atmosphere and spirals into an accretion disk surrounding the black hole. It is the hot gas in this accretion disk which produces most of the light -- and the rapid changes in brightness -- that we see.

For more information

The American Association of Variable Star Observers (AAVSO) is a great resource for all aspects of the study of variable stars. Their website contains lots of useful tools.