PHOTOMETRY: the 'sizes' and magnitudes of stars

reading: Universe 19(2-3) on flux and apparent magnitude

1) Photometry means the measurement of light.
As you remember, each pixel on the digitized CCD image has associated with it a Counts number
(which is proportional to the number of photons that hit that particular pixel).
In the HOU processor, the Counts number appears in the bottom right of the screen along with the x-y number of the pixel.

Open the HOU image processor, and then open the file ptstar2.fts under
C:\ProgramFiles\HOU-IP\images\Images-High_School\5photometry_techniques.

a) ptstar2.fts contains an image of a star.
To remind yourself that YOU have control over how the image appears, mess around with the placement of the red and blue controls that change the min/max values at the top left (or you can change the min/max values directly by typing into the respective boxes).
What are the consequences of varying the min/max values?

b) Measure the diameter of the star in pixels.
I suggest that you use the Slice command under the Data Tools menu.
After selecting the slice command, start with the mouse a distance away from the star,
but on the same horizontal level with the star's center;
hold the left mouse down and drag the mouse until you have made a line through the center of the star.
A window should then pop up that contains a plot of counts versus pixel.
Left click on the graph curve and trace the shape of the graph... notice that a red dot moves along the sliced image as you drag the mouse...

As part of your answer to this question, you will need to come up with (your own) standardized, quantifiable way of deciding where a star begins and ends. \
Document/Explain clearly what you did.

Caveat: Parts 2, 3, and 5 require no measurements using the image processor.
You may want to skip ahead to Parts 4 & 6 (the next measurement sections) and save Parts 2,3,5 for work later.
However, the logic of the lab flows better in the order written.
I will leave it up to you which way you want to go from here.

2) How many pixels should a star's image cover? To find out, do the following:

The nearest star (a Centauri) is 4.3 light years away.
It is a G2 main sequence star, and therefore is essentially identical to the sun in all properties.

a) Find the angular size of the a Centauri in radians, as seen from the earth, from its distance and its diameter.
Draw a large, well-labeled diagram which shows the quantities used in your calculations.
You can use either right-triangle trig or the arc length formula.
(We have already used this procedure multiple times this trimester already, right?)

b) Convert the angular size of a Centauri to seconds of arc (abbreviated as ").

c) The scale of the CCD image (determined by the focal length of the telescope) is 0.67 '/pixel.
How many pixels should the image of a Centauri, a typical star and the nearest one, cover, in an ideal situation?

3) Why does a real star image cover more than 1 pixel, even though it apparently shouldn't?
The answer follows on the next page, but I'd like to suggest that you spend a minute or more thinking of one or more answer on your own.

seeing

The term seeing is commonly used to describe how well light is confined to a few pixels. The number of counts measured for a star would be the same for various seeing conditions, but under ideal conditions all of the counts would register within one pixel. This never happens in reality with even the best ground-based telescopes, because the atmosphere will always blur the light over a wider area. Under "good seeing" conditions the light from the star may be spread over only a few pixels, so that the peak count number is quite high. With "bad seeing," the light is spread over many pixels so that the peak counts number is lower.

When the air is heated by a fire or the sun, the air molecules move faster and they blur the light traveling through it from distant objects. Presumably you have noticed the distortion of a distant object when viewed through air above hot pavement or above a radiator. It is not the object that is moving or wavy; it is the light from the object to your eyes that is being disturbed by the motion of the medium through which it is traveling. As the temperature rises or other atmospheric conditions occur, the air becomes more turbulent, which in turn causes distant objects to appear bigger because the light coming to us is smeared across a wider viewing area. The total amount of light received from the star is the same, but it is distributed over a greater number of pixels. Notice that in the figure below there are the same number of counts  i.e., the same number of boxes -- under each seeing condition; each "count" is represented here by a square. But the Full Width at Half Maximum (FWHM) is greater under greater seeing.

4) The HOU software (the Auto-Aperture option under the Data Tools menu) automatically senses the number of pixels that a star's image covers, sums the counts in those pixels, and subtracts out the background skylight. It then prints the total counts in a dialog box labeled "Results" on the screen.

a) Use the Auto-Aperture option to measure the counts for the star in ptstar1.fts (find it under the same 5photometry_techniques directory as previous image).
After selecting Auto-Aperture option, click on the star in your image.
A results box will appear which gives various information including "brightness"
(which is the total number of counts measured for the star; it's what we have been calling 'flux') and the radius of the star in pixels.
Record all information from the Results box.

b) Measure and record the same quantities for the star in ptstar2.fts (again under 5photometry_techniques).

c) Which star do you think has greater apparent brightness? Why?

5) Suppose I stood in front of the class with a flashlight. What affects your eyes' measurement of the apparent brightness (or flux) of the flashlight?
List some specific things that might cause the apparent brightness of the flashlight to be different for different observers at different times.
Then translate these reasons into astronomical analogues (a table with two columns would be lovely, no?):
Why might the counts recorded for a given star be different on two different nights or even on the same night for two different observers?
You should be able to come up with at least 5 or more additional distinct, specific, non-similar reasons.
I have done one example below. Note the use of complete sentences.

flashlight in class	star
a) The flashlight might appear brighter because a higher-voltage battery was used.	1) The star might appear brighter because the star flares up in brightness due to a new, more energetic nuclear reaction.

measuring a magnitude

6) This section re-tests your understanding of how flux converts to magnitude (and the two rather bizarre rules of magnitudes that we learned weeks ago.)
We need a procedure for finding the magnitude of a star that is independent of sky, CCD, telescope, etc. conditions
(which change from night to night or even minute to minute on the same night, as explained in section 4 above)
so that anyone, anywhere on Earth, under any observing conditions, will get the same magnitude.
'Counts' are not a useful quantity when comparing images from one telescope to images from another.
In order to use your data in the context of other observations and standardized brightness tables
you need to get the brightness of the star in units that are independent of a particular CCD.

Calibration allows you to deal both with changing observing conditions, different CCDs, telescopes, filters, etc. simultaneously.
The process of calibration involves an image of the star whose magnitude you want to measure (call this the target star) and another image of a star with known (already calibrated) magnitude (we'call this the standard star).
The standard star must be in the same region of the sky as the target star, so that it will experience the same sky (or seeing) conditions as the target star at any given time.
The images of the two stars also should be taken within minutes of each other.
Because images are always taken with a specific filter (e.g., U, B, or V; see Kaufmann section 19-4 and figure 19-8).
It also helps to have a star within the optimal brightness for the telescope (not too bright and not too dim) to assure a good image.
Most importantly, the standard star is a star with known (and constant !) flux (or apparent brightness).

With identical observing conditions for the target and standard stars, the ratio of their counts is equal to the ratio of their fluxes. Let

C_t = counts measured for the target star; C_s = counts measured for the standard star

f_t = flux (your text also calls this apparent brightness in section 19-2 and uses 'b') of the target star;
f_s = flux (apparent brightness) of the standard star

Then C_t/C_s = f_t/f_s or equivalently f_t = f_s C_t/C_s

a) pttarg.fts (same directory as previous images) contains a target star whose apparent magnitude we would like to measure.
ptstan.fts contains a standard star (the brightest star in the image) that has an apparent magnitude (with a Blue filter) of m_B = 6.9 .

Measure the counts for both the target star and the standard star using Auto-Aperture.

b) Determine the apparent magnitude of the target star in the Blue using the appropriate magnitude formulas. Remember the magnitude rules we learned in section 19(2-3).

[Oh, and by the way, the two stars whose flux you measured in Part 4 above?  they were the same star, just observed under different conditions.]