Black holes

Photometry with Salsa J (based on the activity from Faulkes Telescope Education Program - Daniel Duggan & Sarah

Roberts).

Photometry is the measurement of the intensity or brightness in a particular waveband (e.g. the optical) of an astronomical object, such as a star or galaxy by adding up all of the light from the object. For example, a star looks like a point of light when you look at it just with your eyes but the Earth’s atmosphere smears it out into something that looks like a round blob when you use a telescope to look at it. In order to measure the total light coming from the star, we must add up all of the light from the smeared out star.

Photometry is used to generate light curves of objects such as variable stars and supernovae, where we are interested in variability of light output by the system over time.

It can also be used to discover exoplanets or to estimate the mass of a black hole candidate, by measuring fluctuations in the intensity of a star’s light over time.

These instructions explain how photometry can be carried out on groups, or clusters of stars, from images taken with different filters, in order to plot a colour magnitude diagram. An explanation on magnitudes can be found at the end of this document in Appendix 1.

Instructions Before we can start the photometry, we have to work out our aperture radius - this defines the radius of the circle that is used to count the pixel values in the image. The radius of the circle is very important - if the radius is too small, it will not count all the light coming from the star and if it is too big, it may count too much background sky or other stars in the image. Therefore you may not get accurate measurements.

SalsaJ automatically sets the radius as the Full Width Half Maximum (FWHM) of the stars in the image. The FWHM is used to describe the width of an object in the image. Stars in astronomical images have a specific profile when plotted as a graph of pixel values and that profile should be the same for each star in the image. The FWHM is a measure of the telescope’s optics, the image recording CCD and the atmosphere through which the light passes.

FWHM When determining the brightness of a star, the software sums the brightness over all pixels receiving light from that star. To do this the effective width of the star must be determined for each image before measuring the brightness of the stars on that image.

One way to estimate the FWHM is to look at a slice across the star. The slice will probably look something like the diagram on the next page (without the arrows and label). The base of the slice is at the value for the background sky. The top of the peak represents the counts measured in the brightest pixel along the slice within the star. The difference between the top of the peak and the base is the height of the peak. The FWHM is the number of pixels across the peak at a point halfway up from the base.

FWHM is displayed graphically like this:

In order to do photometry, we recommend you work out your own optimum star radius in order to get more accurate results.

To do this you must conduct a simple experiment, collect data and plot a graph - using Microsoft Excel (or another spreadsheet package that can plot graphs) makes this exercise much easier and quicker. The idea is to test several different aperture radii and compare the intensity values you get for each radius by plotting a graph of radius against intensity.

To do this, go back to SalsaJ, then to Analyse>Photometry Settings. Select force Star Radius and choose the value 6.

Next, go to Analyse>Photometry and another empty window will then appear entitled ‘Photometry’.

Using the mouse, click on a star in your image. The intensity of the object is calculated by adding up all the pixel values within the radius of the aperture.

We can clearly see that the chosen radius is too small. Let’s increase it a bit to 8. Click on the star again and a new measurement will appear. Still the radius is too small. Increase the value to 10 and continue until you reach a radius of 40 You should have something like this:

In Excel (or other package) create two columns for Radius and Intensity then, add radius and the intensity value from SalsaJ. (You can save the values directly from the Photometry window in file.xls format and convert it to Excel.

You should have a set of results that looks like this:

Index 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Image ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts ptstar2.fts

X

Y 283 283 283 283 283 283 283 283 283 283 283 283 283 283 283 283 283 283

211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211 211

Star's Star's Sky's Sky's intensity radius intensity radius 34841 6 477 9 75460 8 300 12 117922 10 187 15 155160 12 123 18 187485 14 83 21 211802 16 62 24 229401 18 50 27 242610 20 43 30 252117 22 38 33 258799 24 36 36 264426 26 34 39 268427 28 33 42 271693 30 32 45 276987 35 31 52 279995 40 31 60 283728 50 31 75 284816 55 30 82 286119 60 30 90

We are interested in the variation of intensity with increasing aperture radius. When you plot a graph of this data, you should get something that looks like this:

Counts

Aperture Radius

You can see the rapid rise of intensity as the radius of the aperture increases. This is because more of the star is included in the increasing radii of the apertures. The graph begins to flatten out when we have all of the star within the aperture, but keeps rising gradually as more and more of the background sky is included.

From this graph, we can see that the best radius to use is about 10 - this is around the point where the star’s intensity stops increasing so rapidly. There is however, not just one correct answer and a value of 12 or 14 could also be considered appropriate.

Once you have chosen the best aperture radius, this can be set for the remainder of your photometry analysis on this image. It is advisable to carry out this exercise every time you come to work with a new set of images as the FWHM of objects change due to the seeing conditions at the time of observation so new aperture radii will need to be calculated for new images.

However, if you are carrying out photometry on the star, but in two different wavelengths (such as B and V), then you should use the same radius for both images to ensure that you are comparing ‘like with like’.

Measuring the Counts of a Star Let’s continue using the same images as before PTstar1 PTstar2. Now with the established value for the aperture of 18 we will measure the brightness in both images What is the brightness of PTstar1 in Counts?

What is the brightness of PTstar2 in Counts?

You will find out that the values greatly change from one image to the other. These images are actually of the same star and the star itself has not changed. However, they were taken on two different nights and the seeing certainly varied a lot. In these images we can’t compare the brightness of the star with other stars in the field. So in the next activity we will choose a better target.

When the field has more stars it is easy to make a mistake. If you are not sure you selected the correct star you can delete a line in the photometry measurements window by selecting the line, then chosing Edit in the Menu and then Cut.

Comparing Two Images of the Same Region Images for this activity are listed below. In each image the target star is on the left and the reference star is on the right. This images containing a Cepheid Variable, a star with a very well know variability and very often used and to help evaluate distances to nearby galaxies.

For this part of the activity we will use the following images: PTnight1, PTnight2, PTnight3, and PTnight4. You may open and work on these images simultaneously or one at a time.

PTnight1 - https://www.dropbox.com/s/gkgyaya8zuqn5ez/ptnight1.fts PTnight2 - https://www.dropbox.com/s/2hcpbvtrw90p0gt/ptnight2.fts PTnight3 - https://www.dropbox.com/s/xnttgf4h98o74dp/ptnight3.fts PTnight4 - https://www.dropbox.com/s/wk8m53gno9dub0k/ptnight4.fts

Use the photometry tool to measure the brightness of the target star and the reference star

Reference star Variable star