Aperture Photometry


Astronomical Laboratory ASTR:4850, Fall 2015
 by Philip Kaaret

Reading


Introduction

In this lab, we will do photometry on images that you obtained using the Van Allen Observatory.  We will be looking at a pair of images of the open star cluster M39 obtained in the B-band.  You should have one image with the cluster centered in the telescope view of view and another image that is offset by 5 arcminutes in declination.  We will also use frames that you obtained for bias and dark current and a flat field obtained by the magnificent Dominic Ludovici. Ten flat field images were taken in the B-band filter and processed to produce this B-band master flat.

CCD Data Reduction

To accurately measure the flux of light from a star, we need to correct for imperfections in the response of the CCD and also in the response of the telescope.  In the lab on "Readout Noise and Dark Current", you already learned about pedestals, bias, and dark current in CCDs.  It is essential to subtract a bias or dark frame from each astronomical exposure.  The CCD camera on the VAO is cooled and has very low dark current, as you should have found in the previous lab.  The images that you will be using today were taken with short, 5-10 second, exposures.  The dark current is negligible for these short exposures, so in the equation below it is OK to use bias or dark frames for subtraction.

One usually take several bias (or dark frames) and combines them into a single master bias image.  This 'master bias' image was made by combining 10 bias images via median filter, i.e. the value of each pixel is the median of the values for that pixel in the 10 images.  What advantages are there to using a master bias image over a single bias image?  Explain in your lab notebook.

The quantum efficiency of CCDs can vary from pixel to pixel.  Also, every optical system suffers from variations in its response across the field of view and localized variations due to imperfections such as dust.  To correct for these variations, one attempts to uniformly illuminate the telescope field of view and then takes a 'flat field' frame.  This frame is then used to correct for the response across the field of view.  In practice, one divides the value in the each pixel in astronomical image by the value for the corresponding pixel in the flat field.  Think about this for a moment and convince yourself that it is the correct way to apply the flat field calibration - if one region of the camera has a higher quantum efficiency, what will that mean about the number of counts in that region in the astronomical image and in the flat field?  Explain in your lab notebook.

Usually, one takes several flats and then calculates the median in each pixel.  Why is use of the median preferred to use of the mean in calculating flats?  Explain in your lab notebook.

The process of correcting for instrumental imperfections is called 'data reduction'.  Essentially, one is attempting to produce an image that most accurately presents the true spatial distribution of flux on the sky (in the selected waveband).  Represented as an equation, the

Reduced image = (Raw astronomical image - Dark frame)/(Flat field frame)

To keep the units of the reduced image in something close to ADUs, one usually normalizes the flat field frame before doing the division.  Typically one divides the flat field frame by its median so that the flat field correction for pixels with near the median response is near 1.

Write a python program to calculate reduced images and show them on the screen.  Normalize the flat field to its median before applying the flat field correction.  You may want to draw on the various python programs that you have previously used in this class when writing your code.

Stellar Magnitudes

We should review what we learned about stellar magnitudes in General Astronomy. Let F be the flux of radiation from a star (Watts/m2). Given fluxes F1 and F2 from two stars, the difference in their magnitudes is then

m1 - m2 = 2.5 log(F2 / F1)

Attributing a single number to the magnitude of a star is done by essentially expressing its magnitude difference relative to Vega, which by convention has an apparent magnitude of 0. In analyzing CCD data, we use the fact that the number of CCD counts (total charge, corrected for dark current and flat fielding) due to a star is proportional to the flux F. This about that last sentence for a while, if it is not clear to you, discuss within your team and with the instructor.

Finding Magnitudes

Astronomers usually measure magnitudes relative to one or more reference stars. A great thing about the sky is that it contains many stars. Thus, even when pointing at a arbitrary field on the sky, there is often a cataloged star with known magnitude in the field. If there are no cataloged stars in an image, then one needs to take a calibration image with the same telescope under similar observing (sky brightness, seeing, etc.) and instrumental (exposure time, CCD temperature).

The images for this lab are of M39 and contain a number of bright stars.  The brightest star, located near the center of the field of view, is HD 205210 and is saturated, so not suitable for calibration.  Instead, we will use BD +47 3462, located in the green circle in the image below, as the calibration star.  It has a B-magnitude of 9.12 and V-magnitude of 9.02.

The star of interest for this lab is the one inside the red circle on the image below.  Load the two astronomical images into ds9 and find the coordinates each of these two stars in each of the two images.  Note that you want to find the coordinates in physical units for use in your python programs below.

M39


Now we will do aperture photometry, as we did in the "Signal versus noise" lab.  However, you will do the photometry in python rather than ds9 (or MaximDL). 

We will do a few steps to first understand extraction of counts and the signal to noise ratio, so do these first steps on a bias subtracted image, but do not do the flat field correction.

First, we need to find the coordinates of the star.  Write a python function that is given a pair of coordinates (x,y) and a box size (s) and finds the centroid of the source located inside the box using the equations in section 5.1.1 of the textbook.  The centroid should be returned as two floating point variables.



Now, you need to calculate the net number of counts for the calibration star and the target star, after doing a sky background subtraction.  The key steps are:
Write your python code so that the routine to calculate the net counts for a source is a function to which you supply the image and the parameters of the circle and the annulus.  Note that you might want to write a routine that calculates the counts in a circle of a given radius as a first step (such a routine will also be useful below).

To see how the number of counts depends on the extraction radius (the radius of the circle), make a plot similar to figure 5.6 in the textbook, specifically a plot of net counts versus radius.  Choose an inner radius for the sky background annulus that is larger than your largest extraction radius.  Do this for both the calibration star and the target star.

Now calculate the signal to noise.  Use the equation from section 4.4 of the text book (or from the Signal to Noise lab).  We concluded above that the dark current is negligible in these images, so ignore the dark current term.  Write a python program to make a plot of the signal to noise ratio versus extraction radius.

Now we are finally ready to do photometry.  You should do photometry on the reduced image that you calculated above, so you can either add steps for photometry to that program, or modify that program to write out the image (preferably in FITS format) and write a second program to read in the image and do the photometry.

When you have the net counts for the calibration star and the target, you should then calculate the ratio of fluxes of the two objects.  Finally, calculate the magnitude of the target star using the known magnitude of the calibration star.  Repeat this procedure for both images.  Compare the values and estimate the accuracy of your photometry.  Include your python programs with your write up.