25 Photometric Techniques and Photometric Types

Mohd Altaf Sofi

Learning Outcomes

After studying this module, you shall be able to

• Learn a few basic processes which show how photometry as an observational tool in astronomy helps in establishing some of the important characteristics regarding the variable stars.
• Know that there are different types of  photometric devices each having a unique application  of observational value.
• Learn the concept involved in the working of some important photometric devices.
• Know that (i) the photometric techniques such as differential photometry lead to the conclusion that variable star formation in the universe is a general phenomenon, (ii) all the variable stars undergo luminosity variation, (iii) the nature of different types of variable stars is best understood by latest photometric techniques.

1.  INTRODUCTION 

Star light as we know comes to us from astronomically large distances and enters the earth’s atmosphere before being captured by our telescopes for further analysis. In its crude form the atmospheric disturbances introduce technical difficulties in the proper analysis of the spectra received. It is therefore recommended to try to find the best way for observing the pure spectrum of the stars. Since variable stars can only be distinguished by perceptible change in the luminosity output the atmospheric disturbances obscure the results and the analysis is seriously affected. Our task is to remove the signature of the atmosphere and instrument and try to recover as much information as possible from what entered the earth’s atmosphere.

2. PHOTOMETRY AS AN OBSERVATIONAL TOOL IN ASTRONOMY 

2.1  Photometry of Variable Stars:

Variable stars can be distinguished by the amount of light received from them. The intensities of light received from two sources constituting a pair of variable stars (say) follows inverse square law. Let ?be the intensity of illumination of a surface due to a light source and let r be the distance between the source and the surface. Assuming ?to be the luminous intensity or illuminating power of the  source, the relationship between ?and ?is given by

2.3  Some Important Photometric Results:

Telescopes having range 0.6 to 1m and equipped with photometers using photomultiplier tubes are used to achieve very good observational results. The transparency variations need to be determined drifting apart of the channels. This can introduce severe errors. The present limit to the photometric precision is still just slightly under 1 milli-magnitude (mmag) with good photoelectric photometers under excellent weather conditions. In fact, considerable observational care has to be taken in reducing the observational errors sufficiently in order to obtain the `old’ limit near 1 mmag precision per single measurement.

The figure(Fig.09.6) given below is a light curve of the variable star FG Vir and two comparisons taken with the 3-star technique. The solid line is a calculated fit of 24 frequencies detected after the 1995 FG Vir global observing campaign.

Three-Star Photometry is yet another observing technique for understanding the true nature of the variable stars. In this technique intensities of two given stars under the appropriate sky background are measured successively with the same photomultiplier tube (V -C1 -C2 -Sky -V – …). In case of a large sky brightness gradient (moon or dusk/dawn) the intensity has to be measured for each star separately. An integration time of 40 seconds per star has turned out to be a good compromise between high precision and short cycle time. In this case the cycle time is about 6 minutes. The advantage of this observing technique lies in its long term stability. The sensitivity drift of the photometer and the transparency variations of the atmosphere can be corrected for. Pulsation periods of a few hours can be determined with high precision. For shorter periods another observing technique known as Charged Coupled Device or CCD-Photometry has to be applied CCDs are sensors used in digital cameras and video cameras to record still and moving images. They capture light and convert it to digital data that is recorded for future use. Hence, a CCD is often considered the digital version of film. The presence of many comparison stars on the same frame, and the ability to observe through non-photometric (so-called spectroscopic) weather conditions make CCD detectors invaluable. To achieve milli magnitude precision a good guiding-system is needed. Bias frames and flat fields (10 – 20) have to be taken each night before and after the run and linearity checks have to be performed.

3.  DIFFERENTIAL PHOTOMETRY 

3.1  Theory of Differential Photometry:

We start our observation of variable stars in the open sky by estimating the difference in magnitude between a given pair of variable stars that in turn depends upon the color difference and the respective airmasses. This is called  Bouguer’s Law. In the case of B and V measurements taken at two different air masses

The first-order term in equation (17) is the proper atmospheric extinction while the second-order term takes into account the dependence on object color due to the width of the filter band-pass. The first term varies with time but the second term usually remains constant for a given instrumental setup. To determine extinction coefficients accurately we observe a set of standard stars spanning a wide range of colors for several values of the airmass, both before and after meridian passage. A faster, separate determination of the primary and secondary extinction coefficients is possible by observing pairs of stars having the same known color at low and high airmass (ascending, descending) so the second order term vanishes. For pairs of stars of having different known color and located in the same field of view, at different airmasses the first-order term can be neglected. If extinction is unknown we measure pairs of stars under a given program and the standard stars at the same airmass. For unknown and variable extinction, the standard stars are picked up as close as possible in the sky to the program stars. A range of extinctions obtained alternately helps in interpolating any extinction changes that may take place during the course of the extinction measurements.

4.  SUMMARY

The main aim of this lecture has been to understand some of the basic photometric techniques for carrying out the necessary observations regarding the existence of variable stars in the visible universe. We have attempted to critically analyse some of the important photometric results received from variable sources. The spectral characteristics of variable stars have been given proper treatment by introducing the theory of differential photometry and by evaluating some important parameters such as extinction parameter.

Suggested Reading

1. Introduction to Astronomical Photometry by Edwin Budding, Osman Demircan, CUP, Cambridge.
2. Photoelectric Photometers and Amplifiersby H. L Johnson, University of Chicago Press, Chicago.
3. Astronomical Photometry by E. F. Milone , Springer VerlagInternational Publishers.