Measuring comet magnitudes on CCD images

 

Updated 2017 January 14

 

Contents

 

Why comets?

 

Why am I writing about comets you may well ask so I will start with a commercial (the editor permitting). The year before last  I decided to write a book ‘Asteroids and Dwarf Planets and how to observe them’. The draft has been sent to Springer and, all being well, will be published later this year. Having put most of what I (and quite a few other people) know about asteroids into the book I decided it was time for a change. As celestial objects go it wasn’t much of a change of direction as both asteroids and comets now come under the IAU banner of Small Solar System Bodies.

 

Compared with asteroids there aren’t that many comets visible at any one time – those that can be observed visually or imaged with a CCD camera and modest amateur equipment that is. Mainly I have selected targets from the list included in the article ‘Comet prospects for 2010’ by the Director of the BAA Comet Section, Jonathan Shanklin, published in the 2009 December issue of the Journal of the British Astronomical Association. With two exceptions I have used the two Sierra Stars Observatory Network robotic telescopes. My own telescope was brought into play to image comets 169P/NEAT and 157P/Triton. After some months in hibernation I was quite amazed that it worked so well with one exception! – the Skysensor handset resets intermittently and thus the current orientation of the telescope is lost. Possibilities are; handset, power cable, power supply or mains supply with a faulty power cable being favourite – ‘investigation is ongoing’ as they say. Apologies to the neighbours and semi-resident fox for the bad language.

 

Photometric methods

 

As some of you will no doubt be aware astrometry and photometry of asteroids is a fairly simple matter thanks to Herbert Raab’s Astrometrica software. Knowing that comet photometry might not be quite so simple I sought help from the Comet Section’s Assistant Director (CCD), Nick James. His response was ‘It's quite a thorny subject, certainly not as simple as photometry of asteroids!’ He also emailed me a copy of the  report of the Section’s workshop held in Cambridge in 2005 at which two different methods were presented by Giovanni Sostero (the Italian method) and Mark Kidger (the Spanish method).

 

In brief, the Italian method, developed by the Cometary Archive For Amateur Astronomers Group (CARA), uses narrowband filters centred on 647 or 650 nm (unless the comet is fainter than mag 11.5 when a broadband Bessel or Cousins R or I filter is recommended). The size of the aperture used to determine the magnitude of the comet is defined as 100,000 km at the distance of the asteroid. For example on March 14 2010 comet 30P/Reinmuth was 241,500,000 km from the Earth and thus the angle subtended by the aforementioned aperture is 85 arc secs (see Figure 3 for comparison with the apertures used in the Spanish method).

 

The Spanish method

 

Castanets are not a requirement! This method was developed after analysis of the MPC comet database by one of Mark Kidger’s students showed that the photometric data was of little use as the methods used for imaging and data reduction were inconsistent. The resultant measures had a scatter equal to or greater then 4 magnitudes – photometry received by Mark from Spanish amateurs was similarly inconsistent. The quite simple method developed by the Spanish Group requires the use of Astrometrica and their own FoCAs software. This method differs from that developed by the CARA group in that unfiltered  images are used and the comet magnitude is defined in terms of a number of fixed apertures – 10×10 to 60×60 arc secs in steps of 10 arc secs hence the ‘multibox’ terminology. Having obtained and calibrated ones unfiltered images the procedure is as follows;

 

Using Astrometrica one measures the images first with UCAC 2 or USNO-B1.0 and then with USNO-A2.0 or CMC-14 in that order.  FoCAs will use the astrometry from the first two catalogues and photometry from the second pair. The end result of a FoCAs run is shown in Figure 1.

 

FoCAs example

 

Figure 1. Screen shot showing FoCAs analysis of images of comet 94P/Russell obtained with the SSON Rigel robotic telescope on 2010 February 24

 

The positions and magnitudes are listed and shown in graphical format – astrometry top right and photometry bottom right. Any outliers are immediately obvious and, should you not wish to use all the results, specific ones can be selected and are highlighted in the text and the two graphs as shown in Figure 1. The multibox report is shown at the bottom of Figure 1 and, in more detail, in Figure 2. The magnitude values for each aperture are listed with the 10×10 value being an average of the values listed at the top left of Figure 1. The mutlibox report also includes; errors (+/-), Signal to Noise Ratio (SNR), the number of images (N), Sky brightness measured over 1 square arc sec (SB), Full Width Half Maximum (FWHM), MPC code (COD)) and catalogue used for photometry (CAT).

 

Example multibox report

 

Figure 2. FoCAs Multibox report

 

At the time the images were obtained comet 94P/Russell was 191,250,000 km from the Earth and thus a 10×10 arc sec aperture is equivalent to 9270 km square box at that distance.  The equivalent dimensions for the other apertures are; 18,500, 27,800, 37,100, 46,400 and 55,600 km respectively – Figure 3.

 

94P apertures 

 

Figure 3. The various multibox apertures used by FoCAs.

 

The resulting astrometry and photometry, in the standard Minor Planet Center format, and the multibox report can be sent to up to four recipients direct from FoCAs.

 

AFRho

 

The magnitudes are converted to a parameter called AFRho. This is a number originally proposed by Mike Ahern and others in 1984  with the aim of comparing measurements concerning the dust produced under different observing conditions, times and instruments. It groups three unknowns: A is the dust grain albedo, F is the filling factor (i.e. how much of the line of sight is filled up with dust grains) and rho (ρ) is the aperture size (radius) at the distance of the comet. Effectively AFRho is the equivalent column of dust in our line of sight. It is a useful parameter for describing the comet and it can be translated to the dust production rate.

 

Close in to the Sun active comets show very strong Swan band emissions (named after the Scottish physicist William Swan), e.g. C2, C3, CN and CO, and the use of unfiltered photometry in such instances can lead to AFRho values that are too large. This problem could be overcome by imaging bright comets using an R filter but for the vast majority of comets observed by amateurs Swan emission is not a problem since it is not strong enough to affect photometry obtained from unfiltered images.

 

That sums up my total knowledge of AFRho (previously I had thought it was a hair style favoured at one time by footballers and pop stars) but, when I understand it better, I  will write a follow-up article including an example calculation.

 

Roger Dymock

 

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