Updated 2014 January 14
The Multiaperture Method, developed years ago by members of Cometas_Obs,
helped to reduce the large scatter in CCD measurements of comet magnitudes and has allowed the setting
up of a database of high
consistency photometric observations. However it
suffers a strong dependency on the Sun, Earth, comet geometry, and the need to
manipulate the data it provides to get as close as possible to the physical
reality of the behavior of comets.
NUCLEAR ACTIVITY OF COMETS
The diffuse nature of comets has required visual observers to use a number of techniques involving defocusing with the aim of matching the apparent sizes of comparison stars and the comet itself. This enables accurate comparisons between stars and comets to be made and an accurate and consistent measure of the total magnitude of the comet to be calculated. In addition to the estimated magnitude the ‘degree of condensation’ may also be ascertained. This is a number describing the appearance of the coma and varies between 0 (completely diffuse) and 9 (star-like). The advent of CCD cameras, and their popularity with comet observers, has deepened the study of the structure of the coma by using concentric apertures centred on the point of maximum brightness (centroid in Astrometrica terminology – RD). The activity of comets and their visible structure relates to:
- the sublimation of ice from the surface of the nucleus,
- the release of other materials (gas and dust – RD) and their future development in the comet’s environment dominated by the influence of the Sun.
Thus it seems reasonable that, if the interest of our work focuses on the analysis of changes in this activity, we must study the vicinity of the nucleus through the use of reasonably small apertures (within the capabilities of the instruments of observation). If, for example, when monitoring an outburst we may see that the increase in brightness, including the total brightness, can be measured with both small and large apertures but the subsequent expansion of the material affects only small apertures while measurements with large apertures show an unchanged total magnitude.
Outburst of 17P-Holmes in October 2007.
The graph shows how, after the initial outburst, the 10"x10" aperture measurments show a reduction in brightness indicating a loss of material near the nucleus, while the visual magnitude total shows that total ejecta remained little changed (Cometas_Obs).
In May 2001 a group of observers set up the Cometas email list. As a result the first measurements that we performed showed a dispersion of the order of one or two magnitudes. After weeks of debate and testing, the initial findings from observations that we had accumulated pointed to the problem being the diffuse nature of these objects. No one knew exactly what the correct aperture should be and therefore each observer measured different portions of the coma. The first step on the path towards normalization was the decision that all observers apply the same aperture, which was established as arbitrarily as a square box of 10 " side (we now use circular apertures of an equivalent diameter to maintain consistency with these first steps), thus the dispersion of measurements has dramatically reduced to approximately 1/10th of a magnitude.
What is the size of the coma of a comet? In these images we see the
difficulty of determining and thus establishing the appropriate photometric
aperture to measure the total magnitude. Four different
views are shown to the same scale using a different grayscale false color palette. (credit Cometas_Obs).
Further improvements of the method, suggested by Dr.
Variation of aperture with distance
The disadvantage of using of fixed apertures, measured in arcsec, is that the actual area covered by each aperture depends on the distance to the comet. A 10 arc sec diameter aperture with the comet located at a distance of 1 AU subtends a circle of diameter 7272 km at the distance of the comet, 14 544 km if the comet is at 2 AUs and so on.
Real change in diameter covered by an aperture of 10 "x10"
projected at different distances.
We see many variations in size and distance of comets and thus comparisons of magnitudes using a fixed aperture have no physical meaning and cannot allow consistent studies of the evolution of a comet or compare the activity of one comet with others. The solution to this problem would be to use a variable aperture depending on the distance of each comet so that, projected to the distance of the comet, the aperture would be of a constant diameter. However this system has a drawback in that apertures for distant or near comets would be impractical. In the first case the required aperture would be reduced to just a few pixels and in the second the aperture would be very large and almost certainly include background stars that would affect the measurement of the magnitude of the comet.
However, it is possible to calculate the magnitude using the Multiaperture system. In his excellent work: ‘Cometary Photometry: Infinite Aperture Magnitudes’, Professor Ignacio Ferrin (Universidad de Los Andes, Venezuela) suggests a method of adjusting the magnitude ‘growth curve’ in order to calculate the total magnitude of the comet. The ‘growth function’, determined from the Multiaperture method calculates not only the total magnitudel, but also that which corresponds to any discrete photometric aperture. Thus, it is immediately possible to calculate the aperture for any fixed diameter at the distance of the comet and calculate its magnitude.
Example of setting Multiapertura an observation of Comet C/2007 N3 held on
Brightness variation with distance
The second effect that modifies any photometric measurement is purely geometric. The energy reaching the observer from a light source is inversely proportional to the square of distance, and in the case of measures of reflected light, the light coming from the sun to object of interest varies similarly. To get a curve that shows the actual variations in brightness or allow comparisons between comets it is necessary to eliminate this effect by considering the observed brightness of the comet at a fixed distance from the Sun i.e. ‘heliocentric magnitude’. This is the magnitude of a comet observed from, and located at 1 AU from, the sun.
Note; Heliocentric magnitude is defined as the magnitude of the comet when at 1 AU from both the Sun and the Earth and at zero phase angle – RD. How to calculate heliocentric magnitude ? (reduced magnitude in asteroid terms)
The proposed system of Multiaperture photometry which would more closely give an indication of the real physical behavior of cometary nuclei and which could be called ‘Heliocentric magnitude using a constant diameter aperture’ would be:
- Maintaining the current system of Multiaperture measures, valid for consistency and for its simplicity of implementation and for its usefulness as a reference when preparing an observation plan.
- Establishment of a fixed diameter centered on the nucleus of comets (eg, 10,000, 25,000 to 50,000 km.) in order to more clearly show its nuclear behavior. Setting the ‘growth function’ to calculate the magnitude for these apertures.
- Correction of the apparent brightness variation due to the distances between the sun and the comet and comet and
the observer to calculate the heliocentric magnitude.
Example of application: comet C/2007 N3 Lulin
Comet C/2007 N3
Comet C/2007 N3 Lulin on
Comparing both types of measurements we found some interesting details that allow us to verify how to improve the corrections to the data provided by the Multiaperture to better reflect the actual behavior of the comet.
The measurements using a 10x10 arcsec aperture show a dramatic increase from magnitude 18 to magnitude 10 equivalent to a 1500x increase in brightness. However the heliocentric magnitude using a 25K km aperture at the distance of the comet shows an increase in magnitude from 14.6 to 10.0 – a much smaller 70x increase in brightness.
the mag. 11.4 to 10. In applying the corrections we find that this increase in brightness is only apparent and is caused by the comet’s approach to Earth. The heliocentric magnitude using a 25K km aperture at the distance of the comet shows a slight real decline consistent with the gradual increasing distance of the comet from the Sun
To Professor Ignacio Ferrin, Miguel Ángel Vallejo, Esteban Reina, Josep Maria Aymamí and Ramon Naves for their help in editing and proofreading this work.
- Ignacio Ferrin, Cometary Photometry: Infinite Aperture Magnitudes: http://webdelprofesor.ula.ve/ciencias/ferrin/teaching/curveofgrowth.pdf
- Cometas_Obs Web: http://astrosurf.com/cometas-obs
Translation from Spanish to English by Google with a
little help from