Measuring comets with the Afrho quantity
Wed, 2004/03/24 - 01:00 — admin- revised feb 2011
Afρ, is a quantity introduced by Michael A'Hearn et al. in 1984 (AJ 89, 579, 1984) with the aim of comparing measurements concerning the dust continuum under different observing conditions, times and instruments.
The Afρ is simply the product between the albedo "A" (the reflectivity of grains), the filling factor "f" and "ρ" (the Greek letter "rho") that is the radius of the coma (usually in km) under investigation.
The filling factor “f”, is a quantity related to the optical density of the coma, and strictly speaking, is how much the total cross section of grains fills the field of view. It is the ratio between the total area filled by dust in the considered field of view and the area of the field of view itself.
Assuming a constant dust reflectivity, the “Af” product value (the power between the albedo and the filling factor) gets its maximum close to the nucleus and then fades toward the outer edges.
In the inner coma the fading is usually proportional to 1/ ρ , were ρ is the distance from the nucleus. This is what expected for the optical density of a theoretic isotropic coma made only of dust and where the grains have a constant expansion speed (the so called "stationary coma model"). Of course the "stationary model" is often a very rough approximation of a real coma, but it represents an useful basic reference model. In handling and analysing Afρ quantity data one should always consider that it refers to the average brightness of the coma. Highly asymmetric comae and object in non stationary state. Outbursts, splitting of the nuclues or its fragmentation and other temporary events that change the activity status of the comet need to be interpreted with special care.
A relevant property of the Afρ quantity (and it was the reason it was adopted) is just to have a constant (or nearly constant) value over a wide range of distances from the nucleus (ρ). This means it is not affected (or very little affected) by instrumental effetcs, different image-scale and measuring window sizes used in photometry. This was very useful in the past in the analysis of narrowband photoelectric photometry data, but also today in measuring CCD images with aperture photometry techniques.
The Afρ is related to related to the total cross section of the grains and is an useful way to investigate on dust. It is often used as a proxy of dust production rate.
From direct spacecraft exploration of comets (since 1985 with Giotto spacecraft on 1P/Halley up to recent years spacecraft missions) we know that the albedo of the cometary dust is very small and on an average only few percent of the received sunlight is reflected.
So we can usually expect quite low cometary/solar flux ratios. Furthermore cometary comae are not dense and we can see that in nearly all cases the light of the stars is not dimmed if observed through them (the dimming is well below the sensitivity limit level even with the more sophisticated equipments). Some exceptions are possible but a really extraordinary comet with a very high dust production rate is required (e.g. Comet 1995 O1 Hale-Bopp).
Comparing the results among different objects it is quite impressive to see that most relatively faint periodic comets, currently observed from amateur astronomers, display Afρ values of few tenths of centimeters, while many comets of average brightness fall around some meters values. A really great difference from the Hale-Bopp comet that indicatively approached to an Afρ quantity around 10 km (1,000,000 cm) at the epoch of its perihelion passage! Another recent impressive case was the Sun-grazer comet 1996 P1 (McNaught) that displayed an even higher Afρ value at perihelion. Difference among comets are immediately evident and quantified at a first crude analysis.
It appears that these results are really amazing and allow us to understand the basic meaning of the Afρ quantity. It can tell us much more about comets, but , of course, with a bit more complex analysis and taking into account other variables and parameters.
More advanced results are reported in the SCIENCE section.