What is a nuclear magnitude?

A simple answer to this question could be: It is the magnitude of a comet nucleus. But then we are faced with two obvious difficulties: How do we estimate a nuclear magnitude?; and can the comet nucleus actually be observed?. For practical purposes, the nuclear magnitude may be defined as the rather sharp condensation of light in the inner coma, and this concept has been adopted by many observers, mainly amateur astronomers. They estimate the nuclear magnitude by measuring the total flux inside a small disc centered on the brightest peak. Unfortunately, such measurements have little physical meaning. If one wants to get some hint on the actual nucleus size, one should strive, as far as possible, to measuring solely the light reflected by the solid nucleus. In such an ideal case the brightness would indeed be proportional to the observed geometric cross-section of the nucleus. Given the smallness of the nucleus and the distance at which it is generally observed, it would necessarily appear as a star-like source. Thus a true and straightforward nuclear magnitude can only be estimated if the comet has a stellar appearance; i.e., no trace of coma should be detected.

In other words, the brightness of an active comet is the sum of the coma and the nucleus brightness. This total, i.e., coma plus nucleus, intensity on the focal plane can be represented as a 3-D surface. Assuming an axisymmetric surface brightness of the coma and a gaussian-like Point Spread Function (PSF), each brightness profile would have a bell shape as shown in Fig. 1. Unless the nuclear brightness is much higher than that of the coma, the flux measured in a small disc centered on the brightest peak would have a non-negligible contribution from the coma. Thus, such a nuclear magnitude would not have a straightforward physical interpretation but only give an ill-defined upper limit to the true nuclear brightness. Accordingly, we adopt the definition that: A nuclear magnitude corresponds to the total flux coming from the solid nucleus of the comet. We should, however, bear in mind that its determination is a very difficult task.
 

Figure: Schematic representation of the coma and nucleus profiles separately (left-hand side); and the addition of the two profiles (right-hand side) for a: a coma-dominated profile; and b nucleus-dominated profile.

The photometric cross-section S of a nucleus of radius R_N is given by
 
 

$$\log(p_v S) = 16.85 + 0.4 \times [m_{\odot} - H_N]$$ (1)

where p_v is the geometric albedo in the visual, $S = \pi R_N^2$is expressed in km², $H_N \equiv V(1,1,0)$ is the absolute (visual) nuclear magnitude of the comet (the apparent magnitude at 1 AU from the Sun and the Earth and zero phase angle) and $m_{\odot} = - 26.77$ the apparent (visual) magnitude of the Sun. Almost all periodic comets so far studied have very low geometric albedos ($p_v \approx 0.02 - 0.05$) (Hartmann et al. [1987], Jewitt [1996], Weissman et al. [1989]).

2000-03-07