F coma
F ⨀
¼
2
Δ
2 r 2
h
Z b max
0
ρ F b db
ð4:62Þ
and we can substitute this back into Eq. (4.56). This gives
Af ¼
8
b
2
max
Z b max
0
ρ F b db
ð4:63Þ
Using ρ now for b max and substituting using Eq. (4.60), we see that
Af ρ ¼ 8A
ð4:64Þ
In other words, averaging the reflectance on a circle about the nucleus and
multiplying that by impact parameter of that circle gives a very simple relation to
Afρ. (A has been occasionally referred to as the “azimuthal average” of the reflectance although this is actually a misnomer.)
This approach was taken by Gerig et al. (2018) in the construction of Fig. 4.18
which shows Afρ in the innermost coma of 67P derived from Rosetta/OSIRIS data.
This gives one of the most complete descriptions of the evolution of Afρ for any
comet. It should be noted that the measurements have been normalised to a phase
Fig. 4.18 Afρ values calculated from the constant value derived from fits to the azimuthal average
with impact parameter, b. A phase angle normalization to α ¼ 90
has been applied to the data
shown in this plot. The green data points mark Afρ values calculated for single images and the red
data points indicate averaged Afρ values over one comet day. Variation with heliocentric distance is
clearly evident as is the lag in the maximum with respect to perihelion. (Reprinted from Gerig et al.
2018, with permission from Elsevier)
4.3 Afρ (“Afrho”)
309
F ⨀
¼
2
Δ
2 r 2
h
Z b max
0
ρ F b db
ð4:62Þ
and we can substitute this back into Eq. (4.56). This gives
Af ¼
8
b
2
max
Z b max
0
ρ F b db
ð4:63Þ
Using ρ now for b max and substituting using Eq. (4.60), we see that
Af ρ ¼ 8A
ð4:64Þ
In other words, averaging the reflectance on a circle about the nucleus and
multiplying that by impact parameter of that circle gives a very simple relation to
Afρ. (A has been occasionally referred to as the “azimuthal average” of the reflectance although this is actually a misnomer.)
This approach was taken by Gerig et al. (2018) in the construction of Fig. 4.18
which shows Afρ in the innermost coma of 67P derived from Rosetta/OSIRIS data.
This gives one of the most complete descriptions of the evolution of Afρ for any
comet. It should be noted that the measurements have been normalised to a phase
Fig. 4.18 Afρ values calculated from the constant value derived from fits to the azimuthal average
with impact parameter, b. A phase angle normalization to α ¼ 90
has been applied to the data
shown in this plot. The green data points mark Afρ values calculated for single images and the red
data points indicate averaged Afρ values over one comet day. Variation with heliocentric distance is
clearly evident as is the lag in the maximum with respect to perihelion. (Reprinted from Gerig et al.
2018, with permission from Elsevier)
4.3 Afρ (“Afrho”)
309