m 1 1, r h
ð
Þ ¼ m 1 Δ, r h
ð
ÞÀ5 log 10 Δ
ð1:1Þ
This has been performed in Fig. 1.3 which also shows several other points of
interest. Firstly, the plot shows the brightness relative to the time to pericentre, T PERI .
However, this brightness is not symmetric about T PERI . The value, LAG (which
refers to the lag in the maximum brightness with respect to perihelion) indicates that
the maximum in brightness occurred 11.2 days after perihelion. The maximum
brightness is not at the time of maximum solar input. Work by Ferrin suggests that
for 67P, using pre-Rosetta apparitions, the lag was 33 days after perihelion. Hansen
et al. (2016) used ROSINA/COPS measurements of the gas density at 67P and
combined this with a simple free-radial expansion model of the gas to show that gas
production at 67P peaked between 18 and 22 days after perihelion. They also
showed that the gas production was highly correlated with ground-based dust
brightness measurements. Consequently, although there may be small differences
in the exact result, the existence of a pre- and post-perihelion brightness asymmetries
with respect to perihelion is demonstrable and is related to activity and nucleus gas
and dust production.
Fig. 1.3 The light curve of 1P/Halley showing the reduced magnitude (m(1,R h )) as a function of
time with respect to perihelion. Some of the properties of the curves are discussed in the text (from
Ferrin 2010)
4
1 Light Curves, Orbits, and Reservoirs