Bopp) being a good example. The appearance of a similar comet thousands of years
ago would have undoubtedly impressed our forebears. Similarly, the brightening and
fading again within a relatively short period of time (of the order of a few months)
would also have led to considerable amazement and, with the absence of a visible
source, it is not surprising that our ancestors were sufficiently perplexed by these
objects that they tried to illustrate what they saw in works such as the Bayeux
Tapistry and the Augsburg Book of Miracles (Borchert and Waterman 2017).
A final element that is not apparent to the naked-eye of even bright comets is the
presence of a neutral tail. Gas species are also subject to radiation pressure before
dissociation and/or ionization. Some species (atomic sodium being a prime example)
can receive significant anti-sunward acceleration through the resonant fluorescence
process that results in the production of a neutral tail. A neutral sodium tail was first
seen in observations of C/1995 O1 (Hale-Bopp) and was subsequently found in
observations of C/1996 B2 (Hyakutake) (Cremonese and the European Hale-Bopp
Team 1997; Cremonese et al. 1997). For most neutral species, lifetimes are relatively
short and hence gas tails produced in this way are not of major significance.
Making standardized photometric orbital light curves of comets from multiple
independent observations is not straightforward but attempts were driven forward by
the need to place constraints on the activity of 1P/Halley for its return in 1986
(e.g. Newburn and Yeomans 1982). A modern example of an orbital light curve is
shown in Fig. 1.3 and is also for 1P/Halley (Ferrin 2010).
Cometary light curves are usually expressed using the magnitude system. Though
its use is ubiquitous in Earth-based optical astronomy it does have three drawbacks
– it is an inverse scale, with fainter stars having larger magnitudes,
– it is a logarithmic scale and,
– the base of the logarithm is 2.512.
The observed visual magnitude of a comet is denoted by m 1 (Δ,r h ) where Δ is the
comet-Earth distance and r h is the Sun-comet distance. The visual magnitude is
estimated by making differential photometry with nearby objects of known brightness. This has a level of uncertainty. However, accuracy at the 0.1 magnitudes level
is achievable under good conditions.
Combining results from several observers and reducing the data into a standard
system (e.g. the Johnson-Morgan V magnitude system) is not straightforward as the
photometric responses of equipment used to measure the target can differ significantly and atmospheric opacity (extinction) will vary with time and the observing
site (see e.g. Sterken and Manfroid 1992). On the other hand, as Fig. 1.3 shows, the
change in cometary visual magnitude from its first telescopic detection to perihelion
passage can be more than 15 magnitudes (a change in brightness of a factor of 10
6 )
with occasional comets (such as 1P/Halley) appearing to brighten by factors of
100 (5 magnitudes) or more to naked-eye observers and then fading again before
being lost.
Visual magnitudes are usually expressed as reduced magnitudes. Here the magnitude is converted to a unit distance from the observer—normally a comet-Earth
distance of 1 AU—by dividing by Δ
2 . This can be expressed in equation form as
1.1 Light Curves
3
ago would have undoubtedly impressed our forebears. Similarly, the brightening and
fading again within a relatively short period of time (of the order of a few months)
would also have led to considerable amazement and, with the absence of a visible
source, it is not surprising that our ancestors were sufficiently perplexed by these
objects that they tried to illustrate what they saw in works such as the Bayeux
Tapistry and the Augsburg Book of Miracles (Borchert and Waterman 2017).
A final element that is not apparent to the naked-eye of even bright comets is the
presence of a neutral tail. Gas species are also subject to radiation pressure before
dissociation and/or ionization. Some species (atomic sodium being a prime example)
can receive significant anti-sunward acceleration through the resonant fluorescence
process that results in the production of a neutral tail. A neutral sodium tail was first
seen in observations of C/1995 O1 (Hale-Bopp) and was subsequently found in
observations of C/1996 B2 (Hyakutake) (Cremonese and the European Hale-Bopp
Team 1997; Cremonese et al. 1997). For most neutral species, lifetimes are relatively
short and hence gas tails produced in this way are not of major significance.
Making standardized photometric orbital light curves of comets from multiple
independent observations is not straightforward but attempts were driven forward by
the need to place constraints on the activity of 1P/Halley for its return in 1986
(e.g. Newburn and Yeomans 1982). A modern example of an orbital light curve is
shown in Fig. 1.3 and is also for 1P/Halley (Ferrin 2010).
Cometary light curves are usually expressed using the magnitude system. Though
its use is ubiquitous in Earth-based optical astronomy it does have three drawbacks
– it is an inverse scale, with fainter stars having larger magnitudes,
– it is a logarithmic scale and,
– the base of the logarithm is 2.512.
The observed visual magnitude of a comet is denoted by m 1 (Δ,r h ) where Δ is the
comet-Earth distance and r h is the Sun-comet distance. The visual magnitude is
estimated by making differential photometry with nearby objects of known brightness. This has a level of uncertainty. However, accuracy at the 0.1 magnitudes level
is achievable under good conditions.
Combining results from several observers and reducing the data into a standard
system (e.g. the Johnson-Morgan V magnitude system) is not straightforward as the
photometric responses of equipment used to measure the target can differ significantly and atmospheric opacity (extinction) will vary with time and the observing
site (see e.g. Sterken and Manfroid 1992). On the other hand, as Fig. 1.3 shows, the
change in cometary visual magnitude from its first telescopic detection to perihelion
passage can be more than 15 magnitudes (a change in brightness of a factor of 10
6 )
with occasional comets (such as 1P/Halley) appearing to brighten by factors of
100 (5 magnitudes) or more to naked-eye observers and then fading again before
being lost.
Visual magnitudes are usually expressed as reduced magnitudes. Here the magnitude is converted to a unit distance from the observer—normally a comet-Earth
distance of 1 AU—by dividing by Δ
2 . This can be expressed in equation form as
1.1 Light Curves
3