It can be seen that the trends are basically linear with a gradient indicating that the
nucleus is red with respect to a solar spectrum. Interpretation of the departures from
linearity seen would require detailed analysis of the relative errors in the calibration.
Many unresolved observations of asteroids show similar fairly featureless trends.
The asteroid, (21) Lutetia, visited by Rosetta on its way to 67P is an example (see
e.g. Busarev 2016). There are, however, exceptions (e.g. (4) Vesta). The linear trend
has led to use of a spectral gradient to define the spectra at optical wavelengths. The
most common form is
S
0
λ 1 , λ 2 , λ ref
À
Á ¼
1
ρ ref
ρ λ 2 À ρ λ 1
λ 2 À λ 1
ð2:85Þ
where λ 1,2 are the wavelengths of the observations in units of [100 nm] and ρ λ1,2 are
the reflectance factors. ρ ref is the reflectance factor at a reference wavelength which is
used to normalize the spectrum so that the resulting gradient can be expressed as a
percentage (i.e. in units of [% (100 nm)
À1 ].
There is no universal consensus on the choice of the wavelength at which ρ ref
should be taken and hence care should be taken in comparing values. For example,
ground-based observers have tended to use 0.55 μm (e.g. Licandro et al. 2018)
whereas Fornasier et al. (2016) used the central wavelength of the green filter at
0.535 μm for spectrophotometric analyses of Rosetta/OSIRIS data. In these cases,
this is probably of little significance but older papers (e.g. Thomas and Keller 1989)
used very different reference wavelengths and hence comparisons should take this
into account. The conversion from one reference wavelength (λ refA ) to another (λ refB )
is simply
S
0
λ 1 , λ 2 , λ refA
À
Á ¼ S
0
λ 1 , λ 2 , λ refB
À
Á λ refA
λ refB
ð2:86Þ
The fit in Fig. 2.22 gives 20.1(Æ0.8)% (100 nm)
À1 which is consistent with the
pre-perihelion maps from August 2014 given in Fornasier et al. (2016). For comparison, Thomas and Keller (1989) determined 7(Æ3)% (100 nm)
À1 (converted to
the same reference wavelength as Fornasier et al.) for 1P/Halley indicating that
substantial differences between comets exist.
Licandro et al. (2018) have acquired spectra of asteroids in what are considered to
be comet-like orbits and hence one can argue that the spectra provide good signal to
noise observations of bare, albeit dead or dormant, nuclei. All of their spectra
showed linear increasing trends with increasing wavelength in the range 3–15%
(100 nm)
À1 referenced to 0.55 μm with only weak evidence for absorptions. Hence,
while cometary nuclei are usually red, they do have demonstrably different degrees
of reddening.
68
2 The Nucleus
nucleus is red with respect to a solar spectrum. Interpretation of the departures from
linearity seen would require detailed analysis of the relative errors in the calibration.
Many unresolved observations of asteroids show similar fairly featureless trends.
The asteroid, (21) Lutetia, visited by Rosetta on its way to 67P is an example (see
e.g. Busarev 2016). There are, however, exceptions (e.g. (4) Vesta). The linear trend
has led to use of a spectral gradient to define the spectra at optical wavelengths. The
most common form is
S
0
λ 1 , λ 2 , λ ref
À
Á ¼
1
ρ ref
ρ λ 2 À ρ λ 1
λ 2 À λ 1
ð2:85Þ
where λ 1,2 are the wavelengths of the observations in units of [100 nm] and ρ λ1,2 are
the reflectance factors. ρ ref is the reflectance factor at a reference wavelength which is
used to normalize the spectrum so that the resulting gradient can be expressed as a
percentage (i.e. in units of [% (100 nm)
À1 ].
There is no universal consensus on the choice of the wavelength at which ρ ref
should be taken and hence care should be taken in comparing values. For example,
ground-based observers have tended to use 0.55 μm (e.g. Licandro et al. 2018)
whereas Fornasier et al. (2016) used the central wavelength of the green filter at
0.535 μm for spectrophotometric analyses of Rosetta/OSIRIS data. In these cases,
this is probably of little significance but older papers (e.g. Thomas and Keller 1989)
used very different reference wavelengths and hence comparisons should take this
into account. The conversion from one reference wavelength (λ refA ) to another (λ refB )
is simply
S
0
λ 1 , λ 2 , λ refA
À
Á ¼ S
0
λ 1 , λ 2 , λ refB
À
Á λ refA
λ refB
ð2:86Þ
The fit in Fig. 2.22 gives 20.1(Æ0.8)% (100 nm)
À1 which is consistent with the
pre-perihelion maps from August 2014 given in Fornasier et al. (2016). For comparison, Thomas and Keller (1989) determined 7(Æ3)% (100 nm)
À1 (converted to
the same reference wavelength as Fornasier et al.) for 1P/Halley indicating that
substantial differences between comets exist.
Licandro et al. (2018) have acquired spectra of asteroids in what are considered to
be comet-like orbits and hence one can argue that the spectra provide good signal to
noise observations of bare, albeit dead or dormant, nuclei. All of their spectra
showed linear increasing trends with increasing wavelength in the range 3–15%
(100 nm)
À1 referenced to 0.55 μm with only weak evidence for absorptions. Hence,
while cometary nuclei are usually red, they do have demonstrably different degrees
of reddening.
68
2 The Nucleus