Chapter 2
The Nucleus
2.1 Sizes and Shapes of Unresolved Nuclei
For ground-based observations and observations using telescopes in Earth-orbit
(e.g. the Hubble Space Telescope), cometary nuclei are usually much smaller than
the resolution element (e.g. Lamy et al. 2011). Nonetheless, unresolved observations
remain very important because they can place constraints on the diversity of nuclei.
Of particular importance are size, albedo, colour and surface composition.
The flux from an unresolved nucleus in the visible can be computed from
F N λ
ð Þ ¼ F ⨀ λ
ð Þ p φ α
ð Þ
r
2
N
Δ
2 r 2
h
ð2:1Þ
where p is the geometric albedo, φ is the value of the phase function at the phase
angle, α, and F ⨀ is the solar spectral flux at 1 AU within a wavelength interval
reduced to a unit of [W m
À2 nm
À1 ] or similar (Tomasko 1976). The geometric
albedo is the ratio of its actual brightness at zero phase angle (α ¼ 0) to that of a
diffusively scattering, perfectly reflecting, disc with the same cross-section. Fits to
observations of φ(α) have been made in the past using simple linear functions
resulting in values of dφ(α)/dα of between 0.03 and 0.06 magnitudes per degree
(e.g. Jewitt et al. (2003) for 143P/Kowal-Mrkos and Jewitt and Sheppard (2004) for
48P/Johnson). The solar spectral flux (which we will often refer to as just “the solar
flux”) at 1 AU can be obtained from numerous sources (e.g. Kurucz et al. 1984). An
evaluation of the solar flux over an extended wavelength range has been provided by
Claire et al. (2012).
An alternative way of expressing this used by ground-based observers is to take
an approach developed by Russell (1916) (see e.g. Meech et al. 2004 or Lamy et al.
2011) by writing
© Springer Nature Switzerland AG 2020
N. Thomas, An Introduction to Comets, Astronomy and Astrophysics Library,
https://doi.org/10.1007/978-3-030-50574-5_2
27
The Nucleus
2.1 Sizes and Shapes of Unresolved Nuclei
For ground-based observations and observations using telescopes in Earth-orbit
(e.g. the Hubble Space Telescope), cometary nuclei are usually much smaller than
the resolution element (e.g. Lamy et al. 2011). Nonetheless, unresolved observations
remain very important because they can place constraints on the diversity of nuclei.
Of particular importance are size, albedo, colour and surface composition.
The flux from an unresolved nucleus in the visible can be computed from
F N λ
ð Þ ¼ F ⨀ λ
ð Þ p φ α
ð Þ
r
2
N
Δ
2 r 2
h
ð2:1Þ
where p is the geometric albedo, φ is the value of the phase function at the phase
angle, α, and F ⨀ is the solar spectral flux at 1 AU within a wavelength interval
reduced to a unit of [W m
À2 nm
À1 ] or similar (Tomasko 1976). The geometric
albedo is the ratio of its actual brightness at zero phase angle (α ¼ 0) to that of a
diffusively scattering, perfectly reflecting, disc with the same cross-section. Fits to
observations of φ(α) have been made in the past using simple linear functions
resulting in values of dφ(α)/dα of between 0.03 and 0.06 magnitudes per degree
(e.g. Jewitt et al. (2003) for 143P/Kowal-Mrkos and Jewitt and Sheppard (2004) for
48P/Johnson). The solar spectral flux (which we will often refer to as just “the solar
flux”) at 1 AU can be obtained from numerous sources (e.g. Kurucz et al. 1984). An
evaluation of the solar flux over an extended wavelength range has been provided by
Claire et al. (2012).
An alternative way of expressing this used by ground-based observers is to take
an approach developed by Russell (1916) (see e.g. Meech et al. 2004 or Lamy et al.
2011) by writing
© Springer Nature Switzerland AG 2020
N. Thomas, An Introduction to Comets, Astronomy and Astrophysics Library,
https://doi.org/10.1007/978-3-030-50574-5_2
27