Chapter 3
Gas Emissions Near the Nucleus
3.1 Fundamentals
We begin this chapter by looking at highly simplified models of the spatial distribution of gas in the inner coma. The simplest approach is to assume that
(a) gas emission from the nucleus is isotropic,
(b) the nucleus is a point source,
(c) the gas velocity is constant (which is another way of saying that collisions are
negligible), and
(d) the gas species undergo no reactions.
We will see that close to the nucleus the first three of these assumptions are not
tenable and at large distances from the nucleus, the fourth assumption isn’t either!
But nonetheless these assumptions are useful because their simplicity allows us to
derive helpful relationships for density and column density that are straightforward
but fundamental.
Under the above assumptions the local density is given by
n g r
ð Þ ¼
Q g
4πr 2 v g
ð3:1Þ
where r is the cometocentric distance, v is the outflow velocity and Q is the total
production rate. We will see below that similar equations can be used for the dust
outflow and hence we will use a subscript, g, for the gas in this sub-section and
subscript, d, for the dust in Chap. 4.1.
The column density along a line-of-sight can be determined by integration. Here,
we define the impact parameter, b, as the minimum distance to the nucleus along the
line-of-sight and s as the distance along the line-of-sight. Hence,
© 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_3
179
Gas Emissions Near the Nucleus
3.1 Fundamentals
We begin this chapter by looking at highly simplified models of the spatial distribution of gas in the inner coma. The simplest approach is to assume that
(a) gas emission from the nucleus is isotropic,
(b) the nucleus is a point source,
(c) the gas velocity is constant (which is another way of saying that collisions are
negligible), and
(d) the gas species undergo no reactions.
We will see that close to the nucleus the first three of these assumptions are not
tenable and at large distances from the nucleus, the fourth assumption isn’t either!
But nonetheless these assumptions are useful because their simplicity allows us to
derive helpful relationships for density and column density that are straightforward
but fundamental.
Under the above assumptions the local density is given by
n g r
ð Þ ¼
Q g
4πr 2 v g
ð3:1Þ
where r is the cometocentric distance, v is the outflow velocity and Q is the total
production rate. We will see below that similar equations can be used for the dust
outflow and hence we will use a subscript, g, for the gas in this sub-section and
subscript, d, for the dust in Chap. 4.1.
The column density along a line-of-sight can be determined by integration. Here,
we define the impact parameter, b, as the minimum distance to the nucleus along the
line-of-sight and s as the distance along the line-of-sight. Hence,
© 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_3
179