acquired with the spacecraft around 200 km from the nucleus. It should be noted that
even here the velocity component along the line of sight cannot be derived. Ott et al.
assumed velocities and derived a total large particle dust production rate assuming
force-free radial outflow of more than 8 tonne s
À1 in August 2015. Fig. 1.18 shows
the gas production rate to be around 900 kg s
À1 at this time indicating a dust to gas
mass production rate ratio of ~9. This seems to be remarkably high compared to
observations of the dense interstellar medium and protostellar envelopes which
suggest an ice/rock ratio of ~1.5 (Pontoppidan et al. 2014) although it is likely that
this ratio in planetesimals is a function of the heliocentric distance of their formation.
There are two main difficulties with the Ott et al. result. Firstly, Choukroun et al.
(2020) have pointed out that the mass loss rate can only be sustained for 15–30 days
before the hard limit on the total mass lost by 67P during the whole perihelion
passage based on the RSI experiment (Pätzold et al. 2019) is reached. The second is
connected to the trajectories of slow moving particles as shown in Fig. 2.81. The Afρ
value inferred by Ott et al. for the large particles alone is higher than that found by
Gerig et al. (2018) suggesting that these particles should dominate the optical flux
from the dust coma. However, if velocities are of the order of 1–2 m s
À1 then the
nucleus will rotate 20
to 40
while a particle travels from the nucleus to the edge of
the field of view in images such as Fig. 2.81. If the emission is dominated by large
slow moving particles then the jet structures must therefore be curved. In Fig. 2.81,
only one structure shows this behaviour and it is, by far, the best example. Lin et al.
(2016) noted this evidence of curvature resulting from gravitational effects on
unbound particles. Subsequently, Marshall et al. (2018), with a slightly more
sophisticated analysis, showed that these particles were still being measurably
accelerated beyond escape velocity by the gas drag and were moving at velocities
~20 m s
À1 towards the end of the observed part of the flight. This is again
inconsistent with the Ott et al. result.
Models of large particle motion in the vicinity of the nucleus were first discussed
by Richter and Keller et al. (1995) at a time when the main issue was whether large
particles could be retained in stable orbits for long periods of time and thereby
present a danger to the Rosetta spacecraft. An alternative analytical approach would
be to assume that the non-escaping dust particle distribution in the innermost coma
can be modelled with a Chamberlain-like model for an exosphere (Chamberlain and
Hunten 1987; Gerig et al. 2018). This model separates molecules into three different
components using a partition function. Molecules may be on ballistic trajectories,
escaping trajectories or end up in orbits in the event of collisions. In terms of the
trajectories, this bears some similarity to the dust particle case. However, the
Chamberlain model is an equilibrium model at source and, in addition, dust particles
are brought into orbit not by dust-dust collisions but by other forces including
external solar-driven ones that are not accounted for within the scheme.
Because this issue is the subject of detailed debate at the time of writing, we will
look at an alternative approach to quantifying the mass production rate of strongly,
gravitationally-influenced, particles. A numerical model of ejection and ballistic
motion can be easily constructed for the simple case of a 2 km spherical nucleus
of 67P’s mass with uniform (isotropic) emission from the dayside only. Assuming a
4.11 Slow (Large) Moving Particles in the Coma
365
even here the velocity component along the line of sight cannot be derived. Ott et al.
assumed velocities and derived a total large particle dust production rate assuming
force-free radial outflow of more than 8 tonne s
À1 in August 2015. Fig. 1.18 shows
the gas production rate to be around 900 kg s
À1 at this time indicating a dust to gas
mass production rate ratio of ~9. This seems to be remarkably high compared to
observations of the dense interstellar medium and protostellar envelopes which
suggest an ice/rock ratio of ~1.5 (Pontoppidan et al. 2014) although it is likely that
this ratio in planetesimals is a function of the heliocentric distance of their formation.
There are two main difficulties with the Ott et al. result. Firstly, Choukroun et al.
(2020) have pointed out that the mass loss rate can only be sustained for 15–30 days
before the hard limit on the total mass lost by 67P during the whole perihelion
passage based on the RSI experiment (Pätzold et al. 2019) is reached. The second is
connected to the trajectories of slow moving particles as shown in Fig. 2.81. The Afρ
value inferred by Ott et al. for the large particles alone is higher than that found by
Gerig et al. (2018) suggesting that these particles should dominate the optical flux
from the dust coma. However, if velocities are of the order of 1–2 m s
À1 then the
nucleus will rotate 20
to 40
while a particle travels from the nucleus to the edge of
the field of view in images such as Fig. 2.81. If the emission is dominated by large
slow moving particles then the jet structures must therefore be curved. In Fig. 2.81,
only one structure shows this behaviour and it is, by far, the best example. Lin et al.
(2016) noted this evidence of curvature resulting from gravitational effects on
unbound particles. Subsequently, Marshall et al. (2018), with a slightly more
sophisticated analysis, showed that these particles were still being measurably
accelerated beyond escape velocity by the gas drag and were moving at velocities
~20 m s
À1 towards the end of the observed part of the flight. This is again
inconsistent with the Ott et al. result.
Models of large particle motion in the vicinity of the nucleus were first discussed
by Richter and Keller et al. (1995) at a time when the main issue was whether large
particles could be retained in stable orbits for long periods of time and thereby
present a danger to the Rosetta spacecraft. An alternative analytical approach would
be to assume that the non-escaping dust particle distribution in the innermost coma
can be modelled with a Chamberlain-like model for an exosphere (Chamberlain and
Hunten 1987; Gerig et al. 2018). This model separates molecules into three different
components using a partition function. Molecules may be on ballistic trajectories,
escaping trajectories or end up in orbits in the event of collisions. In terms of the
trajectories, this bears some similarity to the dust particle case. However, the
Chamberlain model is an equilibrium model at source and, in addition, dust particles
are brought into orbit not by dust-dust collisions but by other forces including
external solar-driven ones that are not accounted for within the scheme.
Because this issue is the subject of detailed debate at the time of writing, we will
look at an alternative approach to quantifying the mass production rate of strongly,
gravitationally-influenced, particles. A numerical model of ejection and ballistic
motion can be easily constructed for the simple case of a 2 km spherical nucleus
of 67P’s mass with uniform (isotropic) emission from the dayside only. Assuming a
4.11 Slow (Large) Moving Particles in the Coma
365