Plasma dynamics in Saturn’s middle-latitude ionosphere and implications for magnetosphere-ionosphere coupling Shotaro Sakai1,3 and Shigeto Watanabe2,3

1: Department of Physics and Astronomy, University of Kansas, Malott Hall, 1251 Wescoe

Hall Drive, Lawrence, KS 66045

2: Department of Systems and Informatics, Hokkaido Information University, 59-2

Nishinopporo, Ebetsu, Hokkaido 069-8585, Japan

3: Department of Cosmosciences, Hokkaido University, Kita 10 Nishi 8, Kita-ku, Sapporo

060-0810, Japan

Corresponding Author: Shotaro Sakai, Department of Physics and Astronomy, University of

Kansas, Malott Hall, 1251 Wescoe Hall Drive, Lawrence, KS 66045 (shotaro@ku.edu)

This is the accepted version of the following article: “Sakai, S. and S. Watanabe (2016),

Plasma dynamics in Saturn’s middle-latitude ionosphere and implications for

magnetosphere-ionosphere coupling, Icarus, in press, doi:10.1016/j.icarus.2016.03.009.”,

which has been published in final form at http://dx.doi.org/10.1016/j.icarus.2016.03.009.

Highlights

Saturn’s ionospheric plasma temperature is much higher than previously estimated

The ionospheric H+ velocity is very high and directed toward the magnetosphere

Model electron densities agree with observations at high neutral temperature

High electron heating rates also provide an agreement with observed densities

Magnetosphere–ionosphere coupling is key for Saturn’s magnetospheric physics

Abstract

A multifluid model is used to investigate how Saturn’s magnetosphere affects ionosphere.

The model includes a magnetospheric plasma temperature of 2 eV as a boundary condition.

The main results are: (1) H+ ions are accelerated along magnetic field lines by ambipolar

electric fields and centrifugal force, and have an upward velocity of about 10 km/s at 8000

km; (2) the ionospheric plasma temperature is 10000 K at 5000 km, and is significantly

affected by magnetospheric heat flow at high altitudes; (3) modeled electron densities agree

with densities from occultation observations if the maximum neutral temperature at a latitude

of 54˚ is about 900 K or if electrons are heated near an altitude of 2500 km; (4) electron

heating rates from photoelectrons (≈100 K/s) can also give agreement with observed electron

densities when the maximum neutral temperature is lower than 700 K (note that Cassini

observations give 520 K); and (5) the ion temperature is high at altitudes above 4000 km and

is almost the same as the electron temperature. The ionospheric height-integrated Pedersen

conductivity, which affects the magnetospheric plasma velocity, varies with local time with

values between 0.4 and 10 S. We suggest that the sub-corotating ion velocity in the inner

magnetosphere depends on the local time, because the conductivity generated by dust–plasma

interactions in the inner magnetosphere is almost comparable to the ionospheric conductivity.

This indicates that magnetosphere–ionosphere coupling is highly important in the Saturn

system.

1. Introduction

Saturn’s magnetosphere-ionosphere coupling is active in the auroral region at high latitudes

between 75˚ and 80˚ (e.g., Cowley et al., 2004) and corresponding to about 15 and 35 RS in

the equatorial magnetosphere. RS is the Saturn radius of 60268 km. The coupling process

between the inner magnetosphere at less than 10 RS and the ionosphere at latitudes lower than

≈70˚ is not well understood. However, the interaction between the ionosphere and Saturn’s

ring particles was recently observed by studying patterns in the emissions of H3+ in the low

latitude ionosphere (i.e., below 50˚ which is equivalent to ≈2.0 RS in the equatorial

magnetosphere). These emissions were likely due to the “ring rain” demonstrated by

O’Donoghue et al. (2013). Ring rain consists of ion fluxes that are probably generated by

photoionization of the ring surface and then precipitate into the ionosphere (Connerney, 2013).

A similar phenomenon is expected to occur in the inner magnetosphere in the region of the E

ring, since this region also contains mainly water group ions and water ice dust from Saturn’s

moon Enceladus. The south polar region of Encleadus is known to be a source of water vapor

and grains (Dougherty et al., 2006; Porco et al., 2006; Waite et al., 2006), which can then

supply the inner magnetosphere (Horányi et al., 2004; Smith et al., 2010).

Stallard et al. (2008) have found a “secondary auroral oval” that might be caused by

interaction with the inner magnetosphere inside 10 RS, and they showed that the oval extends

to a latitude of 60˚ corresponding to ≈3.5 RS in the equatorial magnetosphere. Sakai et al.

(2013) showed that the magnetospheric electric field generated by ion-dust collisions slows

ions with respect to the co-rotation speed in Saturn’s inner magnetosphere and suggested that

the dust–plasma interactions occur via magnetosphere–ionosphere coupling. This

magnetospheric electric field also strongly depends on the ionospheric Pedersen conductivity

(Sakai et al., 2013). The Pedersen conductivity has been calculated in many models

(Connerney et al., 1983; Cheng and Waite, 1988; Saur et al., 2004; Cowley et al., 2004;

Moore et al., 2010). However, the conductivity values differ considerably between the models

largely due to the dependence on the ionospheric plasma density (e.g., Moore et al., 2010) and

to the effects of the subcorotation of the thermospheric neutral wind field (e.g., Smith and

Aylward, 2008; Müller-Wodarg et al., 2012).

Saturn’s ionospheric plasma, which is important for Pedersen conductivity, has been

observed and modeled many times. The electron density was measured using the radio

occultation technique by the Pioneer 11, Voyager 1 and 2, and Cassini spacecraft (Kliore et al.,

1980; Tyler et al., 1981, 1982; Lindal et al., 1985; Nagy et al., 2006; Kliore et al., 2009, 2014).

These observations showed that the peak electron density was about 1010 m-3 (e.g., Nagy et al.,

2006; Kliore et al., 2009). The altitudes of the peak density depend on the local time (LT) and

latitude. Peak altitudes varied between 1000 km and 3000 km. Saturn’s ionosphere has also

been investigated by Moore et al. (2004, 2008) using the Saturn Thermosphere Ionosphere

Model (STIM). Moore et al. (2008) showed the dominant ion is H3+ and the electron

temperature above 1300 km reaches 500 K during the day. This model included water

influxes which varied with latitude, which affects the loss of H+ and the abundance of H3+.

Moore et al. (2015) showed increases in H3+ intensity to areas of increased water influx, i.e.

water actually increases H3+ density and therefore emissions. This is because the water influx

leads to a reduction in electron density, which then slows down the dissociative

recombination loss rate of H3+.

In this paper we investigate ionospheric plasma densities, velocities, and temperatures using

a model that includes the effects of the magnetosphere, and we discuss dust–plasma

interactions and magnetosphere–ionosphere coupling in the Saturn system.

2. Model

2.1. Continuity, momentum, and energy equations

The plasma densities, velocities, and temperatures in Saturn’s ionosphere are evaluated

using a multifluid model in order to investigate the effects of magnetospheric plasma on the

ionosphere. Orthogonal dipolar coordinates, first introduced by Dragt (1961), are used in the

mid-latitude ionosphere because we neglect the thermospheric wind driven by solar extreme

ultraviolet (EUV) radiation for simplicity (Huang and Hill, 1989). The ion densities and

velocities are calculated from the following continuity and momentum equations:

€

∂ρi∂t

+1A∂ Aρiui,||( )

∂s= Si − Li , (1)

€

ρi∂ui,||∂t

+ ρiui,||∂ui,||∂s

= −nine∂pe∂s

−∂pi∂s

− ρig − ρiν ik ui,|| − uk,||( )k∑ , (2)

where ρi is mini; mi is the ion mass; ni(e) is the ion (electron) number density; A is the

cross-sectional area of a magnetic flux tube; ui,|| is the ion field-aligned velocity; Si is the ion

production rate; Li is the ion loss rate; pi(e) is the ion (electron) pressure; g is the difference

between gravitational and centrifugal forces; νik is the ion collision frequency between species

i and k, including electrons, neutral gas (nonresonant and resonant collisions), dust, and other

ion species (Schunk and Nagy, 2009; Sakai et al., 2013); and s is the coordinate along the

magnetic field line. The ion species taken into account are: H+, H2+, H3

+, He+, H2O+, and

H3O+. We assume that the velocities of water group ions are zero because the relative

momenta of the species are smaller than the other species. The ion temperature Ti is assumed

to be equal to the electron temperature Te:

Ti = Te. (3)

We will discuss the validity of this assumption in Section 4.3.

The electron temperature is given by (e.g., Schunk and Nagy, 2009)

€

∂Te∂t

−231A∂∂s

Aκe∂Te∂s

⎛

⎝ ⎜

⎞

⎠ ⎟ =Qe,net , (4)

where κe is the thermal conductivity and Qe,net is the net electron heating rate. The thermal

conductivity is

€

κe =uethnkσ ek

k∑

, (5)

where ueth is the electron thermal velocity and the subscript k indicates ion, dust, and neutral

species. σek is the collision cross section for ion (general Coulomb collision), dust (e.g.,

Khrapak et al., 2004) and neutral (e.g., Itikawa, 1974). The electron temperature is assumed to

be always larger than the neutral temperature (Te ≥ Tn). The electron number density is given

by the quasi-neutrality condition:

€

ne = nii∑ −

qdend , (6)

where qd is the dust charge and nd is the dust density. The dust charge is given by qd = 4�

ε0Urd (Horányi et al., 2004; Yaroshenko et al., 2009), where ε0 is the vacuum permittivity, U

is the dust surface potential and rd is the dust radius, which is taken to be 100 nm (Sakai et al.,

2013). We assumed that the dust potential is negative because most dust grains have a

negative charge in the inner magnetosphere (e.g., Horányi et al., 2004). We also assumed

negatively charged dust in the inner magnetosphere (at the outer boundary). The field-aligned

electric field is given by

€

E|| = −1ene

∂pe∂s

. (7)

2.2 Model settings and magnetospheric effects

The magnetospheric plasma density and temperature are given as boundary conditions in

order to investigate how the magnetospheric plasma affects the ionosphere. Fig. 1 shows

plasma and dust density profiles in the inner magnetosphere as a function of the L shell

parameter. The electron and dust densities are based on Persoon et al. (2009) and Sakai et al.

(2013). The ion density is derived from charge neutrality. Fig. 2 is a cartoon of coordinate

system used in this model. The Saturn-centered dipole magnetic field line corresponding to

L=3 at equatorial plane is used as an example in this work, which is a good approximation for

L < 10 (Connerney et al., 1984; Saur et al., 2004). The magnetic field strength at the equator

(B0) is about 2.1 × 10-5 T (e.g., Belenkaya et al., 2006). Wahlund et al. (2009) and Gustafsson

and Wahlund (2010) showed that the electron temperature was 1 – 2 eV in the inner

magnetosphere, so we used 2 eV as the magnetospheric electron temperature at the upper

boundary of equatorial region (Sakai et al., 2013). We assume a constant 2 eV as an average

thermal energy (i.e., temperature) in the inner magnetosphere since we are investigating how

the magnetospheric plasma affects the ionospheric plasma. Ion–dust collisions are also

included in our model (Sakai et al., 2013).

An atmospheric pressure of 1 bar is used at 0 km altitude and the lowest altitude is 300 km

in this model. We calculated the time evolution and found the quasi-stationary solution of

plasma density, velocity, and temperature along a hemispheric field line (Fig. 2). For the

initial conditions we assumed that the ion densities had the minute value (10-40 m-3), that ion

velocities were zero, and that the electron temperature was 140 K. The calculations were

iterated for 120 Saturn’s days under the equinox conditions, and we confirmed that variations

after one day are within 1%.

3. Atmospheric model

3.1 Neutral atmosphere and ion chemistry

Fig. 3 shows the density and temperature profiles for the background neutral atmosphere.

We used the background neutral densities and temperatures of Moore et al. (2009). This

model is based on a latitude of 30˚ and the maximum neutral temperature is 410 K. However,

we are interested in a latitude of 54˚ at 1 bar (or L=3 in the dipole field), for which the

maximum neutral temperature is 700 K according to Müller-Wodarg et al. (2006). We

therefore consider two additional background atmosphere profiles for which the maximum

temperatures of the neutral atmosphere are assumed to be 700 K and 900 K. The neutral

densities are in hydrostatic equilibrium corresponding to these temperatures (dashed and

dot-dashed lines, respectively, in Fig. 3). Table 1 also shows the neutral densities at a lower

boundary and 1200 km where the density gradients have changed. Reactions for six ion

species (H+, H2+, H3

+, He+, H2O+, and H3O+) are used in our model. The chemical reactions

are listed in Table 2 and photoionization reactions are explained in Appendix A. The loss of

H+ by reactions with vibrationally excited H2 (ν ≥ 4) is included in our model (solid line in

Fig. 7 of Moses and Bass (2000)).

3.2 Electron heating and cooling rate

The electron heating rate Qe,net is given by the sum of local and non-local heating:

€

Qe,net =QEUV +Qjoule +Qph,ionos +Qcoll , (8)

where QEUV is the heating rate due to photoelectrons produced by solar EUV radiation, Qjoule

is the local Joule heating rate, Qph,ionos is the heating rate due to ionospheric photoelectrons at

altitudes above about 1300 km, which is the altitude of peak electron density, and Qcoll is the

cooling rate due to collisions between electrons and neutral gas species.

QEUV is given by

€

QEUV =2e3nekB

f ionnnE ph exp −τ( )n∑ , (9)

where fion is the ionization frequency (see Appendix A), Eph is the energy of a photoelectron, τ

is the optical depth, nn is the neutral density, and kB is the Boltzmann constant. The energy of

a photoelectron is given by the difference between the solar photon energy and the binding

energy. These are ≈0.2 eV for H to H+, ≈2.3 eV for H2 to H+, ≈2.9 eV for H2O to H+, ≈1.7 eV

for H2 to H2+, and ≈5.6 eV for H2O to H2O+. The heating due to the transition from He to He+

is neglected because of the small energy of the reaction.

The Joule heating term Qjoule is given by

€

Qjoule =2

3kBneσpE⊥

2 (10)

where σp is the local Pedersen conductivity and

€

E⊥ is the perpendicular electric field. This

formula is derived by differentiating the height-integrated Joule heating introduced in

Baumjohann and Treumann (1997) for the energy equation. The slippage from the

co-rotational field estimated from ion speed observations from Cassini Langmuir Probe

(Holmberg et al., 2012) and previous models (Sakai et al., 2013) was taken into account in the

electric field term. Joule heating is originally defined as a consequence pertaining to collisions

between ions and electrons. On the other hand, in our model it is due to the variation of

electric field related to ion-neutral collision and dust-plasma interaction in the magnetosphere

(Sakai et al., 2013). The varying electric field

€

E⊥ is about 10-4 V/m at L=3 based on Sakai et

al. (2013).

Qph,ionos is given by (e.g., Nisbet, 1968; Millward et al., 1996; Huba et al., 2000)

€

Qph,ionos =23BBt

qt exp −C neds∫( ) (11)

where B is the strength of the local dipole magnetic field, Bt is the strength of the magnetic

field at 1500 km, qt is the heating rate per electron at 1500 km (about 10 K/s at noon), ds is

the differential length along the magnetic field line; and C is a constant (3 × 10-18 m2) (e.g.,

Nisbet, 1968; Millward et al., 1996; Huba et al., 2000).

The electron cooling rate due to collisions with neutrals and ions, Qcoll, is given by (e.g.,

Huba et al., 2000)

€

Qcoll =2memn

me +mn( )2νen Tn −Te( )

n∑ +

7.7 ×10−12niAiTe

3 / 2 Ti −Te( )i∑ (12)

where me is the electron mass, mn is the mass of the neutral gas, νen is the collision frequency

between the electron and the neutral gas defined as

€

5.4 ×10−16nnTe−1 2 in previous studies

(e.g., Kelley, 2009), Tn is the temperature of the neutral gas, Ti is the ion temperature, and Ai

is the atomic mass number of the ions.

We also introduce the heat flow from magnetosphere QHF. The QHF is shown using second

term of equation (4) and given by

€

QHF =231A∂A∂sκe∂Te∂s

. (13)

4. Results and Discussions

4.1. Plasma distributions in the ionosphere

Using the model described above, we calculated plasma densities, velocities, and

temperatures. Fig. 4 shows ionospheric plasma densities and ion velocities for three

maximum neutral temperatures Tnmax (case 1: 410 K, case 2: 700 K and case 3: 900 K) at 12

LT below 9000 km at L=3. In case 1 electron densities are about 107 m-3 at the altitude of

9000 km and increase to about 1010 m-3 at 1500 km (solid line in Fig. 4a). H3O+ ions are the

dominant ions at altitudes below 1000 km, with peak densities of about 109 m-3. The dominant

ions above 1000 km are H3+ with a maximum density of about 5 × 109 m-3 at 1100 km. Above

3000-4000 km the density profiles depend on the plasma temperature. The H+ ions are

accelerated in the equatorial direction above 2000 km, and have a speed of about 10 km/s at

7500 km. This is because H+ ions are accelerated from the ionosphere to the magnetosphere

by the centrifugal force and ambipolar electric fields. For high neutral temperatures (cases 2

and 3) the electron speed above 2000 km was higher than in case 1, while the maximum

density became slightly smaller (dashed line for case 2 and dot-dash line for case 3). H3+ is

the predominant ion species above 2000 km and the electron density almost follow the H3+

distribution. The H3+ velocity was reduced at high neutral temperatures because of frequent

collisions with the neutrals, and so the H3+ and electron densities generally increase at higher

altitudes. The slight drop in maximum density could be because the densities are smoothed by

small ion velocities at low altitudes. Other ion species also show the same trends for density

and velocity as H3+.

Fig. 5 shows the electron temperature and heating rate for three neutral temperatures (same

cases as Fig. 4) at 12 LT below 9000 km at L=3. In case 1 the electron temperature is 140 K at

the lower boundary and increases to 10000 K at an altitude of 5000 km (solid line in Fig. 5a).

This is due to heat flow from the magnetosphere, which is dominant over other heat processes

at altitudes above 2500 km (blue solid line in Fig. 5b). We chose a magnetospheric

temperature of 2 eV as the boundary condition. This affects the ionospheric plasma.

Absorption of solar EUV radiation (including the effects of ionospheric photoelectrons)

contributes to heating below 2500 km. Generally, the Joule heating term is important in the

auroral region because of auroral electric fields. However, a strong electric field does not exist

in mid-latitude region, which is associated with aurora and electron precipitation. At Saturn, a

driving source of Joule heating is the variation of electric field by ion-neutral and -dust

collisions in the magnetosphere (Sakai et al., 2013), but the contribution to Saturn's

ionosphere is small in comparison with other heating sources. For high neutral temperatures

(cases 2 and 3) the electron temperature profiles do not agree with the case 1 profile, in

particular above 2000 km. This is because the heat flux for these cases is smaller than for case

1 due to the high neutral densities (see equation 13). The heating rate from solar EUV and the

cooling rate from collisions both also increased at high neutral temperatures because of high

neutral densities.

The ionospheric plasma distribution is determined by the plasma temperature profile, not

by chemistry, above 3000 km (around the exobase). The neutral densities, which are given by

hydrostatic equilibrium corresponding to neutral temperatures, do not affect the plasma

profile at high altitudes.

We assumed the existence of charged dust at the outer boundary (or inner magnetosphere).

This dust did not affect the ionospheric plasma dynamics and chemistry since the dust is too

heavy to move out of the equatorial magnetosphere.

4.2. Comparison with observations and previous models

The electron temperature above 2000 km was much higher than those of previous studies.

We found temperatures exceeding 1000 K at altitudes of 2000 km, while previous models

showed temperatures of 500 K at that altitude (Moore et al., 2008). This is because the heat

flow from the magnetosphere (QHF) significantly affects the ionospheric temperature,

contributing greatly to heating above 2500 km (Fig. 5b).

Our electron density profiles are similar to the profile of Moore et al. (2008), and the

dominant ion species is H3+ at low altitudes in both models. However, Moore et al. (2008)

found H+ to be the dominant ion above 2000 km, unlike our model that showed H3+ is

dominant. This difference could be because H+ is quickly transported to high altitudes in our

model. In Moore’s model the amount of H+ was mainly reduced by the interaction with the

water influx (Moore et al., 2006; Müller-Wodarg et al., 2012). On the other hand, in our

model the amount of H+ is reduced by transport to the magnetosphere. Hence, our mechanism

of H+ depletion differs from theirs.

Cassini measured ionospheric electron densities using the radio occultation technique

(Nagy et al., 2006; Kliore et al., 2009). Three model densities at 18 LT are compared with

occultation observations from Kliore et al. (2009) in Fig. 6. The observed densities are an

average over five observations of mid-latitude (20˚ < |Lat.| < 60˚) electron densities at dusk.

The model electron densities do not agree with observations when neutral profiles have a

maximum temperature of 410 K, which is the temperature at a latitude of 30˚ (orange in Fig.

6). Better agreement with observations is obtained for Tnmax = 700 K, which occurs at the

latitude of 54˚ (Müller-Wodarg et al., 2012). The model electron density profile is mostly

consistent with the observations for altitudes below 3000 km, but the model densities are less

than the observations above 3000 km. For Tnmax = 900 K the model densities are in reasonable

agreement with the observed densities, although they are slightly larger. Note that the

temperature of 900 K is higher the model temperatures of Müller-Wodarg et al. (2006).

Differences between our model and observations could arise for two reasons: (1) more

electron heating is needed around 2000-3000 km because the density gradient is determined

by the scale height which is a function of temperature, and (2) the maximum neutral

temperature at a latitude of 54˚ is not ≈700 K but ≈900 K. No in-situ observations of Saturn’s

upper atmosphere exist, and, although Saturn’s ionosphere will be observed during “the

proximal orbits” of the Cassini spacecraft when it starts in 2016, this will be done at very low

latitudes near the equator. Note that we used a solar flux model for solar maximum conditions,

so our model densities might be overestimated.

Koskinen et al. (2015) suggested that the exospheric temperatures observed by the Cassini

Ultraviolet Imaging Spectrograph (UVIS) are around 520 K for the latitude of 54˚ we used in

this study. If the observations are correct our model results disagree with electron densities

from radio occultations. One possibility is that the electron heating rates attributed to

photoelectrons are too low. Moore et al. (2008) found dayside heating rates of ≈100 K/s at an

altitude of 1000 km, whereas the heating rates are ≈10 K/s from our simulations (Fig. 5). We

tested the case of Tnmax = 520 K and 10Q0 , where Q0 is QEUV + Qph,ionos. Fig. 7a shows model

electron densities (solid: 18 LT, dotted: 12 LT) compared with densities of the dusk time

occultation measurements (Kliore et al., 2009). Model densities agree with observations for

low altitude around 1000 km and for high altitudes above 8000 km (18 LT). The densities are

also lower than observations between 2000 and 7000 km but the difference is within only a

factor of 2. The electron temperatures are more than 5000 K at 2000 km (Fig. 7b) and it is

higher than results of our previous model (Fig. 5a) because the photoelectron heating rates

reach ≈100 K/s, corresponding to heating rates of Moore et al. (2008). We used photoelectron

heating rates based on the Earth’s ionosphere (e.g., Nisbet, 1968; Millward et al., 1996; Huba

et al., 2000). The derived heating rates were low in comparison to Moore et al. (2008). This

might be because the heating from photoelectrons and secondary electrons are not accurate.

Photoelectron heating rates to thermal electrons are generally calculated using the

photoelectron transport (e.g., Nagy and Banks, 1970; Banks and Nagy, 1970), but we do not

have any electron heating rates in Saturn’s middle latitude. Photoelectron transport has been

studied for other planets and moons (e.g., Gan et al., 1990; Richard et al., 2011; Ozak et al.,

2012; Sakai et al., 2015). The photoelectron transport for Saturn is not easy to study due to

the lack of observations, but it has been modeled (e.g., Moore et al., 2008; Galand et al.,

2009). Thus, we cannot compare models with observations even if the photoelectron transport

is modeled. From these results the heating attributed to photoelectrons could be also

important for determining the profile of plasma densities in the ionosphere below 3000 km.

The plasma profile of lower ionosphere would affect plasma distributions in the upper

ionosphere.

4.3. Ion temperature

For the results above the ion temperature was assumed to be the same as the electron

temperature (Ti = Te). However, the ion temperature is generally known to be less than or

equal to the electron temperature (Ti ≤ Te). We discuss the consequences of this assumption in

this section. We also tried Ti = (Te + 2Tn)/3 with the condition Te ≥ Tn, which means that the

ion temperature is about 1/3 of the electron temperature at high temperatures (Te >> Tn). Fig.

8 shows the comparison of our model results at Tnmax = 700 K (green), 900 K (blue) and 520

K (10Q0) (red) with occultation observations from Kliore et al. (2009). The electron densities

(i.e., the sum of ion densities) do not change for altitudes below 4000 km. At low altitudes the

neutral profiles and solar radiation determine the plasma profiles, and so the profiles are

independent of ion temperature. On the other hand, the density gradient deviates from

observations above 4000 km with low ion temperatures (dashed line). The ion temperature

profile is important for determining the density profile at high altitudes because the density

gradient strongly depends on the plasma temperature. The density gradient is in good

agreement with observations at Ti ≈ Te above 4000 km. We therefore suggest that the ion

temperature could be as high as the electron temperature at high altitudes.

4.4. Diurnal variation of the ionosphere

We discuss the diurnal variation of electron densities and temperature in this section. Fig. 9

shows diurnal variations of electron densities and temperature for Tnmax = 700 K, 900 K and

520 K (10Q0) below 4000 km. The altitude of the peak electron density is between 1500 km

and 2000 km, and peak densities are about 1010 cm-3. The peak densities have a diurnal

change between 109 and 1010 m-3 regardless of the neutral temperature and electron heating

rates. The high density region is spread out between 1000 km and 2500 km at 12 LT with

Tnmax = 700 K, while the upper boundary increased to 3000 km with Tnmax = 900 K. This is

because the ion velocities at Tnmax = 900 K are smaller than at 700 K, as explained in Section

4.1. The region with Tnmax = 520 K (10Q0) is between 1000 km and 2000 km, and narrower

than other two cases because of ion velocities. The maximum electron densities occur around

12-13 LT, and the minimum around 5 LT. The electron densities decrease as the altitude

increased in accordance with the scale height.

The electron temperature also depends on the local time (Fig. 9b). It reaches a maximum

around 12 LT due to the combination of heat flow from the magnetosphere and heating by

photoionization and solar EUV. It slightly decreases for 18 LT because of the sunset

conditions for which photoionization rates are lower. The high temperature at high altitudes

after 18 LT is maintained by heat flow from the magnetosphere. The electron temperature is

hardly affected by the variation of neutral temperature. On the other hand, the temperature

with Tnmax = 520 K (10Q0) is higher than the other two cases above 2000 km. It means that

photoelectron heating rates are important for electron heating at the altitude around 2000 km.

4.5. Implications for magnetosphere-ionosphere coupling

The ionospheric conductivity is an important parameter in models of Saturn’s

magnetosphere, such as studies of subcorotation in the auroral region (e.g., Müller-Wodarg et

al., 2012; Sakai et al., 2013). We therefore calculated the ionospheric height-integrated

Pedersen conductivity with our model. The Pedersen conductivity is given by

€

σp =ν i

ν i2 +ω ci

2i∑ nie

2

mi

+ν e

ν e2 +ω ce

2nee

2

me (14)

€

Σi = σpds∫ , (15)

where ωck is the cyclotron frequency of each plasma component, Σi is the height-integrated

Pedersen conductivity (e.g., Moore et al., 2010). The collision frequencies νi and νe are given

by

€

ν i = ν inn∑ , (16)

€

νe = νenn∑ , (17)

where νkn is the plasma-neutral collision frequency. The local time variation of Pedersen

conductivity was calculated using equations (14) and (15) and Fig. 10 shows the local time

variations of the height-integrated Pedersen conductivity. The integrated values were between

0.4 S and 10 S, similar to the results of Moore et al. (2010). We perhaps underestimated the

conductivity because we did not consider hydrocarbon ions in this model, even though they

may be dominant in the lower ionosphere (Kim et al., 2014). Moore et al. (2010) showed the

height-integrated Pedersen conductivity is 15.3 S when the electron density is 1010 m-3 at all

altitudes and the ionosphere consists only of C3H5+, which was just one examined case. We

may have errors of at most a factor of 1.5 in the integrated conductivity. As the ionospheric

Pedersen conductivity depends on the local time, this means that the inner magnetospheric ion

velocity may also depend on the local time because the ionospheric conductivity affects the

magnetospheric ion velocity along with the dust-plasma interaction (Sakai et al., 2013). We

therefore suggest that the magnetosphere–ionosphere coupling is important for inner

magnetospheric physics, such as the ion velocity profile.

5. Summary

Plasma densities, velocities, and temperatures in Saturn’s ionosphere were calculated using

a multifluid model to investigate the ionospheric physics which affects

magnetosphere-ionosphere coupling and the magnetosphere. Our main conclusions are as

follows.

(1) H+ ions had a high upward velocity and were accelerated to 10 km/s at 7500 km since

these light ions were blown to equatorial regions of the magnetosphere by a centrifugal force

and ambipolar electric fields.

(2) The electron temperature was 140 K at the lower boundary, and increased to 10000 K at

5000 km due to heat flow from the magnetosphere.

(3) Model electron densities were in agreement with densities from radio occultation

observations (Kliore et al., 2009) when the maximum neutral temperature at the latitude of

54˚ is 900 K rather than 700 K

(4) The electron heating rates of 100 K/s attributed to photoelectrons also produce agreement

with density observations when the maximum neutral temperature is lower than 700 K as is

520 K corresponding to Cassini/UVIS observations (Koskinen et al., 2015), and it would be

important for determining plasma density profiles.

(5) The ion temperature should be high at altitudes above 4000 km and is almost the same as

the electron temperature.

(6) The ionospheric height-integrated Pedersen conductivity, which is one of the important

parameters needed to model the magnetospheric dynamics, had a minimum of 0.4 S at 5 LT

and a maximum of 10 S at 12 LT. This conductivity depended significantly on the plasma

density in the ionosphere and affects the magnetospheric ion velocity (Sakai et al., 2013). The

magnetosphere and ionosphere could be strongly coupled, and that magnetosphere-ionosphere

coupling is important for inner magnetospheric physics.

Acknowledgements

All data shown in the figures can be obtained from the corresponding author. This research

described in this paper was supported at the University of Kansas by the NASA Cassini Data

Analysis Program under grant NNX13AG04G, by a research fellowship from the Japan

Society for the Promotion of Science (JSPS), and by Grant-in-Aid for Scientific Research

(KAKENHI) from JSPS (15K05303). S.S. acknowledges support from the International

Space Sciences Institute (ISSI) international team on “Coordinated Numerical Modelling of

the Global Jovian and Saturnian Systems”. The authors would also like to thank Thomas E.

Cravens for helpful comments on this manuscript.

Appendix A. Photoionization rates

We consider six photoionization reactions:

€

H + hν →H+ + e− (A1)

€

H2+ + hν →H +H+ + e− (A2)

€

H2O + hν →OH +H+ + e− (A3)

€

H2 + hν →H2+ + e− (A4)

€

He + hν →He+ + e− (A5)

€

H2O + hν →H2O+ + e− (A6)

Photoionization rates are given by

€

Ps z,χ( ) = ns z( ) I∞ λ( )exp −τ z,χ,λ( )[ ]σ si λ( )dλ

0

λsi∫ (A7)

where Ps is the photoionization rate, I� is the solar flux, σsi is the photoionization

cross-section, τ is the optical depth, z is the altitude, χ is the solar zenith angle, λ is the

wavelength, and subscript s indicates the neutral component. Fig. A1 shows the

photoionization cross-sections obtained using the photoionization/dissociation rates from the

Southwest Research Institute (http://phidrates.space.swri.edu/) (red) and fitted values (green).

We used the solar spectra of solar maximum conditions based on UARS SOLSTICE

measurements from 119 to 420 nm and 1994 rocket measurements together with the

Atmosphere Explorer E (AE-E) relative variability from 0 to 119 nm

(ftp://laspftp.colorado.edu/pub/rocket/ref_min_27day_11yr.dat). We also used ionization

cross-sections of H2 from Moore et al. (2004). The optical depth is given by

€

τ z,χ,λ( ) = sec χ ns z( )σ sa λ( )Hs

s∑ (A8)

where σsα is the photoabsorption cross-section and Hs is the scale height. Fig. A2 shows the

photoabsorption cross-sections from the National Institute for Fusion Science (NIFS)

database (http://dpc.nifs.ac.jp/photoab/d_list.html) (red) and fitted values (green). The fine

structures of the H2O cross-section are not reproduced in this fit; however, the effect of this

would be small when it is integrated. The photoionization rates at Tnmax = 700 K are shown in

Fig. A3. The production of H+ and H2+ from molecular H2 is important at altitudes around

1500 km. The produced H2+ quickly changes to H3

+ as a result of chemical reactions.

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Figure 1. Plasma and dust density profiles in the magnetosphere as a function of L. The black

solid line indicates electron density, the black dashed line indicates water group ion density,

the black dash-dotted line indicates proton density, and the gray solid line indicates dust

density. The magnetic latitudes in the Saturn-centered dipole field used in the simulations are

shown for L.

Figure 2. A cartoon of coordinate system used in this model. An atmospheric pressure of 1

bar was used at 0 km altitude, and temperature of 2 eV was used as outer boundary

(magnetosphere). Ion densities (ni), velocities (ui) and electron temperatures (Te) are

calculated along this field line using heating rates (Qe).

Figure 3. (a) Densities and (b) temperature profiles of the neutral atmosphere at the

maximum neutral temperature of 410 K (solid), 700 K (dashed) and 900 K (dot-dash). In (a)

red, blue green and cyan lines indicate H, H2, He, and H2O, respectively.

Figure 4. Altitudinal profiles of (a) plasma densities and (b) ion velocities below 9000 km.

H+ (red), H2+ (orange), H3

+ (pink), He+ (green), H2O+ (blue), H3O+ (cyan), and electron

(black) densities and velocities are shown. Solid, dashed and dot-dash lines indicate densities

and velocities at Tnmax = 410 K, 700 K and 900 K, respectively. Electron velocities are not

shown.

Figure 5. Altitudinal profiles of (a) electron temperature and (b) electron heating rates below

9000 km. In (b), heating due to solar EUV (red), collisions between neutral gas and the ions

(green), ionospheric photoelectrons (orange), heat flow from the magnetosphere (blue), and

Joule heating (black) is shown. Solid, dashed and dot-dash lines indicate densities and

velocities at Tnmax = 410 K, 700 K and 900 K, respectively.

Figure 6. Comparison of our model electron densities with densities from Cassini occultation

observations. The black solid line shows our model densities at Tnmax = 410 K (orange), 700 K

(green) and 900 K (blue), and the black dashed line shows the electron densities from

occultation (Kliore et al., 2009). Averaged densities at dusk at mid-latitudes (20˚ < |Lat.| <

60˚) are used for occultation observations.

Figure 7. (a) Model electron densities (red solid: 18 LT and red dotted: 12 LT) at Tnmax = 520

K and 10Q0 where Q0 is QEUV + Qph,ionos and densities from Cassini occultation observations

(black dashed), and (b) model electron temperatures (red solid: 18 LT and red dotted: 12 LT)

are shown.

Figure 8. Comparison of our model electron densities for Ti = Te (solid) and Ti lower than Te

(dashed) with densities from Cassini occultation observations (Same colors as in Fig. 6 and

7).

Figure 9. Diurnal variation of (left) the electron densities and (right) electron temperature

below 4000 km at (a and b) Tnmax = 700 K, (c and d) Tnmax = 900 K and (e and f) Tnmax = 520

K and 10Q0.

Figure 10. Diurnal variation of height-integrated Pedersen conductivity at L=3 (Same colors

as in Fig. 8).

Figure A1. Photoionization cross-sections for (a, b and c) H+, (d) H2+, (e) He+ and (f) H2O+.

Red lines are based on photoionization/dissociation rates from the Southwest Research

Institute (http://phidrates.space.swri.edu/) (a, c, e and f) and Moore et al. (2004) (b and d);

green lines show fitted values.

Figure A2. Photoabsorption cross-sections for (a) H, (b) H2, (c) He and (d) H2O. Red line

shows data from the National Institute for Fusion Science database

(http://dpc.nifs.ac.jp/photoab/d_list.html) and the green line shows fitted values.

Figure A3. Altitudinal profile of ionization rates below 9000 km at Tnmax = 700 K. Production

rates of H+ from H (red solid), H2 (red dashed) and H2O (red dot-dash), H2+ from H2 (orange),

He+ from He (green), and H2O+ from H2O (blue) are shown.

2 3 4 5 6 7 8 9 10102

103

104

105

106

107

108

Den

sity

[m−3

]

Density in the magnetosphereWater group ion

Electron

ProtonDust

L [Rs]Lat. [deg] 45.0 54.7 60.0 63.4 65.9 67.8 69.3 70.5 71.6

Figure1

L = 3(T

e = 2 eV)

1 bar (alt. = 0 km)

ni, u

i, T

e, Q

e

This figure is not to scale.

Figure2

103

107

1011

1015

1019

1023

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Density [m−3]

Alti

tud

e [km

]

Neutral density

a

H

H2

He

H2O

−: Tn max

= 410 K

−−: Tn max

= 700 K

..: Tn max

= 900 K

0 200 400 600 800 1000Temperature [K]

Neutral temperature

b

Figure3

103 104 105 106 107 108 109 1010

1000

2000

3000

4000

5000

6000

7000

8000

9000

Density [m−3]

Altit

ude

[km

]

Plasma density at L=3

H+H2+ H3

+

He+H2O+

H3O+

e−a

0 2 4 6 8 10 12Velocity [km/s]

Ion velocity at L=3

H+H2+

H3+

He+

H2O+

H3O+

b410 K700 K900 K

Figure4

102

103

104

1000

2000

3000

4000

5000

6000

7000

8000

9000

Temperature [K]

Alti

tud

e [km

]

Electron temperature

Tea

10−8

10−5

10−2

101

104

Heating rate [K/s]

Electron heating rateQEUV

Qph,ionos

−Qcoll

Qhf

Qjoule

b

410 K700 K900 K

Figure5

107 108 109 10101000

2000

3000

4000

5000

6000

7000

8000

9000Electron density

Density [m−3]

Altit

ude

[km

]

− Tnmax = 410 K− Tnmax = 700 K− Tnmax = 900 K−− Kliore et al. [2009] (Dusk)

Figure6

107 108 109 10101000

2000

3000

4000

5000

6000

7000

8000

9000Electron density

Density [m−3]

Altit

ude

[km

]

− Tnmax = 520 K, Q = 10Q0

18 LT

12 LT

− Kliore et al. [2009] (Dusk)a

102 103 1041000

2000

3000

4000

5000

6000

7000

8000

9000

Temperature [K]

Electron temperature

12 LT18 LT

b

Figure7

107 108 109 10101000

2000

3000

4000

5000

6000

7000

8000

9000Electron density

Density [m−3]

Altit

ude

[km

]

Tnmax = 700 K−: Ti = Te, −−: Ti = (Te+2Tn)/3Tnmax = 900 K−: Ti = Te, −−: Ti = (Te+2Tn)/3Tnmax = 520 K, Q = 10Q0−: Ti = Te, −−: Ti = (Te+2Tn)/3Kliore et al. [2009] (dusk)

Figure8

0 6 12 18 24

1000

2000

3000

4000

Altit

ude

[km

]

Electron density [m−3], log(Ne)

aTnmax=700 K

7

8

9

10

0 6 12 18 24

1000

2000

3000

4000Electron temperature [K], log(Te)

b

22.533.544.5

0 6 12 18 24

1000

2000

3000

4000

Altit

ude

[km

]

cTnmax=900 K

7

8

9

10

0 6 12 18 24

1000

2000

3000

4000

d

22.533.544.5

0 6 12 18 24

1000

2000

3000

4000

Local time

Altit

ude

[km

]

eTnmax=520 K, Q = 10Q0

7

8

9

10

0 6 12 18 24

1000

2000

3000

4000

Local time

f

22.533.544.5

Figure9

0 6 12 18 240

2

4

6

8

10

Local time

Con

duct

ivity

[S]

Pedersen Conductivity (L=3)

Tnmax = 700 KTnmax = 900 KTnmax = 520 K

Q = 10Q0

Figure10

0 20 40 60 80 1000

1

2

3

4

5

6

7 x 10−22

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

a: H + hv −> H+

0 20 40 60 800

0.5

1

1.5

x 10−23

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

Ionization cross−section

b: H2 + hv −> H + H+

0 20 40 600

2

4

6

8

x 10−23

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]c: H2O + hv −> OH + H+

0 20 40 60 800

0.5

1

1.5 x 10−21

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

d: H2 + hv −> H2+

0 20 40 600

0.2

0.4

0.6

0.8

1

1.2 x 10−21

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

e: He + hv −> He+

0 20 40 60 80 1000

0.5

1

1.5x 10−21

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

f: H2O + hv −> H2O+

FigureA1

0 20 40 60 80 1000

1

2

3

4

5

6

7 x 10−22

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

Photoabsorption cross−section

a: H

0 20 40 60 80 1000

0.2

0.4

0.6

0.8

1

1.2 x 10−21

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

Photoabsorption cross−section

b: H2

0 10 20 30 40 50 600

2

4

6

8 x 10−22

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

c: He

0 20 40 60 80 1000

0.5

1

1.5

2

2.5

3 x 10−21

Wave length [nm]

Cro

ss−s

ectio

n [m

2 ]

d: H2O

FigureA2

10−9

10−7

10−5

10−3

10−1

101

103

105

107

1000

2000

3000

4000

5000

6000

7000

8000

9000

Production rate [m−3 s−1]

Alti

tud

e [km

]

Photoionization rate (Tnmax = 700 K)

A1 (H+)

A2 (H+)

A3 (H+)

A4 (H2

+)

A5 (He+)

A6 (H2O+)

FigureA3

Table 1. Neutral densities at 0 km and 1200 km. The units are m-3.

H H2 He H2O

0 km 2.53 × 1019 6.04 × 1022 4.35 × 1021 2.16 × 1016

1200 km 4.16 × 1013 3.81 × 1016 4.98 × 1013 1.05 × 1010

Table1

Table 2. Ion recombination, charge exchange and chemical reactions

Chemical reactiona Rate coefficientb Referencec

��

H+ � e� oH

��

1.9 u10-16Te�0.7 1, 2, 3

��

H2+ � e� o2H

��

2.3 u10-12Te�0.4 1, 2, 3

��

H3+ � e� oH2 +H

��

7.6 u10-13Te�0.5 1, 2, 3

��

H3+ � e� o3H

��

9.7 u10-13Te�0.5 1, 2, 3

��

He+ � e� oHe

��

1.9 u10-16Te�0.7 1, 2, 3

��

H2O+ � e� oO �H2

��

3.5 u10-12Te�0.5 1, 3, 4

��

H2O+ � e� oOH�H

��

2.8 u10-12Te�0.5 1, 3, 4

��

H3O+ � e� oH2O �H

��

6.1u10-12Te�0.5 1, 3, 4

��

H3O+ � e� oOH� 2H

��

1.1u10-11Te�0.5 1, 3, 4

��

H+ �H2 oH2+ +H See text 1, 3

��

H+ �H2 �MoH3+ +M

��

3.2 u10-41 1, 2, 3

��

H+ �H2OoH2O+ +H

��

8.2 u10-15 1, 3, 5

��

H2+ �HoH+ +H2

��

6.4 u10-16 1, 3 5

��

H2+ �H2 oH3

+ +H

��

2.0 u10-15 1, 2, 3

��

H2+ �H2OoH2O

+ +H2

��

3.9 u10-15 1, 3, 5

��

H2+ �H2OoH3O

+ +H

��

3.4 u10-15 1, 3, 5

��

H3+ �H2OoH3O

+ +H2

��

5.3u10-15 1, 3, 5

��

He+ �H2 oH+ +H +He

��

8.8 u10-20 6, 7

��

He+ �H2 oH2+ +He

��

9.4 u10-21 1, 2, 3

��

He+ �H2OoH+ +OH +He

��

1.9 u10-16 1, 5

��

He+ �H2OoH2O+ +He

��

5.5 u10-17 1, 5

��

H2O+ �H2 oH3O

+ +H

��

7.6 u10-16 1, 5

��

H2O+ �H2OoH3O

+ +OH

��

1.9 u10-15 1, 5 aM represents any third body such as H2.

bTwo-body rate constants are in units of m3 s-1. Low-pressure limiting rate constants for

trimolecular reactions are in units of m6 s-1. cReferences are 1, Moses and Bass (2000); 2, Kim and Fox (1994); 3, Moore et al. (2004); 4,

Millar et al. (1997); 5, Anicich (1993); 6, Matcheva et al. (2001); 7, Perry et al. (1999).

Table2