Drake G.W.F. (editor) Handbook of Atomic, Molecular, and Optical Physics

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Comets 83.2 Excitation Mechanisms 1253

(3s⬘)

7990

8447

(3s)

11287

(3p)

(3d)

989

1027

1304

(2p

)⬘S

5577

2972

(2p

)⬘D

6300

6364

(2p

)

Fig. 83.4 Simpliﬁed O i energy level diagram showing

transitions of interest in cometary spectra

serve because of the nearby strong CO Fourth Positive

bands. Recently, the shorter wavelength (6,1), (6,2),

and (6,3) bands have been detected in three comets

using FUSE and the derived H

column abundance

was found to be consistent with a water photodisso-

ciation source [83.22, 23]. Another interesting example

occurs for Ne i, where the second resonance transition

at 629.74 Å coincides with the strong solar O v line at

629.73 Å. This line was used to set a sensitive upper limit

on the Ne abundance in the coma of comet Hale-Bopp

(C/1995 O1) [83.40].

83.2.5 Electron Impact Excitation

The photoionization of the parent molecules and

their dissociation products leads to the formation of

a cometary ionosphere whose characteristics are only

poorly known. Planetary ionospheres serve only as

a poor model since the cometary atmosphere is gravita-

tionally unbound and there is no constraining magnetic

ﬁeld. The in situ measurements of Halley provided order

of magnitude conﬁrmation of the theoretical modeling.

In principle, electron impact excitation, which is often

the dominant source of airglow in the atmospheres of

the terrestrial planets Chapt. 84, also contributes to the

observed emissions, particularly in the UV, and so must

be accounted for in deriving column densities from the

observed emission brightnesses. However, one can use

a very simple argument, based on the known energy

distribution of solar UV photons, to demonstrate that

electron impact excitation is only a minor source for

the principal emissions. Since the photoionization rate

of water (and of the important minor species such as

CO and CO

)is≈ 10

−6

−1

at 1 AU, and the efﬁciency

for converting the excess electron energy into excitation

of a single emission is of the order of a few percent,

the effective excitation rate for any emission will be

≈ 10

−8

−1

or less at 1 AU [83.41]. Since the efﬁcien-

cies for resonance scattering or ﬂuorescence for almost

all the known cometary emissions are much larger, elec-

tron impact may be safely neglected except in a few

speciﬁc cases.

The cases of interest are those of forbidden transi-

tions, where the oscillator strength, and consequently

the g-factor, is very small. Examples include the O i

−

2,1

doublet at 1356 Å, which was observed in

comets West and Halley by rocket-borne spectrographs

and more recently in comets Hyakutake and Hale-Bopp,

the O i

D −

P red lines at 6300 and 6364 Å, observed

in many comets, and the CO Cameron bands [83.21].

However, the excitation of these latter two is dominated

by prompt emission in the inner coma, the same region

of the coma where electron excitation is important, as

described in the next section.

83.2.6 Prompt Emission

In cases where the dissociation or ionization of a mol-

ecule leaves the product atom or molecule in an excited

state, the decay of this state with the prompt emission

of a photon provides a useful means for tracing the

spatial distribution of the parent molecule in the inner

coma. The products of interest for the water molecule

are described in Sect. 83.3.1. Prompt emission includes

both allowed radiative decays (such as from the A

state of OH) as well as those from metastable states

such as O(

D ), since the latter will move ∼150 km

(for a comet at a geocentric distance of 1 AU, 1 arc-

second corresponds to a projected distance of 725 km)

in its lifetime. The O i

D–

P transition at 6300 and

6364 Å Fig. 83.4 has been used extensively as a ground-

based monitor of the water production rate with the

caveat that other species such as OH, CO and CO

may also contribute to the observed red line emission.

Part G 83.2

1254 Part G Applications

In addition, when the density of H

O is sufﬁcient to

produce observable red line emission, it is also sufﬁ-

cient to produce collisional quenching of the

D state,

and this must also be considered in the interpretation

of the observations. The analogous

D −

P transitions

in carbon occur at 9823 and 9849 Å and provide simi-

lar information about the production rate of CO. Carbon

atoms in the

D state, whose lifetime is ≈4000 s, are

known to be present from the observation of the reso-

nantly scattered

−

D transition at 1931 Å [83.42],

and the 9849 Å line has been detected in comet Hale-

Bopp [83.43].

The OH A

− X

Π prompt emission competes

with that produced by the resonance ﬂuorescence of

OH and is difﬁcult to detect, except close to the nucleus

(inside 100 km) where the density of water molecules ex-

ceeds that of OH by a few orders of magnitude [83.44].

Again, the reason is that at the wavelengths below the

threshold for simultaneous dissociation and excitation,

the sun has much less ﬂux than at the resonance wave-

length. On the other hand, only a few rotational lines are

excited in ﬂuorescence equilibrium [83.34], while the

prompt emission is characterized by a very “hot” rota-

tional distribution, so in principle the two components

may be separated although observations at very high

spatial and spectral resolution are required. OH prompt

emission has also recently been detected in the infrared

at 3.28 µm [83.45].

83.2.7 OH Level Inversion

An important consequence of ﬂuorescence equilibrium

in the OH radical is the UV pumping of the hyperﬁne and

Λ-doublet levels of the X

3/2

(J = 3/2) ground state,

which results in a deviation of the population from statis-

tical equilibrium [83.34]. Depending on the heliocentric

velocity, this departure may be either “inverted” or “anti-

inverted” giving rise to either stimulated emission or

absorption against the galactic background at 18 cm

wavelength. This technique has been used extensively

since 1974 to monitor the OH production rate in comets,

even of those that appear close to the sun [83.46]. The

resulting radio emissions are easily quenched by colli-

sions with molecules and ions, the latter giving rise to

a fairly large R

that must be accounted for in interpret-

ing the derived OH column density. Nevertheless, the

radio and UV measurements give reasonably consistent

results [83.46].

83.3 Cometary Models

83.3.1 Photolytic Processes

As an example of the photolytic destruction processes

occurring in the coma, consider the dominant molecu-

lar species, water. Water vapor is assumed to leave

the surface of the nucleus with some initial veloc-

ity v

and ﬂow radially outward, expanding into the

vacuum, and increasing its velocity according to thermo-

dynamics [83.7]. Even though collisions are important at

distances typically up to 10

km (depending on the den-

sity and consequently, on the total gas production rate),

the net ﬂow of H

O molecules is radially outward, such

that the density varies as R

−2

near the nucleus, where

R is the cometocentric distance. This is the basis for

spherically symmetric coma models (the number of par-

ticles ﬂowing through a spherical surface is conserved),

which assume isotropic gas production, but appears to

hold equally well for the case of Halley, which clearly

was not outgassing uniformly over its surface [83.4].

The photolysis of H

O can proceed by:

a H

O+ hν→OH + H 2424.6Å



→OH(A

) + H 1357.1Å

b H

O+ hν→H

+ O(

D ) 1770 Å



→H

+ O(

S ) 1450 Å



→H+ H + O(

P ) 1304 Å

c →H

+ e

−

984 Å

d →H+ OH

+ e

−

684.4Å

e →H

+ O

+ e

−

664.4Å

f →OH + H

+ e

−

662.3Å

The right-hand column gives the energy threshold

for each reaction, in wavelength units. The products are

subsequently removed by:

g OH + hν→O + H 2823.0Å

h →OH

+ e

−

928 Å

i H

+ hν→H + H 844.79 Å

j →H

+ e

−

803.67 Å

k →H+ H

+ e

−

685.8Å

l O+ hν→O

+ e

−

910.44 Å

m H + hν→H

+ e

−

911.75 Å

Reactions l and m can also occur by resonant charge

exchange with solar wind protons. Reactions a



, b and



correspond to the production of prompt emission, as

Part G 83.3

Comets 83.3 Cometary Models 1255

discussed in Sect. 83.2.6. The determination of column

densities of H, O and OH simultaneously was con-

vincing evidence that the dominant volatile species in

the cometary nucleus was H

O, long before the direct

infrared detection of this species in the coma.

Detailed cross sections for the absorption of UV

photons by each of the reactants, including proper iden-

tiﬁcation of the ﬁnal product states, is necessary for the

evaluation of the photodestruction rate in the solar ra-

diation ﬁeld of each of the above reactions. These rates

are evaluated at 1 AU using whole disk measurements

of the solar ﬂux by integrating the cross section



πF



dλ. (83.10)

Another quantity of interest in coma modeling is the ex-

cess velocity (or energy) of the dissociation or ionization

products, and this requires knowledge of the partition-

ing of energy between internal and translational modes

for each reaction [83.47].

Qualitatively, the photodissociation and photoion-

ization rates can be estimated from the threshold

energies given in the table above, since the solar ﬂux

is decreasing very rapidly to shorter wavelengths, as can

be seen in Fig. 83.1. It is customary to specify the life-

time against photodestruction τ

, of species i,whichis

just

(τ

)

−1



)

, (83.11)

where the sum is over all possible reaction channels,

as well as the lifetimes into speciﬁc channels. Processes

with thresholds near 3000 Å have lifetimes ≈10

s, those

with thresholds near 2000 Å an order of magnitude

longer, while those with thresholds below Ly-α,suchas

most photoionization channels, have lifetimes ≈10

all at 1 AU. In addition to uncertainties in the details

of the absorption cross sections, further uncertainty is

introduced into the calculation of J

by the lack of

knowledge of the solar ﬂux at the time of a given ob-

servation due to the variability of the solar radiation

below 2000 Å, and most importantly, below Ly-α,where

there have not been continuous space observations for

more than a decade. The solar UV ﬂux is known to vary

considerably both with the 27-day solar rotation period

and with the 11-year solar activity cycle. Also, at any

given point in its orbit, a comet sees a different hemi-

sphere of the sun than what is seen from Earth. Huebner

et al. [83.48] have compiled an extensive list of useful

photodestruction rates using mean solar ﬂuxes to repre-

sent the extreme conditions of solar minimum and solar

maximum. They also include the excess energies of the

dissociation products. A detailed analysis of the rates for

O and OH, using surrogate solar indices such as the

10.7 cm solar radio ﬂux, or the equivalent width of the

He i line at 1.083 µm, is in good agreement with observa-

tions [83.49]. Similar analyses still remain to be carried

out for other important species, such as CO and NH

83.3.2 Density Models

For parent molecules produced directly by sublimation

from the surface of the comet, a spherically symmet-

ric radial outﬂow model is often adopted. Such a model

assumes a steady-state gas production rate Q

and a con-

stant outﬂow velocity v, and gives rise to a density

distribution as a function of cometocentric distance R

given by

(R) =

4πvR

−R/β

, (83.12)

where β

= vτ

is the scale length of species i. The basic

validity of this model was demonstrated by the Giotto

neutral mass spectrometer measurements of H

Oand

[83.4], although detailed analysis revealed that the

velocity of the water molecules increased from 0.8km/s

at about 1000 km from the nucleus to 1.1km/sataradial

distance of 10 000 km. The dependence of outﬂow veloc-

ity on heliocentric distance remains uncertain, although

Delsemme [83.50] has suggested an r

−1/2

dependence

based on thermodynamic arguments. Sub-millimeter ob-

servations of H

O have sufﬁcient spectral resolution to

permit the mapping of outﬂow velocities along various

lines-of-sight to the comet [83.28].

For the dissociation products, the modeling is more

complex. The simplest model assumes continued ra-

dial outﬂow, although at a different velocity, such

as to maintain a constant ﬂux of the initial particle

across an arbitrary spherical surface surrounding the

nucleus [83.51]. This model, which is valid only at

distances equal to a few β

,iswidelyusedasthe

densities can be easily expressed in analytical form.

However, as surface brightness measurements are of-

ten made with small ﬁelds of view close to the nucleus,

this model can lead to a factor of two error from the

neglect of the dissociation kinematics. Since the so-

lar photodissociation often leaves the product fragments

with 1–2 eV of kinetic energy [83.47, 48], the resultant

motion (which is assumed to be isotropic in the parent

molecule’s rest frame), will contain a large nonradial

Part G 83.3

1256 Part G Applications

component. Several approaches have been developed to

account properly for the kinematics; notably, the vecto-

rial model of Festou [83.52], and the average random

walk model (a Monte Carlo method) of Combi and

Delsemme [83.53]. The latter model has been extended

to include time-dependent gas kinetics so as to properly

account for regions of the coma where the gas is not in

local thermodynamic equilibrium [83.54].

In addition to the photodestruction chains, chemical

reactions, particularly ion-molecule reactions, can al-

ter the composition within the collision zone deﬁned in

Sect. 83.2.2. While such reactions may produce numer-

ous minor species, they do not erase the signatures of

the original parent molecules. In fact, detailed chemical

models have clearly demonstrated the need for complex

molecules to serve as the parents of the observed C

and

radicals in the coma, strengthening the connection

between comet formation and molecular cloud abun-

dances. Thus, the photochemical chains provide a valid

means of relating the coma composition to that of the

nucleus.

83.3.3 Radiative Transfer Effects

The results of a model calculation for the density of

a species must be integrated over the line of sight to

obtain the column density at a given projected distance

from the nucleus, and then integrated over the instru-

mental ﬁeld of view for comparison with the observed

average surface brightness or derived average column

density

. This assumes that the coma is optically thin,

and that all atoms or molecules have an equal proba-

bility of absorbing a solar photon. In practice, this is

true for all molecular emissions except perhaps within

1000 km of the nucleus (i. e., for observations made at

better than 1



resolution). Since the cross sections at

line center can be very large for an atomic resonance

transition, the optical depth for the abundant species

can exceed unity and radiative transfer along both the

line of sight to the sun and that to the Earth must be

considered. This is not a trivial problem as the veloc-

ity distribution of the atoms, particularly the component

due to the excess energy of the photodestruction pro-

cess, must be well known, as must be the shape of

the exciting solar line. The most thoroughly studied

case to date is that of H i Ly-α, whose angular ex-

tent, in direct images, can exceed several degrees on

the sky [83.55].

An interesting case arises for resonance transitions

between an excited

state and the ground

2,1,0

state,

as for O and S, particularly the latter, as its concentration

near the nucleus can be quite large due to the rapid decay

of one of its parents, CS

.ForSi the three lines at 1807,

1820 and 1826 Å are not observed to have their statistical

intensity ratio of 5:3:1, except at large distances from the

nucleus. This is explained by noting that ﬁne structure

transitions will lead to all of the S atoms reaching the

J = 2 ground state in a time short compared with that for

absorbing a solar photon, and that the emitted 1807 Å

photons will be re-absorbed and can then branch into

the other two lines. The detailed solution to this prob-

lem has led to the conclusion that H

S was the primary

source of sulfur rather than CS

, whose other product,

CS, was simultaneously observed in the UV [83.56].

Millimeter and sub-millimeter observations of comet

Hale-Bopp (C/1995 O1) subsequently showed that SO,

, and OCS were also minor sources of atomic sul-

fur, comparable in abundance to CS

[83.57]. Another

minor source is S

, initially observed in only one comet,

IRAS-Araki-Alcock (C/1983 H1) [83.58], but recently

seen in three additional comets by HST. The origin of

in the cometary nucleus remains a puzzle.

83.4 Summary

This brief chapter can only hint at the wealth of ob-

servational data spanning the entire electromagnetic

spectrum now routinely acquired at almost every comet

apparition allowing for a statistically signiﬁcant as-

sessment of comet diversity and formation scenarios.

Reference [83.59] will bring the interested reader up

to date on all aspects of comet science. The next

few years will see several spacecraft missions to

comets, Stardust, Deep Impact and Rosetta, whose pri-

mary objective is the study of the cometary nucleus

whose properties can only be inferred from remote

observations. Nevertheless, Earth-based observations

of comets will continue to play an important role

in understanding the physical and chemical environ-

ments of these objects left over from the formation

of the Solar System. There are still signiﬁcant chal-

lenges in understanding the atomic and molecular

physics of the cometary atmosphere, an example being

the identiﬁcation of the large number of unidenti-

ﬁed lines seen in high resolution spectra in both the

far UV [83.22,23] and visible [83.60] regions of the

spectrum.

Part G 83.4

Comets References 1257

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Part G 83

1258 Part G Applications

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Part G 83

1259

Aeronomy

84. Aeronomy

We describe here the neutral and ionic structures

of atmospheres, including the processes that

determine the atmospheric layers, the distribution

of the species, and the temperature proﬁles. We

focus on the upper atmosphere, which comprises

the thermosphere and the ionosphere, two

regions which overlay and interact with each

other. We describe the interaction of near and

extreme ultraviolet solar photons and energetic

electrons with the atmosphere and their role

in ionization and dissociation of atmospheric

species. We also review the production and loss

processes that are important in the formation of

the different layers of the dayside and nightside

ionospheres, including ion and neutral diffusion.

The processes that determine the neutral, ion

and electron temperatures are discussed. We

review the processes that are important in

production of the luminosity of the upper

atmospheres, including dayglow, nightglow and

auroras. Finally, we describe atmospheric escape

processes, including thermal and non-thermal

mechanisms.

84.1 Basic Structure of Atmospheres .............1259

84.1.1 Introduction .............................1259

84.1.2 Atmospheric Regions .................1260

84.2 Density Distributions of Neutral Species. 1264

84.2.1 The Continuity Equation.............1264

84.2.2 Diffusion Coefﬁcients .................1265

84.3 Interaction of Solar Radiation

with the Atmosphere ...........................1265

84.3.1 Introduction .............................1265

84.3.2 The Interaction of Solar Photons

with Atmospheric Gases .............1266

84.3.3 Interaction of Energetic Electrons

with Atmospheric Gases .............1268

84.4 Ionospheres ........................................1271

84.4.1 Ionospheric Regions ..................1271

84.4.2 Sources of Ionization .................1271

84.4.3 Nightside Ionospheres ...............1277

84.4.4 Ionospheric Density Proﬁles........1277

84.4.5 Ion Diffusion ............................1279

84.5 Neutral, Ion and Electron Temperatures 1281

84.6 Luminosity ..........................................1284

84.7 Planetary Escape .................................1287

References ..................................................1290

84.1 Basic Structure of Atmospheres

84.1.1 Introduction

In a stationary atmosphere, the force of gravity is bal-

anced by the plasma pressure gradient force in the

vertical direction, and the variation of pressure P(z)

with altitude above the surface z is governed by the

hydrostatic relation

dP(z)

=−ρ(z)g(z),

(84.1)

where ρ(z) = n(z)m(z) is the mass density, n(z) is the

number density, and m(z) is the average mass of the at-

mospheric constituents. In general, variables such as P,

ρ, g, n and even m are functions of altitude, although it

will often not be shown explicitly in the equations that

follow for the sake of compactness. The acceleration of

gravity g is usually taken to be the vector sum of the

gravitational attraction per unit mass and the centrifugal

acceleration due to the rotation of the planet:

g(r) = GM/r

−ω

r cos

φ, (84.2)

where r = r

+z is the distance from the center of the

planet, r

is the planetary radius, M is the planetary

mass, G = 6.670 × 10

−8

dyn cm

−2

is the gravitational

constant, φ is the latitude, and ω is the angular velocity

of the planet.

When the hydrostatic relation (84.1) is combined

with the ideal gas law in the form

P = nk

T , (84.3)

where k

is Boltzmann’s constant and T is the tempera-

ture, and integrated, the the barometric formula

P(z) = P

exp





−



H(z



)







(84.4)

Part G 84

1260 Part G Applications

for the pressure P(z) above a reference level (denoted

by the subscript 0) as a function of altitude results. The

pressure scale height H(z) is deﬁned as

H(z) =

(84.5)

In the lower and middle atmosphere, the mass m in

(84.5) is the weighted average mass of the atmospheric

constituents.

When the ideal gas law (84.3) is substituted into the

barometric formula (84.4), the altitude distribution

n(z) = n

T(z)

exp





−



H(z



)







(84.6)

for the number density n(z) above a reference altitude

is obtained. Integration of (84.1)or(84.6) from z to

inﬁnity shows that the column density above that alti-

tude is approximately N(z) = n(z)H(z). Thus the scale

height can be thought of as the effective thickness of the

atmosphere.

In its lower and middle regions, the homosphere,

the atmosphere is well-mixed by convection and/or tur-

bulence. The upper boundary of this region is called

Table 84.1 Homopause characteristics of planets and satellites

Planet Altitude K T n

P Composition

(km) (cm

/s) (K) (cm

−3

) (µbar) (Fraction by number)

Venus

135 4(7)

199 1.4(11) 4.7(-3) CO

(76 ),N

(7.6 ),O(9.3 ),CO(6.7 ),N(0.16 ),C(0.01 )

Earth

100 1(6) 185 1.3(13) 0.3 N

(77%), O

(18%), O(3–4%), Ar(0.7%), He(9.5 ppm),

H(1.3 ppm)

Mars

120–125 5(7) 154 1.3(11) 2.8(-3) CO

(95%), N

(2.5%), Ar(1.5%), O(0.9%), CO(0.42%)

(0.12%), NO(0.007%)

Jupiter

500

2(6) 600 1.4(13) 0.4 H

(95%), He(4.1%), H(0.055%), CH

(200 ppb),

(1.2 ppb),C

(2.5 ppb), C

(0.12 ppb)

Saturn

1100

1.3(8) 200 1.2(11) 3(-3) H

(94%), He(6%), CH

(178 ppm)

Uranus

300

1(4) 130 1(15) 20 H

(85%), He(15%), CH

(20 ppm), C

(10 ppb),

(0.1 ppb), C

(0.05 ppt)

Neptune

750

2(7) 280 1.2(12) 3.9(-2) H

(83%), He(16%), CH

(3 ppm)

Titan

1100 1(9) 155 3(9) 6.4(-5) N

(96%), CH

(2.4%), C

(0.07%), C

(0.7%),

(404 ppm), C

(105 ppm)

Triton

30 3(3) 40 3.3(14) 1.8 N

(99.9%), H

(190 ppm), CH

(37 ppm), H(3.1 ppm),

N(4.1 ppb)

Read as 4 × 10

Altitude above the 1 bar level.

K from von Zahn et al. [84.1] and model atmosphere from Hedin

From [84.2]

et al. [84.3], for 1500 h, 15

◦

N latitude, F

10.7

= 150

From [84.4, 5]

From The US Standard Atmosphere [84.6]

From [84.7]

Viking model from [84.8]

From [84.9–12]

From [84.13] and photochemical model of Kim [84.14].

From [84.15, 16]

the homopause (or turbopause), and above this level,

the major transport process is diffusion. The homopause

is deﬁned as the level at which the time constants for

mixing and diffusion are equal, and usually occurs at

n(z) ∼ 10

–10

−3

, depending on the strength of

vertical mixing for a given planet. Since molecular dif-

fusion coefﬁcients vary from one species to another, the

exact altitude of the homopause is species-dependent,

with smaller species having lower homopause altitudes.

In the terrestrial atmosphere, the homopause is near

100 km at n(z) ∼ 10

−3

. Below the homopause, the

mixing ratios (or fractions by number) of the constituent

gases, apart from those minor or trace species whose

density proﬁles are determined by photochemistry or

physical loss processes, are fairly constant with altitude.

Throughout the atmosphere, gravity exerts a force

on each particle that is proportional to its mass. Below

the homopause, however, the tendency of the species

to separate out under the force of gravity is overpow-

ered by large scale mixing processes, such as convection

and turbulence. Above the homopause, each species is

distributed according to its own scale height. Character-

istics of the homopauses of the planets are presented in

Table 84.1.

Part G 84.1

Aeronomy 84.1 Basic Structure of Atmospheres 1261

84.1.2 Atmospheric Regions

The division of atmospheres into regions is based on

the temperature structure of the terrestrial atmosphere,

which is shown in Fig. 84.1. In the troposphere of

a planet, above the boundary layer, T decreases at close

to the adiabatic lapse rate (Γ ) for the constituent gases

from the surface to the tropopause. For an atmosphere

that is a mixture of ideal gases, Γ = g/c

,wherec

the speciﬁc heat of the gas mixture at constant pres-

sure. The presence of a condensible constituent, such as

water vapor in the terrestrial troposphere, and ammo-

nia or methane in the atmospheres of the outer planets

and satellites, decreases Γ because upward motion leads

to cooling and condensation, which releases latent heat.

On Earth, the dry adiabatic lapse rate is about 10 K/km

and the moist adiabatic lapse rate is about 4–6 K/km in

the lower to middle troposphere. The average lapse rate

is about 6.5K/km, and the altitude of the tropopause

varies from about 9 to 16 km from the poles to the equa-

tor. The composition of the lower atmosphere of the

Earth is given in Table 84.2.

Above the terrestrial tropopause lies the strato-

sphere, a region of increasing T that is terminated at

the stratopause, near 50 km. This increase in T is caused

by absorption of solar near UV radiation by ozone in

the Hartley bands and continuum (200–310 nm). In

the terrestrial mesosphere, which lies above the strato-

sphere, T decreases again to an absolute minimum at

the mesopause, where t ≈180 K and n(z) ≈ 10

−3

Above the mesopause, in the thermosphere, T increases

Table 84.2 Molecular weights and fractional composition

of dry air in the terrestrial atmosphere

Species Molecular Weight Fraction by volume

(g/mole)

28.0134 0.780 84

31.9988 0.209 476

Ar 39.948 0.009 34

44.009 95 0.000 3756

Ne 20.183 0.000 018 18

He 4.0026 0.000 005 24

Kr 83.80 0.000 001 14

Xe 131.30 0.000 000 087

16.043 03 0.000 002

2.015 94 0.000 0005

Taken from The US Standard Atmosphere [84.6], except as

noted

2003 annual average value. The CO

mixing ratio is increas-

ing at an annual rate of about 0.45%. Value is from [84.18]

600

500

400

300

200

100

Temperature (K)

1000 15000 500

Altitude (km)

Mesopause

Stratopause

Tropopause

140

200

250

10.7

= 75

Fig. 84.1 Vertical distribution of temperature in the ter-

restrial atmosphere. The altitudes of the tropopause,

stratopause and mesopause are indicated. The thermo-

spheric temperatures depend on solar activity and proﬁles

are shown for four values of the F

10.7

index, from 75 (low

solar activity) to 250 (high solar activity). The solid and

dashed curves are for noon and midnight, respectively.

After the MSIS model of Hedin [84.17]

rapidly to a constant value, the exospheric tempera-

ture, T

∞

.ThevalueofT

∞

in the terrestrial atmosphere

depends on solar activity and is usually between about

700 and 1500 K. Fig. 84.1 also shows altitude proﬁles of

the noon and midnight thermospheric temperature for

four values of the F

10.7

index, (the 2800 MHz ﬂux in

units of 10

−22

−2

−1

at 1 AU), which represent

different levels of solar activity.

The exosphere is a nearly collisionless region of

the thermosphere that is bounded from below by the

exobase. A particle traveling upward at or above the

exobase will, with high probability, escape from the

gravitational ﬁeld of the planet. The exobase on Earth is

located at about 450–500 km, depending upon solar ac-

tivity. The surface P and T on Mars are about 6 mbar

Part G 84.1

1262 Part G Applications

and 230 K, respectively. Due to the effect of dust storms,

the extent of the Martian troposphere is highly variable,

with a lapse rate that is 2–3 K/km compared with the

adiabatic lapse rate of 4.5K/km and a variable thick-

ness of 20–50 km [84.19]. The atmosphere of Mars,

like many planetary atmospheres, does not have a strato-

sphere. A roughly isothermal mesosphere extends from

the tropopause to the base of the thermosphere at about

90 km. The thermospheric T is sensitive to solar activity

and, since Mars has a very eccentric orbit, to heliocentric

distance; T

∞

varies from about 180 to 350 K.

Near the surface of Venus, T

 700 K and

P ∼ 95 bar. T decreases with a mean lapse rate of

7.7K/km, compared with the adiabatic lapse rate of

8.9K/km, from the surface to about 50 km. The region

from 50 to 60 km contains the major cloud layer, and the

tropopause is usually considered to be at about 60 km.

In the mesosphere, between about 60 and 85 km, T de-

creases slowly from about 250 K to 180 K, and is nearly

constant from 85 km to the mesopause at 100 km. The

daytime exospheric temperature is only weakly depen-

dent on solar activity, varying from about 230 to 300 K

from low to high solar activity. The slow retrograde ro-

tation of the planet, which results in a period of darkness

that lasts 58 days, leads to the relative isolation of the

nightside thermosphere, where T is found to decrease

above the mesopause to an exospheric T ≈ 100 K. Be-

cause of this, the nightside Venus thermosphere has been

called the “cryosphere”. The compositions of the lower

atmospheres of Mars and Venus are given in Table 84.3.

The giant planets, Jupiter, Saturn, Uranus and Nep-

tune do not have solid surfaces, so their atmospheric

regions are deﬁned either in terms of pressure, alti-

tude above the 1 bar level, or altitude above the cloud

tops. The temperature structures of all but Uranus are

inﬂuenced by internal heat sources that the terrestrial

planets do not possess. The temperature structures near

the tropopause can be determined from IR observa-

tions and radio occultation data, and at thermospheric

altitudes from ultraviolet solar and stellar occultations

performed by the Voyager spacecraft. In between these

regions, there is a substantial gap in which only aver-

age temperatures can be inferred. Thus the location and

temperature of the mesopauses are largely unknown.

Below 300 mbar on Jupiter, the lapse rate is close

to adiabatic (1.9K/km). T at 1 bar is about 165 K, and

the tropopause occurs near 140 mbar, where T ≈ 110 K.

At 1 mbar, T again reaches 160–170 K. Temperature

inversions have been reported in the stratosphere, and

are probably due to absorption of solar radiation by dust

or aerosols. Temperatures derived from the Voyager UV

stellar and solar occultations show that T increases from

about 200K near 1 µbar to an exospheric value of about

1100 K [84.2].

For P > 500 mbar on Saturn, the lapse rate ap-

proaches the adiabatic value of 0.9K/km, and the

tropopause, near the 100 mbar level, is characterized

by T ≈ 80 K. Above the tropopause the temperature in-

creases to about 140 K near a P ≈1mbar,andabovethat

altitude there are no measurements of T up to a pressure

of about 10

−8

bar, about 1000 km above the 1 bar level,

where T is again about 140 K. Application of the hydro-

static equation to the altitude range 300–1000 km yields

an average temperature near 140 K for the region. Above

1000 km, T increases to a T

∞

≈ 800 K [84.2]. The mix-

ing ratios of the species in the lower atmospheres of

Jupiter and Saturn are given in Table 84.4.

The tropopauses on both Uranus and Neptune oc-

cur near 100 mbar, where T ≈ 50 K. The lapse rates in

the troposphere are 0.7and0.85 K/km for Uranus and

Neptune, respectively. The temperatures in the Uranus

thermosphere range from 500 K near 10

−7

bar (about

1000 km above the 1 bar level) to an exospheric value of

about 800 K. At 300 km on Neptune, T attains a nearly

constant value in the range 150 to 180 K. At 600 km

where P ≈ 1 µbar, T increases again to a value that is

Table 84.3 Composition of the lower atmospheres of Mars

and Venus

Species Mixing Ratio

Mars Venus

0.953 0.96

0.027 0.04

Ar 0.016 50–120 ppm

0.0013 20–40 ppm

CO 0.0008 20–30 ppm

O 0.0003

30 ppm

He 4 ppm

10 ppm

Ne 2.5 ppm 5–13 ppm

Kr 0.3 ppm 0.02–0.4 ppm

Xe 0.08 ppm –

– 150 ppm

S – 1–3 ppm

15 ppm

0.1 ppm

From [84.20], except as noted.

Includes all isotopes of Ar.

Va ri ab le

From [84.21].

From Krasnopolsky and Gladstone. [84.22]

Krasnopolsky and Feldman [84.23]

Yung and DeMore [84.24]

Part G 84.1