Yung Y.L., DeMore W.B. Photochemistry of Planetary Atmospheres
Подождите немного. Документ загружается.
126
Photochemistry
of
Planetary
Atmospheres
Figure
5.3
Radio science radio occultation measurements
of
electron
concentrations
in the
ionosphere
of
Saturn
by
Voyagers
1
and 2
(labeled
VI
and
V2).
For
comparison,
the
Pioneer (la-
beled
P/S)
results
are
also
shown.
After
KJiore,
A. J. et
al.,
1980,
"Vertical
Structure
of the
Ionosphere
and
Upper
Neutral
Atmo-
sphere
of
Saturn
from
Pioneer Radio Occultation." Science 207,
446;
and
Lindal,
G.
F,
Sweetnam,
D.
N.,
and
Eshleman,
V. R.,
1985, "The Atmosphere
of
Saturn:
An
Analysis
of the
Voyager
Radio
Occultation Measurements."
Astron.
J. 90,
1136.
properties
of the
atmosphere averaged over
a
scale height.
The
wave features
in the
RSS
profiles
are
authentic atmospheric waves.
The
IRIS instrument
on
Voyager consists
of a
Michelson interferometer that
records
the
spectrum
from
180 to
2500
cm"
1
(4-56
/urn)
with
a
resolution
of 4.3
cm"
1
,
plus
a
single-channel radiometer.
At
this resolution
it is
possible
to
observe
the
detailed
vibrational
and
rotational spectra
of
simple molecules present
in the
atmosphere. Fig-
ure
5.5
shows three spectra that
are
typical
of the
observations
of
Jupiter
and
Saturn.
The
broad feature between
250 and 700
cm"
1
due to
pressure-induced transitions
in
H
2
is
clearly present
on
both Jupiter
and
Saturn.
The
NH
3
feature near
200
cm""
1
is
prominent
in
Jupiter
but is
absent
from
Saturn.
The
strong
V4
CH4
band
in the
1200-1400
region
is
present
in all
spectra.
C
2
H
6
and
€2^2
appear
in
these spectra
as
strong emission features. This
is
caused
by a
combination
of the
thermal inversion
and
the
high concentrations
of
C
2
H6
and
C
2
H2
in the
stratosphere. Figure
5.6
shows
the
IRIS spectrum
for the 5
fim
window region
of
Jupiter.
In
this region
it is
possible
to see
deep into
the
troposphere
to the
level
of
several bars. Minor constituents such
as
H
2
O,
GeH
4
,
CH
3
D,
and
PH
3
can be
measured
from
such observations.
Figure
5.4
Radio science radio
occultation
measurements
of
the
temperature
profile
in the
troposphere
and the
middle
atmosphere
to 1
mbar.
After
Lindal,
G. F. et
al.,
1981, "The
Atmosphere
of
Jupiter:
An
Analysis
of the
Voyager Radio
Occultation Measurements."
J.
Geop/ryj.
/tos.
86,
8721.
Figure
5.5
IRIS observations
of the
infrared
spectra
of
Jupiter's atmosphere.
After
Hanel,
R.
et
al.,
1981,
"Infrared Observations
of the
Saturnian
System
from
Voyager
1."
Sa'ewce
212,
192.
127
128
Photochemistry
of
Planetary
Atmospheres
CD
Figure
5.6
IRIS observations
of the
infrared
spectra
of
Jupiter's
atmosphere
in the 5
//.m
"window"
region.
After
Hanel,
R.
et
al.,
1979, "Infrared Observations
of the
Jovian System
from
Voyager
2."
Science 206, 952.
It
is
fair
to say
that
the
Voyager results
are the
single greatest contribution
to our
knowledge
of the
atmospheres
of the
outer solar system.
Of
course, these results
do
not
stand alone. Observations
from
ground-based facilities
and
Earth-orbiting satellites
also contribute
to
greatly advance understanding
of the
planetary atmospheres before
and
after
the
Voyager encounters.
We
have chosen
the
Voyager observations here
to
illustrate
how a
concentrated technological
initiative
can
revolutionize
a field.
5.1.2
Chemical
Composition
The
composition
of the
atmosphere
of
Jupiter
as
deduced
from
Voyager
and
other
measurements
is
summarized
in
table 5.2. Less
is
known
about Saturn, Uranus,
and
Neptune,
and
tables
5.3 and 5.4
provide summaries
of our
knowledge
of
these planets.
It
is
convenient
to
classify
the
species
in
these tables according
to the
following
categories:
(a)
low Z
elements,
(b)
high
Z
elements,
(c)
gases
that
can
condense,
(d)
gases
from
equilibrium
chemistry,
(e)
photochemical
products,
(f)
products
of ion
chemistry,
and
(g)
isotopomers,
where
H and He are the low Z
elements,
and
high
Z
elements include
all
elements
heavier
than
He. The
above classification
is not
intended
to be
exclusive.
A
species
may
belong
to
more
than
one
category.
For
example,
HCN can be
derived
as a
photochem-
ical
product
of
NH
3
and
CH
4
in the
stratosphere
or as an
equilibrium product
from
lovian
Planets
129
Table
5.2
Composition
of the
atmosphere
of
Jupiter
Species
H
2
He
CHU
NH
3
PH
3
H
2
O
CO
GeHi
AsH
3
C
2
H
6
C
2
H4
C
2
H
2
C
4
H
2
CH
3
C
2
H
C
6
H
6
H
e
H
3
+
HD
CH
3
D
"Cft,
13
CCH
6
13
CCH
2
15
NH
3
C
3
H
8
H
2
S
Abundance
0.898
±
0.02
0.102
±0.02
3.0
±
l.Ox
10~
3
2.6 ± 0.4 x
10~
3
7.0
±
l.Ox
10~
7
3.0
± 2.0 x
10-
5
4.0
±
l.Ox
10-'
1.6
±0.3
x
10~
9
7.0+2
1
x
10-'°
2.2
± 1.1 x
10-
10
5.8
± 1.5 x
10-
6
7.0
± 3.0 x
10~
9
1.1
±0.3
x
10-
7
3.0
± 2.0 x
10-'°
2.5+]
x
10-
9
2.0+]
x
10-
9
Dayglow
= 15 kR
maximum
density
= 3 x
10
5
cm"
3
detected
?
s
+3
-°
v
m~
5
^•°_08
X
IU
2.0
± 4.0 x
10-
7
3.3 x
10~
5
5.8
x
10-
8
1.0
x
10~
8
2.0 x
1Q-
6
< 6.0 x
1Q-
7
< 3.3 x
10~
8
< 2.0 x
10~
9
Remarks
primordial,
electroglow
observed
primordial,
resonance line observed
photolyzed
in
mesosphere
condensation
in
upper troposphere,
photolyzed
in
troposphere
and
stratophere
photolyzed
in
troposphere
and
stratophere
at
6 bar
level
at
2-4
bar
level
mixed
from
deep atmosphere
mixed
from
deep
atmosphere
mixed
from
deep atmosphere
photochemical, stratosphere
photochemical, stratosphere
photochemical, stratosphere
photochemical, stratosphere
polar auroral region
polar
auroral region
nonbulge,
disk-centered, solar maximum
ionosphere
polar
auroral region
gives
D/H ~ 1.6 x
10~
5
gives
D/H ~ 1.7 x
10~
5
gives
12
C/
13
C
~ 90
gives
12
C/
13
C
~ 94
gives
C
2
H
2
/
13
CCH
2
~ 10
gives
14
N/
15
N
~ 125
polar auroral region
troposphere
stratosphere
From
Fegley,
B. Jr.
(1995).
the
planetary interior.
In
addition,
HCN can
condense
at the
tropopause
of
Neptune's
atmosphere. Therefore,
HCN
belongs simultaneously
to
(b)-<e).
We
briefly
discuss
the
species
in
tables
5.2-5.4
in
terms
of the
preceding classification.
The
photochemical
products
are
special topics that
are
elaborated
in
sections
5.3-5.6.
(a)
Low Z
Elements
H2
and He are
obviously derived
from
the
gaseous component
of the
solar nebula.
But
the
abundance
of He
relative
to H2 is not
constant among
the
giant planets. Table
5.5
summarizes
the
He/H
ratios
for the
giant planets, along with internal heat
fluxes. The
first
notable
difference
is
between Jupiter
and
Saturn.
The
He/H
ratio
in
Jupiter
is
71% of the
cosmic abundance value
but
only
21%
for
Saturn.
It is
difficult
to
imagine
that
He was
nonuniform
in the
solar nebula.
The
explanation
is
found
in the
internal
heat
of the
giant
planets,
as
summarized
in
table 5.5.
It is
known that some giant
planets
radiate more heat than what
is
absorbed
from the
sun.
The
ratio
of the
total
heat
flux to the
absorbed solar
flux
provides
a
measure
of the
excess heat generated
Table
5.3
Composition
of the
atmosphere
of
Saturn
Species
H
2
He
CH4
NH
3
PH
3
CO
GeH4
AsH
3
C
2
H
6
C
2
H
2
H
e
HD
CH
3
D
CH
3
C
2
H
C
3
H
8
H
2
S
H
2
O
HCN
Sift,
Abundance
0.963
±
0.024
0.0325
±
0.024
4.5-
2
;
4
x
lO-
3
0.5
-
2.0
x
10~
4
1.4
±0.8
x
10~
6
1.0
±0.3
x
10~
9
4.0
± 4.0 x
10-'°
3.0
± 1.0 x
10~
9
7.0
± 1.5 x
10~
6
3.0
± 1.0 x
10~
7
Day
glow
= 3.3
kR
maximum density
= 2.3 x
10
4
cm~
3
1.10
±0.58
x
10~
4
3.9
±2.5
x
10~
7
5.1
x
10~
5
tentatively
detected
tentatively
detected
< 2.0 x
10~
7
< 2.0 x
10~
8
<
4.0 x
10-
9
<
4.0 x
JO'
9
Remarks
disk-centered,
solar
maximum
south polar latitudes
gives
13
C/
I2
C~89
From
Fegley,
B. Jr.
(1995).
Table
5.4
Composition
of the
atmospheres
of
Uranus
and
Neptune
Species
H
2
He
CH4
C
2
H
6
C
2
H
2
CO
HCN
H
Uranus
0.825
±
0.033
0.152
±0.033
2.3 x
10~
2
2.0 x
10~
5
1.
0-20.0
x
10-
9
1.0
x
10~
8
< 3.0 x
10'
8
< 1.0 x
10-'°
—
Neptune
0.80
±0.03
0.19
±0.032
1.
0-2.0
x
10~
2
6.0-50.0
x
10~
4
1.5+^
x
10~
6
6.0±|
4
x
10-
8
1.2x
10~
6
l.Ox
10~
9
—
Remarks
troposphere
stratosphere
HD
CH
3
D
1.48
x
10-
4
8.3 x
10~
6
H
2
S
< 8.0 x
10-
7
NH
3
<1.0xlO-
7
From
Fegley,
B.,
Jr.
(1995).
1.92x
10-
4
1.2
x
10-
5
< 3.0 x
10~
6
< 6.0 x
10~
7
Gives
D/H = 9.0 x
10~
5
for
Uranus,
1.2
x
10~
4
for
Neptune
Gives
D/H = 9.0 x
10~
5
for
Uranus,
1.2 x
10~
4
for
Neptune
130
Jovian
Planets
131
Table
5.5
Helium
to
hydrogen
ratio
and
internal
heat
flux for
giant
planets
Jupiter
Saturn Uranus Neptune
He/H
(He/H)/(He/H)
0
Total heat
flux/absorbed
solar
flux
Excess heat density
(10~
13
W/g)
0.0568
0.709
1.67
±0.09
1.76 ±0.14
0.0169
0.211
1.78
±0.09
1.52±0.11
0.0921
1.15
1.06
±0.08
<0.16
0.119
1.48
2.61
±
0.28
0.34
±0.11
in
the
planet.
A
value
of
unity
for
this
ratio
implies
the
absence
of an
internal
heat
source.
The
ratios
for
Jupiter
and
Saturn
are
1.67
and
1.78,
respectively, implying that
these planets radiate
67% and 78%
more energy than what they receive from
the
sun.
A
more useful quantity
is the
excess heat density
(in
units
of
10~
13
W
g~')
derived
from
the
excess heating rate divided
by the
mass
of the
planet. This quantity
is
1.76
and
1.52
for
Jupiter
and
Saturn, respectively. There
are two
major sources
of
heating
for
the
giant planets.
The first is
heat derived from gravitational contraction
of the
planets. According
to
models
of the
origin
and
evolution
of
these
planets,
there
was a
period
of
rapid contraction
at the
beginning
(10
5
yr), followed
by a
longer
period
of
slow contraction over
the
next
few
billion
years.
This
is the
principal
source
of
internal
heat
for
Jupiter,
but
this
source
would
be
insufficient
for a
smaller planet like Saturn.
The
second major
source
of
internal heat derives
from
the
separation
of
helium from
hydrogen.
At
pressures
greater than
3
Mbar,
which occurs
in the
interior
of
Jupiter
and
Saturn,
hydrogen
becomes
metallic.
If the
temperature
is
sufficiently
high
(>
10
4
K),
helium
forms
an
immiscible mixture with hydrogen. However,
at
lower temperatures,
He and H2 are
only partially miscible.
The
heavier element tends
to
sink
to the
interior,
much
as
differentiation
occurs
in the
interior
of the
terrestrial planets.
In
Saturn this
process
is
shown
to be
important,
and as the
helium-rich
gas
sinks
to the
core,
its
viscous interactions
with
the
surrounding
air
convert
the
gravitational energy into heat.
Thus,
the
depletion
of He in the
gaseous
envelope
of
Saturn
and the
internal heating
of
the
planet
are
beautifully
and
simply related. Since
He is
also
somewhat
depleted
on
Jupiter, this
process
may
also
be
occurring
on
that planet, albeit
at a
reduced level.
Pressure
at the
centers
of
Uranus
and
Neptune
does
not
exceed
200
kbar,
and
there
is
no
separation
of
helium
from
hydrogen
by
this mechanism.
The
only planet
in
table
5.5
with
He/H
ratio equal
to the
cosmic
abundance ratio
is
Uranus.
The
question then arises
as to why
Neptune
is
enriched
in
helium
by
about
30%
relative
to
Uranus. There
is no
simple explanation.
There
is,
however,
an
alternative interpretation
of the
Voyager data
on
which this helium abundance
is
based.
The
Voyager
data
could
be
explained
with
a
model
containing
the
cosmic
abundance
of He and
0.3%
N2. As we
shall argue,
the
latter hypothesis
may be
needed
to
account
for the HCN
observed
in
Neptune.
The
ultimate
difference
between Uranus
and
Neptune
is
attributed
to the
absence
and
presence,
respectively,
of an
internal heat
source, which
affects
the
interior convection
of
these planets.
(b)
High
Z
Elements
From tables
5.2-5.4
we may
note that
the
giant planets
are
enriched
in the
high
Z
elements relative
to the
cosmic abundances. Table
5.6
expresses
the
same
information
132
Photochemistry
of
Planetary Atmospheres
Table
5.6
High
Z
elements
and
bulk properties
of the
giant planets
Property
Jupiter
Saturn
Uranus
a
All
masses
are in
units
of
Earth
masses.
b
Low
Z
elements
= H + He.
'High
Z
elements
= all
elements
heavier
than
He.
Neptune
C/C
Q
N/N
O
P/PO
o/o
e
S/S
0
Total
mass
3
Low
Z
mass
b
High
Z
mass (core)
2.3
±0.2
2.0
1.4
±0.4
0.02
<
3.7 x
10-
3
318.1
254.1-292.1
26.0-64.0
5.1
±2.3
3.0
±1.0
2.8
± 1.6
—
—
95.1
72.1-79.1
16.0-23.0
35.0
±15.0
—
—
—
—
14.6
1.3-3.6
11.0-13.3
40.0
±
20.0
33.0
?
—
—
—
17.2
0.7-3.2
14.0-16.5
relative
to the
cosmic standard. Thus, carbon (primarily
as
CHO
is
enriched
by
factors
of
2-3 in the
atmospheres
of
Jupiter
and
Saturn,
and by
about
30-40
times
in the
atmospheres
of
Uranus
and
Neptune.
The
reason
may
become
clear
if we
examine
the
bulk
properties
of the
giant planets inferred
from
independent sources.
As
summarized
in
table
5.6 all
giant planets have substantial
cores,
which
may
contribute
significantly
to the
budget
of
high
Z
elements.
The
cores
of
Jupiter
and
Saturn
are
much smaller
than
the
gaseous envelopes
of low Z
elements,
but the
situation
is
reversed
for
Uranus
and
Neptune,
which
have large
cores
relative
to
gas.
Nitrogen
and
phosphorus appear
to be
enriched also,
but
observing
NHs
and
PHj
in the
atmospheres
of
Uranus
and
Neptune
is
difficult
due to
condensation.
The 33
times enrichment tentatively assigned
to
Neptune
is
based
on a
plausible
but
unverified
interpretation
of the
origin
of HCN in
Neptune. Oxygen
(in
HjO)
has
been positively
identified
only
in
Jupiter
and
appears
to be
depleted relative
to the
cosmic abundance
by a
factor
of 50.
This
may not be
real
because water
may be
sequestered
in the
clouds.
The
upper limit
for
sulfur
(in
H^S)
established
for
Jupiter suggests that Jupiter
is
depleted
in
sulfur
by a
factor greater
than
300.
Again,
in
this case
the
problem
may lie
with
the
sequestering
of
sulfur
in
NHUSH
clouds. This topic
is
discussed
in
section
5.1.2(c).
(c)
Gases
That
Can
Condense
At
the low
temperatures that
are
typical
of the
visible troposphere
and the
tropopause
region
in the
giant planets
a
large number
of
gases
can
condense.
The
vapor pressures
for
a
selected
number
of
simple molecules over
the
temperature range
of
interest
are
given
in figure
5.7.
Of all the
molecules compared
in
this
figure,
H
2
O
condenses
most
easily, followed
by
NH/j,
PH
3
,
C
2
hydrocarbons,
and
CRj.
This
has an
important
consequence
on the
interpretation
of the
observed composition
of the
atmospheres
of
these planets. Figure
5.8
shows
a
model
of
Jupiter
with
regions
of the
atmosphere
where
clouds
of
NHs,
NFUSH,
and H2O are
expected
to
form.
The
concentrations
of
the
condensing
species
are
solar.
For
water,
the
dashed lines show
the
location
of
EfeO
ice
formation
if its
abundance
is
only
10~
3
times solar.
For an
understanding
of
atmospheric composition, there
are two
crucial regions
of the
atmosphere where
an
estimate
of the
saturation vapor pressure
of
molecular
species
is
useful.
For the
Jovian
Planets
I 33
Figure
5.7
Saturation vapor pressures
of
selected
molecules
of im-
portance
in the
atmosphere
of the
outer solar system. After Atreya,
S.,
1986, Atmospheres
and
Ionospheres
of the
Outer Planets
and
their Satellites (New York:
Springer-Verlag).
visible
atmosphere part
we
shall choose
the
pressure level
of 1
bar,
with
approximate
temperatures
of
165, 135,
and 75 K,
respectively,
for
Jupiter, Saturn,
and
Uranus.
For
the
purpose
of
this
discussion
we
take
the
thermal structures
of
Uranus
and
Neptune
to
be the
same.
The
tropopauses
of the
giant planets
are
between
100 and 200
mbar;
we
arbitrarily adopt
a
pressure level
of 150
mbar.
The
minimum temperatures
are
110,
85, and 50 K,
respectively
for
Jupiter, Uranus,
and
Saturn. Using this information
it
is
possible
to
compute
the
saturation vapor pressures
of
simple molecules
at 1 bar
and
the
tropopauses.
The
results
are
summarized
in
table 5.7. Comparing
the
results
of
this
table
with
those
in figure 5.7 and
tables
5.3 and
5.4,
we can
understand
the
nondetection
of
HaO,
H2S,
and HCN in
Saturn
and the
apparent depletion
of
NHs,
PH
3
,
and
some
of the
higher hydrocarbons
in
Uranus
and
Neptune.
These
species
may
all
be
present
in the
atmosphere
but may all be in the
frozen
solids
at the
ambient
atmospheric temperatures. There
is a
major surprise when
we
compare table
5.4
with
134
Photochemistry
of
Planetary
Atmospheres
Figure
5.8 A
model
of the
clouds
of
Jupiter based
on
cosmic abundances
of the
ele-
ments.
The
main cloud layers, composed
of
aqueous
NHa
solution plus
HiO
ice,
solid
NH4SH,
and
solid
NHs,
are
formed
by
condensation
of
thO,
NHs,
and
HiS,
which
are
stable
in the
lower atmosphere.
After
Weidenschilling,
S.
I.,
and
Lewis,
J.
S.,
1973,
"Atmospheric
and
Cloud Structures
of the
Jovian
Planets."
Icarus
20,
465.
table
5.7.
The CH4
abundance
in the
stratosphere
of
Neptune
is in
excess
of its
saturation
value
by
factors
of
10-100.
The
tropopause cold trap must have failed
to
remove
CH4
from
air
that
is
entering
the
stratosphere from
the
troposphere.
A
special
convective
injection mechanism
may be
operating
on
Neptune
but not on
Uranus,
whose
CtLt
abundance
in the
stratosphere
is
consistent with that given
by the
cold
trap.
The
ultimate difference between Uranus
and
Neptune
may be in the
absence
and
presence, respectively,
of
excess
heat
flux
that drives convection
in the
troposphere
(see table
5.5).
Table
5.7
Saturation mole
fraction
of
simple molecules
in the
troposphere
(at the 1 bar
level)
and the
tropopause
of
giant planets.
Troposphere
(1
bar)
Jupiter
Saturn
Uranus/Neptune
Tropopause
Jupiter
Saturn
Uranus/Neptune
CRt
NS
NS
7.7
x
IO-
3
NS
NS
1.9x
IO-
5
C
2
H
2
NS
2.2
x
IO-
2
—
4.8 x
IO-
3
1.3
x
IO-
5
—
H
2
O
2.3 x
IO-
9
—
—
S
S
S
Notes:
The
temperatures
at 1 bar are
165, 135,
and 75
K
for
Jupiter, Saturn,
and
Uranus/
Neptune,
respectively.
The
corresponding adopted temperatures (not
the
real temperatures)
at
150
mbar
are
110,
85, and 50 K. NS
denotes
mixing
ratios
>
0.1
and S
denotes values
<
l.Ox
10-
10
.
lovian
Planets
135
Figure
5.9
Partitioning
of
carbon species
in the
deep
atmosphere
of
Jupiter. Equilibrium chemistry
with
cosmic abundances
of
ele-
ments
is
assumed
in the
model.
After
Prinn,
R. G., and
Barshay,
S. S.,
1977,
"Carbon
Monoxide
on
Jupiter
and
Implications
for
Atmospheric
Convection."
Science 198,
1031.
(d)
Gases from Equilibrium Chemistry
As
pointed
out in
section
5.1,
in the
interior
of the
giant planets
at
pressures
and
temperatures
in
excess
of 1
kbar
and
1000
K,
respectively, equilibrium chemistry
is
important.
The
partitioning
of
chemical
species
is
carried
out
according
to the
laws
of
thermodynamics,
as
described
in
section 3.2.
An
example
of
this type
of
chemistry
for
carbon
is
given
in
figure
5.9 for
Jupiter. Assuming cosmic abundances
of the
elements,
the
model predicts appreciable amounts
of
species such
as CO and
CiVLf,.
Vigorous
mixing
from
the
level
of
about
1100
K can
bring
up
parcels
of air
with
mixing
ratios
of CO and
C2He
equal
to
10~
9
and
10~
10
,
respectively. This source
can
account
for the
observed concentration
of CO in
Jupiter
but is too
small
to
explain
the
observation
of
C2He-
This process
has
been invoked
to
account
for the
observed
HCN, GeH4,
and
AsHs
in the
atmosphere
of
Jupiter.
The
observed
species
CO,
GeH4,
and
AsHs
in
Saturn
and CO in the
atmosphere
of
Neptune
may
have
a
similar origin
in
the
planetary interior. However,
the
observed
HCN in
Neptune cannot
be
accounted
for
by
this mechanism, because
the
stratospheric abundance
far
exceeds
that
of the
saturation
vapor
at the
tropopause.
As
discussed
in
section 5.4.2,
HCN in
Neptune
must
be
locally
synthesized
in the
upper
atmosphere.
A key
uncertainty concerning
the
validity
of
equilibrium
chemistry
for the
giant planets
is the
time constant required
for
equilibrium
to be
reached.
A
crucial quenching temperature must
be
estimated
so
that
the
chemical time equals that
for
atmospheric transport.
We
note that Uranus
is a
very
quiescent planet compared
with
Neptune. Hence,
we
expect both
CO and HCN
to be
significantly
depleted
in
Uranus relative
to
Neptune. This
is
borne
out by the
observations summarized
in
table 5.4.