submitted to Astrophysical Journal
arXiv:astro-ph/0511136v1 4 Nov 2005
Atmospheric Chemistry in Giant Planets, Brown Dwarfs, and
Low-Mass Dwarf Stars II. Sulfur and Phosphorus
Channon Visscher and Bruce Fegley, Jr.
Planetary Chemistry Laboratory, Department of Earth & Planetary Sciences, McDonnell
Center for the Space Sciences, Washington University, St. Louis, MO 63130-4899
[email protected], [email protected]
ABSTRACT
We use thermochemical equilibrium and kinetic calculations to model sulfur
and phosphorus chemistry in the atmospheres of giant planets, brown dwarfs,
low-mass stars, and extrasolar giant planets (EGPs). The chemical behavior of
individual S- and P-bearing gases and condensates is determined as a function
of pressure, temperature, and metallicity. Our results are independent of any
particular model atmosphere and the behavior of different gases can be used to
constrain atmospheric structure and metallicity. Hydrogen sulfide is the dominant sulfur gas in substellar atmospheres and approximately represents the atmospheric sulfur inventory. Depending on the prevailing S and C chemistry,
the abundance of minor sulfur gases may constrain atmospheric temperatures
or metallicity. Disequilibrium abundances of PH3 are expected in the observable atmospheres of substellar objects, and PH3 is representative of the total P
abundance in giant planets and T dwarfs. A number of other phosphorus gases
become relatively abundant in substellar atmospheres with increasing effective
temperatures.
Subject headings: astrochemistry — planets and satellites: individual (Jupiter)
— stars: low-mass, brown dwarfs — stars: individual (Gliese 229B, HD 209458)
1.
Introduction
Previously, we modeled the carbon, nitrogen, and oxygen chemistry in giant planet,
brown dwarf, and low-mass dwarf star atmospheres (Lodders & Fegley 2002, hereafter LF02).
–2–
Here we continue and extend this study by employing thermochemical equilibrium and kinetic
calculations to model the behavior of sulfur- and phosphorus-bearing gases and condensates
in substellar objects. We adopt an approach similar to that in our earlier study. We determine the chemical behavior of each sulfur- and phosphorus-bearing species as a function of
pressure and temperature, plotted in abundance contour diagrams. Our abundance results
are thus independent of any particular pressure-temperature profile. The atmospheric profile
of any object may be superimposed on the abundance diagrams to determine equilibrium
chemistry along the profile. In principle, the chemical behavior of key gases and condensates
may also be used to constrain atmospheric temperature, pressure, or metallicity.
In the next section (§2) we describe our computational method. In §3 we give an
overview of sulfur chemistry in a solar system composition gas. We then describe the chemical behavior of individual sulfur-bearing condensates and gases as a function of pressure,
temperature, and metallicity. Where relevant, we discuss which sulfur species may serve
as diagnostic probes of atmospheric structure or metallicity. We finish by examining the
overall sulfur chemistry in representative substellar objects. A similar treatment of phosphorus chemistry follows in §4. We briefly discuss photochemistry in §5, and conclude with
a summary (§6).
2.
Computational Method
Thermochemical equilibrium calculations were performed using a Gibbs free energy minimization code, previously used for modeling the atmospheric chemistry of Saturn (Visscher
& Fegley 2005). Where relevant, we considered the effects of vertical mixing on the abundances of gases (e.g., PH3 ) which serve as chemical probes of the deep atmospheres of Jupiter
and Saturn. This was done using a chemical dynamical model described elsewhere (Fegley
& Prinn 1985).
Thermodynamic data for the equilibrium calculations were taken from the compilations
of Gurvich et al. (1989-1994), Robie & Hemingway (1995), the fourth edition of the JANAF
Tables (Chase 1999), and the thermodynamic database maintained in the Planetary Chemistry Laboratory (LF02). This database includes additional thermodynamic data from the
literature for compounds absent from the other compilations, as well as several important
data revisions for the sulfur and phosphorus species SH, S2 O, NS, PS, PH, PH3 , PN, and
Mg3 P2 O8 (s), which are incorrect as tabulated in the JANAF Tables (Lodders 1999a, 2004a).
Thermodynamic data for P4 O6 gas was taken from the JANAF tables for reasons cited in
Fegley & Lodders (1994) (hereafter FL94).
–3–
All calculations were conducted using elemental abundances from Lodders (2003) for a
solar system (i.e., protosolar) composition gas. The effect of metallicity on sulfur and phosphorus chemistry was examined by running computations at [Fe/H] = -0.5 dex (subsolar),
[Fe/H] = 0 dex (solar), and [Fe/H] = +0.5 dex (enhanced) metallicities. The metallicity factor, m, is defined as log m = [Fe/H]. When considering the chemical behavior of individual
gases, we focus on temperatures of 800 K and higher, where thermochemical processes are
expected to dominate. Further discussion of thermochemical vs. photochemical processes is
given in §5.
3.
3.1.
Sulfur Chemistry
Overview of Sulfur Chemistry
Figure 1 illustrates the pressure and temperature regions where different sulfur gases
constitute the major form of sulfur in a solar metallicity gas at equilibrium. Condensation
temperatures are also shown (dotted lines) for several S-bearing compounds as a function
of total pressure (see Table 1 and §3.2). Model atmospheric profiles for Jupiter (Teff = 124
K), the T dwarf Gliese 229B (Teff = 960 K; Marley et al. 1996), the close-orbiting EGP (or
“Pegasi” planet) HD209458b (Teff = 1350 K; Iro et al. 2005), an L dwarf (Teff = 1800 K,
log g = 5.0; Burrows et al. 2005), and an M dwarf (Teff = 2600 K, dust-free, log g = 5.0; Tsuji
et al. 1996) are indicated by dashed lines. We note that Jovian atmospheric chemistry differs
slightly than that for a solar metallicity gas because Jupiter has a heavy element enrichment
comparable to [Fe/H] ≈ +0.5 dex (Lodders 1999b; LF02).
The most abundant S-bearing gases are generally H2 S, SH, and S, depending on the
temperature and total pressure. For example, at high temperatures and low pressures, H2 S
is converted into SH by the net thermochemical reaction:
H2 S = SH + 0.5H2 ,
(1)
and the line dividing the H2 S and SH fields in Figure 1 indicates where these two gases have
equal abundances A(H2 S)=A(SH) ≈ 12 ΣS (where ΣS is the total sulfur elemental abundance).
The position of this line is approximated by
log PT = 6.82 − 17570/T,
(2)
and is independent of metallicity. The abundance of each sulfur gas does not drop to zero as
this line is crossed; H2 S is still present within the SH field and vice versa. As temperatures
increase, SH dissociates and monatomic S becomes the dominant sulfur-bearing gas via
SH = S + 0.5H2 .
(3)
–4–
The position of the SH-S equal abundance boundary is given by
log PT = 4.80 − 14522/T,
(4)
independent of metallicity. At low pressures, S replaces H2 S as the dominant sulfur gas via
H2 S = S + H2 .
(5)
The position of the metallicity-independent H2 S-S boundary line is approximated by
log PT = 5.81 − 16046/T.
(6)
The H2 S-SH, SH-S, and H2 S-S boundaries intersect at the H2 S-SH-S “triple point” at T ∼
1509 K and PT ∼ 10−4.82 bar, indicated by the triangle in Figure 1 and represented by the
thermochemical equilibrium
H2 S + S = 2SH.
(7)
At the triple point, all three gases have equal abundances [A(H2 S) = A(SH) = A(S) ≈ 13 ΣS],
and the abundance of each gas is about one third of the total sulfur abundance.
3.2.
Sulfur Condensation Chemistry
3.2.1. Ammonium Hydrogen Sulfide, NH4 SH
Figure 1 shows that sulfur condenses as NH4 SH via the net thermochemical reaction
NH3 + H2 S = NH4 SH(s),
(8)
at low temperatures where H2 S and NH3 are the dominant sulfur and nitrogen gases, respectively. The NH4 SH condensation temperature is approximated by
104 /Tcond (NH4 SH) = 48.91 − 4.15 log PT − 4.15[Fe/H],
(9)
slightly different from LF02 due to revised elemental abundances. Equation (9) shows that
increasing either pressure or metallicity results in higher NH4 SH condensation temperatures.
On Jupiter, NH4 SH condensation should occur near the ∼ 220 K level (cf. FL94), though a
NH4 SH cloud was not detected by the Galileo entry probe because of its entry in the cloudfree 5 µm hot spot (e.g. Atreya et al. 1999). Condensation of NH4 SH is expected to be very
effective at removing H2 S from the upper atmospheres of giant planets because nitrogen
is ∼ 4.4 times more abundant than sulfur in a solar system composition gas. However,
NH4 SH cloud formation is not expected on warmer objects such as brown dwarfs because
their atmospheric pressure-temperature profiles do not intersect the NH4 SH condensation
curve.
–5–
3.2.2. Hydrogen Sulfide, H2 S
At sufficiently low temperatures, H2 S condensation may occur via the net reaction
H2 S = H2 S (s).
(10)
The condensation temperature for hydrogen sulfide is approximated by
104 /Tcond (H2 S) = 86.49 − 8.54 log PT − 8.54[Fe/H].
(11)
Hydrogen sulfide cloud formation is only possible in cool objects (such as Uranus and Neptune) if NH3 is absent or less abundant than H2 S, since ammonia will consume atmospheric
sulfur to form NH4 SH via reaction (8) (see discussion in Fegley et al. 1991). We also examined the condensation of S, OCS, and SO2 , finding that none of gases condense under
equilibrium conditions over this P-T range in a protosolar composition gas.
3.2.3. Sodium Sulfide, Na2 S
A number of metal sulfides are also expected to condense in the atmospheres of giant
planets and brown dwarfs. This strongly affects the observed spectra by removing gases from
the atmosphere and introducing solid particles (e.g. Lodders, cited in Marley et al. 1996;
Burrows et al. 2000a). The formation of a metal sulfide cloud requires that its component
elements are not removed by condensation of more refractory compounds deeper in the
atmosphere (e.g. FL94; Lodders 1999b; LF02), since solids in a planetary atmosphere will
settle into a cloud layer and cannot form secondary condensates at higher altitudes. For
example, FeS would form a substantial cloud layer at ∼ 700 K if iron were not already
removed by condensation as Fe metal at deeper, warmer levels in the atmosphere. Since
Fe is nearly twice as abundant as S in a solar composition gas, FeS condensation would
effectively remove all H2 S from the atmosphere above the 700 K-level. This scenario is
inconsistent with an observed H2 S abundance of at least twice the protosolar H2 S/H2 ratio
in Jupiter’s atmosphere, measured by the Galileo probe mass spectrometer (Niemann et al.
1998; Wong et al. 2004; LF02). In contrast to Fe, there are several other elements which
are expected to condense primarily as sulfides (see Table 2 in FL94). The most abundant of
these are Na, Mn, and Zn.
Sodium sulfide cloud formation occurs via the net thermochemical reaction
2Na + H2 S = Na2 S(s) + H2 .
(12)
The condensation temperature of Na2 S as a function of pressure and metallicity is approximated by
104 /Tcond (Na2 S) = 10.05 − 0.72 log PT − 1.08[Fe/H],
(13)
–6–
and is shown in Figure 1 for a solar-metallicity gas. Sodium sulfide is expected to condense
at the ∼ 1370 K level in Jupiter’s atmosphere (FL94; Lodders 1999b) and the ∼ 1030 K level
in Gliese 299B (Lodders 1999b), and may also condense in the uppermost atmospheres of
late-type L dwarfs (see Table 1). This is consistent with the observed weakening of Na atomic
features throughout the L dwarf spectral sequence and their disappearance by early T dwarfs
(e.g. Kirkpatrick et al. 1999; McLean et al. 2003), though this trend is primarily caused by
pressure broadening (e.g. Allard et al. 1997; Burrows et al. 2000b; Liebert et al. 2000).
Although the atmospheres of Pegasi planets are generally too warm for Na2 S condensation,
night-side Na2 S cloud formation occurs if temperatures are low enough (e.g. Fortney et al.
2003, 2005; results of Lodders 1999b cited by Iro et al. 2005). The abundance of sodium is
13% of that for sulfur in a solar system composition gas and thus Na2 S condensation removes
sodium and approximately 6.5% of all sulfur from the atmosphere.
3.2.4. Alabandite, MnS
The condensation curve for MnS in a solar-metallicity gas is illustrated in Figure 1.
Alabandite cloud formation proceeds via the net thermochemical reaction
Mn + H2 S = MnS(s) + H2 ,
(14)
where the condensation temperature is approximated by
104 /Tcond (MnS) = 7.45 − 0.42 log PT − 0.84[Fe/H].
(15)
Predicted MnS condensation temperatures on Jupiter, Gliese 229B, HD209458b, and an L
dwarf (Teff = 1800 K) are listed in Table 1. The Mn abundance is 2% that of sulfur in a solar
system composition gas and thus MnS cloud formation removes Mn and 2% of all sulfur.
3.2.5. Sphalerite, ZnS
Sphalerite cloud formation in a protosolar composition gas is represented by the reaction
Zn + H2 S = ZnS(s) + H2 .
(16)
The condensation temperature of ZnS as a function of pressure and metallicity is given by
104 /Tcond (ZnS) = 12.52 − 0.63 log PT − 1.26[Fe/H],
(17)
and is shown in Figure 1 for a solar-metallicity gas. Sphalerite condensation is expected
at the ∼ 980 K level on Jupiter and the ∼ 800 K level on Gliese 229B (see Table 1). The
–7–
atmospheres of L dwarfs, M dwarfs, and irradiated EGPs are too warm for ZnS condensation
and Zn will remain in the gas. Sphalerite cloud formation effectively removes Zn and ∼ 0.3%
of H2 S from the atmosphere. Taken together, condensation of Na2 S, MnS, ZnS, and other
less abundant sulfides consumes up to ∼ 9% of atmospheric sulfur in substellar atmospheres.
3.3.
Chemical Behavior of Individual Sulfur-Bearing Gases
3.3.1. Hydrogen Sulfide, H2 S
Hydrogen sulfide is expected to be the most abundant sulfur-bearing gas throughout the
atmospheres of substellar objects (e.g. see Figure 1; FL94; Fegley & Lodders 1996). Aside
from minor amounts of sulfur (. 9%) removed by metal sulfide clouds (see above), H2 S
is approximately representative of the atmospheric sulfur inventory until it is removed by
condensate cloud formation and/or photochemical destruction. As already discussed, H2 S
dissociates to SH and S at higher temperatures. Within the H2 S field and below the Na2 S
cloud, the H2 S abundance is given by
log XH2 S ≈ −4.52 + [Fe/H],
(18)
whereas above the Na2 S cloud, the H2 S abundance is given by
log XH2 S ≈ −4.55 + [Fe/H].
(19)
Figure 2a shows mole fraction contours (on a logarithmic scale) of H2 S as a function of
pressure and temperature. At low pressures and high temperatures, the abundance of H2 S
decreases as it is replaced by SH and S. The conversion between H2 S and SH occurs via
reaction (1). The equilibrium constant expression for reaction (1) can be written as
K1 = (XSH XH0.52 /XH2 S )PT0.5
(20)
Rearranging and substiting for the temperature dependence of K1 (log K1 = 3.37 − 8785/T
from 800 to 2500 K), the H2 S/SH ratio is given by
log(XH2 S /XSH ) = −3.37 + 8785/T + 0.5 log PT + 0.5 log XH2 .
(21)
Along the H2 S-SH equal abundance boundary, log(XH2 S /XSH ) = 0 and 0.5 log XH2 ≈ −0.04,
and equation (21) becomes equivalent to equation (2). The H2 S/SH ratio is independent of
metallicity because the H2 abundance is essentially constant over small metallicity variations
in an otherwise solar system composition gas. Over most of the H2 S stability field, XH2 ≈
–8–
0.8384. However, at high temperatures and low pressures, H2 thermally dissociates into
monatomic hydrogen via
H2 = 2H
(22)
The abundance of H2 as a function of pressure and temperature in a solar system composition
gas can therefore be determined by solving the quadratic equation:
0 = 1.1835XH2 2 − 1.9845XH2 − 10n XH2 + 0.8319
(23)
where the variable n is given by
n = −23672/T − log PT + 6.2645
(24)
At pressures and temperatures where H2 dominates, 10n in equation (23) approaches zero
and the hydrogen abundance remains XH2 ≈ 0.8384.
With increasing temperatures, SH is replaced by S as the dominant sulfur gas. The
conversion between H2 S and S occurs via reaction (5), and the H2 S/S ratio is given by
log(XH2 S /XS ) = −5.73 + 16046/T + log PT + log XH2 .
(25)
Along the H2 S-S boundary, log(XH2 S /XS ) = 0 and log XH2 ≈ −0.08, and equation (25)
becomes equivalent to equation (6). Inside the S field, the H2 S abundance decreases when
moving away from the H2 S-S boundary toward higher temperatures and lower pressures.
Hydrogen sulfide was measured on Jupiter by the Galileo entry probe mass spectrometer
down to ∼ 20 bars (Niemann et al. 1998; Wong et al. 2004), where the observed H2 S abundance should represent the total sulfur abundance in Jupiter’s atmosphere (e.g. Barshay &
Lewis 1976; FL94; Lodders 2004b). Ground-based observations of Jupiter and Saturn have
not detected H2 S because of its removal by NH4 SH cloud formation, its short photochemical
lifetime, and the lack of H2 S features in the 5 µm window. Similarly, observations of Jupiter
at 2.7 µm by the Kuiper Airborne Observatory (Larson et al. 1984) and at 8.5 µm by the
Voyager spacecraft (Bézard et al. 1983) provide only upper limits because these wavelengths
probe atmospheric levels where H2 S is depleted by condensation and/or photochemistry.
In contrast, NH4 SH does not condense in the warmer atmospheres of brown dwarfs,
Pegasi planets, or low-mass dwarf stars. This allows for observations of H2 S at deeper
atmospheric levels where it is not destroyed photochemically or removed by condensation,
and a measurement of H2 S in one of these objects is expected to approximately represent its
atmospheric sulfur inventory. Despite strong background opacities from H2 O, CH4 , and CO,
a potentially observable H2 S absorption feature is present at 2.1 µm (Saumon et al. 2000).
–9–
3.3.2. Mercapto, SH
Mole fraction contours of the SH radical as a function of temperature and pressure are
shown in Figure 2b. The mercapto radical is the major sulfur gas only in a small P-T field
(see Figure 1). However, it is predicted to be the second or third most abundant sulfur gas
in substellar atmospheres. The chemical behavior of SH is governed by equilibrium with H2 S
via reaction (1). Within the H2 S field, the SH abundance is given by
log XSH ≈ −1.11 − 8785/T − 0.5 log PT + [Fe/H],
(26)
proportional to PT−0.5 and m. At higher temperatures, SH is replaced by S via reaction (3).
The SH/S ratio is found by subtracting equation (21) from equation (25) to give
log(XSH /XS ) = −2.36 + 7261/T + 0.5 log PT + 0.5 log XH2 ,
(27)
independent of metallicity. Along the SH-S boundary, log(XSH /XS ) = 0 and 0.5 log XH2 ≈
−0.04, and equation (27) becomes equivalent to equation (4). Inside the S field, the SH
abundance decreases when moving away from the SH-S boundary to higher temperatures
and lower pressures.
The first astronomical detection of SH was made at the 3.7 µm fundamental band in
the S-type star R And, which has a mercapto column density of 4 × 1020 cm−2 and an
estimated abundance of SH/H = 1 × 10−7 at T ∼ 2200 K and PT ∼ 10−5 bar, consistent
with thermochemical equilibrium in a warm atmosphere (Yamamura et al. 2000; Tsuji 1973,
and present work). The position of this measurement is indicated by the box in Figure 2b.
Equilibrium mercapto abundances of ∼ 1 ppb and ∼ 10 ppb are expected at the ∼ 1000
K-level of L dwarfs and Pegasi planets, respectively.
3.3.3. Monatomic Sulfur, S
Mole fraction contours for monatomic S are shown in Figure 2c. Inside the H2 S field,
the chemical equilibrium abundance of S in substellar objects is governed by reaction (5),
and is given by
log XS ≈ 1.29 − 16046/T − log PT + [Fe/H],
(28)
proportional to PT−1 and m. As illustrated in Figure 1, monatomic S becomes the dominant
sulfur-bearing species (XS ≈ XΣS ) at high temperatures and low pressures in a solar system
composition gas. Thermal ionization of S becomes increasingly important at temperatures
higher than those shown in Figure 1.
– 10 –
3.3.4. Diatomic Sulfur, S2
Mole fraction contours of S2 as a function of temperature and total pressure are shown
in Figure 2d. In giant planets, brown dwarfs, EGPs, and low-mass stars, the equilibrium
chemical behavior of S2 is controlled by the net thermochemical reaction
2H2 S = S2 + 2H2 .
(29)
The S2 mole fraction abundance within the H2 S field is given by
log XS2 ≈ −3.74 − 9440/T − log PT + 2[Fe/H],
(30)
The small discontinuities in the S2 contours are caused by magnesium silicate cloud formation. Inflection points in the S2 contour lines occur when S replaces H2 S as the dominant
sulfur gas. In both fields, S2 has a strong m2 dependence on metallicity. Although the
equilibrium abundance of S2 is negligible in the upper atmospheres of giant planets and
brown dwarfs, ultraviolet absorption bands from S2 were observed by Noll et al. (1995) in
the Shoemaker-Levy 9 impact region on Jupiter, where large amounts of S2 were produced
by shock chemistry (Zahnle et al. 1995).
3.3.5. Dihydrogen Disulfide, H2 S2
The chemical equilibrium behavior of H2 S2 in a solar metallicity gas is illustrated in
Figure 3a. When H2 S is the dominant sulfur-bearing gas, the H2 S2 abundance is governed
by the net thermochemical reaction
2H2 S = H2 S2 + H2 .
(31)
log XH2 S2 ≈ 0.10 − 3433/T + 2 log XH2 S .
(32)
and is given by
The discontinuities in the H2 S2 contours in Figure 3 result from the condensation of magnesium silicates (∼ 1600 K at 1 bar) and Na2 S (∼ 1000 K at 1 bar). The H2 S abundance
in equation (32) is given by equation (18) below the Na2 S clouds and equation (19) above
the Na2 S clouds. The H2 S2 abundance is virtually independent of pressure and in principle
is diagnostic of temperature. Because of its low abundance in substellar objects, H2 S2 is
plausibly detectable only via deep atmospheric probes in the gas giants of the solar system
(e.g. FL94).
– 11 –
3.3.6. Methyl Mercaptan, CH3 SH
Abundance contours for CH3 SH in a solar system composition gas are displayed in
Figure 3b. The chemical behavior of methyl mercaptan (and other carbon-bearing gases)
in substellar objects strongly depends on whether the major carbon-bearing gas is CO or
CH4 . When CH4 and H2 S are the dominant C- and S-bearing gases, respectively (left side
of Figure 3b), the CH3 SH abundance is controlled by the net thermochemical reaction
CH4 + H2 S = CH3 SH + H2 .
(33)
The CH3 SH mole fraction is found by rearranging the equilibrium constant expression for
reaction (33) and substituting to give
log XCH3 SH ≈ −7.51 − 4085/T + 2[Fe/H],
(34)
independent of the total pressure. Methyl mercaptan is thus potentially diagnostic of atmospheric temperature in methane-dominated objects. It is plausibly detectable on Jupiter
and/or Saturn via deep atmospheric entry probes (e.g. FL94). When CO is the dominant
carbon-bearing gas (right side of Figure 3b), CH3 SH forms via
2H2 + CO + H2 S = CH3 SH + H2 O.
(35)
The slight discontinuities in the CH3 SH contours near 1300-1600 K are caused by magnesium
silicate cloud formation. At lower temperatures above the Mg-silicate clouds, the CH3 SH
abundance is given by
log XCH3 SH ≈ −17.44 + 7619/T + 2 log PT + [Fe/H],
(36)
The CH3 SH abundance contours in Figure 3b are roughly parallel to the atmospheric profiles
for L and M dwarfs in Figure 1. Therefore constant (but low) CH3 SH abundances are
expected throughout the thermochemically-driven regions of their atmospheres.
3.3.7. Carbonyl Sulfide, OCS
The chemical equilibrium behavior of carbonyl sulfide is illustrated in Figure 3c, and
can be divided into three distinct regions in a protosolar composition gas. In the first region,
CH4 , H2 O, and H2 S are the most abundant C-, O-, and S-bearing gases, respectively, and
OCS chemistry is governed by the net thermochemical reaction
CH4 + H2 O + H2 S = OCS + 4H2 .
(37)
– 12 –
The OCS equilibrium mole fraction for reaction (37) is given by
log XOCS ≈ 1.07 − 11634/T − 2 log PT + 3[Fe/H],
(38)
and has a strong m3 dependence on metallicity. In the second region, CO replaces methane
as the dominant carbon gas, and the chemical behavior of carbonyl sulfide is controlled by
CO + H2 S = OCS + H2
(39)
The OCS equilibrium abundance is found by rearranging the equilibrium constant expression
for reaction (39):
XOCS = (XCO XH2 S /XH2 )K39 .
(40)
Substituting (where XCO ≈ XΣC and XH2 S ≈ XΣS ) yields
log XOCS ≈ −9.11 + 2[Fe/H].
(41)
At a given metallicity, the OCS abundance is essentially constant throughout this region
because it is independent of pressure, the abundances of H2 , CO, and H2 S effectively remain
constant, and the equilibrium constant K39 is very weakly dependent on temperature. Higher
metallicities give greater OCS abundances by increasing the mole fractions of CO and H2 S,
which drive reaction (39) to the right, forming more OCS. In the third region, H2 S is replaced
by monatomic S, and OCS forms via the net thermochemical reaction
CO + S = OCS,
(42)
and the OCS abundance decreases when moving toward higher temperatures and lower
pressures. Reaction (37) will be important for CH4 -dominated objects while reaction (39)
will be important for CO-dominated objects. We therefore expect relatively constant OCS
abundances of ∼ 1 ppb (for solar metallicity objects) throughout the atmospheres of Pegasi
planets, L dwarfs, and M dwarfs. In principle, OCS, a strong infrared absorber, is potentially
diagnostic of metallicity if a solar C/S ratio is assumed.
3.3.8. Silicon Sulfide, SiS
The chemical behavior of SiS in a solar metallicity gas is shown in Figure 3d. Also shown
are dashed lines indicating the condensation curves for forsterite (Mg2 SiO4 ) and enstatite
(MgSiO3 ), which efficiently remove Si from the atmospheres of gas giant planets and related
objects (Fegley & Prinn 1988; FL94). The SiS abundance is effectively controlled by the net
thermochemical reaction
H2 + H2 S + SiO2 (s,l) = SiS + 2H2 O.
(43)
– 13 –
The SiS abundance above the magnesium-silicate clouds is given by
log XSiS ≈ 5.38 − 2 log XH2 O − 28151/T − log PT − [Fe/H].
(44)
Curvature in the SiS contours occurs at the CH4 -CO equal abundance boundary, which
affects the abundance of water in reaction (43) (e.g. LF02). The H2 O abundance is given
by log XH2 O ≈ −3.12 in CH4 -dominated objects and log XH2 O ≈ −3.58 in CO-dominated
objects. A peak SiS abundance of ∼ 10 ppm (in a solar metallicity gas) is achieved near the
Mg-silicate cloud base and therefore SiS is a potential tracer of weather in Pegasi planets
and L dwarfs, analogous to the chemical behavior of FeH in T dwarfs (Burgasser et al. 2002).
3.4.
Sulfur Chemistry in Substellar Objects
Figures 4a-4d summarize the equilibrium sulfur gas chemistry computed along the
pressure-temperature profiles of four representative substellar objects: Jupiter, the T dwarf
Gliese 229B, the irradiated EGP HD209458b, and an L dwarf (Teff = 1800 K). Hydrogen
sulfide is the dominant sulfur-bearing gas in the atmospheres of substellar objects and is approximately representative of their atmospheric sulfur inventories. The next most abundant
sulfur gases are typically SH (at low temperatures) or SiS (at high temperatures), and the
relative importance of SiS increases with increasing effective temperature. Furthermore, the
peak SiS abundance occurs near the Mg-silicate cloud base and therefore may be a tracer of
weather in Pegasi planets and L dwarfs, where condensation occurs at lower temperatures
than on giant planets and T dwarfs. The chemical behavior of carbon-bearing sulfur gases
strongly depends on the prevailing carbon chemistry. In CO-dominated objects, such as
Pegasi planets and L dwarfs, the OCS abundance is nearly constant and is potentially diagnostic of metallicity. Other minor gases such as CH3 SH and H2 S2 are pressure-independent
and diagnostic of atmospheric temperature, but are plausibly detectable only via deep atmospheric entry probes on Jupiter and Saturn (e.g. FL94).
4.
4.1.
Phosphorus Chemistry
Overview of Phosphorus Gas Chemistry
Figure 5 illustrates the pressure and temperature regions where different phosphorus
gases constitute the major form of phosphorus in a solar metallicity gas at thermochemical
equilibrium. Also shown is the condensation curve for NH4 H2 PO4 (dotted line) and model
atmospheric profiles (dashed lines). Phosphorus chemistry is considerably more complex
– 14 –
than that for C, N, O, and S, and several P-bearing species become abundant at elevated
temperatures (Barshay & Lewis 1978; Fegley & Lewis 1980; FL94). Here we give an overview
of the chemical behavior of phosphorus at temperatures and pressures relevant for substellar
atmospheres.
Under equilibrium conditions, P4 O6 is the dominant phosphorus gas at low temperatures, and is replaced by PH3 or P2 as temperatures increase. The conversion of P4 O6 to
PH3 is represented by the net thermochemical reaction:
P4 O6 + 12H2 = 4PH3 + 6H2 O.
(45)
In CH4 -dominated objects, the position of the PH3 -P4 O6 equal abundance boundary is approximated by
log PT ≈ −11.40 + 12360/T + 3[Fe/H],
(46)
At lower pressures, in CO-dominated objects, the conversion of P4 O6 to P2 occurs via the
net reaction
P4 O6 + 6H2 = 2P2 + 6H2 O,
(47)
and the position of the P2 -P4 O6 equal abundance boundary is approximated by
log PT ≈ 45.17 − 51048/T − 7[Fe/H].
(48)
The relative importance of reactions (45) and (47) depends on the position of an object’s
pressure-temperature profile relative to the PH3 -P4 O6 -P2 triple point at T ∼ 1101 K and
PT ∼ 10−1.20 bar, where all three gases have equal abundances [A(PH3 ) = A(P4 O6 ) = A(P2 )
≈ 71 ΣP]. The positions of all the triple points shown in Figure 5 are listed in Table 2. In L
dwarf atmospheres, PH3 and P2 have similar abundances and are converted into each other
by the reaction
2PH3 = P2 + 3H2 .
(49)
The position of the PH3 -P2 equal abundance boundary in a solar metallicity gas is approximated by
log PT ≈ −1.56 × 107 /T 2 + 2.13 × 104 /T − 7.68,
(50)
from 1101 to 1330 K. At deeper atmospheric levels, PH2 becomes the most abundant phosphorus gas. In giant planets, T dwarfs, and late L dwarfs, PH2 replaces PH3 via
PH3 = PH2 + 0.5H2 ,
(51)
and the position of the PH3 -PH2 line is given by
log PT = 7.71 − 10888/T,
(52)
– 15 –
In Pegasi planets, early L dwarfs, and M dwarfs, PH2 replaces P2 via
P2 + 2H2 = 2PH2 ,
(53)
and the position of the P2 -PH2 line in a solar metallicity gas is approximated by
log PT ≈ −1.68 × 107 /T 2 + 2.62 × 104 /T − 10.68.
(54)
from 1330 to 1780 K. The PH3 -P2 , PH3 -PH2 , and P2 -PH2 boundaries intersect at T ∼ 1330
K and PT ∼ 10−0.48 bar, where all three gases have equal abundances [A(PH3 ) = A(PH2 ) =
A(P2 ) ≈ 14 ΣP]. At even higher temperatures, PH2 thermally dissociates via
PH2 = P + H2 ,
(55)
and monatomic P becomes the major P-bearing gas. The position of the PH2 -P boundary
is given by
log PT = 5.00 − 11233/T,
(56)
and is independent of metallicity.
4.2.
Phosphorus Condensation Chemistry
Figure 5 shows that phosphorus condenses as ammonium dihydrogen phosphate in a
solar system composition gas. The equilibrium condensation temperature of NH4 H2 PO4 as
a function of pressure and metallicity is approximated by
104 /Tcond (NH4 H2 PO4 ) = 30.20 − 2.28 log PT − 2.98[Fe/H].
(57)
Equilibrium condensation of NH4 H2 PO4 is expected to be very effective at removing phosphorus from the upper atmospheres of giant planets because protosolar oxygen and nitrogen
abundances are both much greater than the phosphorus abundance. Clouds of NH4 H2 PO4
are not expected in warmer objects such as brown dwarfs because their pressure-temperature
profiles do not intersect the NH4 H2 PO4 condensation curve. Furthermore, we find that P4 O10
and elemental phosphorus will not condense under equilibrium conditions over this P-T range
in a solar system composition gas.
4.3.
Chemical Behavior of Individual Phosphorus-Bearing Gases
4.3.1. Tetraphosphorus Hexaoxide, P4 O6
The equilibrium abundance of P4 O6 as a function of pressure and temperature in a
solar metallicity gas is illustrated in Figure 6a. The behavior of P4 O6 at high temperatures
– 16 –
(& 1000 K) depends on which phosphorus-bearing gas is dominant. For example, within
the PH3 field, the P4 O6 abundance is controlled by reaction (45) and is proportional to
PT−3 and m10 . Inside the P2 field, the P4 O6 abundance is controlled by reaction (47) and
is proportional to PT and m8 . In both fields, the P4 O6 abundance rapidly decreases with
temperature.
Figure 5 shows that P4 O6 becomes the stable phosphorus-bearing gas low temperatures
(. 1000 K). Its maximum abundance is XP4 O6 ≈ 14 XΣP since each molecule of P4 O6 contains
four phosphorus atoms. In Pegasi planets and L dwarfs, P4 O6 replaces P2 as the dominant
phosphorus gas. The conversion from P2 to P4 O6 is fast and therefore equilibrium abundances of P4 O6 are expected in the upper atmospheres of these objects, where it is plausibly
destroyed by photochemistry. In contrast, studies of PH3 kinetics on Jupiter and Saturn
(Prinn et al. 1984; Fegley & Prinn 1985; FL94; Visscher & Fegley 2005) indicate that the
conversion from PH3 to P4 O6 is slow (see §4.3.2 below). Negligible amounts P4 O6 are thus
expected to form in the upper atmospheres of giant planets and T dwarfs.
4.3.2. Phosphine, PH3
The equilibrium chemical behavior of PH3 is shown in Figure 6b as a function of pressure
and temperature. Phosphine is expected to be the dominant P-bearing gas in the deep atmospheres of giant planets and T dwarfs, where its abundance is approximately representative
of the total phosphorus abundance and is given by
log XPH3 ≈ −6.25 + [Fe/H].
(58)
At lower temperatures, under equilibrium conditions, PH3 is replaced by P4 O6 and its abundance decreases when moving to lower temperatures and pressures. The bend in the PH3
contour lines within the P4 O6 field (e.g., at 0.1 bar and 1000 K) is caused by the CH4 -CO
boundary and its effect on the water abundance in reaction (45).
At higher temperatures, the PH3 abundance generally increases with pressure and decreases with temperature when other phosphorus-bearing gases are dominant. For example,
PH3 is replaced by PH2 deep in the atmospheres of brown dwarfs and Pegasi planets. The
PH3 mole fraction in the PH2 field is approximated by
log XPH3 ≈ −10.33 + 5444/T + 0.5 log PT + [Fe/H].
(59)
At lower pressures, the PH3 abundance in the P2 field is approximated by
log XPH3 ≈ −9.03 + 3737/T + log PT + 0.5[Fe/H].
(60)
– 17 –
Phosphine infrared absorption features near 10 µm and 4.3 µm in the upper atmospheres
of Jupiter (e.g. Bjoraker et al. 1986; Lara et al. 1998) and Saturn (e.g. Noll & Larson 1991;
Courtin et al. 1984) reveal a PH3 abundance of 1.1 ppm by volume on Jupiter and 4.5 ppm by
volume on Saturn. The measured PH3 abundance in each planet is ∼ 30 orders of magnitude
higher than that predicted by thermodynamic equilibrium and implies rapid vertical mixing
from deeper atmospheric levels where PH3 is more abundant (e.g. Fegley & Prinn 1985). The
observable amount of phosphine depends on both the rate of vertical mixing, characterized
by a convective timescale (tmix ), and the rate of PH3 conversion into P4 O6 , characterized
by a chemical lifetime (tchem ). Figure 7 shows the PH3 chemical lifetime as a function of
temperature and pressure using PH3 destruction kinetics described by Visscher & Fegley
(2005), showing that the destruction of PH3 is fastest at high pressures and temperatures
(i.e., the bottom left of Figure 7). The quench temperature (where tchem = tmix ) for PH3
destruction is expected to occur inside the PH3 field in the deep atmospheres of giant planets
and T dwarfs. As a result, virtually no P4 O6 forms and phosphine is mixed upward into their
observable atmospheres at abundances approximately representative of the total atmospheric
phosphorus abundance (XPH3 ≈ XΣP ). In the atmospheres of L dwarfs and Pegasi planets,
phosphine oxidation is quenched outside of the PH3 field, and thus PH3 will no longer be
representative of the total phosphorus abundance. However, it will remain an abundant
disequilibrium gas at altitudes above the quench level, and we expect PH3 abundances of
∼ 0.1 ppm throughout the atmospheres of L dwarfs, and ∼ 10 ppb in the upper atmospheres
of Pegasi planets. Phosphine is plausibly removed from the upper atmospheres of these
substellar objects by photochemistry, as occurs on Jupiter and Saturn.
4.3.3. Phosphino, PH2
Figure 6c illustrates the chemical behavior of the PH2 radical, which becomes the most
abundant P-bearing gas in the deep atmospheres of brown dwarfs and close-in EGPs. At
lower temperatures, the PH2 abundance within the PH3 field is given by
log XPH2 ≈ −2.40 − 5444/T − 0.5 log PT + [Fe/H].
(61)
When P2 is the dominant phosphorus gas, the PH2 abundance is given by
log XPH2 ≈ −5.19 − 1707/T + 0.5 log PT + 0.5[Fe/H].
(62)
Equations (61) and (62) show that the PH2 abundance decreases with pressure when PH3
dominates and increases with pressure when P2 dominates. This behavior is illustrated in
the curvature of the PH2 mole fraction contours in Figure 6. Inside the P4 O6 field, the PH2
abundance rapidly decreases with decreasing temperature. An equilibrium PH2 abundance
of ∼ 1 ppb is expected at the ∼ 1000 K level in substellar objects.
– 18 –
4.3.4. Phosphinidene, PH
Mole fraction contours for the PH radical are shown in Figure 6d. Inside the PH3 field,
the chemical behavior of PH is controlled by the net thermochemical reaction
PH3 = PH + H2 ,
(63)
log XPH ≈ 0.51 − 12268/T − log PT + [Fe/H].
(64)
and the PH mole fraction is given by
In warmer L dwarfs, Pegasi planets, and cool M dwarfs, phosphinidene is in equilibrium with
P2 via the reaction
P2 + H2 = 2PH.
(65)
The PH abundance is given by
log XPH ≈ −2.27 − 8531/T + 0.5[Fe/H],
(66)
and is independent of the total pressure. In principle, PH is thus diagnostic of temperature
within the P2 field, where PH has a maximum abundance of ∼ 10 ppb at the 1500 K level.
4.3.5. Diatomic Phosphorus, P2
Mole fraction contours for P2 are illustrated in Figure 8a as a function of pressure and
temperature. Diatomic phosphorus becomes the dominant P-bearing gas with an abundance
of XP2 ≈ 21 XΣP from the ∼ 1100 to 1500 K levels in the atmospheres of early-type L dwarfs, M
dwarfs, and close-orbiting EGPs (see Figure 5). At deeper atmospheric levels, P2 is replaced
by PH2 via reaction (53). In cooler objects, the P2 abundance is governed by reaction (49).
The mole fraction abundance of P2 within the PH3 field is
log XP2 ≈ −1.01 − 7474/T − 2 log PT + 2[Fe/H],
(67)
proportional to PT−2 and m2 . The strongest P2 bands are likely present near 0.2 µm (e.g.
Marais & Verleger 1950; Carroll & Mitchell 1975), similar to the ultraviolet bands observed
for S2 in the Shoemaker-Levy 9 impact region on Jupiter (Noll et al. 1995), though these
features are probably very difficult to detect in an extrasolar atmosphere.
– 19 –
4.3.6. Methinophosphide, HCP
Mole fraction abundance contours for HCP are illustrated in Figure 8b.
dominated objects, HCP forms via
PH3 + CH4 = HCP + 3H2
In CH4 -
(68)
and is proportional to PT−2 and m2 . In warmer objects, CO replaces CH4 and the HCP
abundance is governed by the net thermochemical reaction
PH3 + CO = HCP + H2 O
(69)
At a given metallicity, the HCP abundance is essentially constant in this region because it
is independent of pressure and reaction (69) has a weak temperature dependence. At lower
pressures, P2 replaces PH3 and the HCP abundance is governed by the net reaction
1.5H2 + P2 + CO = HCP + H2 O
(70)
proportional to PT1.5 and m. The different pressure dependencies in reactions (68), (69),
and (70) give rise to the shape of the HCP contours in Figure 8b. At thermochemical
equilibrium, HCP abundances of ∼ 10 ppb are expected in the deep atmospheres of T
dwarfs and throughout much of the atmospheres of L dwarfs and irradiated EGPs.
4.4.
Phosphorus Chemistry in Substellar Objects
Figures 9a-9d illustrate equilibrium phosphorus gas chemistry in the atmospheres of
Jupiter, Gliese 229B, HD209458b, and an L dwarf (Teff = 1800 K). In giant planets and T
dwarfs, PH3 is the dominant phosphorus bearing gas until replaced by PH2 deeper in the
atmosphere, and the relative importance of PH2 increases with increasing effective temperature. At lower temperatures, the conversion of PH3 to P4 O6 is kinetically inhibited and
PH3 will be mixed into the observable atmosphere at abundances representative of the total
atmospheric phosphorus inventory. On Pegasi planets and L dwarfs, P2 is the dominant phosphorus gas until replaced by PH2 at high temperatures or P4 O6 at low temperatures. Other
sulfur gases, such as HCP, PS, and PO become more important with increasing effective
temperature. Although PH3 is no longer the most abundant phosphorus gas, disequilibrium
abundances of ∼ 10 ppb and ∼ 0.1 ppm are expected in the upper atmospheres of Pegasi
planets and L dwarfs, respectively.
– 20 –
5.
Photochemistry
Our examination of the chemical behavior of individual sulfur and phosphorus species
explicitly assumes thermochemical equilibrium. However, disequilibrium photochemical reactions become important in the uppermost atmospheres of planets and companion brown
dwarfs, and in isolated brown dwarfs if their coronae are warm enough to produce a significant ultraviolet flux (e.g., Yelle 1999).
Photochemistry is expected to be particularly important in the strongly irradiated upper
atmospheres of Pegasi planets. For example, HD209458b orbits a solar-type star at 0.05 AU
and has a stellar UV flux ∼ 10, 000 times that for Jupiter (e.g. Liang et al. 2003). In order to
determine the depth in the atmosphere where thermochemical processes become important,
we compared the thermochemical behavior of the reactive species OH, O, and H in our
model with photochemical results from Liang et al. (2003) for HD209458b. Plots comparing
photochemical (dotted lines) and thermochemical (solid lines) abundances for these reactive
species are shown in Figure 10, using the P-T profile for HD209458b given in Figure 1 of
Liang et al. (2003).
At low pressures, in the uppermost atmosphere of HD209458b, photochemistry produces
excess disequilibrium abundances of OH, O, and H, primarily via H2 O photolysis (Liang et al.
2003). Thermochemistry becomes increasingly important with depth, as pressures and temperatures increase and the available stellar flux decreases. Eventually, the thermochemical
abundances surpass the photochemical abundances, indicating the establishment of equilibrium chemistry. As shown in Figure 10, this crossover occurs near the ∼ 1 to 10 mbar levels
for the reactive species OH, O, and H. This suggests that thermochemistry is important
at pressures of ∼ 10 mbar and higher, consistent with results indicating that most of the
incoming stellar flux is absorbed by the 1 bar level on HD209458b (Iro et al. 2005). Thermochemical processes are therefore expected to dominate atmospheric chemistry in the deep
atmospheres of brown dwarfs and Pegasi planets. Furthermore, our results for sulfur and
phosphorus chemistry may serve as a baseline for photochemical models of these objects.
6.
Summary
Thermochemistry governs the chemical behavior of sulfur and phosphorus species at
pressures greater than ∼ 10 mbar in the atmospheres of brown dwarfs and irradiated EGPs.
Hydrogen sulfide is the most abundant sulfur-bearing gas in substellar atmospheres, and observations of H2 S in these objects should provide a reasonable estimate of their atmospheric
sulfur inventory. The condensation of metal sulfide clouds slightly lowers the atmospheric
– 21 –
H2 S abundance to ∼ 91% of the total S inventory. These clouds also affect opacity by introducing condensed particles and removing gases from the atmosphere (e.g., Na, Mn, Zn, S).
Mercapto (SH) and SiS are the next most abundant sulfur gases, and the relative importance
of SiS increases with increasing effective temperature. Furthermore, the maximum SiS abundance occurs near the Mg-silicate cloud base and is a potential tracer of weather in Pegasi
planets and L dwarfs. Less abundant sulfur gases are potentially diagnostic of temperature
(H2 S2 , CH3 SH) or metallicity (OCS), depending on the prevailing S and C chemistry.
Phosphorus speciation is considerably more complex than that for C, N, O, or S, and
several phosphorus gases become relatively abundant at high temperatures. Disequilibrium
abundances of PH3 are expected in the upper atmospheres of substellar objects, and measurements of PH3 in giant planets and T dwarfs are expected to approximately represent
their atmospheric phosphorus inventory. In Pegasi planets and L dwarfs, P2 is the dominant
phosphorus gas until replaced by P4 O6 at low temperatures or PH2 at high temperatures.
Phosphino (PH2 ) is the most abundant phosphorus gas in the deep atmospheres of brown
dwarfs and Pegasi planets. The relative importance of PH2 , PO, PS, and HCP in these
objects increases with increasing effective temperature.
This work was supported by the NASA Planetary Atmospheres Program.
A.
Additional Compounds
Here we list additional sulfur and phosphorus compounds investigated but not discussed
above. This list includes unstable condensates and minor gases predicted to have very low
abundances in a solar system composition gas over the P-T range studied. In some instances,
these gases are independent of pressure (e.g., CS and CS2 inside the H2 S field; PN and
HPO inside the P2 field), though their abundances are generally too low to serve as useful
temperature probes in substellar atmospheres.
Sulfur
S3 , S4 , S2 O, SO, SO2 , SO3 , SOH, HSO, H2 SO, H2 SO4 , SF, SF2 , CS, CS2 , NS, PS, K2 S, CaS,
FeS, MgS, MnS, TiS, VS, ZrS, SiS2 , TiS2 , ZrS2 , S(s,l), OCS(s,l), SO2 (s,l)
Phosphorus
P3 , P4 , PO, PO2 , P2 O3 , P2 O4 , P2 O5 , P3 O6 , P4 O7 , P4 O8 , P4 O9 , P4 O10 , PCl, PCl2 , PCl3 ,
PF, PF2 , PF3 , HPO, CP, PN, PS, P(s), P4 O10 (s,l)
– 22 –
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– 25 –
Table 1. Equilibrium Condensation Temperatures of Sulfur-Bearing Compounds
object
NH4 SH
Na2 S
MnS
ZnS
Jupiter
Gliese 229B
L dwarf
HD209458b
M dwarf
220
···
···
···
···
1370
1030
∼ 1000a
∼ 800b
···
1800
1440
1270
1260
···
970
800
···
···
···
a
in late-type L dwarfs
b
night-side condensation
– 26 –
Table 2. Phosphorus Equal Abundance “Triple Points”
triple pointa
T, K
log(PT , bar)
PH3 -P4 O6 -P2
PH3 -PH2 -P2
P2 -PO-PS
P2 -PH2 -PO
PH2 -P-PO
1101
1330
1389
1780
1811
-1.20
-0.48
-3.93
-1.26
-1.20
a
e.g., where XA = XB = XC for
phosphorus-bearing gases A, B, C.
– 27 –
Fig. 1.— Overview of sulfur chemistry as a function of temperature and pressure in a
solar system composition gas. The solid lines indicate where major S-bearing gases have
equal abundances. Also shown are condensation curves for several sulfur-bearing compounds
(dotted lines) and model atmospheric profiles for representative substellar objects (dashed
lines). The triangle denotes the position of the triple point where H2 S, SH, and S have equal
abundances. See text for details.
– 28 –
Fig. 2.— Mole fraction contours (on a logarithmic scale) for (a) hydrogen sulfide (H2 S), (b)
mercapto radical (SH), (c) monatomic sulfur (S), and (d) diatomic sulfur (S2 ) as a function
of pressure and temperature in a solar metallicity gas. The box in the bottom right of the
SH plot denotes the P-T position of the SH abundance estimate by Yamamura et al. (2000)
in the S-type star R And.
– 29 –
Fig. 3.— Mole fraction contours (on a logarithmic scale) for (a) dihydrogen disulfide (H2 S2 ),
(b) methyl mercaptan (CH3 SH), (c) carbonyl sulfide (OCS), and (d) silicon sulfide (SiS) as
a function of pressure and temperature in a solar metallicity gas. The dashed lines in the
SiS plot labeled Fo and En indicate the condensation temperatures of forsterite (Mg2 SiO4 )
and enstatite (MgSiO3 ), respectively.
– 30 –
Fig. 4.— Sulfur chemistry along the atmospheric pressure-temperature profile from 1000 to
2500 K for (a) Jupiter, (b) Gliese 229B, (c) HD209458b, and (d) an L dwarf (Teff = 1800 K).
– 31 –
Fig. 5.— Overview of phosphorus chemistry as a function of temperature and pressure in
a solar system composition gas. The solid lines indicate where major P-bearing gases have
equal abundances. Also shown is the condensation curve for NH4 H2 PO4 (dotted line) and
model atmospheric profiles for representative substellar objects (dashed lines). See text for
details.
– 32 –
Fig. 6.— Mole fraction contours (on a logarithmic scale) for (a) tetraphosphorus hexoxide
(P4 O6 ), (b) phosphine (PH3 ), (c) phosphino (PH2 ), and (d) phosphinidene (PH) as a function
of pressure and temperature in a solar metallicity gas.
– 33 –
Fig. 7.— Logarithmic time scale (seconds) for the chemical conversion of PH3 to P4 O6 .
Phosphine destruction is favored at high pressures and temperatures.
– 34 –
Fig. 8.— Mole fraction contours (on a logarithmic scale) for (a) diatomic phosphorus (P2 )
and (b) methinophosphide (HCP) as a function of pressure and temperature in a solar
metallicity gas.
– 35 –
Fig. 9.— Phosphorus chemistry along the atmospheric pressure-temperature profile from
1000 to 2500 K for (a) Jupiter, (b) Gliese 229B, (c) HD209458b, and (d) an L dwarf (Teff =
1800 K).
– 36 –
Fig. 10.— Comparison of thermochemical (solid lines) and photochemical (dotted lines;
Liang et al. 2003) abundances for the reactive species OH, O, and H in the upper atmosphere
of HD209458b. See text for details.