JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 106,NO. All, PAGES 24,831-24,841,NOVEMBER 1, 2001
Sizedependence of the mesospheric dusttemperature And its influence on the noctilucent
clouds
and polar mesosphere summerechophenomena Trude Eidhammer and Ove Havnes Departmentof Physics,Universityof Troms0,Troms0,Norway
Abs!ract. The temperatureof dustin the Earth'smesosphere, whichis determined by collisions with the neutralgas,absorption of radiationfromthe Sun,the Earth andits ownthermalradiation,in generalincreases with dustsize[GramsandFiocco, 1977].Thismayleadto situations wherethereis a maximumsizeof the dustre abovewhichthe dust temperatureis too high for condensation of water vapor to occur. Dust of this size can still accreteother elements.If they accretea sufficient amountof elements,with low ionizationpotential as a surface"contamination," their photoelectricpropertiesmay change.We suggestthat this can lead to their
chargeschangingfrom the "normal"low negativevalueof pure ice particlesto the positivechargeswhichrocketin situ observations haveshownto exist. In suchcases we will have a situation with small, newly created and negativelychargeddust
particles coexisting withlargerandpositively charged dustcharges. Agglomeration of dust particleswill then be an effectiveprocess.We alsodemonstratethat the changes in the polar surfacetemperatureof the Earth duringthe polar mesosphere summerecho(PMSE) seasoncan influencethe mesospheric dust temperatureand by this havea potentialeffecton the shapeof the occurrence rate curveof the PMSE.
1.
In another rocket launch the dust probe showed the
Introduction
Some phenomena near the Earth's mesopause between80 and 90 km height are associatedwith the presenceof large amountsof dust or aerosols. In the following we call all solid particles, whether they consist of ice or other solid material, dust particles.
presenceof positively chargeddust. On that occasion, PMSE was observed by radar and NLC by lidars
[Nussbaumer et al., 1996]. A rocket flight in 1999 [Hayneset al., 2001]directlythrougha radar beam
demonstratesa very closecorrespondence betweendust chargedensity and radar P MSE signal strength. The The noctilucentclouds[e.g., Gadsdenand SchrSder, observationof large amounts of charged dust during 1989],whichwerepossiblyfirst observedin 1883, are PMSE conditions supported the ideas that the probably consistingmainly of particles of icy nature. presenceof chargedparticles such as water cluster ions
The noctilucentclouds(NLC) form in the coldsummer mesosphere betweenheightsfrom 80 to 90 km when the temperature drops down below -•155øK. This seemsto be an approximateupper temperaturelimit for the for-
or aerosols/dustwas necessaryfor PMSE to form. The effect of dust could be by slowing down the diffusion, which without such large charged particles would rapidly smooth electron density fluctuations
mationof NLC to be possible[Liibken,1999].Another [Kelleyeta!., 1987],it couldbe by directscatteringdue phenomena,the so-calledpolar mesosphericsummer to highly (positively)chargeddus•tparticleshavinga echoes (PMSE), which are strong radar echoes (dressed) electron cloud[Tsytovich et al., 1989;Haynes [Ecklundand Balsley,1981; Czechowsky et al., 1989; et al., 1990;Haglots,1992;La Hoz, 1992]or by dustand Hoppeet al., 1988; Cho and RSttger,1997],alsoseem electronholesbeingformedin spacein the presenceof to be linked to dust. This was demonstratedby Haynes neutralgasvortices[Hayneset al., 1992]. More recent et al. [1996]whichwith a new dust detectorobserved theories on causes for the PMSE phenomenon also large mounts of subvisualnegativelychargeddust in a generallyfocuson the presenceof chargeddust (see situation with PMSE present but with no NLC reviewby Cho andRb'ttger[1997]). detectedby the lidar systemat the rocket launch site.
For the dust particles to be able to influence the spatial distribution of the electrons, they must be
Copyright 2001 by the American GeophysicalUnion.
electrically charged. We expect that NLC/PMSE
Paper number 2001JA900036.
particles are normally negatively charged with only a
0148-0227/01/2001JA900036$09.00
fewunit charges[e.g.,Jensenand Thomas,1991].The 24,831
24,832
EIDHAMMER
AND HAVNES- SIZE DEPENDENCE
OF DUST TEMPERATURE
reason for this is that pure ice particles have such a growth of the dust particles and how agglomeration high photoelectricwork function q5,-• 8.9 eV [Baron can becomedominant if the large dust becomescharged et al., 1978]that the photoelectriceffectis negligible. positivewhile smallerdust particlesremain negatively The chargingwill then be by attachment of plasma par- charged. We also take up the limit of sizesdue to
ticles, but this can only lead to surface potentials U
on the dust particlesof a few times -(kT/e),
electrostatic stress on the dust.
In section 4 we look
and where at two differentdustgrowthand chargingscenarios
how thesecan lead to differentchargesignson the dust, neutralgastemperatureTN •.< 155øK.For TN -- 155øK the one for a moderate mesospherictemperature miniwe have kTN/e • 0.013 V and U •- -0.05 V. For mum,mostlikelyto occurat the beginningand the end a dust particle of radius ro• in nanometers this will of the P MSE season,and one for a deep temperature minimum which we expect to find mainly in the lead to an average charge number of Zo• - -0.04 (nanometers).The large negativechargedensityof up middle of the PMSE season. In section 5 we briefly to NdZd •. --4.5 x 109 m-3 due to dust, as observed discussthe possibilitythat the dust temperatureand by Hayneset al. [1996]in a casewhere the dust was its dependenceon the Earth's radiation can affect the occurrence rate not detected by lidar, therefore indicate dust densities seasonal variation of the PMSE of severalthousandper cm3 and sizesof the orderof 10 [Kirkwood et al., 1998;Hoffmannet al., 1999]. to 20 nm [Hayneset al., 1996;Liibkenet al., 1998]. Oneof the radar scatteringtheories[ Tsytovichet al., 2. Temperature of Mesospheric Dust 1989;Haglots,1992;La Hoz, 1992]requireslargedust and Its Variation With Dust Size charge numbers which can only result if photoelectric The temperature of the dust in the mesospherewill charging is effective at mesospheric heights where absorptionlimits the photon energyto h• •< 6.7 eV be affected by the ambient neutral gas, by the direct [Lean, 1987]. If the photoelectricwork functionq5is and reflected solar light, by radiation from the Earth T is the plasma temperature which is equal to the
much smaller than this, one can in principle obtain dust and by radiation loss from the dust. It turns out that surface potential of several volts and correspondingly the least important factors for the temperature of the large charges. Havnes et al. [1990] suggestedthat small dust particles in the mesosphereare the direct and positive charges could result if ice particles became reflectedsolar radiation. Earlier calculations[Grams "contaminated" by other elements so that its photo- and Fiocco, 1977; Jensen, 1989] have demonstrated electric properties changed profoundly. Rocket that the dust temperatures, although closeto, can be
observations [Hayneset al., 1996] demonstratedthat different from that of the ambient neutral gas. This the mesosphericdust can occasionally be positively differenceis normally smallest low down in the mesocharged. This rocket flight, during a PMSE event spherebut increaseswith height due to the decreasein whichalsowasobservableby lidar [Nussbaumer et al., neutral gas density. They also showthat the differences betweenneutral gas and dust also normally increase 1996], found dust chargedensitiesof up to NdZa
7 x 109 m-3
Sincethis dust layer was detectedby
with dust size.
We followthe approachby Gramsand Fiocco[1977] lidar, the dust sizes are probably considerablylarger than the former case with negative dust which was for calculating the dust temperature. We will connot detected by lidar. For scattering in the Rayleigh centrate on the height region of the PMSE and use the
limitthecross section isproportional to r• [e.g.,Evans, most recent gas temperaturemeasurements[Liibken,
1994]. If we adopt the averagevaluesof (ro•}•- 50 nm 1999].We focuson the smalldustsizesand especially and {No•}"-•108m-3 for PMSE dustparticlesin cases look at the heights and dust sizes at which the dust when they are observableby lidar [von Cossartet al., temperature falls below •-155øK. We also look at the differences in temperatures betweenpureiceand "dirty" 1999],we find that the positivedustmay have(Zoo/ 70 and surface potentials of U •- 2 V. This requires metal-coatedice (G. E. Thomas, private communicaa low work function and a high photoelectric yield tion, 1998). The equilibrium temperature of a dust function. Rapp and Liibken[1999]find, with a work particle is given by a balancebetweenfour different heat function of q5- 2.3 eV as for Na, and a yield function lossor heat gain processes
of 0.01 (q5- h•) 2 that dust chargesare of the order of +4e. However, with yields •-5 times this, as found
by $chleicheret al. [1993],the resultingchargeswould be •-+20e.
A lower work function
than 2.3 eV would
Qs abs+ QE abs-- Qemis+ Qcon= 0.
(1)
The absorptionof solar direct and reflectedlight is
increasethe dust charge further. Qs + 2A x) One of the major questionswhich we take up in this paper is what processescan lead to a switchover from low negativedust chargesto comparativelylarge posi- where the dust radius is rd, the solar dilution factor tive charges. In section 2 we discussthe size-dependent is e = (Rs/Re) 2, the solarradiusis Rs = 7 x 10s m, dusttemperature[GramsandFiocco,1977]at different and distancefrom Sun to Earth is Re = 1.5 x 10TMm. mesospheric conditions. In section 3 we discuss the The planetary albedo is A which we assume to be
EIDHAMMER AND HAVNES: SIZE DEPENDENCE OF DUST TEMPERATURE
24,833
radiationhasa negligibleinfluenceon independent of wavelength [WallaceandHobbs,1977]. The atmospheric For the absorptionfactor Qabswe will use those for the dust temperature. The last two terms in (1) are pure ice and for dirty ice which in our casewill be taken as iron-coated ice (G. E. Thomas, private Qemis - 4•rr• Qabs.•X (T•)dA, communication, 1998]. Atmosphericabsorptionlimits
(8)
the available solar direct radiation near the mesopause
to that longwards of E -• 6.7 eV [Lean,1987]corre- representing radiation loss by the dust particle at spondingto A • 185 nm, with a minor contribution temperature T•, and from Ly a at A = 122 nm. Mesosphericdust is most likely considerably muchsmallerthan 185 nm, and we will for simplicityassumethat we are in the Rayleigh limit (A >> rd). As we will later show,the largestdust particlesmay have a complexloose structure so that Mie calculationsof absorptionmay not be justified. In
the Rayleighregimewe have[e.g.,Evans,1994] Q•bs -- -4X
(3)
hn
where X=
27rrd •
'
coll-
\ 7rmN /
X CvmN + •k (TN-Ta) -0, which representsenergy transfer due to collisionswith
the ambientneutralgasat temperatureTN [Gramsand Fiocco,1977]. If TN > Ta this leadsto a net input of energy from the gas to the dust, while if TN. < Td it leads to cooling. The neutral gas number density is the nN atmospheric and mN is the specific gas molecular heat. Theweight factor while /3 is the c,
(4) accommodation
coefficient
which
describes
the
and the complex index of refraction is
efficiencyof energy transfer during a collision. The n = m - ik. (5) value of/3 can in principle be from 0 to 1. For small in which casethe energy exchangebetween the gas and Inserting(5) in (3) and (4) leadsto the dust particles is the least effective, we also find the largest differencesbetweenTa and TN (see Figure 1). 6mk In an experimentby Daughertyand Graves[1993],for grains in a low pressureradio frequency plasma the For the variousfluxes involvedin the problem (solar, value of/3 was found to be ,-• 0.17. In general, one Earth, aerosol/dustflux) we assumethat they have a expectssmall values of/3 for hard smooth dust surfaces shapegiven by the Planck function where gas atoms are reflected specularly. For rougher and softer surfaces where the gas-surface interaction C1 can last longer one expects larger values for /3. The
Qabs --4X(m2_ k2+2)2+ (2ink)2 .
;rx= A5[exp(c2/ATj)_ 1]' (6) relaxation time,
the time for the dust temperature to
HereC1= 3.74x 10-16 W m2 andc2 - 1.44x 10-2 m øK, reach its equilibrium value, is short, of the order of while the temperatures can be the solar Ts - 5780øK, seconds [Bevilacqua, 1978],and the dust will therefore that of the planet Earth Tp or the dust temperature be at its equilibriumvalue as givenby (1). Td. The last two temperatures can vary. The emission
To
demonstrate the
dependence of the
dust
(see(8)) from dustwill be reducedrelativeto the black- temperature on factors such as dust size, neutral gas body radiationof (6) by a factorequalto its absorption density, and temperature of the Earth's surface, we coefficientat the relevant wavelength. The next term
have calculated the temperature of ice when varying
in (1) is the absorbedenergyfrom the radiation from
the above factors.
the Earth and its atmosphere
1.32- 0.01i for absorption of solar radiation and n =
Q••bs - •rr• ••
Qabs.T'x(Yp) d/•.
We use refractive
indices
of n =
1.5- 0.078i for the IR radiationfrom the Earth [Liou, (?) 1992].Figuresla, lb, andlc showthe dusttemperature as function of dust size for different heightsin the meso-
For the flux • in (7) we use the resultsobtainedby sphere. We have chosenh = 82, 84, and 88 km with of mNnN -- 10-4'6, 10-4'86 satellitemeasurements [Kundeet al., 1974]which we neutralgasmassdensities [Liibken,1999].The representby a sum of Planck functions(equation(6)) and 10-5'26kg m-a, respectively within finite wavelengthintervals with the appropriate effective temperatures. The radiation comes from the surface of the Earth in the clear atmospheric windows and from the atmospherewhere the opacity of the atmosphereis high. The atmosphericwindow between -• 8 to 13 pm includes the peak of the Earth's radiation, which is at •max - 10 pm for T • 290øK, and it is this
surfaceradiation which dominatesthe integral in (7).
adopted gas temperatures at the different heights are given in the figures. For each of the heights we have shown
the
results
for
three
different
values
of the
accommodation factor /3 = 0.1, 0.5 and 1.0. We clearly see that the deviation of the dust temperature from the neutral gas temperature increaseswhen the heating or coolingeffect of the neutral gasis diminished. This happens when the neutral gas density decreases
24,834
EIDHAMMER
AND HAVNES: SIZE DEPENDENCE
180
with the largest deviationsin temperature occurring at the largest heights where n•v is low and also for the largest dust sizes. With the same accommodation
82km
170 160
factor the dirty ice dust deviatesmore from the neutral gas temperature than the pure ice dust. On the other
150 140
hand, it is not improbablethat dirty ice has a larger /• than pure ice becauseof a probableroughersurface.
Gas temperature --•=0.5 ....I•=l .o
130
120
10
OF DUST TEMPERATURE
' 20
' 30
' 40
' 50
' 60
' 70
' 80
' 90
This would reduce the temperature difference. 100
3.
Dust
Particle
Growth
and
Destruction 180
3.1.
84km
170
140
1'
Gas temperature
120
S: PH•.O/P$
'
10
Growth by Condensation
A likelyfactorin the processof formingthe NLC and PMSE dust is that water vapor condenses,or freezes out, when the mesospherictemperature becomes low enoughand that the watervaporcontentis highenough so that the degreeof saturation
160
130
Dust Particle
20
30
40
50
60
70
80
90
,
i
i
,
,
i
i
,
100
(10)
becomes higherthan 1 [e.g.,Evans,1994].In (10), Pm.o 180
is the partial pressureof water vapor while the saturation pressureof water as a function of temperature T
170
(in øK)is [Marti andMauersberger, 1993]
'-' 160
logp$: -2663.5/T + 12.537.
• 150 • 140 13O
1'Gastemperature 120 10
' 20
i
i
I
i
I
I
1
30
40
50
60
70
80
90
1 oo
Radius (nm)
Figure 1. The temperatureof pure ice dust as a function of dust size for different values of the accommoda-
tion coefficient3 (equation(9)). We showthe results for threedifferentheights(82, 84, and 88 km) for July 1. The neutral gas densitiesand temperaturestaken from L•bken[1999].The neutralgastemperatures are given in the figures.
(ll)
Accordingto L•bken[1999]it appearsthat PMSE does not form if the minimumin the neutral gastemperature is aboveapproximately155øK.This is alsoindicatedby the resultsof Hoffmannet al. [1999].SincePMSE does not form above.-•155øK,it seemslikely that formation of icy dustis not takingplaceand that alreadyexisting icy dust will melt if the temperaturebecomeshigher than .-•155øK.Of course,the exact gas temperature at whichmelting(and formation)of the dustoccursis dependenton the water vaporcontent.We will call this temperaturefor the criticaltemperatureTc. However,
we have shownin section2 that the neutral gas temperature alone will not in general determine the exact dust temperature but that factors as dust
with height and also if fi is decreased.We see[ha• the temperatures of the large dust deviate more from T•v than do the temperatures of the small dust. The reasonfor this is that a larger rd increasesthe absorption efficiency(see(3) and (4)) for a givenwavelength. In Figure 2 we keep the accommodation factor constantat fi - 0.5 and calculate the dust temperature for ice and dirty ice as a function of mesospheric height. We have used dust sizes of 10, 50, and 70 nm. The neutral gastemperaturesand densitieswhich are given
size,composition, andneutralgasdensity(i.e.,height) can be decisive.We suggestthe following"normal" scenariofor summer mesosphericdust formation. At
a sufficientlylow temperature,water vapor starts to condense,or freeze out on, for example, the small meteoriticsmokeparticleswhichmay be presentmost of the time in the mesosphere.Suchmeteoriticsmoke
particles arepredicted by Huntenet al. [1980]to have average sizes of 1 nm and densities of .-•109 m -3
at heightsbetween80 and 90 km. If water vapor particles all stick to the dust they collidewith, in Figures2a and 2b are takenfrom Liibken[1999].We have calculatedthe variation of dust temperature with the increase in dust sizewith time if no evaporation heightfor two differentdates,wherethe one at May 15 takesplaceis [Hesstvedt, 1961;Reid,1975] is early in the PMSE/NLC season,while the other at July 1 is closeto the time when the mean mesospheric • = n}•.ommo 4pz>, temperature is at its lowest. Again the picture is clear •'mH• 0 /
d•'
(12)
EIDHAMMER
AND HAVNES: SIZE DEPENDENCE
OF DUST TEMPERATURE 1. July Ice
15. May Ice 9O
9O
: i
24,835
--
,
r=10nm r=50nm
:.I• -- Gas r=70nm temperature
88
88
E 86
E 86
• 84
e 84
-'•.,,
82
82
a) 8O
1•o
8O
1,•o
130
140
150
180
160
Temperature(K)
Temperature(K)
1. July Dirty ice
15. May Dirty ice 9O
9O
•
88
... ' III
88
•'86
E 86
•- 84
e 84
82
82
d) 8O
130
140
150
160
170
130
180
140
150
160
170
180
Temperature (K)
Temperature (K)
Figure 2. The heightdependence of the dusttemperature for differentdustsizesfrom 10 nm to 70 nm, calculatedfor pureice and for dirty ice. We showthe resultsfor May 15 and for July 1
(earlyandin themiddleof thePMSEseason).
if S >>1. UsingPD-- 1000kgm-a, nHo. O -- 3 x 10TM of differentcomplexity,havebeenmade [e.g., Turcoet m-a andTN -- 150øK,wefinddr/dr - 10-a nms-1. al., 1982; Jensen and Thomas, 1988; Inhester et al., 1994;Klostermeyer,1998],and we referto thesefor a this casebe •-104 s or slightlylessthan 3 hours.With discussionof the various processesinvolved and their nucleationsitesof densities-•10ø m-a, suchcondensa- possibleconsequencesfor particle growth. From these The time to increase the size from 1 to 10 nm will in
tion would have reduced the water vapor content by
models we can concludethat a size spectrum with con-
•-50%. However, due to a fall velocity of the dust siderable differences in dust sizes can be produced. It and/ora transportof gasfromotherheights, the local appearsthat the expectedmaximumdust sizeswill be watervaporat the varyingdustheightmay not change below-•100 nm [Turcoet al., 1982]. As we will argue dramaticallyin the initial phasesof condensation.It below,it is likely that an additionalfactor in the evois alsopossiblethat p < 1000kg m-a or in other lution of mesosphericdust, namely, the influence of a words that the dust is fluffy. If this is the case the size-dependentdust temperature, must be added. watervaporwill not be soeasilyexhausted.Assuming an approximateconstantsupplyof water vapor, the dust size would reach 50 nm in about 14 hours if PD --
3.2.
Dust Particle
Growth by Agglomeration
Agglomerationis normally not thought to be an 1000kgm-a andin -•1.5hoursif PD -- 100kg m-a. However,the amountof water vaporcontainedin such important processfor the mesosphericdust. For all comparatively largeandnumerous dustparticlesin, say, dust being negatively charged, the repulsiveforce in a cloud of •-1 km thickness will most likely practice stops any agglomeration. During nighttime, exceed the available amount of water vapor. We have with little or no particle precipitation the dust may
made no attempts at modeling transport of water have a chargedistribution of -•-le,
0, +le which may
[Reid, vapor togetherwith condensation or evaporationof leadto somebut not very efficientagglomeration dustparticlesand possibleagglomeration duringtheir 1997]. However,basedon rocketin situ measurements vertical and horizontal motion. Various models of this, of Hayneset al. [1996],whereboth positiveand nega-
24,836
EIDHAMMER
AND HAVNES' SIZE DEPENDENCE
OF DUST TEMPERATURE
tive dust were found on one occasion, and on the ideas and low negative chargestogether with neutral dust. on dust charging presentedin this paper, we find it Such a situation can arise during nighttime in the likely that we at least on some occasionswill have absenceof precipitation when the electron density is some dust particles with considerablepositive charges, low. In our caseswe look at two different populations coexistingwith smaller dust particleswith "normal" of dust with very different chargesand sizes. The colli-
small negative chargesof-le or -2e. We will in the followingbriefly discussthe consequences of this for an agglomeration. The agglomerationprocessdependson the relative velocity Vrelof the different dust particlesand on their charges.We considerthe growth of large dust of radius rL, charge Zz•e, and mass density of p•. The small particles which collide with it have the corresponding parametersrs, Zse, and p$. If rœ • rs the collision
crosssectionis [e.g.,$pitzer, 1978]
a - •r•
1-
---.•. 2U•. Zse)
(13)
mSVrel
sioncrosssectionof (13) cannowbe muchabovethat of
the geometric crosssection•r•. Again,takingvalues which may be close to the maximum favorable for
agglomeration, for example,Uœ -
4 V [Hayneset
i 2 I -- kT•v, where al., 1996],Z$ __ -2, and •mSVre
TN • 150øK,weget that the secondterm in (13) totally
dominates andthat er>>•rr• sinceer- •rr•(1 + 310). The agglomeration now favors a situation where the dust all have low velocities.
This
means
that
a non-
turbulent situation should favor agglomeration when ZL. Z$ < 0. The lowest average relative velocity is the thermal velocity in which case the growth rate of the large dust becomes
Here Uœ is the surface potential of the large dust. In cases where Z$ - 0 or Vrel • kT•v, we will have
dt
2pLVrel
ßns,
(15)
a • •rr•. We alsoseethat if the dustparticlesare all negative and have vrel • the thermal velocity, the crosssection will be reduced drastically, in fact, most of the small dust particles will not reach the surface of the large dust. This will be the case if Vrel •
whereVrel-- (2kTN/m$)1/•. Againusingthefavorable values above for the different parameters and in addi-
tion ns - 109 m-•, pœ - 100 kg m-•, p$ : 1000kg m-• with Vrel- 0.2 m s-1 for TN -- 150øK
(2UœZse/m$) 1/2. If we consider collisions betweenandrs - 3 x l0-s m, we find dr/dr - ll5 nm h-1. large dust particles of the same size, the collisioncross Even with an increaseof pœand some decreaseof Uœ, sectioncan be larger than for that of small to large ns, and rs the growth rate could still be significant. particle collisions,but we will still have for the above The collisiontime of a small dust particle with a large
-1 •" 2 X 104 S for the favorable examples • • •r(r•l + r•2). Hererœ1andrœ•.arethe is tcon-- (VreleYNL) values. This is comparable to the growth time by conradii of the twocollidingdustparticles.For a - •r• the growth rate of the large dust due to agglomeration densationand showsthat for such casesagglomeration must influencethe size distribution of dust profoundly.
dr-•--(P•LS)Vrelnsr • (14) dt
3
3.3. Destruction
of Dust by Electrostatic
Stress
where ns is the number density of the small dust. If we put in what we consider to be rather extreme set
ff the dust obtain positive chargesdue to a changeof photoelectric propertiescomparedto that of pure ice, of valuesfor the parametersof (3), as PS/PL = 10,
vrd = 10 m s-i, ns = 109 m-3, and rs = 3 x
the surfacepotential can in principle have any value up
10-8 m (= 30 nm), we find dr/dr • 10 nm h-1. The to about4 V [Havneset al., 1990,1996].Thisraisesthe large relative velocitiesadopted can only come about questionof whether or not the electrostatic stressmay if different dust sizes are influenced differently by exceedthe tensile strength of the dust material. The turbulent or other nonthermal motion of the neutral magnitude of the electrostaticstress,or outward force gas. We do not find it very likely that suchlarge rela- F per unit areais [e.g.,Evans,1994] tive velocities are present and we therefore concludein
agreementwith others[Jensenand Thomas,1991]that agglomerationduring daytime conditions,if the dust is negatively charged due to a high electron density or if it is neutral, is probably not an important process. As arguedin the Introduction, dust surfacepotentials of plus severalvolts may occasionallybe presentin the mesosphere. If these coexist with smaller and negatively charged dust, this will make agglomeration an effective process. This situation is somewhat similar
F-•-
,
(16)
when we express the dust charge in terms of the potential by Z•e - 4•zor•U•. Since the critical size of dust rc will be at the large end of the dust size
distributionwe may have r• • 50 nm in which casewe
getF • 2.8x 104 N m•'if Uœ- 4 V. Haynes etal.[1996]
arrivedat r• • 70 nm for whichF - 1.4 x l0 4 N m-•'. to the situationconsideredby Reid [1997]where he Accordingto Evans [1994],thesevaluesare closeto looks at the agglomeration rates if the dust charge the tensile strength of weakly bonded solids. It theredistribution contains dust particles of both low positive
fore appearsthat even suchcomparatively large surface
EIDHAMMER
AND HAVNES' SIZE DEPENDENCE
potential as UL -• 4 V should not lead to grain destruction,although loose "fluff" on the grain surface may be ejected, leading to more regularly shaped dust particles. Eventually, such contaminated large dust particles will be destroyed. This will probably be in a combination of a substantial evaporation of ice, which will reducethe tensile strength of the particle, together with the electrostatic
OF DUST TEMPERATURE
24,837
Dust temperature < 155 K
15. May
tensile stress. Since contaminated
dust may have a somewhatlarger temperature than negatively charged pure ice (Figure 2), we expect
the positivelychargeddust cloudsto haveits lower boundary at a higher temperature than the lower boundary temperature for negatively charged dust
83
clouds. 82
4. Possible Scenarios Leading to Different Charge Signs on Mesospheric Dust It is generallyacceptedthat mesospheric dust most often is negativelychargedof low Z0•• -1,-2 because
Dusttemperature< 155 K
1. July
81
80 10
'
20
3'0
'
40
'
50
6'0
7'0
8'0
90
00
Radius (nm)
Figure 3. Curvesshowingat what mesospheric heights
it is most likely to consistof almost pure water ice with and for what dust sizes an ice dust particle will have a high photoelectric work function. However, we have temperature of Td -- 155øK. This is shown for May 15 direct observationsshowingthat dust can be positively and July 1. To the left of the respective curves Td < charged,possiblyto large chargenumbers. As discussed 155øK. in the Introduction, this has a consequencethat the photoelectric properties of the dust particles must be totally different in the two cases. This again indicates water vapor. Other gasescould still condense. In the that either the total chemical composition of the dust following we will discussthe two scenarioswhich we particles must be different or the surface composition suggestare the ones leading to either negative charges and possibly the structure must be different. We dis- or positive chargeson the mesosphericdust. The first, or case 1, is when the ambient gas card the first possibility due to the small amount of other trace gases(e.g., Na and metals) comparedto temperature TN is considerably lower than the This is most likely to water vapor. The secondpossibility could either come "critical" temperature Tc. about if all water vapor has condensedout on dust, happen in midsummer when the temperature near the
or if the condensationof water vapor can be exactly balancedby sublimation so that there is no net water condensation. It does not seem likely that all water vapor shouldbe exhaustedthroughout the whole dust cloud. This would require that no transport of new water vapor into the dust cloud takes place, or that no dust falls into regions with water vapor available. Althoughnot totally out of the question,we find it to be unlikely and we would instead expect that exhaustion of water vapor could occur in patchesand that this, if being the responsiblemechanism for dust charge changes,would result in positive and negative dust chargeregionsintermingled with each other. This is contrary to the one direct observationof positive dust
mesopause reachesa minimum [Liibken,1999]. The other, case 2, is when TN is lower than but closer to Tc. We expect this to be most common early and late in the NLC
season.
We show two such different
cases
in Figure 3 when the dust radius is given as a function of the height for which icy dust have T0•= 155øK, for May 15 and July 1. To the left of the curve for May 15, and above the curve for July 1, the dust temperature is T0• < 155øK. We see that for July 1, when TN is
low, all ice particleswill have T0• ,.•< 155øK abovea height of ,o81 km. Very early in the season,however, when TN is not much below 155øK, one may have that
T0•• 155øK at all heightsfor rd • 90 nm and that dust temperaturesbelow155øKis foundonly at h • 84.5 kin. [Hayneset al., 1996]showinga continuous positively For case 1, if TN is sufficiently low, no dust becomes chargeddust cloud with a thin layer of negativedust large enoughto obtain a temperatureT0• ;• Tc. We expect available H•.O to condenseon all types of dust slightly above. We find that the observation of the positive dust sinceall are well below Tc. Therefore any metals which cloudis more consistentwith a processwhereinitially condenseon the dust, or which are nucleation sites for smallerand negativelychargeddust falls and growsin condensation,will be "hidden"belowor within layersof size and thereby also becomewarmer with respectto ice, and a situation with a contaminatedsurface,which the neutral gasas shownin section2. This may finally can changethe photoelectricproperties[Milllet et al., lead to a temperature with no net condensation of 1987; Haynes et al., 1990], is thereforelesslikely to
24,838
EIDHAMMER
AND
HAVNES:
SIZE DEPENDENCE
OF DUST
TEMPERATURE
arise. We therefore expect all dust particles to remain tMON•'"1.4x 101*/nMET,S (17) negatively charged, that is, be relatively unaffected by the photoelectric effect and to be charged mainly by if we use for the radius of the metals 2 x 10-9 m, collisions with electrons and ions. 50 m•/ for their mass and T•v = 155 øK and assume a In case 2, however, the evolution of dust sizes and sticking coefficient of 1. With nMET•0 10TMm-3 this surface compositionmay be quite different. The con- corresponds to about 4 hoursbut if only a 10% surface densation starts off as in case 1 where water vapor contaminationis sufficientonly ,-.20 min would suffice. condenses on, for example, small meteoritic smoke This showsthat a substantial surface contamination by particles. This processis the fastest due to the larger metals can in principle take place within a relatively density of water molecules,and metal which condenses short time after the critical size rc has been reached. becomes "hidden" by ice. With an increasing dust This can have the effect that the work function W temperature as the dust size grows the H20 conden- of the dust particle decreasesfrom •08.7 eV for pure sation will stop at some dust temperature which we set ice to a much lower value for the contaminated dust as Td ,• To. Any metals which are accreted after this particle. While a dominanceof metals like Mg, A1 or
will remain on the surfaceand not be hidden by ice Fe could give q• •0 4 to 5 eV, a considerableamount layers. This can have two effectson the largest dust: of Na or K could lower the work function to
(1) The photoelectric propertiescanchange[Miiller et 2.3 eV. We would not exclude that a thin film contamial., 1987], and the dust chargingmay eventuallybe nation mixture couldgive an evenlowerwork function. dominated by the photoelectric effect. As discussed Experimentsby Qiu et al. [1989],where a mixture of in section 1, the dust charge can then become posi- Na and NH3 was codepositedin a thin film, resultedin tive [seeHayneset al., 1990, 1996]. (2) Its absorption q•=0.9 eV. and emissionpropertiesof the dust particle can change and thereby also its temperature. Since metals are not 15. Variation of the Average Dust evaporated easily, this could influence the water con- Temperature During the NLC tent of the dust, either allowing more H20 to condense Season and Its Possible if Td < Tc or lead to evaporation of water if Ta > To. Influence on the PMSE Accordingto Figure 2, the last situation appearsto be Occurrence Rate most likely and will lead to some of the ice in the dust We have in Figure 2 shown the temperature of dust to evaporate and be returned to the gas. Some of the contaminating atoms will probably be carried off in this as a function of height during the early and middle process,but we foresee,as for comets,that during the PMSE season. However, in these calculations we did evaporation of volatile ices the less volatile elements as not include a possible effect of a difference in the metals tend to remain on the dust surface. For dust thermal radiation from the Earth due to a temperature particles this will contribute to a changein the photo- variation of the polar regionsof the Earth during the NLC/PMSE season. As we will show,this can have electric properties as discussed. We also expect, as discussedin section 3.2, that a small but potentially important effect on the dust accretion of smaller negative dust will lead to a size temperature during the PMSE/NLC season. The increasewith a correspondingtemperature increaseto effects of a changing albedo A during the spring Ta > Tc which will cause some ice to evaporate and period when snow and ice are melting is found to be be returned to the gas face for condensationon to negligible. We compute the dust temperature as smaller dust. We expect all the water ice on the function of time during the P MSE seasonand showthe small dust, which agglomeratewith the large dust, to resultsin Figure 4 for different dust types and different evaporate. The metals, however, should to a large mesosphericheights. We have which are shownadopted extent remain on the large dust and contribute to its the neutral gas temperaturesfrom L•ibken[1999]in surface "contamination." the figures. The adopted variation of the temperature The timescalefor the first step toward changingthe of the Earth in northern Scandinaviais taken to vary charge sign after the dust has reachedits critical size from 278øK to 290øK from May 15 to August 20. As rc is for a sufficient number of metals to be accreted on stated in section2, we used these temperatures instead to the surfaceof the large dust to causeits photoelectric of the •0300øKtemperaturebetween8 and 13 ttm which propertiesto changeand allow it to becomepositively dominate the radiation spectrum from the Earth and its
charged. Milllet et al. [1987] find that a surface atmosphere nearto equator[Kundeet al., 1974].In the contamination much less than that correspondingto left columnof Figure 4 we showthe resultsfor an icy a monolayer can cause the photoelectric properties to change. If metallic moleculeshave a total number density of
particle of radius ra = 50 nm. The dust temperature variationfollowscloselythat of the neutral gas,but the
will cover the surface of a dust particle of radius with a monolayerin a time
part. For smaller ice particles the difference would be
differenceis lessby a few degreesin the early parts of nMET = • ns (a = differentmetallicmolecules),this the PMSE/NLC seasoncomparedto thosein the late smaller. In the right-handpart of Figure 4 we showthe
EIDHAMMER
AND HAVNES: SIZE DEPENDENCE
OF DUST TEMPERATURE
24,839
170
._, 200
82km
160
• 180
150 • 160
140
•- 14o
130
170
,.., [ 84km
200 t 84km
• 150
•E 140[ ..... '"
140['"-.....
•- 130
6
7
8
6
9
7
8
9
7
8
9
170
---I 88km •. 160'
._. 200
• 18o
ß •150,
[ 160
E 140
•- 130
E
"--
•-140'-.. -. _
----
6
7
8
9
6
Date (month)
Date (month)
Figure 4. The variation of dust temperatureduring the NLC/PMSE seasongiven at three different heights. The temperature of the polar regionsof the Earth are here assumedto vary from 278øK in mid-May to 290 toward the end of the seasonin August. This results in a smaller
difference betweenthe neutralgastemperature(shownasa dashedline) andthe dusttemperature (solidline) earlyin the seasonthan late in the season.(left) The resultsfor a pureice dustparticle of radius50 nm, with n = 1.5- 0.078i for absorptionof the Earth's IR radiation,and (right) the resultsfor a dirty ice particle of the same size but with n -- 1.5- 1.0i. We have also, as a dotted line, shownthe results when the May temperature of the polar Earth is reduced to 270øK.
resultsof a dust particle alsowith r• - 50 nm but which now has been given an "artificial" large absorptionin the IR to seethe effect of this on the dust temperature. Relative to the results in the left-hand column, with
dust sizes,their compositionand electriccharging.The
most important factor for icy dust formation in general is,' of course, the temperature of the mesospheric gas and content of H20. It is when this n = 1.5-0.078i we use n = 1.51.0i. We see that temperature drops during the spring that formation of also in these casesthere is a few degrees asymmetry icy dust becomes possible, but the subsequent in the dust temperature curve. In view of the close evolution of the dust population will probably be bond between the presence of dust and the P MSE influenced strongly by the dependence of the dust phenomenonand nonlinear dependenceof radar signal temperature on dust size. This should be especially strengthon dust density as demonstratedby rocket in true at conditionswhere the neutral gastemperature in
situ observations [Hayneset al., 1996; 2001], we find largeparts of the NLC/PMSE region(-•80 to 90 km) it likely that conditions which are favorable for dust formation, that is, a low dust temperature, also favor the occurrenceof the PMSE phenomenon. This could then possiblylead to a more favorablesituation for dust
growth,and for the PMSE phenomenonto occur,in the early part of the PMSE/NLC seasonthan in the late part of the season.This could possiblycontribute to a variation of the occurrencecurve with time, for PMSE
[Ho•rnannet al., 1999]beingsteeperin the springthan in the fall.
is lower than but still closeto the critical temperature
(To -• 155øK)abovewhichmeltingof icy dustprobably will occur. Suchtemperature conditionswill mainly be found in the early and late part of the P MSE season. The effect should,however, also be consideredduring other parts of the P MSE seasonsincethe temperature can fluctuate considerably. Also, even though the neutral gas temperature minimum can be much lower than To, the temperaturesin the high and low part of the PMSE/NLC regionwill be higherand therefore closerto Tc.
6.
It is intriguing to note that the neutral gas
Discussion We
have
demonstrated
temperatures [Liibkenet al., 1996;Rapp,2000]arequite that
the
effect
of dust
different on the two occasions in 1994 when Haynes
temperature changeswith dust size have the potential et al. [1996]observedchargedmesospheric dust. The to be a major factor in determiningthe evolutionof minimum temperatures, occurring close to the top of
24,840
EIDHAMMER
AND HAVNES: SIZE DEPENDENCE
OF DUST TEMPERATURE
the dust layers, are some 15ø-20øK higher for the case Gadsden,M., and W. SchrSder,NoctilucentClouds,165 pp., Springer-Verlag,New York, 1989. with positive dust than for the casewith negative dust. Grams, G., axtd G. Fiocco, Equilibrium temperaturesof This is what we would expect if our ideas for rnesospherical ice particles in the upper atmosphereand sphericdust evolution are correct. implicationsfor noctilucentcloudformation,J. Geophys. Before positive dust can be formed there must first Res., 82, 961-966, 1977. waves be a stage,lastingpossiblyseveraltimes104s, for the Hagfors,T., Note on the scatteringof electromagnetic fromchargeddustparticlesin a plasma,J. Atmos.Terr. dust to build up into large enough sizes so that the Phys., 5J, 333-338, 1992. dust size- dependent temperature effect can stop their Havnes, O., U. de Angelis, R. Bingham, C. K. Goertz, further growth. Due to their larger weight they will G. E. Morrill, and V. Tsytovich, On the role of dust in probably have a net downwardvelocity relative to the the summer mesopause,J. A tmos. Terr. Phys., 52, 637smallernegativeparticles in the dust cloud. The large 643, 1990. dust will thereforeleave the cloud of negatively charged Havnes, O., F. Melands0, C. La Hoz, T. K. Aslaksen, and T. Hartquist, Charged dust in the Earth's mesopause: dust and fall downwards with its positive charge Effects on radar backscatter, Phys. Scr., J5, 535-544, becoming larger as its surface becomes increasingly 1992. "contaminated"
with metals.
The in situ observations
Havnes, O., J. Tr0im, T. Blix, W. Mortensen, L. I. N•esheim, E. Thrane, and T. T0nnesen, First detection of charged dust particles in the Earth's mesosphere, J. Geophys. a caselike this where a negative dust layer of thickness Res., 101, 10,829-10,847, 1996. ,-•200 rn exists slightly above the main positive cloud Havnes, O., A. Brattli, T. Aslaksen,W. Singer, R. Latteck, layer of thickness ,-•1.5 km. T. Blix, E. Thrane, and J. Tr0im, First common volume The schematic picture of •!ust creation and evolution observationsof layered plasma structures and polar mesowhich we have suggestedcan certainly be improved. We sphericsummerechoesby rocket and radar, Geophys.Res. Lett., 28, 1419-1422, 2001. have consideredconstantbackgroundgas temperatures Havnes, O., A. Brattli, T. Aslaksen,W. Singer, R. Latteck, which can be acceptableon short timescalescompared T. Blix, E. Thrane, and J. Tr0im, First common volume to gravity wave periods, but on longer timescalesthe observationsof layered plasma structures and polar mesotemperature changes resulting from such waves must sphericsummer echoesby rocket and radar. Manuscript,
of Havneset al. [1996]by their DUSTY 2 launchreports
be considered [Klostevmeyer, 1998]. The underlying
2000.
effects of the size- dependent dust temperatureswill Hesstvedt, E., Note on the nature of noctilucent clouds, J. Geophys.Res., 66, 1985-1987, 1961. still be presentand play, we believe,an important role Hoffmann, P., W. Singer, and J. Bremer, Mean seasonal for the evolutionof dust sizesand their chargesand and diurnal variations of PMSE and winds from 4 years thereby for the creation and evolution of PMSE and of radar observationsat ALOMAR, Geophys.Res. Left., NLC phenomena.
26, 1525-1528, 1999.
Hoppe, U. P., C. Hall, and J. RSttger, First observationsof Acknowledgments.
'We thank the two referees for
summer polar mesosphericbackscatter with a 224 MHz
radar, Geophys.Res. Left., 15, 28-31, 1988. commentswhich helped to improve the paper. 'We would alsolike to thank Liv Larssenfor preparingthe manuscript. Hunten, D. M., R. P. Turco, and O. B. Toon, Smoke and Thisworkhasbeensupportedby grantsfromthe Norwegian dust particles of meteoric origin in the mesosphereand Research Council. stratosphere,J. Atmos. Sci., 37, 1342- 1357, 1980. Michel Blanc thanks GeorgeReid and another refereefor Inhester, B., J. Klostermeyer, F. J. Lfibken, and U. von Zahn, Evidencefor ice cloudscausingpolar mesospheric their assistancein evaluating this paper. summerechoes,J. Geophys.Res., 99, 20,937-20,954, 1994. Jensen,E. J., A numericalmodel of polar mesospheric cloud References
formation andevolution, Ph.D.thesis,Dep.of Astrophys.,
Baron, B., D. Hoover, and F. Williams, Vacuum ultraviolet photoelectric emission from amorphous ice, J. Chem. Phys., 68, 1997-2003, 1978. Bevilacqua, R. M., Ice particles in the mesosphere,M.S. thesis,78 pp., Penn. State Univ., University Park, 1978. Cho, J. Y. N., and J. RSttger, An updated review of polar mesospheresummer echoes: Observation, theory and their relationship to noctilucent clouds and subvisible aerosols,J. Geophys.Res., 102, 2001-2020, 1997. Czechowsky,P., I. M. Reid, R. Riister, and G. Schmidt,VHF radar echoesobservedin the summer and winter polar mesosphereover Andoya, Norway, J. Geophys.Res., 9•, 5199-5217, 1989. Daugherty,J. E., and D. B. Graves,Particulate temperature in radio- frequencyglow-discharges,J. Vac. Sci. Technol., 11, 1126-1131, 1993.
Planet. and Atmos. Sci., Univ. of Colo., Boulder, 1989. Jensen, E., and G. E. Thomas, A growth-sedimentation model of polar mesosphericclouds: Comparisonswith SME measurements,J. Geophys.Res., 93, 2461-2473, 1988.
Jensen,E. J., and G. E. Thomas, Charging of mesospheric particles: Implications for electron density a•d particle coagulation,J. Geophys.Res., 96, 18,603-18,616, 1991. Kelley, M. C., D. T. Farley, and J. RSttger, The effect of cluster ions on anomalous VHF
backscatter
from the
summerpolar mesosphere,Geophys.Res. Left., 1J, 10311034, 1987.
Kirkwood, S., V. Barabash, P. Chilson, A. R•chou, and K. Stebel, The 1997 PMSE season:Its relation to wind, temperature and water vapor, Geophys.Res. Lett., 25, 1867-1870, 1998.
Ecklund,W. L., and B. B. Balsley,Long-termobservations Klostermeyer,J., A simple model of the ice particle size of the Arctic mesospherewith the MST radar at Poker distributionin noctilucentclouds,J. Geophys.Res., 103, 28,743-28,752, 1998. Flat, Alaska, J. Geophys.Res., 86, 7775-7780, 1981. Evans, A., The Dusty Universe,John Wiley, New York, Kunde,V. G., B. J. Conrath,R. A. Hanel, W. C. Maguire, 1994. C. Prabhakara, and V. V. Salomonson,The Nimbus 4
EIDHAMMER
AND
HAVNES'
SIZE DEPENDENCE
infrared spectroscopyexperiment, 2, Comparisonof observed andtheoreticalradiances from425to 1450cm- •, J. Geophys.Res., 79, 777- 784, 1974.
La Hoz, C., Radar scattering from dusty plasmas, Phys. Scr., J5, 529-534, 1992.
Lean, J., Solar ultraviolet irradiancevariations:A review, J. Geophys.Res., 92, 839-868, 1987.
Liou, K. N., Radiation and CloudProcesses in the Atmosphere.Theory, Observationand Modeling,Oxford Univ. Press, New York, 1992.
Lfibken, F.-J., Thermal structure of the Arctic summer mesosphere,J. Geophys.Res., 10•, 9135-9149, 1999. Lfibken, F.-J., K. H. Fricke, and M. Langer, Noctilucent clouds and the thermal
structure
near the Arctic meso-
OF DUST
TEMPERATURE
24,841
dependence on temperature and dynamics, thesis, Bonn Univ., Bonn, 2000. Rapp•.M., and F.-J. Lfibken, Modelling of positively charged aerosolsin the polar summer mesopauseregion, Earth Planets and Space, 51, 799-807, 1999. Reid, G. C., Ice clouds at the summer polar mesopause, J. Atmos. Sci., 32, 523-535, 1975. Reid, G. C., On the influence of electrostatic charging on coagulationof dust and ice particles in the upper mesosphere, Geophys.Res. Left., œ•, 1095-1098, 1997. Schleicher,B., H. Burtscher, and H. C. Siegmann, Photoelectricquantum yield of nanometer metal particles, Appl. Phys. Left., 63, 1191-1193, 1993. Spitzer, L., Jr., Physical Processes in the Interstellar Medium, John Wiley, New York, 1978. Tsytovich, V. N., U. de Angelis, and R. Bingham, Transition scatteringof waveson chargeddust particles in a plasma, J. Plasma Phys., J2, 429-443, 1989. Turco, R. P., O. B. Toon, R. C. Whitten, R. G. Keesee, and D. Hollenbach, Noctilucent clouds: Simulation studies of their genesis,properties and global influences,Planet. Space Sci., 3, 1147-1181, 1982. von Cossart, G., J. Fiedler, and U. von Zahn, Size distribution of NLC particles as determined from 3-color observationsof NLC by ground-basedlidar, Geophys.Res. Left., 26, 1513-1516, 1999.
pause, J. Geophys.Res., 101, 9489-9508, 1996. Lfibken, F.-J., M. R.app, T. Blix, and E. Thrane, Microphysical and turbulent measurementsof the Schmidt number in the vicinity of polar mesosphere,Geophys.Res. Left., 25, 893-896, 1998. Marti, J., and K. Mauersberger,A surveyand new measurementsof ice pressureat temperature between170 and 250 K, Geophys.Res. Left., 20, 363-366, 1993. Mfiller, U., A. Schmidt-Ott, and H. Burtscher, First measurementof gas absorptionto free ultrafine particles: O2 on Ag, Phys. Rev. Left., 58, 1684-1686, 1987. Nussbaumer,V., K.-H. Fricke, M. Langer, W. Singer, and U. von Zahn, First sbnultaneous and common-volume Wallace, J. M., and Hobbs, P.V., AtmosphericScience. An observations of NLC and PMSE by lidar and radar, Introductory Survey, Academic, San Diego, Calif., 1977. J. Geophys. Res., 101, 19,161-19,167, 1996. Qiu, S. L., C. L. Lin, L. Q. Jiang, and M. Strongin, T. Eidhammer and O. Havnes, Department of Physics, Photoemission studies of the metal-nonmetal transition University of Troms0, N-9037 Tromso, Norway. of sodium on solid ammonia, Phys. Rev. B, 39, 1958-1961, (
[email protected]) 1989.
Rapp, M., Aerosol layers in the polar summer mesosphere: (ReceivedNovember 18, 1999; revisedDecember 14, 2000; Interaction with the plasma of the D-region and acceptedFebruary 20, 2001.)
