TheGaseousUniverse
Sec1on3.4ofthetext
PhasesofMa:er
Therearefour: •  Solid-rare,inastronomy
•  Liquid-rarestinastronomy:examplesinclude
Earth,Mars(?),Europa(?),Titan,Pluto(?)
•  Gas-ubiquitous
•  Plasma–ionizedgas
Intheclassroom
1moleofN2gas=6.023x1023molecules
occupies22.4litresatSTP(1atmpressure,273K
temperature)
1litre=10x10x10cm3
Sothegasnumberdensityis~6x1023/22.4x103
~3x1019percm3
ConsiderWater
AmoleculeofH2Ohasamassof
2x1.67x10-24+2.66x10-23
=2.89x10-23grams
So1.0cm3(=1.0gm)contains~3.5x1022
-about10001mesthenumberasinair.
AstrophysicalGases
Notetheenormousrange!
Terminology
Romannumeralsrepresentioniza1onstages
I = neutral gas (e.g. HI = neutral hydrogen)
II = once ionized
(HII = fully ionized hydrogen;
HeII = He that’s lost one of its two electrons)
Fe XXVI = iron with 25 electrons removed (i.e. all
but one!)
Circumstances!
Inthecenterofthesun,allatomsarecompletelyionized;butin
thecoolphotosphericregions,weseeabsorp1onlinesofmany
neutralspecies.Soevenwithinasinglebodywehaveto
considerrangesofexcita1on/temperature/etc
TheMeaningofTemperature
Variouswaysofcharacterizing/measuringT:
•  Considerkine1cs(thecharacteris1cveloci1esofpar1clesinthermal
[random]mo1on)
•  Considerambientradia1on(thecharacteris1ccolour/energyofatypical
photonpassingthrough)e.g.whatisthe‘temperature’ofinterstellar
space?
•  Considerthetypicalradia1onemi:edbysomematerial(e.g.what
radia1onisemi:edbycoolinterstellardust?)
•  Considerthestageofexcita1onofaneutralgas(e.g.howmanyelectrons
areinthegroundstatevsthenumberinhigherorbitals?)
•  Considerthestageofioniza1onofvariousgasesinaplasma
•  Variousothermeasuresinvolvingemissionfromotherallowedor
forbiddentransi1ons(wewillcomebacktothis–e.g.the21cmradia1on
fromneutralhydrogen)
TheObviousQues1on
Willthesevariousmeasuresallagreeinagiven
body/locale/medium/circumstance?
Forexample:inaregionofinterstellarspace,
considerthetemperaturesindicatedbythe
ambientradia1on,theexcita1on/ioniza1on
stateoftheatomspresent,andthekine1c
mo1onsofanypar1cles.Willtheyagree?
InGeneral,NO
Wehavetoconsidertheminturn:whateach
represents,howtheyareestablished,andhow
toinfertheimportantphysicsfromthem.
KINETICTemperature
Considerahotgas,withpar1clescolliding
elas1cally(i.e.nolossofenergyinthecollisions)
(sideissue:wheremighttheenergygo?)
Whatspectrumofveloci1esdoyouexpecttosee
whenitisatequilibrium?
(Forexample,willallpar1cleshavepreciselythe
samevelocity??)
Maxwell-BoltzmannVelocityDistribu1on
onceequipar11onisreachedandauniqueequilibrium“T”applies
IntheClassroomInanInterstellarCloud
TheFunc1onalForm
Notethat<v>=2.00v mp
ThingstoNote
•  Atanygiveninstant,essen1allynopar1clesareatrest
•  Thereisalongtailtohigherveloci1es.
•  Equipar==onofenergymeans(inamul1-component
system)thatthelower-masspar1cleshavehigher
meanveloci1es
•  Ingravita1onally-boundsystems,thelightpar=clescan
evaporateaway
Examples
•  Earth’satmospherehasnofreeHydrogenor
Helium
•  ThemoonandMercuryhavenosignificant
atmospheresatall
OtherApplica1ons
Clustersofstarscanevaporate.
Note:thestarsdonotsufferdirectphysicalcollisions!
BacktotheM-BFunc1on
NotetheBoltzmannfactor:
exp(-mv2/(2kT))
or,equivalently,
exp(-½mv2/(kT))
TheImplica1on
Theprobabilityoffindingapar1cleofhigh
kine1cenergyfallsoffexponen1allyinpart
(remembertheotherfactorsintheequa1on!),
onascalethatisdeterminedbykT.
Thisdeterminesthelonghigh-energytailofthe
distribu1on.
ARecurrentTheme
WeencountertheBoltzmannfactorinother
defini1onsoftemperature(ioniza1on,
excita1on,…)andwriteitmoregenerallyas
exp ( - Χ / kT) (where Χ is a “chi”)
AchievingEquipar11on(Thermal
Equilibrium)inGases
Imaginemergingahotgasandacoolgas.Forthemto
cometoequipar11on(theMBdistribu1on)takessome
1me-manyelas1ccollisionsmustoccur!
Seepage86forvariouscircumstances.Inmost
astrophysicalgases,thermalequilibriumisquitequickly
established.
Butthereareimportantexcep1ons!(p.87).
IdealGases
ThePerfect(Ideal)GasLaw(CHEM101!)is
P=nKT
(wherenisthenumberdensityofpar=cles)
Think:whyistherenodependenceonthe
individualpar1clemass?
Equivalently
P=(ρ/μmh)kT
where
ρisthedensityinphysicalunits
μisthemeanmolecularweightofthematerial
mhisthemassofthehydrogenatom
SomeCases
Wewritecomposi1onasX+Y+Z(forH,He,‘metals’)
Inaneutralgas,
Inacompletelyionizedgas
(Whythenumericalfactors?Considertheelectrons!)
MoreGenerally
Theidealgaslawappliesonlyto‘wellseparated’
par1cles.
RemembervanderWaals?
Wehavetoconsiderallcontribu1ons.Instars,thiscan
includeradia1onpressure,orthequantum-mechanical
pressureprovidedbydegenerateelectrons(inwhite
dwarfs)orneutrons(inneutronstars)
Par1cleCollisions:MeanFreePath
Howlikelyisapar1cletocollidewithafieldof
otherpar1clesthroughwhichitismoving?
Seethesimplederiva1ononpage90.
Conclusions:
MeanFreePathbetweencollisions
=1/(nσ) whereσ=par1clecross-sec1on
n=par1clenumberdensity
Mean1mebetweencollisions(forasinglepar1cle)
=1/(nvσ)
Collisionrate(forasinglepar1cle)
=nvσ
Analogy:
Do Bullets Collide?
Yes – But Very Rarely!
Applica1ons
Dostarseverysufferphysicalcollisionswithone
another?(workitout!)
HowdidtheSolarSystemform?
Willwebehitbyasteroids?
DoGalaxiesCollide?
h:p://globalnews.ca/video/2359184/anima1on-of-milky-way-and-andromedagalaxies-colliding
OtherConsidera1ons
Effec1vecross-sec1onsmaybedifferentfrompure
physicalradii–considerCoulombforces,
gravita1onalfocussing,etc
Thesecanbefoldedintoahybridcollisionrate
coefficientthatpertainsingivenphysical
circumstances.
(Seetable3.2,p92,andconsiderthevarious
regimesdiscussed.)