EL5!:!! Atomes,!! Molécules,!! Solides!
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Niveau fondamentaux Li2, B2 et C2 EL5!:!! Atomes,!! Molécules,!! Solides! Emmanuel Dartois IAS J. Belushi 2008! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Niveau fondamentaux Li2, B2 et C2 Niveau fondamentaux Li2, B2 et C2 3σ ! u 3σ ! u 1π ! g 2p! Li2 : (1σg)2 (1σu)2 (2σg)2 ! λ=+ou81! 1π ! g 3σ ! g 2p! 2p! B2 : (1σg)2 (1σu)2 (2σg)2 (2σu)2 (1πu)2 ! 1π ! u λ=+ou81! 2σ ! u 2s! + 1!Σ g! 2s! 2s! 8 3!Σ g! 1s! 1π ! u 2s! 2σ ! g 1σ ! u 1s! 1s! 1σ ! g Cours!M2!8!E.!Dartois!8!18/11/2016! 2p! 2σ ! u 2σ ! g 1σ ! u 1s! 3σ ! g 1σ ! g Cours!M2!8!E.!Dartois!8!18/11/2016! Niveau fondamentaux Li2, B2 et C2 Population des niveaux rotationnels 3σ ! u C2 : (1σg)2 (1σu)2 (2σg)2 (2σu)2 (1πu)4! NJ!=!NTOTAL!.(2J+1).!e8BJ(J+1)/kT!/!Qrot! 1π ! g 2p! λ=+ou81! 1!Σ+ 3σ ! g 2p! 1π ! u 2σ ! u g! 2s! 2s! 2σ ! g 1σ ! u 1s! 1s! 1σ ! g Cours!M2!8!E.!Dartois!8!18/11/2016! Qrot=!ΣJ!(2J+1).!e8BJ(J+1)/kT!!! Déterminer le niveau le plus peuplé en fct de la température Cours!M2!8!E.!Dartois!8!18/11/2016! Niveaux rotationnels & transitions ΔE!(J+1⟵J)!!!=!B!(J+1)(J+2)!8!B!J(J+1)!=!2B!(J+1)!! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Niveau fondamentaux Li2, B2 et C2 3σ ! u 1π ! g 2p! (B2+)* : (1σg)2 (1σu)2 (2σg)2 (2σu)2 (3σg)1 ! λ=+ou81! (B2+)* : (1σg)2 (1σu)2 (2σg)2 (2σu)2 (1πg)1 ! (B2+) : (1σg)2 (1σu)2 (2σg)2 (2σu)2 (1πu)1 ! 3σ ! g 2p! 1π ! u 2σ ! u 2s! 2s! 2σ ! g 1σ ! u 1s! 1s! 1σ ! g Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Herschel PACS / CO in protostars J=46845! NJ!=!NTOTAL!.!gJ!.!e8EJ/T!/!Qrot!!!!!!!!!!!!!!!gJ!=!(2J+1)!!!!!!!!!!!!!!!EJ!=!BJ(J+1)/k! J=14813! J=46845! J=14813! Diagramme rotationnel Manoj!et!al.!2013!! Cours!M2!8!E.!Dartois!8!18/11/2016! Manoj!et!al.!2013!! Cours!M2!8!E.!Dartois!8!18/11/2016! HF Léger,!donc!B!très!élevé! Distorsion centrifuge Une!force!de!rappel!influence!la!rota]on,!termes!supplémentaires! B=!20.561!cm81! A!fort! tout!dans!le!fondamental!! Peut!permeWre!de!suivre!H2! Cours!M2!8!E.!Dartois!8!18/11/2016! F(J)!=!B!J(J+1)!8!D!J2(J+1)2!+!H!J3(J+1)3!+!…!! Sonnentrucker!et!al.!2011!! Molécules polyatomiques Toupies symétriques IA!=!IB!<!IC!!! !A!=!B!>!C!!oblate!type!oursin,disque!:!benzène 3!moments!d'iner]e!IA,!IB!et!IC! 3!axes!perpendiculaires!:!axes!principaux!! Cours!M2!8!E.!Dartois!8!18/11/2016! IA!<!IB!=!IC!!! !A!>!B!=!C!prolate!type!cigare!:!propyne!CH3C2H SF6!Wikipedia! 2!moments!d’iner]e!dis]ncts!dans!l’équa]on!de!Schrödinger!:!!! Défini]on!de!2!nombres!quan]ques! Trois!catégories!de!molécules!! IA!=!IB!!!=!!IC! !toupies sphériques!! IA!≠!IB!!!=!!!IC! !toupies symétriques!!! IA!≠!IB!!!≠!!!IC toupies asymétriques!! J!moment!angulaire!total!! +!!K!moment!angulaire!de!l’autre!axe!d’iner]e!(oblate:C,!prolate:A)!! K!=!J,!J81,!J82,!…,!0,!…,!8(J81),!8J! Oblate!F(J)!=!B!J(J+1)!+!(C8B)K2!+!…!!!!!!!!!!!!!!!!!!!!!!avec!(C8B)!néga]f Prolate!F(J)!=!B!J(J+1)!+!(A8B)K2!+!…!!!!!!!!!!!!!!!!!!!!!avec!(A8B)!posi]f!! Règles!de!sélec]on:!ΔJ!=!±1!;!ΔK=!0! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Spectres toupies symétriques Règles!de!sélec]on:!ΔJ!=!±1!;!ΔK=!0! Distorsion et termes d’ordre supérieur F(J)!=!B!J(J+1)!+!(A8B)K2!8!D!J2(J+1)2!+!DJK!J(J+1)K28!DK!K4+!…!! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Avantage astrophysique de la mesure des toupies symétriques prolate Toupies asymétriques κ!=!(2B!8!A8!C!!)/(A!8!C!)!!!! !81!(prolate)!<!κ!<!1!(oblate) Paramètre asymétrique A!=!127484!MHz!! B!=!24679.98!MHz!! C!=!23769.70!MHz! κ!(CH3OH)!≈!8!0.98!!!! !81!(prolate)!<!κ!<!1!(oblate) T kin =35±7!K ! Cours!M2!8!E.!Dartois!8!18/11/2016! ! ! ! ! ! !!Tkin=55±10!K.! Dartois!et!al.!2000!! Cours!M2!8!E.!Dartois!8!18/11/2016! Toupies asymétriques Nota]on : τ!=!KA8KCours!M2!8!E.!Dartois!8!18/11/2016! C!!;!+J!<!τ!<!8J!;!!KA+KC=J!ou!J+1 Cours!M2!8!E.!Dartois!8!18/11/2016! H2O Herschel / Orion KL Hubble! H2O Herschel Cours!M2!8!E.!Dartois!8!18/11/2016! CNES! Neill!et!al.!2013!! Subaru! KL! Cours!M2!8!E.!Dartois!8!18/11/2016! Neill!et!al.!2013!! H2O Herschel / Protoétoile Mouvement de vibration Par]e!radiale! [8 2 2 R /2µ+V(R)] Ψvib(R)=Evib Ψvib(R)! Les!atomes!vibrent!comme!un!oscillateur!! harmonique!obéissant!à!la!loi!de!Hooke!:! F!!=!!8k(x!–!xeq) !! ou!k!est!la!constante!de!force! V(R)!=!V0!+!½k(x!–!xeq)2 ( Ĥ!=!p^2/2µ + E0!+!½k(x^!–!xeq)2( Cours!M2!8!E.!Dartois!8!18/11/2016! Van!der!Tak!et!al.!2013!! Niveaux vibrationnel d’une molécule diatomique : harmonique Niveaux!permis! Cours!M2!8!E.!Dartois!8!18/11/2016! Le!poten]el!réel!est!anharmonique!et!il!faut! rajouter!des!termes!d’anharmonicité! G(v) !=!ωe!(v!+!½)!8!ωexe!(v!+!½)2! Evib! !=!ħω0!(v!+!½)!! !=!ωe!(v!+!½)!cm81! xe!:!constante!d’anharmonicité! Interac]on!de!vibra]on8rota]on! ω0!=!(k/µ)½! Distance!d’équilibre!moyenne!plus!grande!si!v!plus!grand! Lié!à!au!principe!d’incer]tude! Bv V!=!0,!1,!2,!…! Transi]ons!autorisées! Δv!=!1!et!un!seul!pic!aWendu! Il!y!a!interac]on!entre!un!photon!et!la! vibra]on!seulement!si!on!a!une! varia]on!du!moment!dipolaire! pendant!l’oscilla]on.! Donc!HCl,!CO!et!HF!absorbent!les!EMR! et!ont!un!spectre!IR!mais!H2!et!N2!! non.! Cours M2 - E. Dartois - 18/11/2016 !=!B0!8!α!(v!+!½)!+!…! Règles!de!sélec]on!relaxées!à!cause!de! l’anharmonicité!:! Δv!=!±!1,!±!2,!±!3,!…! Cours M2 - E. Dartois - 18/11/2016 Point zéro d’énergie et fractionnement isotopique H2!et!HD! ωe!(H2)!=!4396!cm81! ZPE!=!2198!cm81!! ωe!(HD)/ωe!(H2)!!=!(µH2/µHD)½!=!(3/4)½! ωe!(HD)!=!3807!cm81! ZPE!=!1903!cm81!! Δ ZPE!=!289!cm81!! Teq (Δ ZPE)!=!hν/k!=!hcσ/k!=!!420K! H2!+!D!8>!HD!+!H!+!420K! Cours M2 - E. Dartois - 18/11/2016 Vibration-Rotation Enrichissement!localement!>!D/H!cosmique!0.001%! Cours!M2!8!E.!Dartois!8!18/11/2016! Vibration-Rotation EvJ !=!G(v)!+!F(J) !! !=!ωe!(v!+!½)!8!ωexe!(v!+!½)2!+!!ωeye!(v!+!½)3!+!…! ! !+!Bv!J(J+1)!8!Dv!J2(J+1)2!+!Hv!J3(J+1)3!+!…!! Bv !=!B0!8!α!(v!+!½)!+!γ!(v!+!½)2!+!!…! Dv !=!D0!+!β!(v!+!½)!+!…! ΔE!=!ω0!+!(Bv=1+!Bv=0!)m!+!(Bv=18!Bv=0!)m2!–!2(Dv=18!Dv=0!)m3!! Cours!M2!8!E.!Dartois!8!18/11/2016! avec!!ω0!=!ωe!(!182xe!)!,!m=J+1!branche!R,!!m=8J!branche!P! Cours!M2!8!E.!Dartois!8!18/11/2016! Vibration-Rotation Exemple du labo 4.27 µm Transmittance 1.00 0.95 0.90 0.85 0.80 R P 0.75 0.70 2380 2360 Cours!M2!8!E.!Dartois!8!18/11/2016! 2340 2320 2300 2280 Wavenumber (cm-1) 2260 2240 Cours!M2!8!E.!Dartois!8!18/11/2016! Exemple du labo Exemple de l’astro 15 µm Transmittance 1.0 R 0.8 P Van!Dishoeck!et!al.!2004!! 0.6 0.4 Q 700 690 680 670 660 Wavenumber (cm-1) Cours!M2!8!E.!Dartois!8!18/11/2016! 650 640 Cours!M2!8!E.!Dartois!8!18/11/2016! Boonman!et!al.!2004!! Transitions vibroniques : le principe Franck Condon Exemple de l’astro Wiki! Pontoppidan!et!al.!2002!! Cours!M2!8!E.!Dartois!8!18/11/2016! L'intensité!de!la!transi]on!vibronique!est!propor]onnelle!au!carré!de!l'intégrale!de! recouvrement!entre!les!fonc]ons!d'ondes!vibra]onnelles!des!deux!états!impliqués!dans! Cours!M2!8!E.!Dartois!8!18/11/2016! la!transi]on! Progression vibronique : le principe Franck Condon Solides( !Introduc]on! Solides!réfractaires!(et!très!grosses!molécules...)! Observa]ons! Minéraux!(composi]ons!et!phases)! ≠!formes!de!ma]ère!carbonée!et!leur!mode! d’émission/absorp]on!(PAHs,!fullérènes,!HAC)!!!!!!!!!!!!! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! MaWer!lifecycle! Roland Diehl! Phases!neutres!du!MIS! Phase nH (cm−3 ) T (K) x Mass (%) WNM CNM MC 0.1–1 10–100 >103 104 − 103 500-100 <50 0.01 10−4 <10−5 25 25 30 Verstraete 2011, Wolfire 2003 Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Van Boekel! La!loi!d’ex]nc]on! Ex]nc]on!en!magnitude!dans!l’UV! cm2! S!=!S0!exp![8τν]!=!S0!exp![8∫0D!κν!dx];!!τν =!κνD!=!NσextD!! Flux!versus!magnitude! cm83! 82.5log10S!=!82.5log10S0!8!2.5log10!(exp8[τ])!! m!=!m0!+!2.5τ/ln(10)!=!m0!+!A!=!m0!+!1.086τ!!! “A”!est!!l’ex]nc]on!en!magnitude! Rappel!:!m!=!8!2.5 log10(F/F0) ! !magnitude!apparente!! IUE, Egret 1985! F0!représente!le!flux!d'une!étoile!de!référence! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Excès!de!couleur!(rougissement)! E(B8V)!=!(B8V)!8!(B8V)0!=!AB!8!AV! Magnitude!apparente! ="[indice"de"couleur"observé]"2"[intrinsèque]" indépendant"de"la"distance! V!(540nm)! Rapport!de!l'ex]nc]on!totale!sur!l'ex]nc]on!sélec]ve! R!=!AV!/!E(B8V)!≈!3.1! B!(442!nm)! AV!=!1.086τ! λ81! !τλ!8!τV!!/!τB!8!τV! !Aλ!8!AV!!/!AB!8!AV! E(λ!8!V)!/!E(B8V)! Corrélé!avec!la!taille!moyenne!des!grains!responsable!de!l’ex]nc]on! Cours!M2!8!E.!Dartois!8!18/11/2016! Fitzpatrick & Massa 2007! Cours!M2!8!E.!Dartois!8!18/11/2016! Quan]té!de!poussière!?! Aλ!varie!en!λ81! Ex]nc]on!galac]que!moyenne!visible!≈!1.8!mag/kpc! Molécules!!! Par]cules!a<<λ! λ84! Par]cules!a>>λ! λ0! Par]cules!a~λ! λ81! Cours!M2!8!E.!Dartois!8!18/11/2016! τν =!NσextD!! AV!=!1.086τ! pc!:!3.08x1016!m! Nσext!?!! Cours!M2!8!E.!Dartois!8!18/11/2016! Abondances!!interstellaires!des!éléments!! (DISM,!NH~!100!cm83)! Rapport!gaz/grain! Si!on!prend!a!≈!0.1!µm!! Élément Ngrain!?!! Si!on!prend!a!≈!0.1!µm!et!ρ!≈!283!g/cm3! He C N O Mg Si S Fe mgrain!?! ρ poussières!/!ρ gaz!≈!! Mgrain!x!Ngrain!/!MH!x!NH! ρ poussières!/!ρ gaz!≈!?! [X/H ]IS (ppm) 7.8 104 288.4 79.4 575.4 41.7 40.7 18.2 34.7 δX (%) 0 38.7 22.2 41.9 94.6 95.6 80.7 99.4 Lodders 2003, Jenkins 2009, Verstraete 2011 Cours!M2!8!E.!Dartois!8!18/11/2016! Les!trois!grandes!phases! Longueurs!d’ondes!d’intérêt!:! Mineraux!!/!!(Hydro8)carbures!!/!!Glaces! Compromis!longueur!d’onde!/!signatures! ICE house! Cours!M2!8!E.!Dartois!8!18/11/2016! Van Boekel! ESO! Cours!M2!8!E.!Dartois!8!18/11/2016! Astronomie!infrarouge!spa]ale! Transmission!atmosphérique! Beginning with the Infrared Astronomical Satellite (IRAS) in 1983. (the Netherlands, UK, USA/ 10 months / first maps of entire sky at 4 IR wavelengths.) ESA's Infrared Space Observatory (ISO), 1995-1998, world’s first general-purpose IR space observatory. Japanese mission Akari. 2006-2007, it mapped more than 94% of the sky at infrared wavelengths in greater detail than IRAS. NASA's Spitzer Space Telescope is a general-purpose infrared observatory with a slightly bigger telescope than ISO. Herschel telescope, more than four times larger than any previous IR space telescope bridging the gap between infrared satellites and radio telescopes on ground. Caltech! Cours!M2!8!E.!Dartois!8!18/11/2016! IR astronomy become increasingly important to astronomers. ESA/NASA James Webb Space Telescope, IR space telescope designed to look into the very furthest reaches of space Cours!M2!8!E.!Dartois!8!18/11/2016! Observer!:!les!constantes!op]ques! IRAS! Akari! Jaeger 2003! ISO! Spitzer! JWST! Cours!M2!8!E.!Dartois!8!18/11/2016! Herschel! (sub)8mm! FIR!!!!!8!Infrared!!8!!!!!NIR! !Visible!8!UV! Cours!M2!8!E.!Dartois!8!18/11/2016! Roland Diehl! Poussières carbonées et inorganiques Cours!M2!8!E.!Dartois!8!18/11/2016! - Les étoiles à perte de masse contribuent significativement à enrichir le milieu interstellaire en poussières. Vue!schéma]que!d’un!flot!stellaire/refroidissement! La poussière est observée à des stades d’évolution ultérieurs Jones!2001,!Tielens!2005,! Robitaille!2010,!Matsuura!2011! - Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Adapté de Patzer 2004! Cours!M2!8!E.!Dartois!8!18/11/2016! χ! Exemple!de!modèle!de!vent! 1200 quartz 1100 olivine olivine 1e 05 1000 iron 900 800 T [K] a [cm] periclase 700 periclase iron 1e 06 600 quartz 500 400 300 1e 07 200 100 seed nuclei 0 8 7 6 5 log P [dyn cm 4 2 3 2 1200 1100 ] 1000 900 800 700 600 500 400 300 200 T [K] Condensa]on!loin!de!l’ETL!T 1000K,!P 10(810)atm! Gail & Sedlmayr 1999! Phase!cri]que!:!agrégat!de!molécules!pour!former!des!par]cules!de!108100!atomes!! Ces!noyaux!de!condensa]on!sont!moins!stables!que!les!gros!et!requièrent!une! sursatura]on!/!solide! Compé]]on!temps!caractéris]que!de!forma]on!et!éjec]on!(réac]ons!«!gelées!»)! Cours!M2!8!E.!Dartois!8!18/11/2016! φ! Cours!M2!8!E.!Dartois!8!18/11/2016! Ebel 2000! “Minéralogie”!des!Silicates!! Olivines!(Mg2xFe2−2xSiO4)! ! ! ! ! ! ! !Mg2SiO4!Forsterite! ! ! ! ! ! ! !Fe2!SiO4!Fayalite! Pyroxenes!(MgxFe1−xSiO3)! Molster!et!al.!2002,!Posch!et!al.!2002,!Cami!2002!...! Cours!M2!8!E.!Dartois!8!18/11/2016! ! ! ! ! ! ! !Mg2Si2O6!Ensta]te! ! ! ! ! ! ! !Fe2Si2O6!Ferrosilite!(hypersthene)! ! ! ! ! ! ! !CaMgSi2O6!Diopside! ! ! ! ! ! ! !CaFeSi2O6!Hedenbergite! Cours!M2!8!E.!Dartois!8!18/11/2016! Olivine! Pyroxène! Cours!M2!8!E.!Dartois!8!18/11/2016! La!révolu]on!cristalline! Cours!M2!8!E.!Dartois!8!18/11/2016! Sequence! Adapted from Ebel 2000! Jaeger et al. 1998! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Exemple!!de!sequences!mélangées! Roland Diehl! Silicates! PAHs!?! Silicates! Gielen et al. 2011! PAHs! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Silicates!dans!le!MIS! Silicates!dans!le!MIS! Silicates!dans!l’ISM!sont!presque! en]èrement!«!amorphes!»! (<2.2%!!cristallins!! Kemper!et!al.!2004!+!erratum)! Kemper et al. 2004! Kemper et al. 2004! Cours!M2!8!E.!Dartois!8!18/11/2016! Et!dans!la!limite!de!Rayleigh!(pe]ts)!! Cours!M2!8!E.!Dartois!8!18/11/2016! Silicates!dans!les!disques! Arp220, Hubble! Excep]on!:!l’ISM!des!ULIRGs! Modèle!de!Kurucz!! Spoon et al. 2006! Meeus et al. 2001! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Silicates!dans!les!disques! Evidence!spectrale!du! grossissement!des! grains! Group I Group II Meeus et al. 2001! Cours!M2!8!E.!Dartois!8!18/11/2016! Przyggoda et al. 2003! Cours!M2!8!E.!Dartois!8!18/11/2016! Evidence!spectrale!du! grossissement!des!grains! Minéralogie!:!La!poussière!dans!les!Herbig!Ae!Be!! La!masse!dynamique!dans! certains!disques!implique!des! tailles!encore!plus!grandes! Forsterite Enstatite Van Boekel et al. 2003! Bouwman et al. 2001! Cours!M2!8!E.!Dartois!8!18/11/2016! Cours!M2!8!E.!Dartois!8!18/11/2016! Bouwman et al. 2001! Cours!M2!8!E.!Dartois!8!18/11/2016!
