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today : molecular observations of H2 CO , 13CO, HCN 3mm spectrum of Orion (80-115 Ghz) SiO HCN amplified vert. axis è > 1000 lines ! how to determine properties of gas clouds Galactic distribution CS CO 1976ApJ...210L..39K CO CO Rotational Levels CO (J=1-0) in Orion KL Nebula TB (K) CO A1-0 = 7x10-8 sec-1 13CO x 5.1 for radio freq. lines and continuum, intensities usually expressed in temperature units 2h! 3 1 2! 2kT B ! T = 2 h!/kT # (Rayleigh-Jeans) 2 c e "1 c rad. transfer eq., I ! = B ! Tx 1" e " $ + I BG e " $ ( ) ( )( ( () ) ) # TB ! = Tx 1" e " $ + TBG e " $ for difference measurements (on_cloud - off_cloud), ( ) ( )( %TB = Tx 1" e " $ + TBG e " $ " TBG & Tx " TBG 1" e " $ ) two limits : ( ) $ << 1 : %TB = Tx " TBG $ ' nmol ( dr ) column density of mol. $ >> 1 : %TB = Tx " TBG ~ TX (=Tk if level pop. in TE, e.g. CO) $ A " 3g ' $ n n ' u ))& l * u ) + ,-1* e *T0 /Tx ./ nl ) ( since ! = && ul % 8# dv / dr (% g l g u ( summary : for the 2 limits : τ < 1, brightness varies as Txnm often taken as applicable to rare isotope lines e.g. 13CO τ > 1, brightness varies as Tx if density low Tx < Tk if density high (above ncrit), Tx è Tk brightness measures gas temperature e.g. 12CO Orion GMCs : ~40 pc extent, 2-4x105 M¤ IR 100 mic CO 5 deg M42 optical nebula few arcmin. Orion CO and 13CO Ripple,, Heyer, Gutermuth,, and Snell 2012 CO Orion CO and 13CO Ripple,, Heyer, Gutermuth,, and Snell 2012 13CO – 33 – Taurus – closest molecular cloud ~ 150pc distance H2 column density Goldsmith etal 2008 5pc Fig. 14.— Locations of young stars in Taurus superimposed on map of the H2 column density. The stellar positions are from Kenyon (2007). The diamonds indicate diffuse or extended sources (of which there are 44 in the region mapped), the squares indicate Class I or younger stars (18), and the asterisks indicate T-Tauri stars (168). It is evident that the distribution of gas vs young stars young stars in highest density regions typical NH2~1021-22 cm-2 Taurus dust cloud – CO velocities Goldsmith etal 2008 blue 3-5, green 5-7, red 7-9 km/s molecular excitation : collisional excitation by H2 radiative excitation observe :TB ~ Tx (1 – collisions : e-τ ) 1976ApJ...210L CO Rotational Levels = Txτ for τ<1 Tx for τ> 1 excitation of J=1 requires ? H2 have : 1) kT >~ 5K (easy) 2) collision rate similar to A1-0 (next page) TB (K) A1-0 = 7x10-8 sec-1 standard rate eq. for level populations : u nu (Cul + Aul + BulUν ) = nl (Clu + BluUν ) l w/ Cul= nH2<σv> (see lecture 3) neglecting stimulated em. & abs. , significant pop. in upper level requires : è n1 nH2<σv> > n1A1-0 for nH2 > A/<σv> , then Tx è Tk critical density ~ 3000 cm-3 for CO (A=7x10-8 sec-1) ~ 104-5 for HCN, CS ... radiative transitions ? What about radiation ?? molecular line emission & background continuum Line Emission : spontaneous decay photons absorbed if τ > 1 based on rare isotope line strengths, τ > 1 e.g. TB (13CO/CO) ~ 1/5 – 1/10 but [13C/12C] ~ 1/40 – 1/90 how to include this ? energy density at line freq. ? large linewidths (>> cs) è Sobolev/LVG rad. trans. photon escape prob. : β = (1 – e-τ) / τ ~ 1 for τ << 1 and 1/τ for τ >> 1 for reference : $ A " 3g ' $ n n ' u ))& l * u ) ! = && ul % 8# dv / dr (% g l g u ( *T /T = +A ul ,-1* e 0 x ./ n l w/ + 0 energy density in line : 4# , 4# . U 1 = -1* 2/S 1 + I 1*BG2 c c 2h1 3 1 S 1 = B 1 Tx = 2 T /T c e 0 x *1 2h1 3 1 = c 2 g ul n l *1 nu ( ) g ul c 3 3 8#1 dv / dr , T0 = h1 / k € in optically thick regime, net radiative R : R = nu ( A ul + Bul U ν ) − nl Blu U ν nu − nl g ul R = nu A ul + (1 − β) A ul n g ul l − 1 nu using Einstein relations : B lu Bul c3 = , Bul = A ul gu gl 8!h" 3 = nu A ul + (1 − β) A ul nu (−1) = nu A ulβ ∴ simply replace A ul with βA ul in 2 level solution!!! ⇒ ncrit = A / σv → βA ul / σv β = 1 / τ ⇒ effective A reduced by factor 1 / τ Conclude : in stat. equil. eq. , replace A w/ Aβ ~ A/τ for τ > 1 è critical density nH2 > Aβ/<σv> è reduced by τ & indep. of A if τ ~10 , CO critical density ~ 300 cm-3 i.e. CO thermalized even in low density clouds called line photon trapping also much easier to excite high dipole mom. mol. can show analytically : Tx varies as (α nm nH2 Cul )1/2 è Tx depends only on mol. abundance ! (not A-coef.) Note : 13CO vs CO -- lower intensity does not mean τ < 1 ! HI CO radio far-IR mid-IR near-IR opt. x-ray gamma Galactic H2 from CO surveys : ~3000 GMCs (compared w/ ~200 HII region > M42) GMCs : n(M) α M-1.6 <M> ~ 2x105 M¤ (50%mass above, 50% below) < D> ~ 40 pc < nH2> = 180 (D/40pc) -0.9 cm-3 how are these measured ? clue : large CO linewidths ~ 10 x thermal at 10-20K Orion GMCs : ~40 pc extent, 2-4x105 M¤ CO measure doppler width of ~ 5 km/s 5 deg !V km/s 1987ApJS...63..821S GMC size-linewidth relation at 10K , thermal width ~ 0.1 km/s !! è supersonic turb. Diameter (pc) GMCs are self-gravitating (not in thermal press. equil.) M = α R2 Δv2 /G w/ α ~ 1 linewidth and size è virial mass Mvir can check virial mass w/ measure of column density 13CO or A V standard dust to gas ratio è NH+2H2= 2x1021 cm-2 per mag AV LCO estimating H2 masses – for resolved clouds Mvir correlated with LCO (= area TCO Δv) Mvir (105 M!) How can an optically thick CO line measure mass ?? How can an optically thick CO line measure mass ?? LCO = area ! TCO "V ( K km/s pc 2 ) = #R 2Tk "V 1/2 % 3#G ( =' * Tk M GMC & 4$ ) %T ( k i.e. LCO + ' 1/2 * M GMC &$ ) è if T & ρ constant , MGMC = constant x LCO as you add mass, size and linewidth increase è increases LCO constant ~ 4.9 M¤ / K km/s pc2 measure LCO for collection of unresolved clouds to get H2 note : for τ > 1 mol. (w/ photon trapping) Tx varies as (abundance)1/2 => constant varies slowly with metallicity (z) Milky Way ISM radial distributions (~ spirals) summary : • HI flat (~1021 cm-2 ) • excess gas è H2 H2 HI HII • SF (HII regions) similar to H2 distribution [ most other nearby spirals expon. falloff of H2 w/ r] in summary star forming GMCs : < diameter > ~ 40 pc , 200-300 H2 cm-3 , <M> ~ 2x105 M¤ clouds are self-gravitating but not-spherical high internal Pturb >> Pth , Pdiffuse ISM intuition : internal state of GMC not affected by external disturbances in diffuse ISM once formed , very hard to disrupt GMC i.e. GMCs have large ‘inertia’ internal SF ~ constant how long do the GMCs last ??