Download molecular observations of H CO , 13CO, HCN how to determine

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 ??