Lecture 9 CO Observations of Molecular Clouds. CO Surveys 2. Nearby molecular clouds 3. Antenna temperature and radiative transfer 4. Determining cloud conditions from CO References Tielens, Ch. 0 Myers, Physical Conditions in Molecular Clouds, OSPS99 Blitz & Williams, Molecular Clouds, OSPS99 OSPS = Origins of Stars & Planetary Systems http://www.cfa.harvard.edu/events/crete/
Orion-Taurus-Aurigae The location of the nearby molecular clouds. 2
. CO Surveys There have been several surveys of CO emission of the Milky Way using the low- transitions 2 CO -0 at 5.27203 GHz 2 CO 2- at 230.53800 GHz 3 CO -0 at 0.2037 GHz CO surveys are the primary way of identifying giant molecular clouds and their properties The relatively low abundance of CO compared to H 2 is more than offset by its dipole moment (and higher Einstein A-values) CO lines can be optically thick, so the thinner lines of 3 CO and C 8 O are important 3
Three Important CO surveys. Goddard-Columbia-CfA (Thaddeus et al.) - Dame et al. Ap 547 792 200, which lists earlier surveys. Carried out with two mini.2 m telescopes, one at CfA (originally on the top of Columbia s Pupin Hall) and the other in Chile, with angular resolution 8.5 ( pc at the distance of Orion). 2. SUNY-UMASS (Solomon, Scoville, Sanders) - Scoville & Sanders, Interstellar Processes (987). pp 2-50. 4 m telescope with angular resolution of 45 (0. pc at the distance of Orion). 3. BU-FCRAO Survey of the Outer Galaxy Heyer et al. ApS 5 24 998. Uses the 4-m with multi-feeds. It is not just the resolution that counts, but sampling, sensitivity, & coverage. The CfA survey took 0.5M spectra; BU-FCRAO.7M. A recent meeting report devoted to surveys: Milky Way Surveys, ASP CP37, eds. D. Clemens et al. 4
Overview of CO Surveys CO maps are clumpier and show a different global structure than the broad HI distribution Individual molecular clouds and cloud complexes can be identified throughout much of the galaxy (taking advantage of the variation of velocity vs. galactic radius), but clouds may be confused and ill-determined in some regions CO observations are crucial for studies of star formation and galactic structure: Together with radio, optical-ir observations of HII regions, OB associations and other Pop I objects, CO surveys show that virtually all star formation occurs in molecular clouds CO surveys have helped refine our knowledge of the spiral structure of the Milky Way, since clouds preferentially form in spiral arms, and their distances can be determined from associated Pop I objects 5
Distribution of CO Clouds latitude Opiuchus The Molecular Ring 80º Taur-Per-Aur 0º Orion 80º The Milky Way in Molecular Clouds: A New Complete CO Survey Dame, Hartmann and Thaddeus, Ap 547 792 200 CO has a vertical extent ±45-75 pc over much of the disk, similar to OB associations, and flares out to ±00-200 pc. 6
Kinematics of CO Clouds Velocity-longitude plot Dame et al. Ap 547 792 200 7
Kinematics of Molecular Clouds CfA survey Dame et al. 200 Inner (250-750 pc) disk/ring of high surface density expanding/rotating ~ 240 km/s Molecular ring between 3-8 kpc ( 5 kpc ring ) Spiral arms and discrete OB associations 3 CO Galactic Ring Survey (46 resolution) www.bu.edu/galacticring 8
Inner Galaxy in CO Spiral Arm Ridges Molecular Ring Inner Disk 9
2. Nearby Molecular Clouds Taurus is the nearest and the site of lowmass star formation Closest site of massive star formation is Orion Nearest large cloud complex is Cygnus rift/cygnus OB7 Dame et al. (987) 0
Early CO map of Orion by the Goddard-Columbia.2 m mini-telescope plus Blaauw s OB associations a - 2 Myr b - < Myr Trapezium - < Myr c - 2 Myr The Trapezium cluster has about 3500 YSOs, including a few O,B stars
Taurus-Perseus-Aurigae Next slide: Low-mass star formation in a cloud complex, ranging from cloud cores to clusters of low-mass young stellar objects and T Tauri stars. 2
PERSEUS NGC 579 B5 IC 348 NGC 333 TMC- T Tau TAURUS L55 3
Very Young Proto-Cluster in Perseus NGC 333, Lada & Lada, ARAA 4 57 2003 Notice the many outflows and jets, characteristic of young protostars. 4
TMC in 2 CO Taurus region in 2 CO (FCRAO 4-m, HPBW = 50 ) 5
TMC in 3 CO Taurus region in 3 CO (FCRAO 4-m, HPBW = 50 ). Notice the greater detail compared to the CO map. 6
3. Antenna Temperature and Radiative Transfer Radio astronomers like to invoke Rayleigh-eans formula to describe the intensity of lines, even though it does not apply to the mm spectrum of molecules like CO.This is OK so long as the radiative transfer is done correctly. We follow and modify the analysis of Lec0 on the 2-cm line and solve the equation of transfer with an integrating factor di d = B (T ex ) I, d = ds where T ex is the excitation of the line in question n u /n l = g u /g l e T ul /Tex, T ul = E ul /k B The integrating factor is just exp(- ), I = e e d d = B(T ex ) ( ) (0) = (e )B(T ex ) for constant T ex 7
Solution of the Equation of Transfer The solution to the equation of transfer is now I ( ) = ( e )B (T ex ) + e I (0) We may think of I ( ) as the measured intensity of a uniform slab of thickness where I (0) is the incident intensity, the CBR at the frequency. The observations are assumed to be made in the offon manner discussed for the 2-cm line, so the relevant quantity is the difference I ( ) - I (0), I ( ) = I ( ) I (0) = ( e )[B(T ex) I (0)] Next we define the antenna temperature with the Rayleigh-eans formula as I 2 k T A 2 B and the above solution becomes T A ( ) = ( e )[ e T ul /T ex e T ul /T R ] () 8
Formula for the Antenna Temperature In deriving this result, T A ( ) = ( e )[ e T ul /T ex e T ul /T R ] we defined T ul = h ul /k B and replaced the background radiation field by the BB intensity with radiation temperature T R I (0) = B (T R ) 2 h 2 e T ul /T R The solution above allows 3 possibilities: line T ex = T R no line T ex > T R emission T ex < T R absorption This result is still incomplete because the optical depth and T ex are both unknown; they require a calculation of the level population. The optical depth is obtained in the usual way d = h ul c 2 (N lb lu N l B ul ) = ul 8 A uln u (e T ul /T R ) (2) 9
Population Calculation The balance equation assuming adjacent ladder-rung transitions is: (A ul + k ul n c + u B ul )n u = (k lu n c + u B lu )n l This equation can be solved for the population ratio n u g u = e T ul /T k lu n c + A ul (e Tul /TR ) n l g l A ul + k lu n c + A ul (e T ul /T R ) = et ul T ex and the excitation temperature can be expressed in terms of T R and the density n coll of colliders by way of the critical density e T ul T ex = e T ul /T (e T ul /T R ) + (n cr n coll ) (e T ul /T R ) + (n cr n coll )e T ul /T R (n cr = A ul /k ul ) (3) We can easily check the high and low density limits: n coll >> n cr : T ex = T n coll << n cr : = T ex T + T (T << T R ) and T R (T >> T R ) T R 20
Summary of Radiative Transfer We derived three equations for one rotational transition: Eq, () - T A in terms of T ex and the optical depth Eq, (2) - optical depth in terms of T ex and N l Eq, (3) - T ex in terms of T and n coll There are several unknowns: kinetic temperature T excitation temperature T ex of the line density of the molecular carrier n density of the collision partner n coll It is obvious that the three equations, containing just one observable T A, is insufficient to obtain all the desired information. All is not lost, however, since usually more than one line and at least one isotope ca be observed. If that isotope has a low enough abundance, then one can assume that the optical depths of its lines are small, thereby simplifying the analysis.there are other tricks 2
3. Determining Cloud Propeties from CO Maps of the 2 CO or 3 CO lead to the concept of molecular clouds. The kinematics of the clouds give distances and thus the linear dimensions of the clouds. To obtain more information on the physical conditions, we apply the discussions of Lecs 3-8 on the rotational levels to the interpretation of the mm observations. UV NIR mm 22
a. The Ground Rotational Band of CO E = ( + ) B, E = E E = 2B for small B =.922529 cm - B/k B = 2.766 K 3 ------------------- 0.867 mm 345 GHz 2 -------------------.30 mm 230 GHz ------------------- 2.60 mm 5 GHz 0 ------------------- A,- = 3 4 /(2+) A 0, A 0 = 7.7x0-8 s - f -, = 2 /(2-) f 0 f 0 = 2.8x0-08 approximate collisional rate coefficient: k, (H 2 +CO) ~0 - T 0.5 cm 3 s - for - =.2 23
CO rotational Frequencies and Critical Densities -0 2-3-2 CO 5.27 230.58 345.796 b. Critical Densities 767 3 ncr 0) cm 0.5 T - n cr (-) -0 2-3-2 Frequencies in GHz 3 CO 0.20 220.4 330.6 C 8 O 29.6 29.6 329.4 See NIST /MolSpec/Diatomics 25 T 3 2 ( =.430 ( ).4x0 3 2.3x0 3 7x0 4 cm The fundamental transition at 2.6 mm is easily thermalized, especially when line trapping is considered. 3 24
25 c. Optical Depth of the CO mm Lines ( ) + = 2 / 2 / CO, 2,, P P N b m c e f e ) 2.766K / exp( 2 / 2 / T P P + H CO) ( N P x N = Start with the standard formula for a gaussian line The stimulated emission factor must be included, especially because the transition and thermal temperatures are the same order of magnitude (0 K): For a constant CO abundance and excitation temperature, the column densities of the rotational levels are For a thermal equilibrium population, B T Z e Z P kt B + +, ) (2 / ) (
CO rotational line optical depths Putting all the pieces together leads to:, f, e 2 m e c, b x(co)n H 2 T /B e( )B /T ( e 2B /T ) 335 [x(co) 4 0K T km s b ] mag A V ( e 2.766 /T ) for = 0 CO(-0) and other low- transitions can easily be optically thick d. Further consequences of large optical depth Consider the critical density of the CO(-0) transition, including the effects of line trapping: n cr 0 A k 0 0 A k 0 0 0 = 2.30 Large 0 reduces the critical density. 3 0 cm 3 0K T 2 26
Consequences of the Large CO Optical Depth. The case for thermalization is very strong when the line optical depth is large. 2. Low- CO transitions provide a thermometer for molecular gas 3. Widespread CO in low density molecular regions is readily observed. 4. Optically thick line intensities from an isothermal region reduce to the Blackbody intensity B (T). 5. Densities must come from the less-abundant and more optically-thin isotopes. 27
Idealized Density Measurement with C 8 O With its low abundance (x 6 /x 8 ~ 500), C 8 O may be optically thin, in which case the observed flux is (ds is distance along the l.o.s) F = ds j beam with j = 4 A ul n u h ul Assuming that the relevant population is in thermal equilibrium, that there is no fractionation, and that x(co) is a constant, then all the variables are known: n u n(c 8 O) = g ue Eul / kt Z F N(CO) and and n(c 8 O) = x 8 x 6 n(co) N H = N(CO) x(co) Under all of these assumptions, the optically thin C 8 O flux determines the H column density. If one more assumption is made about the thickness of the cloud L, e.g., that it is the same as the dimensions on the sky (at a known distance), then the H volume density can be estimated as n H = N H /L. 28
Probes of Higher Density Although the CO isotopes are useful for measuring the properties of widely distributed molecular gas, other probes are needed for localized high-density regions, especially cloud cores that give birth to stars. The solution is to use high-dipole moment molecules wth large critical densities. Species μ(d) 0 (GHz) CO CS HCN.0.96 2.98 5.3 48.99 89.09 A ul = 64 3h 4 μ 2 ul 3 ul HCO + 3.93 89.9 N 2 H + 3.4 93.8 See Schoier et al. A&A 432, 369 2005 for a more complete table of dipole moments and other molecular data from the Leiden data base. 29