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Sub-mm and mm study of ISM;

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					    Sub-mm/mm astrophysics:
    How to probe molecular gas

           Yasuo Fukui
         Nagoya University

            Summer School
        The Gaseous Universe
        Oxford, 21-23 July 2010
•
                                  1
        Lecture 2
Sub-mm diagnostics; density
     and temperature
    Sub-mm/mm astrophysics:
    How to probe molecular gas
 Sub-mm diagnostics; density and
         temperature
  In lecture 1, we have learned the
fundamentals of molecular data at sub-mm
and mm wavelengths.
  Now we apply the method to real data taken
with best telescopes in order to derive
physical parameters of the molecular gas.
  By comparing different J transitions we can
determine density and temperature by LVG
approximation
            Radiative transfer




(εν(x): Emission coefficient, κν(x): Absorption coefficient)




Optical depth:
       Absorption coefficients




φ(ν): line profile function
 - When φ(ν) takes a Gaussian function.
Rotational excitation of a diatomic-molecule
• Eigenvalue of energy (Quantum mechanics)



• Rotational quantum number, J (J = 0,1,2,3,…)
• ΔJ = ±1



• A coefficient
    Excitation temperature & Optical depth
•   13CO   J=1-0 (LTE assumption)
    – Radiation (Observed) Temperature, TR*
                      (*Back ground of spectral line is removed)




• Since τ12CO(optical depth of 12CO J=1-0) ≥ 1



• Then, derive τ13CO (optical depth of 13CO J=1-0)
                Column density



• Partition function, Q
                     LVG approximation
LVG (Large Velocity Gradient)
(Castor 1970; Goldreich & Kwan 1974; Scoville & Solomon 1974
• Simple molecular cloud model                                   Molecular cloud
   – Uniform Tk and n(H2)
   – Uniform velocity gradient
                                                               Velocity
 Photon escape probability, β
    - Spherical
                                                                    Tk, n(H2)
    - Slab

    – Input parameters: Tk, n(H2), [CO]/[H2] abundance
      ratio X(CO), velocity gradient dv/dr
          Part I
N159 and other GMCs in the
           LMC
           Magellanic Clouds             The Large Magellanic Cloud
   D=50 kpc (one of the nearest)
   Different environment from the MW.
      High gas-dust ratio
      Low metallicity
   Active star formation
      Massive star formation
      Young populous clusters




                                           The Small Magellanic Cloud




                                                                        11
12
                   Excitation 2
• Hydrogen molecules are not observable in radio. Too
  high energy levels. Only in absorption.
• Carbon monoxide CO and others can be observed
  rotational energy levels, high excitation vibration.
  cf. electronic, spin-spin interaction


• Sub-mm transitions
generally higher excited states
ratio between J and J’ gives
density/tempearture.

                                                         13
                N159        N206D      GMC225
              (Type III)   (Type II)   (Type I)
12CO(J=3-2)




                                                  100


                                                  80



                                                  60




                                                        (K km/s)
12CO(J=1-0)




                                                  40


                                                  20

                                                  14
                                                   0
NN159 CO 3-2/1-0 vs. Ha




                          15
30Dor No.1                                                   15-40K, 103cm-3
                                                              (cool, diffuse)



     > 50K, 103-5cm-3               > 30K, 103cm-3                  GMC225 No.1
      (warm, dense)                 (warm. diffuse)

                                            N206 No.1


                                                                           16
             XCO =   3×10-6;   solid:R3-2/1-0,clump;broken:R12/13
                High temp.
Low density     High density




       低温・低密度




                               17
        NANTEN2 CO J=4-3 observations
                        Mizuno et al. 2010
N159 region in the LMC
N159E           N159W     CO(J=1-0)   CO(J=3-2)   CO(J=4-3)




             N159S



Spitzer(8, 24mm)           Mopra         ASTE     NANTEN2
 (Meixner et al.2006)
+NANTEN2 CO (4-3)
                  Results:N159W



                      1s level


–Temperature
72+3-9 (K)

–Density
4.0+0.0-0.0×103
(cm-3)
                                  19
                  Results:N159E




–Temperature
79+13-12 (K)

–Density
4.0+1.0-0.0×103
(cm-3)
                                  20
                  Results:N159S




–Temperature
31+8-9 (K)

–Density
1.6+0.4-0.3×103
(cm-3)
                                  21
Comparison with the observed intensities




N159W, E:
12CO J=1-0, 2-1 are weaker than that expected from LVG

                                                    22
 Physical conditions in the clumps
• N159W, N159E:2 components

                         12CO   J=4-3, J=3-2
           Hot
                         13CO
           Dense
           ~ 80 K        12CO   J=1-0
          Cold ~ 30 K


• N159S:1 component
                          12CO   J=4-3, J=3-2
                          13CO

          Cold ~ 30 K    12CO    J=1-0


                                                23
                 Contours:12CO(J=4-3)
                          Image:optical
Star formation      B, V, Ha, O III (ESO)




                                   24
    Molecular clouds and star formation
N159S                       N159W                  N159E
*No massive star            *massive star          *Massive star
formation                   formation              formation
*cold                       *Ionized gas           *extended ionized
                                    +              gas
                            *pre star forming
                            region

   Cold molecular gas




                        High excited region
                                                Ionized region
                                                                   25
      Sky Condition at Atacama
          –Atmospheric Tau vs PWV-
           12CO                                       13CO




Sky condition at 100GHz in summer is not different from that in winter
NANTEN2
       NANTEN & NANTEN2




@Las Campanas, alt.2400m   @Atacama, alt.4800m
            Part II
Westerlund 2, case of super-star
           cluster
                  Super star cluster in the MW
O stars are rare in the MW
It is important to study nearby young and rich
cluster but, only five super star clusters in the MW
 Arches Cluster       Quintuplet Cluster            Central Cluster



                                                               Genzel et al. 2003



                       Figer et al. 1999

       0.6[pc]                  1.2[pc]


                                                         0.4[pc]
                                Figer et al. 1999        Genzel et al. 2003
                      Westerlund 2(Wd2)
Spitzer IRAC 3.6, 4.5, 5.8, 8.0 mm                  HESS J1023-575

                                     •Total mass of star: 4500 Msun
                                                            (Rauw et al. 2007)
                                     •Age            :2-3 Myr
                                                           (Piatti et al. 1998)
                                     •O type star         :12
                                                            (Rauw et al. 2007)
                                     •Wolf-Rayet (WRs) star :2
                                                        (Rauw et al. 2007)
                                     •Distance:2.8 kpc(Ascenso et al.2007)
                                       4.3 ± 1.4 kpc(Furukawa et al.2009)
                                       8.3 ± 1.6 kpc (Rauw et al. 2007)
                                     HII region RCW 49
                                     •HII region associated with
                                      the cluster (Churchwell et al. 2004)
                                     •YSOs: 300 (Whitney et al. 2004)
      Distribution of line intensity ratio
   image: integrated intensity, cont.:CO(2-1) Red cross:Wd2
Ratio 12CO2-1/12CO1-0                    Ratio 12CO2-1/13CO2-1
                                   2.0                           15




                                  1.5

                                                                 10



                                  1.0


                                                                  5

                                  0.5




                                    0                             0




      Ratio is high near the cluster
LVG Analysis          line:12CO2-1/12CO1-0
                      wiggle line: 12CO2-1/13CO2-1
                      Gray :error range15%
  High Temp.                            Low Temp.




Estimation of temperature and density by using
the LVG analysis including 13CO(J=2-1)
 Temperature distribution of the molecular clouds
   Image: Temperature, cont.:12CO(2-1) red cross:Wd2

        4 km/s Cloud                 16 km/s Cloud




Suggesting gas is heated by the raditation from the cluster.
Temperature with distance from Wd2




                Molecular clouds are associated
                with Wd2 and RCW 49
                            Ohama, Furukawa et al. 2010
           Part III
Galactic centre loops
  Torii et al. 2010 and others
                 The Galactic Centre
      NANTEN CO J=1-0




                         CMZ



• Galactic centre has strong gravity
• Strong differential rotation amplifies the magnetic field
• Molecular gas is nearly neutral, but frozen-in is a good
  description. Ionization degree 10-7 from HCO+
   Molecular loops 1 & 2
(Fukui et al. 2006, Torii et al. 2010a)
     NANEN CO J=1-0

                               ・ Two loop like
                200 pc
                               structures
                               ・ foot points with
                               broad velocity
                               dispersion (~40km/s)
                               ・Total M ~106 Msun
                      300 pc
           Parker Instability (Parker 1966)

• Parker instability drives the                Magnetic field
                                     Gravity
  neutral gas
• Magnetic flotation in the sun
  takes place 12 orders of
  magnitude greater scale
• Key parameters are scale height                  Gas particle
  H and Alfvén speed VA
• Time scale of the process is H/VA,
  1-10 Myrs
2D MHD calculations (Matsumoto et al. 1988)




                        •Gas accumulation at the two
                        foot points, shock heating

                        •Any part of the loop is also
                        being shocked, high
                        temperature
                                                    40
   12CO(J=3-2)       observations   ASTE CO(J=3-2) -180 - -40 km/s

NANTEN CO J= 1-0




Torii et al. 2010b
          12CO(J=3-2)/12CO(J=1-0)         ratio: R3-2/1-0
Color:R3-2/1-0, Contours:ASTE CO(J=3-2)                 P-V diagram




                 High R3-2/1-0 inside the U shape
    Broad emission Spectra
カラー:R3-2/1-0, コントア:ASTE CO(J=3-2)            LVG analysis
           空間分布図
    A
                                    •   12CO(J=1-0,
                                                  3-2, 4-3, 7-6),
                                    13CO(J=1-0), C18O(J=1-0)

                                    • Take 10 km/s average intensities
                                    • [12CO]/[13CO] 〜 53
                                    (Riquelme 2010)

                                    • [12CO]/[C18O] 〜 250
        B                           (i.e. Wilson & Matteucci 1992)

                                    • [12CO]/[H2] = 1×10-4
                                    • dv/dr= 9.0 km/s/pc
            C
                                    • Chi-square minimization
     LVG analysis – Results –
• Typically T 〜30-50 K, n〜103 /cm3
• Broad emission : > 100 K
• Magnetic reconnection may offers a
possible candidate for the hot and
broad gas component.
    Degree of excitation

    R3-2/2-1 Distributions
    in the loops 1 and 2

•   12CO(J=3-2)/12CO(J=2-1)




                              45
              R3-2/2-1 Histogram

                                      All
                                      Loops 1 & 2
                                      Disk (-40 - -20 km s-1)
                                      Disk (-20 - 0 km s-1)
                                      Disk (0 - 20 km s-1)




• Loops 1 and 2: peak at 0.42
• Disk components: peak at 0.24-0.3                     46
      R3-2/2-1 and physical conditions




                           >103cm-3 , >70 K

0.7




                                              47
       LVG analysis
T: 10 – 50 K, >100 K
n(H2): ~ 103.0 cm-3
R3-2/2-1>0.7 indicate T of >70 K


        R3-2/2-1>0.7   R3-2/2-1>0.7




                                      48
appendix




           49
 Derivation of physical parameters
• Rayleigh-Jeans approximation



• Column density:
• τ << 1 case
Physical parameters from CO emission
• Mass:
                 u: mean molecular weight, mH: H atom mass,
D: distance to object, Ω: solid angle, N(H2): H2 column density

•   12CO

    - Optically thick (τ ≥ 1)
    - Can trace only envelopes.
    - X-factor (empirical rule):
                                     WCO: 12CO integrated intensity
       > 0.24×1020 cm-2 (K km s-1)-1 (Oka et al. 1998, the Galactic centre)
       > 1.6×1020 cm-2 (K km s-1)-1 (Hunter et al. 1997, disk average)
                HI 21cm line
hyperfine levels of the
  hydrogen 1s ground state
• Angular momentum
   Upper: 1/2 + 1/2 = 1 (1 = ±1, 0), g2 = 3
   Lower: 1/2 - 1/2 = 0, g1 = 1
•ΔE = 9.4×10-25 J (T = ΔE/k = 0.068 K)
•ν = 1420.405 MHz, λ = 21.106 cm
•A21 = 2.85×10-15 s-1 (Optically thin)
                HI 21cm line
• In the thermodynamic equilibrium



                       (Rayleigh-Jeans approx. )

				
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