1. Mellinger Lesson 6 molecular line & clouds Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University Kagoshima Univ./ Ehime Univ. Galactic radio astronomy

2. Mellinger Physical state of Int.-stellar gas categorytemperaturedensitymajor objects molecular gas20K>100 cm -3 molecular clouds atomic gas100K1 cm -3 WNM, CNM ionized gas6000-10000K100 cm -3 HII regions ionized gas10 6 K<0.01 cm -3 coronal gas expansion Gravitational collapse Phase change Pressure equilibrium Radiative cooling (very slow) SNR heating

3. Mellinger Molecular clouds ▶ It is a “interstellar molecular gas cloud”. ■ Condensation of IS gas mainly composed by H 2 ■ The most dense part of the ISM ▶ Non-equilibrium with surrounding gas ■ Self gravity works efficiently. ■ Self-gravity ＞ gas pressure gives contraction(?)

4. Mellinger Prove of molecular clouds(1) ▶ Hydrogen molecules H 2 ■ Symmetric 2 atom molecule is  =0 ■ No electric-dipole emission! ■ No radio emission for rotational transition ▶ Q:What’s the next? A ： CO ■ Abundance is not well fixed. ■ CO/H 2 ~10 -4

5. Mellinger Prove of molecular clouds(2) ▶ Problem on CO ■ Saturate with even a moderate column density ▶ Isotope molecules of 12 C 16 O ■ 13 CO, C 18 O ▶ Other molecules ■ CS, HCO +, HCN, etc.

6. Mellinger Mol. lines : rotational transition ▶ diatomic molecule ▶ Electronegativity difference ■ C=2.55, O=3.44 Pauling electronegativity ▶ Mass difference ■ C=12, O=16 ▶ Cnt of electr. distr. ≠ Mass center ■ Electric dipole moment ■ Rot. gives charge vib.→radio emission C O axis ： mass center

7. Mellinger Rot. trans. of diatomic molecule(1)

8. Mellinger Rot. trans. of diatomic molecule(2)

9. Mellinger Rot. trans. of diatomic molecule(3)

10. Mellinger Rot. trans. of diatomic molecule(4)

11. Mellinger Rot. trans. of diatomic molecule(5)

12. Mellinger Molecular line in a mol. cloud ▶ Collisional excitation ■ Equilibrium between collision and line emission ▶ Two level mode dn 1 =n 2 A 21 -n 1 B 12 I+n 2 B 21 I-n 1 C 12 +n 2 C 21 n=n 1 +n 2 total number is const. ▶ Solve under steady state with dn 1 =0 n2n2 n1n1 C 12 C 21 B 21 B 12 A 21

13. Mellinger Consider the extreme case

14. Mellinger Reduction of coefficients ▶ Derived equation n 2 /n 1 =( g 2 / g 1 ){(c 2 /(2h  3 )I A 21 +C 21 exp[-(h )/(kT k )]} /{A 21 [1+ c 2 /(2h  3 ) I]+C 21 } ■ Show I with T r using Planck function formally ■ Show n 2 /n 1 with T ex using Boltzmann distr. ▶ They give… exp[-(h )/(kT ex )]=[A 21 /{exp(-h /kT r )-1}+C 21 exp(-h /kT k ) /{A 21 exp(h /kT r )/[exp(h /kT r )-1]+C 21 }

15. Mellinger Consider the extreme case Equation given on the previous page exp[-(h )/(kT ex )]=[A 21 /{exp(-h /kT r )-1}+C 21 exp(-h /kT k ) /{A 21 exp(h /kT r )/[exp(h /kT r )-1]+C 21 } ■ When radiation dominant (A 21 ≫ C 21 ) T ex →T r ■ When collision dominant (A 21 ≪ C 21 ) T ex →T k ■ Weak radiation approximation (I=0) n 2 /n 1 =[n 2 /n 1 ] Bol (A 21 /C 21 +1) -1 [n 2 /n 1 ] Bol : Boltzmann distr. with T k

16. Mellinger Critical density(1) ▶ Classical collision model: C 21 C 21 =n(H 2 )  ▶ no line with small n 2 /n 1 n 2 /n 1 =[n 2 /n 1 ] Bol (A 21 /C 21 +1) -1 ■ Critical value is given by A 21 <C 21 ■ n(H 2 )>A 21 /(  )=n(H 2 ) crit : critical density ▶ Easy misunderstanding ■ “strong line with large A coefficient” is false.

17. Mellinger Critical density(2) ▶ In the case of CO(J=1-0) ■ A 10 =7.203×10 -8 s -1,  ~10 -15 cm 2 ■ If T k ~20K, ~0.5 km s -1 ■ They gives n(H 2 ) crit, CO(1-0) ~10 3 cm -3 :crit. density ▶ In the case of CO(J=4-3) ■ With A 43 =( 43 / 10 ) 3 A 10 =6.4×10 -6 s -1, we get ■ n(H 2 ) crit, CO(4-3) ~10 5 cm -3

18. Mellinger Critical density(3) ▶ Appropriate line to address typical density ■ high density tracer CS, HCN, HCO + CO(4-3), CO(3-2) NH 3 ▶ Molecular gas without any line emission ■ Very less dense gas may exist. ■ Candidates of baryonic dark matter=dark gas

19. Mellinger Multi-line observations(1) ▶ LTE approximation ■ T ex is constant between any two levels ■ Line intensities differ due to  T B =T ex (1-e -  ) ■ Compare lines with  ≫ 1 and  ≪ 1 T B,thick =T ex, T B,thin =T ex , ▶ Optical depth from intensity→column density ▶ Optically thick line→excitation temperature

20. Mellinger Multi-line observations(2) ▶ Multi-levels (allow  j=±1: diatomic mol.) dn j =n j+1 A j+1,j -n j B j, j+1 I j+1,j +n j+1 B j+1,j I j+1,j -n j C j,j+1 +n j+1 C j+1,j n=  n j total number is const. ■ Solve it under steady state dn j =0 ▶ Change of I j+1,j :simliar to the 2 level model   = (h  )/(4  )  ( ) n j A j+1,j   = (h  )/(4  )  ( ) (n j B j,j+1 -n j+1 B j+1,j ) ▶ Change of intensity dI =(   –   I )dx ■ Depend on the large scale structure of the cloud