1. Outflows and Jets: Theory and Observations Winter term 2006/2007 Henrik Beuther & Christian Fendt 20.10 Introduction & Overview (H.B. & C.F.) 27.10 Definitions, parameters, basic observations (H.B) 03.11 Basic theoretical concepts & models I (C.F.) 10.11 Basic theoretical concepts & models II (C.F.) 17.11 Observational properties of accretion disks (H.B.) 24.11 Accretion disk theory and jet launching (C.F.) 01.12 Outflow-disk connection, outflow entrainment (H.B.) 08.12 Outflow-ISM interaction, outflow chemistry (H.B.) 15.12 Theory of outflow interactions; Instabilities; Shocks (C.F.) 22.12, 29.12 and 05.01 Christmas and New Years break 12.01 Outflows from massive star-forming regions (H.B.) 19.01 Radiation processes (H.B. & C.F.) 26.01 AGN jet theory (C.F.) 02.02 Observations of AGN jets (Guest speaker: Klaus Meisenheimer) 09.02 Summary, Outlook, Questions (H.B. & C.F.) More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ws0607.html beuther@mpia.de, fendt@mpia.de

3. Planck's Black Body

4. Wien's Law max = 2.9/T [mm] Examples: The Sun T  6000 K  max = 480 nm (optical) Humans T  310 K  max = 9.4  m (MIR) Molecular Clouds T  20 K  max = 145  m (FIR/submm) Cosmic Background T  2.7 K  max = 1.1 mm (mm)

5. The Interstellar Medium I Atomic Hydrogen Lyman  at 1216 A o The 21cm line arises when the electron spin S flips from parallel (F=1) to antiparallel (F=0) compared to the Proton spin I.  E = 5.9x10 -5 eV

6. The Interstellar Medium II Molecular Hydrogen Carbon monoxide CO Formaldehyde H 2 CO Cyanoacetyline HC 3 N Excitation mechanisms: - Rotation --> usually cm and (sub)mm wavelengths - Vibration --> usually submm to FIR wavelengths - Electronic transitions --> usually MIR to optical wavelengths

7. The Interstellar Medium III Ionized gas - H 2 recombination lines from optical to cm wavelengths - Emission lines from heavier elements --> derive atomic abundances He/H 0.1 C/H 3.4x10 -4 N/H 6.8x10 -5 O/H 3.8x10 -4 Si/H 3.0x10 -6 - Free-free emission between e - and H + cm mm submm

8. Heating processes Energy injection from outflows/jets Energy injection from supernovae UV radiation from stars Cosmic rays interaction with HI and H 2 (consist mainly of relativistic protons accelerated within magnetized shocks produced by supernova-remnant--molecular cloud interactions) p + + H 2 --> H 2 + + e - + p + (dissociation: ions also important for ion- molecule chemistry) Interstellar radiation (diffuse field permeating interstellar space) Mainly dissociates carbon (lower ionization potential than H 2 ) C + h --> C + + e - The electron then disperses energy to surrounding atoms by collisions. Photoelectric heating: - Heats grains which re-radiate in infrared regime - UV photons eject e - from dust and these e - heat surrounding gas via collisions

9. Cooling processes Major constituents H & H 2 have no dipole moment and hence cannot effectively cool in quiescent molecular cloud. Other coolants required. --> Hydrogen collides with ambient atoms/molecules/grains exciting them. The cooling is then done by these secondary constituents. O + H --> O + H + h  collisional excitation (FIR)  C + + H --> C + + H + h  fine structure excitation (FIR)  CO + H 2 --> CO + H 2 + h  rotational excitation (radio/(sub)mm)  The low-J CO lines are mostly optically thick, the energy diffuses  from region to region and escapes from cloud surface. Higher J  lines cool directly. CO is the most effective coolant in molecular clouds.  Collisions with gas atoms/molecules cause lattice vibrations on grain  surfaces, that decay through the emission of infrared photons (since  grains are also heated by radiation gas and dust temperature are  usually not equal).

10. Molecular Hydrogen (H 2 ) Since H 2 consists of 2 identical atoms, it has no electric dipol moment and rotationally excited H 2 has to radiate via energetically higher quadrupole transitions with excitation temperatures > 500 K. --> cold clouds have to be observed other ways, e.g., CO H 2 can be detected in hot environment. Rotational energy: Classical mechanics: E rot = J 2 /2I ( J: Angular momentum; I: Moment of inertia) Quantum-mechanical counterpart: E rot = h 2 /2I x J(J+1) = BhI x J(J+1) (J: rotational quantum number; B: rotational constant) Small moment of inertia --> large spread of energy levels Allowed quadrupole transitions  J = 2 --> lowest rotational transition J=2-0 has energy change of 510 K

11. Carbon monxide (CO) Forms through gas phase reactions similar to H 2 Strong binding energy of 11.1 eV helps to prevent much further destruction (self-shielding) Has permanent dipole moment --> strong emission at (sub)mm wavelengths Larger moment of inertia than H 2 --> more closely spaced rotational ladder J=1 level at 4.8x10 -4 eV or 5.5K above ground In molecular clouds excitation mainly via collisions with H 2 Critical density for thermodynamic equilibrium with H 2 n crit = A/  ~ 3x10 3 cm -3 (A: Einstein A coefficient;  : collision rate with H 2 ) The level population follows a Boltzmann-law: n J+1 /n J = g J+1 /g J exp(-  E/k B T ex ) (for CO, the statistical weights g J = 2J + 1) The excitation temperature T ex is a measure for the level populations and equals the kinetic temperature T kin if the densities are > n crit

12. Radiation transfer I dI = -  I ds +  ds with the opacity d    -  ds and the source function S =  /   dI / d  = I  + S Assuming a constant source function   I  = S  (1 - e -  ) + I,0 e - 

13. Radiation transfer II The excitation temperature T ex is defined via a Boltzmann distribution as n J /n J-1 = g J /g J-1 exp(h /kT ex ) with n J and g J the number density and statistical weights. In case of rotational transitions g J = 2J + 1 In thermal equilibrium T ex = T kin In a uniform molecular cloud the source function S equals Planck function S = B (T ex ) = 2h 3 /c 2 (exp(h /kT ex ) - 1) -1 And the radiation transfer equation  I = B (T ex ) (1 - e -  ) + I,0 e -  In the Rayleigh-Jeans limits (h <<kT) B equals B = 2k 2 /c 2 T And the radiation transfer equation is T = J (T ex ) (1 - e -  ) + J,0 (T bg )e -  With J = h /k (exp(h /kT) - 1) -1 Subtracting further the background radiation T r = (J (T ex ) - J n,0 (T bg )) (1 - e -  )

14. Molecular column densities To derive molecular column densities, 3 quantities are important: 1)Intensity T of the line 2)Optical depth  of the line (observe isotopologues or hyperfine structure) 3)Partition function Q The optical depth  of a molecular transition can be expressed like  = c 2 /8  2 A ul N u (exp(h /kT) -1)  With the Einstein A ul coefficient A ul = 64  4 3 /(3c 3 h)  2 J u /(2J u -1) And the line form function   = c/ 2sqrt(ln2)/(sqrt(  )  ) Using furthermore the radiation transfer eq. ignoring the background T = J (T ex )  (1 - e -  )/  And solving this for , one gets N u = 3k/8  3  1/  2 (2J u -1)/J u  /(1 - e -  ) (T  sqrt(  )/(2sqrt(ln2)) The last expression equals the integral ∫ T dv. The column density in the upper level N u relates to the total column density N tot N tot = N u /g u Q exp(E u /kT) For a linear molecule like CO, the partition function can be approximated to Q = kT/hB. However, for more complex molecules Q can become very complicated.

15. Conversion from CO to H 2 column densities One classical way to derive conversion factors from CO to H 2 column densities and gas masses essentially relies on three steps: 1)Derive ratio between colour excess E B-V and optical extinction A v A v = 3.1 E B-V (Savage and Mathis, 1979) 2)The ratio N(H 2 )/E B-V : One can measure the H 2 column density, e.g., directly from UV Absorption lines. 3)The ratio N(CO)/A v : In regions of molecular gas emission, one can estimate A v by star counts in the Infrared regime  Combining these three ratios, the CO observations can directly be converted to H 2 column densities. Assumptions about the 3D cloud geometry allow further estimates about the cloud masses and average densities.

16. A few important molecules Mol. Trans. Abund. Crit. Dens. Comments [cm -3 ] ------------------------------------------------------------------- H 2 1-0 S(1) 1 8x10 7 Shock tracer CO J=1-0 8x10 -5 3x10 3 Low-density probe OH 2  3/2 ;J=3/2 3x10 -7 1x10 0 Magnetic field probe (Zeeman) NH 3 J,K=1,1 2x10 -8 2x10 4 Temperature probe CS J=2-1 1x10 -8 4x10 5 High-density probe SiO J=2-1 6x10 5 Outflow shock tracer H 2 O 6 16 -5 23 1x10 3 Maser H 2 O 1 10 -1 11 <7x10 -8 2x10 7 Warm gas probe CH 3 OH 7-6 1x10 -7 1x10 5 Dense gas/temperature probe CH 3 CN 19-18 2x10 -8 2x10 7 Temperature probe in Hot Cores

17. Molecular Masers I - In the Rayleigh-Jeans limit, brightness temperature T and intensity S relate like T = Sc 2 /2k 2 with S=F/  (  : solid angle). With the small spot diameters (of the order some AU), this implies brightness temperatures as high as 10 15 K, far in excess of any thermal temperature --> no thermal equilibrium and no Boltzmann distribution. - Narrow line-width - Potential broad velocity distribution. - They allow to study proper motions.

18. Molecular Masers II - The excitation temperature was defined as: n u /n l = g u /g l exp(h /kT ex ). - For maser activity, population inversion is required, i.e., n u /g u > n l /g l. --> This implies negative excitation temperatures for maser activity. - In thermal conditions at a few 100K, for typical microwave lines E line = h /k n u /g u ~ n l /g l --> Only a relatively small shift is required in get population inversion T ex /E line = -1/ln(n u g l /n l g u ) With rising T ex the level populations are approaching each other, and then one has only to “overcome the border”. Different proposed pumping mechanisms, e.g.: - Collisional pumping in J- and C-shocks of protostellar jets for H 2 O masers. - Radiative pumping at shock fronts between UCHII regions and ambient clouds. In both cases, very high densities and temperatures are required.

19. Interstellar dust: Thermal emission S( ) = N (  /D 2 ) Q( ) B(  With N dust grains of cross section  at a distance D, a dust emissivity Q~ 2 and the Planck function B(,T). In the Rayleigh-Jeans limit, we have S( ) ~ 4 The thermal dust emission is optically thin and hence directly proportional to the dust column density. With a dust to gas mass ratio of ~1/100, we can derive the gas masses. Colour: MIR Contours: mm continuum L1157 Gueth et al. 2003

20. Interstellar dust: Extinction Extinction dims and reddens the light Dust composition: Graphite C Silicon carbide SiC Enstatite (Fe,Mg)SiO 3 Olivine (Fe,Mg) 2 SiO 4 Iron Fe Magnetite Fe 3 O 4 Size distribution: Between 0.005 and 1  m n(a) ~ a -3.5 (a: size) (Mathis, Rumpl, Nordsieck 1977) Optical Near-Infrared

21. Outflows and Jets: Theory and Observations Winter term 2006/2007 Henrik Beuther & Christian Fendt 20.10 Today: Introduction & Overview (H.B. & C.F.) 27.10 Definitions, parameters, basic observations (H.B) 03.11 Basic theoretical concepts & models I (C.F.) 10.11 Basic theoretical concepts & models II (C.F.) 17.11 Observational properties of accretion disks (H.B.) 24.11 Accretion disk theory and jet launching (C.F.) 01.12 Outflow-disk connection, outflow entrainment (H.B.) 08.12 Outflow-ISM interaction, outflow chemistry (H.B.) 15.12 Theory of outflow interactions; Instabilities, Shocks (C.F.) 22.12, 29.12 and 05.01 Christmas and New Years break 12.01 Outflows from massive star-forming regions (H.B.) 19.01 Radiation processes (H.B. & C.F.) 26.01 AGN jet theory (C.F.) 02.02 Observations of AGN jets (Guest speaker: K. Meisenheimer) 09.02 Summary, Outlook, Questions (H.B. & C.F.) More Information and the current lecture files: http://www.mpia.de/homes/beuther/lecture_ws0607.html beuther@mpia.de, fendt@mpia.de