MASER Microwave Amplification by Stimulated Emission of Radiation Statistical equilibrium equations general expressions: coupling with radiation field the excitation temperature: emission, absorption, and masers the 2-level system: thermalization the 3-level system: population inversion  MASER Astronomical masers observational characteristics: identification of a maser line masing species and their environments the outcome of maser observations: examples

i j Aij Bij Bji Cij Cji …

Radiative transfer equation: the line case

2 A21 B21 B12 C21 C12 1

3-level system 3 2 1 A32 B32 B23 C32 C23 A31 B31 B13 C31 C13 A21 B21

J=2 A21 A21 ≈ 10 A10 J=1 A10 J=0

nH2 ~ ncr Tex(1-0) > TK

nH2 ~ ncr Tex(1-0) < 0 MASER!!!

Astronomical masers By definition a line is masing when Tex<0 i.e. τ<0 Identification of OH maser (Rieu et al. 1976) towards cloud with background quasar: off-source: TBoff=Tex(1-e-τ) on-source: TBon=(Tex-Tquasar)(1-e-τ)  Tex=-10 K, τ=-0.1 for 1720 MHz line of OH TBon quasar TBoff

How to recognise maser lines Large TB: TB = |Tex| e|τ| e.g. TB=1010 K for H2O masers! Point-like source: maser emission is very beamed  “spot” with angular size < 1 mas ! Narrow line width: amplification favours line center  line width ΔV < 1 km/s (cf. ΔVthermal > a few km/s) Multiple lines: velocity coherence needed along l.o.s. High time variability: exponential dependence on τ  very sensitive to small changes of pumping, amplification path, velocity coherence, orientation  changes over < 1 day !

How to recognise maser lines Large TB: TB = |Tex| e|τ| e.g. TB=1010 K for H2O masers! Point-like source: maser emission is very beamed  “spot” with angular size < 1 mas ! Narrow line width: amplification favours line center  line width ΔV < 1 km/s (cf. ΔVthermal > a few km/s) Multiple lines: velocity coherence needed along l.o.s. High time variability: exponential dependence on τ  very sensitive to small changes of pumping, amplification path, velocity coherence, orientation  changes over < 1 day !

Cesaroni et al. (1991) maser line thermal line

maser emission Hofner et al. (1994) thermal emission

How to recognise maser lines Large TB: TB = |Tex| e|τ| e.g. TB=1010 K for H2O masers! Point-like source: maser emission is very beamed  “spot” with angular size < 1 mas ! Narrow line width: amplification favours line center  line width ΔV < 1 km/s (cf. ΔVthermal > a few km/s) Multiple lines: velocity coherence needed along l.o.s. High time variability: exponential dependence on τ  very sensitive to small changes of pumping, amplification path, velocity coherence, orientation  changes over < 1 day !

2 months 1 year Variability of H2O maser in the star forming region L1204-G

Maser species and environments Many lines of many molecules are masing Maser lines from different environments: Galactic: SFR: H2O, OH, CH3OH, H2CO, NH3, SiO, Hnα, … Late Type Stars: H2O, OH, SiO, HCN, … Extragalactic: Star-burst galaxies: H2O, OH, H2CO AGN: H2O, OH Water masers are strongest: in Orion, up to 1010 K brightness or 1 LO isotropic luminosity in 1 line!!!

H2O molecule 22 GHz maser 61,652,3

Results from maser line observations Intensity useless to derive physical parameters of gas! In fact, Tex< 0 cannot be Tk and τ<0 cannot be Ncol… Strong and pointlike: excellent targets for VLBI (mas!) Proper motion measurements Reconstruction of the 3D velocity field of the gas Distance estimates (statistical parallax, phase lag, kinematical models) Magnetic field measurements from polarization (Zeeman) Clues on acceleration/deceleration from variability Different maser species trace different phenomena (e.g. disk & outflow)

Proper motions of H2O maser spots in star forming region Torrelles et al. (2001)

central mass from Keplerian law: H2O masers in galaxy NGC4258 Miyoshi et al. (1995) red blue 0.13 pc red blue central mass from Keplerian law: M = V2R/G = 3.6 107 MO density > 4 109 MO pc-3 black hole!

massive protostar IRAS 20126+4104 Keplerian rotation: M*=7 MO OH & CH3OH masers massive protostar IRAS 20126+4104 Keplerian rotation: M*=7 MO OH & CH3OH

7mm free-free & H2O masers Hypercompact HII region Moscadelli et al. (2007) Beltran et al. (2007) 7mm free-free & H2O masers 500 AU

7mm free-free & H2O masers Hypercompact HII region expands! 7mm free-free & H2O masers 30 km/s

Bibliography Genzel 1991, in The Physics of Star Formation and Early Stellar Evolution, p. 155 M. Elitzur 1992, Astronomical Masers Cohen 1989, Rep. Prog. Phys. 52, 881 Cosmic Masers: From Proto-Stars to Black Holes, 2002, proc. IAUS 206 Stahler & Palla 2004, The Formation of Stars Astrophysical Masers and their Environment, 2008, proc. IAUS 242