1. 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

2. i j
Aij
Bij
Bji
Cij
Cji …

4. Radiative transfer equation: the line case

5. 2
A21
B21
B12
C21
C12 1

9. 3-level system 3 2 1 A32 B32 B23 C32 C23 A31 B31 B13 C31 C13 A21 B21

12. J=2
A21
A21 ≈ 10 A10
J=1
A10
J=0

13. nH2 ~ ncr
Tex(1-0) > TK

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

15. 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

16. 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 !

18. 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 !

19. Cesaroni et al. (1991)
maser line
thermal line

20. maser emission
Hofner et al. (1994)
thermal emission

21. 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 !

22. 2 months 1 year Variability of H2O maser in the star forming region
L1204-G

25. 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!!!

26. H2O molecule
22 GHz maser
61,652,3

27. 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)

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

29. 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 = MO
density > MO pc-3
black
hole!

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

31. 7mm free-free & H2O masers
Hypercompact
HII region
Moscadelli et al. (2007)
Beltran et al. (2007)
7mm free-free & H2O masers
500 AU

32. 7mm free-free & H2O masers
Hypercompact
HII region
expands!
7mm free-free & H2O masers
30 km/s

33. 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