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New Developments in Maser Theory

New Developments in Maser Theory. Vladimir Strelnitski Maria Mitchell Observatory. “Radio Stars” Haystack Observatory 4 October, 2012. Plan . 1. Summary of Maser Theory - Uniqueness of Inversion - Pumping Cycles - Thermalization - Theoretical Pump Power

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New Developments in Maser Theory

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  1. New Developments in Maser Theory Vladimir Strelnitski Maria Mitchell Observatory “Radio Stars” Haystack Observatory 4 October, 2012

  2. Plan • 1. Summary of Maser Theory • - Uniqueness of Inversion • - Pumping Cycles • - Thermalization • - Theoretical Pump Power • - Saturation • - Observational Requirements for the Pump Power • 2. Hydrogen Masers and Lasers • 3. Prospects

  3. Uniqueness of Inversion = )]-1 Tx = Tk- Thermalization 0<Tx<Tk-Overcooling Tk<Tx<∞-Overheating Tx< 0 - Inversion Tk→

  4. hν/k << Tk; |Tx| Tk→ β = 1- Thermalization β > 1-Overcooling 0<β<1-Overheating β< 0 - Inversion β = 1

  5. Pumping Cycles 3 SOURCE SINK 2 2 MASER 1 1 SOURCE SINK 3 • General Recepe: Look for TWO temperatures! • Energy Reservoirs: • radiation (star; dust) • collisions (maxwellized gas; streams) • chemical processes (ionization; dissociation; dust coat sublimation…)

  6. Deguchi (1977) Sobolev & Strelnitski (1983)

  7. Sobolev & Deguchi (1994)

  8. Gray (2007)

  9. Energy Drain in CCr Pumping of H20

  10. Thermalization Two-level System: ABJ C 2 C>> A ;BJ C << A; BJ τmin<< 1 1 τmin≳ 1 TxTkTrwhen (Avrett & Hummer 1965) Maser (unsaturated) • CC or XX pumping: • NO thermalization! • Strelnitski (1984) • Norman & Kylafis (1987) • CR, RC … pumping: • possible delay of thermalization • to higher densities (example below: Hydrogen masers). • Strelnitski et al. (1996) Λ2 Λ1 2 1 Γ2 Γ1

  11. Estimates of the Pump Power RRv: Litvak (1969) RCv: Goldreich & Kwan (1974) CCr: Strelnitski (1982)

  12. Saturation R ≡ B21J21 << Γ +C → (Unsaturated inversion) R ≳Γ +C → (Saturation) • Saturation results in: • Linear intensity growth • The rule of “1 maser photon per pumping cycle“

  13. Observational Requirements for the Pump Power

  14. Hydrogen Masers and Lasers

  15. D. Menzel: The Man Who Could Make the Whole Story Happen Earlier [of the light absorption in a line]

  16. Baker & Menzel (1937) All the transitions above n=5 are inverted!

  17. v Population Density

  18. MWC 349: The First Natural Hydrogen Maser Martín-Pintado et al. (1989)

  19. Strelnitski et al. (1996) [based on computations by Hummer & Story (1992)]

  20. gain = max C ~ Γ Inversion = max

  21. Lines of Constant Intensity MASERS LASERS Messenger & Strelnitski (2011)

  22. Polarization Goldreich, Keeley & Kwan (1973; GKK) : 1-D maser; magnetic field B; J=1-0 transition; isotropic pumping 4 key parameters with dimension frequency: Δω - bandwidth of radiation; gΩ - Zeeman splitting g - Landég value for the upper state Ω= eB0/mc – girofrequency Γ - population decay rate R - stimulated emission rate

  23. ∢ z B; z’ Watson & Wyld (2001) y’ θ Q = Ix - Iy y x, x’ GKK: nonparamagnetic molecules saturation R << gΩ << Δω, R/Γ>>1 for sin2 θ ≥ 1/3 (θ ≥ 35°) -1 for sin2 θ ≤ 1/3 (θ ≤ 35°) sin2θ = 2/3 → 0 (θ = 54.7°, van Vleck angle) 35° 55°

  24. Circular Polarization of H2O Masers (Fiebig & Güsten, 1989) V

  25. Non-magnetic Explanation of Linear Polarization • Competition between intersecting rays of a saturated maser in non-spherical media and/or media with velocity gradients + lack of axial symmetry along the line of sight causes linear polarization.(Western &Watson, 1983) • Non-magnetic Explanation of Linear Polarization • Anisotropic pumping of an unsaturated maser (e.g. Ramos & Degl’Innocenti, 2005) • Non-Zeeman Explanation of Circular Polarization • Change of the quantization axis from the direction of the MF to the direction of propagation with the increasing R, when R ~ gΩ(‘Intensity-dependent polarization’) (Nedoluha & Watson, 1994 ) • Non-Zeeman Explanation of Circular Polarization • (Observed) linear polarization + variations of the orientation of magnetic field along the line of sight (Wiebe & Watson, 1998) When Bis “unusually” high, think of the above possibilities!

  26. Reviews on astrophysical maser polarization: Watson W.D. 2009, Rev.MexAA (Serie de Conferencias), 36, 113 Elitzur, M. 2002, 2007: Reviews at the Brazil and Australia Maser Symposia

  27. Some Prospects • Methods of Extraction of the principal pumping cycles • More work on “spooks” versus “things” dilemma • Probing turbulence in H2O fountains • More work on theory of polarization • Theory of cyclotron masers • Recombination lines on Sun

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