New Developments in Maser Theory
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New Developments in Maser Theory
Vladimir StrelnitskiMaria Mitchell
Observatory
“Radio Stars” Haystack Observatory
4 October, 2012
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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
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Uniqueness of Inversion
= )]-1
Tx = Tk - Thermalization
0 < Tx < Tk - Overcooling
Tk < Tx < ∞ - Overheating
Tx < 0 - Inversion
Tk
→
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β = 1 - Thermalization
β > 1 - Overcooling
0 < β < 1 - Overheating
β < 0 - Inversion
Tk
→
β = 1
hν/k << Tk ; |Tx|
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MASER
SOURCE
SOURCE
SINK
SINK
3
21
21
3
Pumping Cycles
General Recepe: Look for TWO temperatures!
Energy Reservoirs: • radiation (star; dust)• collisions (maxwellized gas; streams)• chemical processes (ionization; dissociation; dust coat
sublimation…)
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Deguchi (1977)
Sobolev & Strelnitski (1983)
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Sobolev & Deguchi (1994)
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Gray (2007)
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Energy Drain in CCr Pumping of H20
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𝛥 𝑁0(cm−3)≈Λ2 − Λ1
𝜞+𝑪
C >> A ; BJ
Two-level System:
Maser (unsaturated)
Tx Tk Tr when
𝑪𝟐𝟏1
2Λ1
Λ2
Γ2Γ1
1
2A BJ C
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)
𝑁2
𝑁1≈
𝑔2
𝑔1𝑒− h𝜈
𝑘𝑇𝑟
C << A; BJτmin <<
1
τmin ≳1(Avrett & Hummer 1965)
Thermalization
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Estimates of the Pump Power
RRv: Litvak (1969)
RCv:Goldreich & Kwan (1974)
CCr:Strelnitski (1982)
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𝜟𝑵 ≈𝜟𝑵𝟎
𝟏+𝑩𝟐𝟏 𝑱 𝟏𝟐
𝜞 +𝑪
≈𝜟𝑵 𝟎
𝟏+𝑱𝟏𝟐
𝑱 𝒔
𝑱𝒔≡ 𝜞+𝑪𝑩𝟐𝟏
𝜟𝑵𝟎≈Λ2 − Λ1
𝜞+𝑪R ≡ B21J21 << Γ +C → (Unsaturated
inversion)R ≳ Γ +C →
(Saturation)
Saturation results in:
Linear intensity growth
The rule of “1 maser photon per pumping cycle“
Saturation
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Observational Requirements for the Pump Power
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Hydrogen Masers and Lasers
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D. Menzel: The Man Who Could Make the Whole Story Happen Earlier
[of the light absorption in a line]
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All the transitions above n=5 are inverted!
Baker & Menzel (1937)
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v
Popu
lati
on
Den
sity
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MWC 349: The First Natural Hydrogen
Maser
Martín-Pintado et al. (1989)
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Strelnitski et al. (1996)[based on computations by Hummer & Story (1992)]
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C ~ Γ
gain = max
Inversion = max
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LASERSMA
SER
S
Messenger & Strelnitski (2011)
Lines of Constant Intensity
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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 - Landé g value for the upper state Ω = eB0/mc – girofrequencyΓ - population decay rate
R - stimulated emission rate
Polarization
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for sin2 θ ≥ 1/3 (θ ≥ 35°)
-1 for sin2 θ ≤ 1/3 (θ ≤ 35°)
GKK:
sin2θ = 2/3 → 0(θ = 54.7°, van Vleck
angle)
Watson & Wyld (2001)
55°35°
R << gΩ << Δω, R/Γ >>1
nonparamagnetic molecules
saturation
x, x’
y’
z
y
∢
B; z’
θ Q = Ix - Iy
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Circular Polarization of H2O Masers (Fiebig & Güsten, 1989)
V
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Non-magnetic Explanation of Linear PolarizationCompetition 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 B is “unusually” high, think of the above
possibilities!
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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
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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