1 Spatial variations of the Spatial variations of the electron-to-proton mass ratio: electron-to-proton mass ratio: bounds obtained from high- bounds obtained from high- resolution radio spectra of resolution radio spectra of molecular clouds in the Milky molecular clouds in the Milky Way Way S. A. Levshakov Dept. Theoretical Astrophyscis A.F. Ioffe Physical-Technical Institute St. Petersburg
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1 Spatial variations of the electron-to- proton mass ratio: bounds obtained from high-resolution radio spectra of molecular clouds in the Milky Way S.
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Spatial variations of the electron-Spatial variations of the electron-to-proton mass ratio: bounds to-proton mass ratio: bounds obtained from high-resolution obtained from high-resolution
radio spectra of molecular clouds radio spectra of molecular clouds in the Milky Wayin the Milky Way
S. A. Levshakov
Dept. Theoretical AstrophyscisA.F. Ioffe Physical-Technical Institute
St. Petersburg
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Contents
Short Introduction
Part I. What is known
Part II. What is new
Conclusions
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= me/mp = e2/(hc)
Atomic Molecular Discrete Spectra
allow to
probe variability of
through
relativistic corrections to
atomic energy, (Z)2R
corrections for the finite nuclear mass, R
and
important for molecules
less important for atoms
Z – atomic number
R – Rydberg constant
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fine-structure levels:
=
molecular rotational transitions:
2
=
atomic levels, in general:
’= + qx + …
=
2Q
x = (’)2 - 1
Q = q/ dimensionless sensitivity coefficient
q-factor [cm-1]individual for each atomic transition
1) updated sensitivity coefficients (Porsev et al.’07)
2) Accounting for correlations between different pairs {1608,X}
/ = -0.12 1.79 ppm
The most stringent limit: |/| < 2 ppm
Calibration uncertainty of 50 m/s translates into the error in / of 2 ppm
cf. pixel size 2-3 km/s
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Conclusions (Part I)
No cosmological temporal variations of at the level of 2 ppm have been found
(same for )
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Part II. Spatial Variations (search for scalar fields)
dependence of masses and coupling constants on environmental matter density
Chameleon-like scalar field models:
= ()
= ()
- ambient matter density
Khoury Weltman’04
Bax et al.’04
Feldman et al.’06
Olive Pospelov’08
lab / ISM 1014 - 1016
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Ammonia Method to probe me/mp
vibrational, and rotational intervals in molecular spectra
Evib : Erot 1/2 :
vib /vib = 0.5 /
rot /rot = 1.0 /
the inversion vibrational transition in ammonia, NH3, inv = 23.7 GHz
inv /inv = 4.5 /
Flambaum Kozlov’07
Qinv / Qvib = 9
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N
N
H
H
H
H
H
H
HHH
HHH
N N
10-4 eV
1.3 cm
U(x)
x
inv exp(-S)
the action S -1/2
Quantum mechanical tunnelingdouble-well potential of the inversion vibrational mode of NH3
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By comparing the observed inversion frequency of NH3 with a rotational frequency of another molecule arising co-spatially with ammonia, a limit on the spatial variation of / can be obtained :
/ = 0.3(Vrot – Vinv)/c 0.3 V /c
V = Vnoise V
Var(V) = Var(Vnoise) Var(V )
Vnoise = 0
V = V
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23 GHz
18 GHz
93 GHz
Hyper-fine splittings in NH3 , HC3N N2H+
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Dense molecular clouds, nH 104 cm-3, Tkin 10K
High-mass clumps, M 100Msolar, Infrared Dark Clouds (IRDCs)