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S. A. Levshakov Dept. Theoretical Astrophyscis A.F. Ioffe Physical-Technical Institute

Spatial variations of the electron-to-proton mass ratio: bounds obtained from high-resolution radio spectra of molecular clouds in the Milky Way. S. A. Levshakov Dept. Theoretical Astrophyscis A.F. Ioffe Physical-Technical Institute St. Petersburg. Contents. Short Introduction

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S. A. Levshakov Dept. Theoretical Astrophyscis A.F. Ioffe Physical-Technical Institute

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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. A. Levshakov Dept. Theoretical Astrophyscis A.F. Ioffe Physical-Technical Institute St. Petersburg

  2. Contents • Short Introduction • Part I. What is known • Part II. What is new • Conclusions

  3. Atomic  Molecular Discrete Spectra allow to probe variability of  = e2/(hc)  =me/mp through relativistic corrections to atomic energy,   (Z)2R Z – atomic number R – Rydberg constant and corrections for the finite nuclear mass,  R less important for atoms important for molecules

  4. fine-structure levels:  = ’-  either spatial or temporal differences     = ’-  = 2   molecular rotational transitions: x = (’)2 - 1    =   dimensionless sensitivity coefficient Q = q/ atomic levels, in general: individual for each atomic transition q-factor [cm-1] ’=  + qx+ …   = 2Q  

  5. Part I. Cosmological Temporal Variations Quasar spectra VLT/UVES Redshift: z = ( - 0)/0 z  2 t 1010 yr

  6. Single ion/ measurements z1 – z2 v FeII 2600 2586 2382 2374 2344 1608  1 = =  2 (Q2 – Q1)(1+z) 2cQ Q  0.04 FeI2967 3021 2484 3441 3720 3861 Q  0.08 Q  0.05 Q  -0.02 Q  0.03 Q  0.06

  7. QSO HE 0001-2340 neutral iron FeI resonance transitions at z=0.45 Doppler width  1 km/s (!) Simple one-component profiles v = -200  200 m/s / = 7  7 ppm Q  0.08 Q  0.03

  8. Q 1101-264 the highest resolution spectrum, FWHM = 3.8 km/s FeII resonance transitions at z=1.84 Current estimate: v = -130  90 m/s / = 4.0  2.8 ppm

  9. brightest QSO HE 0515-4414 FeII resonance transitions at z=1.15 34 FeII pairs {1608,X} X = 2344 2374 2586 Current estimate: 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

  10. Conclusions (Part I) No cosmological temporal variations of  at the level of 2 ppm have been found (same for )

  11. Part II. Spatial Variations (search for scalar fields) Chameleon-like scalar field models: dependence of masses and coupling constants on environmental matter density Khoury  Weltman’04 Bax et al.’04 Feldman et al.’06  = () Olive  Pospelov’08  = ()  - ambient matter density lab / ISM  1014 - 1016

  12. 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

  13. N U(x) H H H H N H N H H H H H 10-4 eV H  1.3 cm H x N double-well potential of the inversion vibrational mode of NH3 Quantum mechanical tunneling inv  exp(-S) the action S  -1/2

  14. 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 Vnoise = 0 V = V Var(V) = Var(Vnoise)  Var(V )

  15. Hyper-fine splittings in NH3, HC3N  N2H+ 23 GHz 18 GHz 93 GHz

  16. Dense molecular clouds, nH  104 cm-3, Tkin  10K High-mass clumps, M  100Msolar, Infrared Dark Clouds (IRDCs) Low-mass cores, M  10Msolar Protostellar cores containing IR sources Starless cores (prestellar cores) Dynamically stable against grav contraction Unstable nH 105 cm-3 nH 105 cm-3

  17. Molecular differentiation within a low-mass core HCO+ CO CCS CS NH3 N2H+ N2D+ H2D+ H3+ NH3 D3+ D2H+ 105 cm-3 H2 H+ e- 2,000 AU 104 cm-3 5,000 AU 7,000 AU 15,000 AU

  18. Preliminary obtained results (Levshakov, Molaro, Kozlov 2008, astro-ph/0808.0583) Perseus molecular cloud D 260 pc 62 o or 279 pc M  104 Msolar nH  100cm -3

  19. Perseus molecular cores ammonia spectral atlas of 193 molecular cores in the Perseus cloud Rosolowsky et al. 2008 Observations:100-m Green Bank Telescope (GBT) GBT beam size at 23 GHz is FWHM = 31arcsec (0.04 pc) Spectral resolution = 24 m/s (!) Single-pointing, simultaneous observations of NH3 and CCS lines

  20. pure turbulent broadening, (CCS) = (NH3) pure thermal, (CCS) = 0.55(NH3) symmetric profiles CCS vs NH3 Vn=98= 44  13 m/s Vn=34= 39  10 m/s Vn=21= 52  7 m/s / = (5.2  0.7)10-8

  21. Pipe Nebula Rathborne et al. 2008 46 molecular cores in Pipe Nebula Observations:100-m Green Bank Telescope (GBT) GBT beam size at 23 GHz is FWHM = 30arcsec (0.02 pc) Spectral resolution = 23 m/s (!) Single-pointing, simultaneous observations of NH3 and CCS lines

  22. CCS vs NH3 Vn=8 = 69  11 m/s

  23. New results (Astron.Astrophys., astro-ph/0911.3732) Nov 24-28, 2008 Collaboration with NH3 HC3N 32m MEDICINA (Bologna) Italy Alexander Lapinov Christian Henkel Takeshi Sakai Feb 20-22, 2009 Paolo Molaro NH3 HC3N Dieter Reimers 100m EFFELSBERG (Bonn) Germany 41 cold and compact molecular cores in the Taurus giant molecular complex Apr 8-10, 2009 NH3 N2H+ 45m NOBEYAMA (NRAO) Japan 55 molecular pairs in total

  24. Observations: 32-m Medicina Telescope: two digital spectrometersARCOS (ARcetri COrrelation Spectrometer) and MSpec0(high resolution digital spectrometer) Spectral res. = 62 m/s (NH3), 80 m/s (HC3N)ARCOS Spectral res. = 25 m/s (NH3), 32 m/s (HC3N)MSpec0 beam size at 23 GHz, FWHM = 1.6 arcmin position switching mode 100-m Effelsberg Telescope: K-band HEMT (High Electron Mobility Transistor) receiver, backend FFTS (Fast Fourier Transform Spectrometer) Spectral res. = 30 m/s (NH3), 40 m/s (HC3N) beam size at 23 GHz, FWHM = 40 arcsec frequency switching mode 45-m Nobeyama Telescope: HEMT receiver (NH3), and SIS (Superconductor-Insulator- Superconductor) receiver (N2H+) Spectral res. = 49 m/s (NH3), 25 m/s (N2H+) beam size at 23 GHz, FWHM = 73 arcsec position switching mode Independent Doppler tracking of the observed molecular lines

  25. Effelsberg 100-m

  26. Nobeyama 45-m

  27. co-spatially distributed total n=55 Black: 1<1.2 Red: 1.2<1.7 b(NH3)  = b(HC3N)  = 1.7 for pure thermal broadening

  28. Results total sample, n=55 mean V = 14.1  4.0 m/s scale = 29.6 m/s (standard deviation) median V = 17 m/s mean V = 21.5  2.8 m/s co-spatially distributed, n=23 (red  black points) scale = 13.4 m/s median V = 22 m/s mean V = 21.2  1.8 m/s thermally dominated, n=7 (red points) scale = 3.4 m/s median V = 22 m/s effelsberg, n=12 mean V = 23.2  3.8 m/s scale = 13.3 m/s NH3 HC3N median V = 22 m/s nobeyama, n=9 mean V = 22.9  4.2 m/s scale = 12.7 m/s NH3 N2H+ median V = 22 m/s

  29. Poor accuracy in lab frequencies -main source of uncertainties sys = 0.6 m/s NH3 sys = 2.8 m/s HC3N N2H+ sys = 14 m/s V = 23.2  3.8stat  2.8sys m/s Effelsberg: / = (2.2  0.4stat  0.3sys)10-8

  30. GBT vs Effelsberg CCS  NH3 HC3N NH3 V  52  7m/s V  23.2  3.8 m/s 22344.033(1) MHzYamamoto et al.’90 – radioastronomical estimate 22344.029(4) MHz Lovas et al.’92 - laboratory 22344.0308(10) MHzCDMS’05 - catalogue V  22  7m/s v  13.4 m/s 1 kHz at 22.3 GHz V  6  7m/s

  31. new precise lab freqencies badly needed ! lab  1 m/s

  32. Constraint on -variation fine-structure transition of carbon [CI] 609 m low-lying rotational lines of 13CO J=1-0 (2.7 mm), J=2-1 (1.4 mm) F = 2/ F/F = 2/ - / = v/c v = vrot - vfs TMC-1 Schilke et al.’95 observations of cold molecular clouds FWHM = 200-400 m/s L 183 Stark et al.’96 Ori A,B Ikeda et al.’02 FWHM = 100 m/s mean V = 0  60 m/s sample size n=13 scale = 215 m/s (standard deviation) median V = 0 m/s |/| < 0.15 ppm |F/F| < 0.3 ppm

  33. Conclusions (Part II) reproduced at different facilities • velocity offset V = 23  4stat  3sys m/s • no known systematic at the level of 20 m/s verification – other molecules new targets / = (2.2  0.4stat  0.3sys)10-8 • conservative upper limits at z=0 : |/|  310-8 |/| < 1.510-7  expected /  10-8 • at high-z, ISM(z=0)  ISM (z>0) if no temporal dependence of (t) is present

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