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

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

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

6 Single ion  /  measurements FeII Q  0.04 Q   Q  0.06   = 1 2 z 1 – z 2 (Q 2 – Q 1 )(1+z) = vv 2c  Q FeI Q  0.08 Q  0.03  Q  0.05

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

8 Q 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 FeII resonance transitions at z= FeII pairs {1608,X} X = Current estimate: 1) updated sensitivity coefficients (Porsev et al.’07) 2) Accounting for correlations between different pairs {1608,X}  /  =  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) 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 

12 Ammonia Method to probe m e /m p vibrational, and rotational intervals in molecular spectra E vib : E rot   1/2 :   vib /  vib = 0.5  /   rot /  rot = 1.0  /  the inversion vibrational transition in ammonia, NH 3,  inv = 23.7 GHz  inv /  inv = 4.5  /  Flambaum  Kozlov’07 Q inv / Q vib = 9

13 N N H H H H H H H H H H H H N N eV  1.3 cm U(x) x  inv  exp(-S) the action S   -1/2 Quantum mechanical tunneling double-well potential of the inversion vibrational mode of NH 3

14 By comparing the observed inversion frequency of NH 3 with a rotational frequency of another molecule arising co-spatially with ammonia, a limit on the spatial variation of  /  can be obtained :  /  = 0.3(V rot – V inv )/c  0.3  V /c  V =  V noise   V  Var(  V) = Var(  V noise )  Var(  V  )  V noise = 0  V =  V 

15 23 GHz 18 GHz 93 GHz Hyper-fine splittings in NH 3, HC 3 N  N 2 H +

16 Dense molecular clouds, n H  10 4 cm -3, T kin  10K High-mass clumps, M  100M solar, Infrared Dark Clouds (IRDCs) Low-mass cores, M  10M solar Protostellar cores containing IR sources Starless cores (prestellar cores) Dynamically stable against grav contraction Unstable n H  10 5 cm -3 n H  10 5 cm -3

17 CS CO HCO + CCS NH 3 N2H+N2H+ N2D+N2D+ H3+H3+ H2D+H2D+ D2H+D2H+ D3+D3+ H2H2 H+H+ e-e- 15,000 AU 7,000 AU 5,000 AU 2,000 AU 10 4 cm cm -3 Molecular differentiation within a low-mass core

18 Perseus molecular cloud D  260 pc 6  2 o or 27  9 pc M  10 4 M solar n H  100 cm -3 Preliminary obtained results (Levshakov, Molaro, Kozlov 2008, astro-ph/ )

19 Perseus molecular cores Rosolowsky et al ammonia spectral atlas of 193 molecular cores in the Perseus cloud 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 NH 3 and CCS lines

20 pure turbulent broadening,  (CCS) =  (NH 3 ) pure thermal,  (CCS) = 0.55  (NH 3 )  V n=98 = 44  13 m/s  V n=34 = 39  10 m/s  V n=21 = 52  7 m/s CCS vs NH 3 symmetric profiles  /  = (5.2  0.7)  10 -8

21 Pipe Nebula Rathborne et al molecular cores in Pipe Nebula Observations: 100-m Green Bank Telescope (GBT) Spectral resolution = 23 m/s (!) Single-pointing, simultaneous observations of NH 3 and CCS lines GBT beam size at 23 GHz is FWHM = 30arcsec (0.02 pc)

22  V n=8 = 69  11 m/s CCS vs NH 3

23 New results (Astron.Astrophys., astro-ph/ ) 32m MEDICINA (Bologna) Italy 100m EFFELSBERG (Bonn) Germany 45m NOBEYAMA (NRAO) Japan Nov 24-28, 2008 Feb 20-22, 2009 Apr 8-10, 2009 Collaboration with Alexander Lapinov Christian Henkel Takeshi Sakai NH 3  HC 3 N NH 3  N 2 H + 41 cold and compact molecular cores in the Taurus giant molecular complex 55 molecular pairs in total Paolo Molaro Dieter Reimers

24 Observations: 32-m Medicina Telescope: beam size at 23 GHz, FWHM = 1.6 arcmin position switching mode two digital spectrometers ARCOS (ARcetri COrrelation Spectrometer) and MSpec0 (high resolution digital spectrometer) Spectral res. = 62 m/s (NH 3 ), 80 m/s (HC 3 N) ARCOS Spectral res. = 25 m/s (NH 3 ), 32 m/s (HC 3 N) MSpec0 100-m Effelsberg Telescope: beam size at 23 GHz, FWHM = 40 arcsec frequency switching mode K-band HEMT (High Electron Mobility Transistor) receiver, backend FFTS (Fast Fourier Transform Spectrometer) Spectral res. = 30 m/s (NH 3 ), 40 m/s (HC 3 N) 45-m Nobeyama Telescope: beam size at 23 GHz, FWHM = 73 arcsec HEMT receiver (NH 3 ), and SIS (Superconductor-Insulator- Superconductor) receiver (N 2 H + ) Spectral res. = 49 m/s (NH 3 ), 25 m/s (N 2 H + ) position switching mode Independent Doppler tracking of the observed molecular lines

25 Effelsberg 100-m

26 Nobeyama 45-m

27 total n=55 co-spatially distributed Black: 1  <1.2 Red: 1.2  <1.7  = b(NH 3 ) b(HC 3 N)  = 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 thermally dominated, n=7 (red points) mean  V = 21.5  2.8 m/s scale = 13.4 m/s median  V = 22 m/s co-spatially distributed, n=23 (red  black points) mean  V = 21.2  1.8 m/s 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 median  V = 22 m/s nobeyama, n=9 mean  V = 22.9  4.2 m/s scale = 12.7 m/s median  V = 22 m/s NH 3  HC 3 N NH 3  N 2 H +

29 Poor accuracy in lab frequencies - main source of uncertainties NH 3  sys = 0.6 m/s HC 3 N  sys = 2.8 m/s N2H+N2H+  sys = 14 m/s  V = 23.2  3.8 stat  2.8 sys m/s Effelsberg:  /  = (2.2  0.4 stat  0.3 sys )  10 -8

30 GBT vs Effelsberg  V  52  7 m/s  V  23.2  3.8 m/s CCS  NH 3 HC 3 N  NH (1) MHz Yamamoto et al.’90 – radioastronomical estimate (10) MHz CDMS’05 - catalogue (4) MHz Lovas et al.’92 - laboratory 1 kHz at 22.3 GHz  v  13.4 m/s  V  22  7 m/s  V  6  7 m/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 13 CO J=1-0 (2.7 mm), J=2-1 (1.4 mm) observations of cold molecular clouds F =  2 /   F/F = 2   /  -   /  =  v/c TMC-1 Schilke et al.’95 L 183 Stark et al.’96 Ori A,B Ikeda et al.’02  v = v rot - v fs mean  V = 0  60 m/s scale = 215 m/s (standard deviation) median  V = 0 m/s sample size n=13 FWHM = m/s FWHM = 100 m/s |  F/F| < 0.3 ppm |  /  | < 0.15 ppm

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