Observational Determinations of the Proton to Electron Mass Ratio ( m ) in the Early Universe

1. Observational Determinations of the Proton to Electron Mass Ratio (m) in the Early Universe Rodger Thompson- Steward Observatory, University of Arizona

2. Collaborators • Jill Bechtold • John Black • Daniel Eisenstein • Xiaohui Fan • Robert Kennicutt • Carlos Martins • Xavier Prochaska • Yancey Shirley • Wim Ubachs

3. Fundamental Constants • Fundamental Constants are pure numbers whose value determines the nature of our physical universe. • Any civilization that can count will come up with the same values for the fundamental constants.

4. Motivation • Pure intellectual interest in establishing the value of a fundamental “constant” in the early universe • Input and information to guide our way through the vast landscape (10500?) of elementary particle and dark energy theories

5. This Talk • A bit of history • Concept for measuring m • A sense of the advantages and problems of the concept • A sense of the accuracy of the measurement • What can we do in the future and is it relevant?

6. History of Rolling Constants Dirac in 1937 appears to be the first to discuss the possible time variation of fundamental constants although m was not one of them since its value is not near unity. Dirac was followed by Teller (1948) and Gamow (1967) who both speculated that the ratio of the fine structure constant to the dimensionless gravitational constant would vary.

7. Possibility of measuring m in the early universe In 1975 Thompson proposed a method for measuring the fundamental constant m = mp/me in the early universe using molecular spectra. In particular the redshifted absorption lines of the Lyman and Werner bands of H2 in Damped Lyman Alpha Absorber (DLA) clouds. (Note: No picture of Thompson was found in the archives of famous physicists!)

8. Molecular Spectra and m Following a treatment in Shu (1991) we can write the binding energy of a molecule as where we used and a0 is the Bohr radius. If we displace the nuclei by a0 then they will vibrate in the potential well with an energy The frequency is then but For rotation the moment of inertia is The angular momentum is so Then

9. DLA Concept Quasar DLA containing cold H2 Observer The light is absorbed from the first few rotational levels of the electronic and vibrational ground state to vibrational and rotational levels of the first (Lyman) and second (Werner) excited electronic state.

10. H2 Energy Levels Overlap areas are very important. DJ=0,+/-1 Dn= any integer

11. Sensitivity Constants • Although implicit in previous work, Varshalovich and Levshakov (1993) explicitly developed the sensitivity constant which for a line i is defined as • The rest frame wavelengths are related to the observed wavelengths by • Each line has a unique sensitivity constant Ki which can be slightly negative, zero or positive. • The higher the vibrational quantum number the larger the sensitivity constant. • The overlap of the Lyman and Werner bands places lines with very different sensitivity constants in close proximity to each other.

12. Sensitivity Constants cont. • In principle one can match the wavelengths of the H2 absorption lines against the pattern of shifts predicted by the sensitivity constants. • In practice the available signal to noise and resolution allows only a fit to the trend of the predicted shifts.

13. Redshift vs. Sensitivity Coefficients From Reinhold et al. 2006

14. Observational History • Historically there have been 3 types of observations • Optical observations of redshifted absorption lines of the electronic transitions of H2 in DLAs. • Radio observations of rotational and inversion transitions of molecules in molecular clouds. • Laboratory measurement of the current rate of change of m.

15. H2 Observations • When first proposed in 1975 the method required 3 advances to be practical • Larger telescopes • More sensitive and higher resolution astronomical spectrometers • More accurate measurements of the rest wavelengths of the transitions • All of these have now occurred

16. H2 Difficulties • Very few DLAs contain measurable amounts of H2. • Only about a dozen known • The Lyman and Werner lines lie in the Ly alpha Forest of atomic absorption lines • The primary shift is in the vibrational and rotational levels. These shifts are diluted by the electronic energy. • Typical Ki are about 10-2.

17. Sample Spectrum and Difficulties Q0347-383 Wavelength in Å

18. H2 Advantages • Potential for many lines from the same ground state • Well measured rest wavelengths • (Ubachs et al. 2007) • Lines with significantly different sensitivity factors in close spectral proximity • Mix of Lyman and Werner lines

19. The Common Gas Problem • Kinetic motions can mimic wavelength shifts due to fundamental constant variations. • Spatial variations in excitation temperature can also mimic shifts. • The solution is to only compare transitions of the same species in the same lower level.

20. Some Opportunities Low Shift Lines High Shift Lines All 4 lines have the same ground state.

21. Very Few Systems Actually Studied • PKS 0528-250= Q0528-250 (z = 2.811) • Foltz et al. (1988), Cowie & Songaila(1995), Potekhin et al. (1998), King et al. (2008) • Q1232+082 (z=2.338) • Ivanchik et al. (2002) • Q0347-383 (z=3.025) and Q0405-443 (z=2.595) • D’Odorico(2001), Ivanchik et al.(2002,2003,2005), Levshakov et al.(2002), Ubachs & Reinhold(2004), Reinhold et al.(2006), Ubachs et al.(2007), King et al. (2008), Wendt & Reimers(2008),Thompson et al.(2009) • Q1331+170 (z=1.776) • Cui et al. (2006) • J2123-0050 (z=2.059) • Malec et al. 2010 • A total of 6 systems in all

22. Sources of Systematic Errors • Systematic errors in the wavelength calibration • The sensitivity factors Ki are roughly proportional to the vibrational quantum number of the upper state (ground state is always v = 0) • The higher the upper vibrational quantum number the shorter the wavelength • Systematic wavelength errors therefore translate into positive or negative changes in m • Partially mitigated by the mixture of Lyman and Werner bands.

24. Application to the Positive Detection • Systematic wavelength errors in the old UVES reduction pipeline may be the source of the previous positive result for a change in m. • New results from the same data (Thompson et al. 2009) • See also King et al. (2008) Dm/m = (-7 +\- 8) x 10-6

25. Bootstrap Statistics 10,000 bootstrap realizations have a Gaussian Distribution

26. Lyman Werner Pairs • The superposition of Lyman and Werner lines produces closely spaced pairs with very different sensitivity factors. • We looked at the Dm/m values for these pairs in Q0347-383 and Q0405-443. • The negative Dm/m for Q0347-383 is marginally significant.

27. Dz values for Lyman-Werner Pairs

28. Instrument Systematics • In most spectrometers the light path of the calibration lamp is not the same as the object light path • Different angles between the object and calibration lamp principal rays can introduce systematic wavelength differences.

29. Other systematics • Errors in rest wavelength • Errors in rest wavelength Dl produce errors in Dm/m of (1/Ki)Dl/l. • Typical Ki are 0.02, typical Dl/l are 10-8. • Errors are then ~5x10-7 which may limit future high resolution observations • Errors in the sensitivity constants. • Errors in the sensitivity factor Ki result in errors in Dm/m proportional to DKi/Ki.

30. Systematics Continued • Mixing of different rotational quantum number lower states • Cold and hot gas can have different kinematics. • The effect would be slight since the lower rotational J levels do not have a large influence on the sensitivity factors.

31. Summary of the State of H2 Studies • Except for Q0347-383 and Q0405-443 there have been no claims of a detected shift in m. • Reanalysis of the Q0347-383 and Q0405-443 data by two groups find no shift. • From H2 data Dm/m < 10-5 for a lookback time of 10.5 gigayears (z~3.1).

32. Implications of the Current State of Dm/m Observations • Most Super Symmetry (SUSY) models predict a rolling of the fundamental constants • Rolling is a change with time as opposed to running which is a change with energy • Theories of dark energy that evoke a rolling scalar potential also predict rolling fundamental constants

33. Implications of the Current State of Dm/m Observations • Quantitative predictions from either SUSY or dark energy are hard to achieve. • Inversely, accurate determination of the values of the fundamental constants in the early universe determines the proper parameter space for these theories

34. m in Particle Physics • In GUT theories rolling m is usually given by • Where LQCD is the QCD scale, n is Higgs Vacuum Expectation Value (VEV), R is a model dependent factor and a is the fine structure constant • In many GUT models R is large and negative, R~-50 eg. (Avelino, Nunes and Olive (2006))

35. m in Dark Energy • Quintessence is usually expressed in terms of a potential V(f) that is a function of the rolling scalar f then • Where k is , mPl is the Planck mass and zm is a model dependent parameter • A non-rolling or rolling m is therefore a discriminator between a cosmological constant and quintessence Nunes & Lidsey (2004)

36. Rolling m Landscape Data from King+, Reinhold+, Malec+, Murphy+ and Thompson+

37. Current Constraints at 11 Gyr • Particle Physics • Dark Energy

38. H2 Optical Observation Status • m is constant at the Dm/m < 10-5 level for look back times up to 11 gigayears. • This limit is a legitimate constraint on high energy and cosmological physics. • The measurement can be improved by a factor ~10 with existing or nearly complete instrumentation. • Further improvement relies on • Larger, 30m class telescopes • Higher throughput, higher resolution spectrometers. • More precise molecular wavelength measurements • Precision laser frequency combs • Measurement of fundamental constants in the early universe is a low cost and powerful tool for the study of cosmology and high energy physics.

39. History of Radio Molecular Studies • Radio studies of m are much more recent than the first optical studies of H2 • Studies have concentrated on the inversion transition of ammonia (ignore colors)

40. Radio Concept Direct Emission Lines As Well As Absorption NH3, CO, CCS, HCN, HCO+

41. Advantages of Radio Measurements • Radio telescopes are capable of high frequency resolution • Dn/n < 10-7 • Radio molecular transitions have high sensitivity factors • KNH3 = 4.46 for inversion transitions • Ki ~ 1. for rotational transitions

42. Disadvantages of Radio Observations • In general there are not multiple lines from the same ground state • Often a different molecule is used as the reference • This is a particular problem in systems that have multiple close spaced velocity components. If the abundance ratios between the two components is different between the two molecules, errors occur. • To date observations have been limited to redshifts less than 1

43. Observations of NH3 to Determine Dm/m • Absorption system in the spectrum of B0218+357 at z = 0.68466 • Flambaum and Kozlov (2007), Murphy et al. (2008) • Find |Dm/m| < 1.8 x 10-6 at z=0.68466 • From Murphy et al. 2008 who used HCN and HCO+ as the wavelength standard • The universe is ~1/2 its present age at this point and in the transition between matter dominated and dark energy dominated epochs.

44. Spatial variations of m within the Milky Way • Levshakov, Molaro and Kozlov (2008) find Dm/m values of (4-14)x10-8 for various locations in the Milky Way • They compare NH3 emission lines with those of HC3N and N2H+

45. OH Observations • Four observed transitions that have different dependencies on m, a and gp (the proton g factor).

46. State of Radio Observations • Most accurate limits on Dm/m but at redshifts below 1 • H2 not available at radio wavelengths • The lower abundance of other molecules is a limiting factor • Hard to find transitions from a common ground state to eliminate kinematic effects

47. CMB constraints on me and a • Changes in me and a produce changes in amplitude and position of the CMB acoustic peaks through changes in the Thomson cross section and other parameters. • Statistical modeling of the changes, eg. Landau & Scoccola (2010) give a/a0=0.986+/0.009 and me/me0=0.999+/-0.035 at a redshift of ~1000

48. Combination of Atomic and Molecular Measures • The combination of HI 21 cm absorption and Atomic resonance dipole absorptions puts constraints on X=gpa2/m • New work by Kanekar et al. (arXiv:1003.0444v1) using UV CI line give DX/X =(6.8+/-7)x10-6 where systematics dominate the error.

49. Implications • Current Da/a =(-5.7 +/- 1.1)x10-6 • Murphy et al. (2004) • Current Dm/m = (-7 +/- 8)x10-6 • Several • DX/X=2(Da/a) + Dgp/gp – Dm/m <7x10-6 • Slightly out of the Da/a box, consistent with no change in m and implies no change in gp at the ~10-5 level.

50. Options for the future • Very high resolution spectrometers on large telescopes. • PEPSI on the LBT at R=300,000 • Next generation of telescopes • GMT, TMT, ELT • Dedicated facilities to increase the available observing time. • These options are cost effective compared with space borne facilities. • Herschel?