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

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

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.

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 ( ?) of elementary particle and dark energy theories

This Talk A bit of history Concept for measuring  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?

History of Rolling Constants Dirac in 1937 appears to be the first to discuss the possible time variation of fundamental constants although  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.

Possibility of measuring  in the early universe In 1975 Thompson proposed a method for measuring the fundamental constant  = m p /m e in the early universe using molecular spectra. In particular the redshifted absorption lines of the Lyman and Werner bands of H 2 in Damped Lyman Alpha Absorber (DLA) clouds. (Note: No picture of Thompson was found in the archives of famous physicists!)

Molecular Spectra and  Following a treatment in Shu (1991) we can write the binding energy of a molecule as where we used and a 0 is the Bohr radius. If we displace the nuclei by a 0 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 isso Then

DLA Concept Quasar DLA containing cold H 2 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.

H 2 Energy Levels Overlap areas are very important.  J=0,+/-1  = any integer

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 K i 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.

Sensitivity Constants cont. In principle one can match the wavelengths of the H 2 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.

Redshift vs. Sensitivity Coefficients From Reinhold et al. 2006

Observational History Historically there have been 3 types of observations Optical observations of redshifted absorption lines of the electronic transitions of H 2 in DLAs. Radio observations of rotational and inversion transitions of molecules in molecular clouds. Laboratory measurement of the current rate of change of .

H 2 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

H 2 Difficulties Very few DLAs contain measurable amounts of H 2. 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 K i are about

Sample Spectrum and Difficulties Wavelength in Å Q

H 2 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

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.

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

Very Few Systems Actually Studied PKS = Q (z = 2.811) Foltz et al. (1988), Cowie & Songaila(1995), Potekhin et al. (1998), King et al. (2008) Q (z=2.338) Ivanchik et al. (2002) Q (z=3.025) and Q (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) Q (z=1.776) Cui et al. (2006) J (z=2.059) Malec et al A total of 6 systems in all

Sources of Systematic Errors Systematic errors in the wavelength calibration The sensitivity factors K i 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  Partially mitigated by the mixture of Lyman and Werner bands.

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 . New results from the same data (Thompson et al. 2009) See also King et al. (2008)  /  = (-7 +\- 8) x 10 -6

Bootstrap Statistics 10,000 bootstrap realizations have a Gaussian Distribution

Lyman Werner Pairs The superposition of Lyman and Werner lines produces closely spaced pairs with very different sensitivity factors. We looked at the  /  values for these pairs in Q and Q The negative  /  for Q is marginally significant.

 z values for Lyman-Werner Pairs

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.

Other systematics Errors in rest wavelength Errors in rest wavelength  produce errors in  of (1/K i ) . Typical K i are 0.02, typical  are Errors are then ~5x10 -7 which may limit future high resolution observations Errors in the sensitivity constants. Errors in the sensitivity factor K i result in errors in  proportional to  K i /K i.

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.

Summary of the State of H 2 Studies Except for Q and Q there have been no claims of a detected shift in . Reanalysis of the Q and Q data by two groups find no shift. From H 2 data  < for a lookback time of 10.5 gigayears (z~3.1).

Implications of the Current State of  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

Implications of the Current State of  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

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

 in Dark Energy Quintessence is usually expressed in terms of a potential V(  ) that is a function of the rolling scalar  then Where  is, m Pl is the Planck mass and   is a model dependent parameter A non-rolling or rolling  is therefore a discriminator between a cosmological constant and quintessence Nunes & Lidsey (2004)

Rolling  Landscape Data from King+, Reinhold+, Malec+, Murphy+ and Thompson+

Current Constraints at 11 Gyr Particle Physics Dark Energy

H 2 Optical Observation Status  is constant at the  < 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.

History of Radio Molecular Studies Radio studies of  are much more recent than the first optical studies of H 2 Studies have concentrated on the inversion transition of ammonia (ignore colors)

Radio Concept NH 3, CO, CCS, HCN, HCO + Direct Emission Lines As Well As Absorption

Advantages of Radio Measurements Radio telescopes are capable of high frequency resolution  < Radio molecular transitions have high sensitivity factors K NH 3 = 4.46 for inversion transitions K i ~ 1. for rotational transitions

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

Observations of NH 3 to Determine  Absorption system in the spectrum of B at z = Flambaum and Kozlov (2007), Murphy et al. (2008) Find |  | < 1.8 x at z= From Murphy et al 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.

Spatial variations of  within the Milky Way Levshakov, Molaro and Kozlov (2008) find  values of (4-14)x10 -8 for various locations in the Milky Way They compare NH 3 emission lines with those of HC 3 N and N 2 H +

OH Observations Four observed transitions that have different dependencies on  and g p (the proton g factor).

State of Radio Observations Most accurate limits on  but at redshifts below 1 H 2 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

CMB constraints on m e and  Changes in m e and  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  0 =0.986+/0.009 and m e /m e0 =0.999+/ at a redshift of ~1000

Combination of Atomic and Molecular Measures The combination of HI 21 cm absorption and Atomic resonance dipole absorptions puts constraints on X=g p  2 /  New work by Kanekar et al. (arXiv: v1) using UV CI line give  X/X =(6.8+/-7)x10 -6 where systematics dominate the error.

Implications Current  =(-5.7 +/- 1.1)x10 -6 Murphy et al. (2004) Current  = (-7 +/- 8)x10 -6 Several  X/X=2(  ) +  g p /g p –  <7x10 -6 Slightly out of the  box, consistent with no change in  and implies no change in g p at the ~10 -5 level.

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?

PEPSI on the LBT PEPSI is the Postdam Echelle Polarimetric and Spectroscopic Instrument. Will be installed on the Large Binocular Telescope and is fiber fed from both primary mirrors. Can achieve resolutions of 300, times the resolution of UVES on VLT.

PEPSI Layout

Observing PSS J with PEPSI on the LBT H 2 absorption system at z=4.224 V mag = 19.3 H 2 lines redshifted to ~5000 Å Resolution of 300,000 S/N=50 per resolution element after 30 hrs of observing (5-6 nights).

GMT Example

Relevant Instruments Qspec R= 20,000 – 200,000 = 3000 – 10,000 Angstroms GMT CfA Large Earth Finder (GCLEF) “Precision” = 10 cm/sec, R? Temperature controlled vacuum enclosure Laser comb wavelength reference