Limits on the Space-time Variations of Fundamental Constants 1307.8266

7/27/2019 Limits on the Space-time Variations of Fundamental Constants 1307.8266

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Limits on the space-time variations offundamental constants

S. A. Levshakov1,2, C. Henkel3,4, D. Reimers5, and P. Molaro6,7

1 Ioffe Physical-Technical Institute, Russian Academy of Sciences, Polytekhnicheskaya Str.26, 194021 St. Petersburg, Russia

2 St. Petersburg Electrotechnical University LETI, Prof. Popov Str. 5, 197376

St. Petersburg, Russia

3 Max-Planck-Institut fur Radioastronomie, Auf dem Hugel 69, D-53121 Bonn, Germany4 Astronomy Department, King Abdulaziz University, P.O. Box 80203, Jeddah 21589,

Saudi Arabia5 Hamburger Sternwarte, Universitat Hamburg, Gojenbergsweg 112, D-21029 Hamburg,

Germany6 INAF Osservatorio Astronomico di Trieste, Via Tiepolo 11, I-34131 Trieste, Italy7 Centro de Astrofsica, Universidade do Porto, Rua das Estrelas, 4150-762, Porto, Portugal

e-mail: [email protected]

Abstract. We report on new tests that improve our previous (2009-2010) estimates ofthe electron-to-proton mass ratio variation, = me/mp. Subsequent observations (2011-2013) at the Effelsberg 100-m telescope of a sample of eight molecular cores from the

Milky Way disk reveal systematic errors in the measured radial velocities varying with an

amplitude 0.01 km s1

during the exposure time. The averaged offset between the radialvelocities of the rotational transitions of HC3N(2-1), HC5N(9-8), HC7N(16-15), HC7N(21-20), and HC7N(23-22), and the inversion transition of NH3(1,1) gives V = 0.002 0.015

km s1 [3 confidence level (C.L.)]. This value, when interpreted in terms of/ = (obs lab)/lab, constraints the -variation at the level of/ < 2 10

8 (3 C.L.), which is themost stringent limit on the fractional changes in based on radio astronomical observations.

Key words. Line: profiles ISM: molecules Radio lines: ISM Techniques: radial ve-locities elementary particles

1. Introduction

This study is aimed to test whether dimension-

less physical constants are really constants, orwhether they vary with space and time. Thelatter would imply, at some level, a violationof the Einstein equivalence principle (EEP),i.e., local position invariance (LPI) and local

Send offprint requests to: S. A. Levshakov

Lorentz invariance (LLI), as suggested in anumber of unification theories (for reviews,see Uzan 2011; Liberati 2013). In particular,

LPI postulates that the outcome of any localnongravitational experiment is independent ofwhere and when it is performed, i.e., that thefundamental physical laws are space-time in-variant. Experimental validation of EEP is oneof the most important topics of modern physics
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Levshakov et al.: Limits on the space-time variations of fundamental constants 283

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5

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5 5 5 5

0.02

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Fig. 1. Astronomical constraints on - and -variations (1 C.L.) for the period from 1956

to 2013. Above each point, the spectral resolu-tion (FWHM in km s1) is indicated. -variationconstraints are based on the alkali-doublet (AD)

and many-multiplet (MM) methods, whereas -

variation on the ammonia method. The datapoints for the AD method are taken from Savedoff(1956), Bahcall et al. (1967), Levshakov (1992),Varshalovich & Potekhin (1995), Varshalovich et al.(1996), Murphy et al. (2001), Chand et al. (2005);

MM method Webb et al. (1999), Quast et al.(2004), Srianand et al. (2007), Agafonova et al.(2011), Molaro et al. (2013); ammonia method

from Levshakov et al. (2010a), Levshakov et al.(2013a). The figure shows that limits on the - and

-variations just follow the spectral resolution ap-

proximately as / (or /) 1/10th of thepixel size.

allowing us to probe the applicability limits ofthe Standard Model (SM) of particle physics.At the same time, precision limits deliveredfrom such experiments serve as restrictions forthe numerous new theories beyond the SM andcan help to distinguish between them.

Figure 1 demonstrates how upper limits onvariations of physical constants obtained fromastronomical spectra just followed the avail-able spectral resolution. Up to now, no signalshave yet been detected in the range of frac-tional changes from 3 102 to 3 108.Thus, any progress in improving the existing

limits can be achieved from observations ofnarrow spectral lines involving higher spectralresolutions to resolve completely their profiles.At the moment, the resolution of radio tele-scopes exceeds that of optical facilities by or-der(s) of magnitude; an additional and very at-tractive property of microwave radio observa-

tions is that some molecular transitions fromthis frequency range are extremely sensitiveto the putative variations of the fundamentalphysical constants (see a review by Kozlov &Levshakov 2013).

Flambaum & Kozlov proposed in 2007 theso-called ammonia method to test the vari-ability of the electron-to-proton mass ratio, .Using this method for a sample of cold molec-ular cores from the Milky Way disk we ob-tained the following estimate on the spacial-variations (Levshakov et al. 2010a, 2010b):/ = (26 1stat 3sys) 10

9 (1 C.L.).However, further studies revealed significantinstrumental instabilities in the measurementsof line radial velocities which were not ac-counted for in the above value. Thus, we per-

formed a new set of observations of the sametargets and with the same instrument (100-mEffelsberg radio telescope) in order to get aninsight into this previously unknown systemat-ics. Here we present the recent results.

2. Observations

Observations in 2011-2013 targeted a sampleof nine cold (Tkin 10K) and dense (nH2 104 cm3) starless molecular cores locatedin the Milky Way disk. The selected clouds

are known to have narrow molecular emissionlines (full width at half maximum, FWHM < 1km s1) what makes them the most suitabletargets to precise measurements of relative ra-dial velocities (RV). The following moleculartransitions were observed: NH3(1,1) 23.7 GH,HC3N(2-1) 18.2 GHz, HC5N(9-8) 23.9 GHz,HC7N(16-15) 18.0 GHz, HC7N(21-20) 23.7GHz, and HC7N(23-22) 25.9 GHz.

The source coordinates are taken fromLevshakov et al. (2010b, 2013b). Observationsused the Effelsberg 100-m radio telescope asdescribed in Levshakov et al. (2010a, 2013b).

In 2011, the measurements were obtainedin frequency switching (FSW) mode usinga frequency throw of 2.5 MHz. The back-end was a fast Fourier transform spectrometer(FFTS), operated with a bandwidth of 20 MHz,which simultaneously provided 16 384 chan-nels for each polarization. The resulting chan-


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284 Levshakov et al.: Limits on the space-time variations of fundamental constants

Fig. 2. The line-of-sight velocities (VLSR) of NH3(J, K) = (1, 1) (squares) and HC3N J = 2 1 (tri-angles) transitions at different radial distances along

the main diagonal cuts towards the molecular coresL1512 and L1498 measured in 2010 (dashed lines)and in 2011 (solid lines) at the Effelsberg 100-m

radio telescope. The half-power beam width at 23GHz is 40, the backend is the fast Fourier trans-form spectrometer (FFTS) with the channel separa-

tion v = 0.015 km s1.

nel width was 0.015 km s1. However, the truevelocity resolution is about 1.6 times coarser.

In 2012-2013, we performed the measure-ments in the position switching (PSW) modewith the backend XFFTS (eXtended band-width FFTS) operating with 100 MHz band-width and providing 32 768 channels for eachpolarization. The resulting channel width was0.039 km s1, but the true velocity resolution is1.16 times coarser (Klein et al. 2012).

3. Results

To check the reproducibility of the relativeRVs of the NH3(1,1) and HC3N(2-1) lines we

re-observed two molecular cores L1512 andL1498 in 2011. The procedure was the same asin 2010 observations: cores were mapped at thesame offsets and in the same lines. Namely inthe (1,1) inversion transition of NH3 comple-mented by rotational lines of other molecularspecies. The comparison of radial velocities of

Fig. 3. The line-of-sight velocities (VLSR) of theNH3(1,1) transition (dots with 1 error bars) to-wards the ammonia peaks in the molecular cores

L1512 and L1498 measured continuously in theposition switching mode (PSW) at the Effelsberg100-m radio telescope in April, 2012. The exposure

time at each point is 150 sec. The PSW offsets areshown in parentheses. The backend was an extendedfast Fourier transform spectrometer (XFFTS) with a

channel separation v = 0.039 km s1 (marked byvertical lines). The instability of the VLSR measure-ments of an amplitude 0.01 km s1 (i.e., 1/4thof the channel width) is revealed.

NH3 inversion lines, Vinv, with radial velocitiesof rotational transitions, Vrot, provides a sensi-tive limit to the variation of (Flambaum &Kozlov 2007):

/ = 0.289(Vrot Vinv)/c 0.3V/c ,

where c is the speed of light.The measured RVs (Levshakov et al.

2010a) at different radial distances along themain diagonal cuts towards L1512 and L1498are shown in Fig. 2. It is seen that the veloc-ity offsets V exhibit quite different behavior

between 2010 and 2011, what is probably aneffect of unknown systematic errors.

To figure out the source of these errors, weperformed in 2012 a set of continuous observa-tions of L1512 and L1498 targeting their am-monia peaks. Observing in PSW mode, we alsoused different OFF positions to check possible


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Fig. 4. Radial velocity differences, V, betweenrotational transitions of different molecules andthe NH3(1,1) line for the sources observed at the

Effelsberg 100-m telescope (2011-2013). 1 sta-tistical errors are indicated. In the panel, given inparentheses are the coordinate offsets in arcsec.

Filled circles data from Levshakov et al. (2013a);open triangle this paper; open circle and square Levshakov et al. (2010a, 2010b);

contamination from an extended backgroundammonia emission (which was not detected).

The resulting time series are shown in Fig. 3.The RV values fluctuate with an amplitude of 0.01 km s1, i.e., 1/4th of the channelwidth.

To check whether the sky frequency isidentical with the frequency coming out of thebackend we carried out a test with an artificialsignal at 22000.78125 MHz. The synthesizerfrequency was accurate to about 1 Hz, and thefrequency scale was found to be accurate toabout 32 Hz ( 0.0004 km s1).

In our observations, the sky frequencieswere reset at the onset of each subscan.

Therefore, the longer a subscan the higher theerror caused by Doppler shifts during the ex-posure time (e.g., for a 5 min scan, it is about0.004 km s1 at Effelsberg latitude). We cor-rected some of our observations to account forresidual Doppler shifts. This didnt show a sig-nificant change in the results, however.

Another source of errors which can affectthe / estimates with the ammonia methodis the possible segregation of molecules inmolecular cores. Figure 4 shows our measure-ments in 2013 (filled circles) of the relativeRVs between NH3(1,1) and other molecules to-wards eight molecular cores (L1498A is a gascondensation in L1498, see Fig. 3 in Kuiper etal. 1996) at different offsets. Previous values,obtained in 2009-2011, are marked by opensymbols. A spread of the velocity offsets Vis clearly seen.

Thus, we conclude that noise in theVval-ues consists of at least two components: oneis due to chemical differentiation and velocitygradients within the molecular cores, possibly

being amplified by small variations in the tele-scope pointing. Additionally, some scatter inthe RVs may be caused by the different op-tical depths of the hyperfine structure transi-tions. However, all these effects may be ran-dom from one observation to another, and, be-ing averaged over a sample of targets, shouldbe reduced to some extent. Applied to our sam-ple ofn = 18 independent V offsets shown inFig. 4, this gives the weighted mean V =0.002 0.015 km s1 (3 C.L.). Being inter-preted in terms of/ = (obs lab)/lab, thisvalue ofV constraints the -variation at thelevel of/ < 2 108 (3 C.L.), which isthe most stringent limit on the spatial variationof based on radio astronomical observations.The same order of magnitude upper limit on/ was obtained from independent observa-tions of L1512 and L1498 at the Medicina 30-m telescope (Levshakov et al. 2013a).

We note in passing that mapping of thedense molecular cores in different molecularlines shows that there is, in general, a good cor-relation between NH3, N2H

+, and HC3N dis-tributions (Fuller & Myers 1993; Hotzel et al.2004; Tafalla et al. 2004; Pagani et al. 2009).

However, in some clouds NH3 is not tracedby HC3N, as, e.g., in the dark cloud TMC-1, where peaks of line emission are offset by7 (Olano et al. 1988). In our case, we ob-serve systematic velocity shifts between NH3and other species. This can be expected sinceC-bearing molecules are usually distributed in


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286 Levshakov et al.: Limits on the space-time variations of fundamental constants

the outer parts of the cores, whereas N-bearingmolecules trace the inner parts.

4. Discussion

The obtained local constraint on the spatial -variation, / < 2 108 (3 C.L.), can beused to set limits on changes in . This, how-ever, is strongly model dependent. For exam-ple, within the grand unification model (GUT)a variation of would imply considerablylarger fractional changes in the mass scale ofthe strong force in QCD, QCD, and in quarkand electron masses leading to

/ R/ ,

where R 40 (e.g., Langacker et al. 2002;Flambaum et al. 2004). This gives a limit on|/| < 1010 (1 C.L.). The value of R is,however, poorly constrained. Depending on thetheory, it varies from 235 to +46 (examplesare given in Section 5.3.1 in Uzan 2011). Theonly way to distinguish between theories is tomeasure / and / independently.

At higher redshifts, the most stringent limiton cosmological -variation was set at z =0.89, |/| < 107 (Bagdonaite et al. 2013).This would imply that |/| < 2.5 109 (1

C.L.) at epoch 7 109 yr, which means in turnthat |/| < 4 1019 yr1. At very high red-shift, z = 5.2 (epoch 12.9 Gyr), the currentlimit is |/| < 8 106 (1 C.L.) corre-sponding to |/| < 6 1016 yr1 (Levshakovet al. 2012). We note that most stringent lim-its set by the Oklo fossil reactor and by ter-restrial atomic clock experiments are, respec-tively, |/| < 5 1017 yr1 (Uzan 2011),and |/| < 4 1017 yr1 (Rosenband et al.2008). Thus, despite many efforts, the space-time variations in and have never been de-tected either in laboratory or astronomical ex-

periments.It only remains to hope that significant im-

provements in radio astronomical observationswill allow us to probe variations of at levelsof/ 109 1010, leading to even morestringent results and eventually to the detectionof a real variation.

5. Conclusions

We have used the Effelsberg 100-m telescopeto observe the NH3(1,1) 23.7 GHz, HC3N(2-

1) 18.2 GHz, HC5N(9-8) 23.9 GHz, HC7N(16-15) 18.0 GHz, HC7N(21-20) 23.7 GHz, andHC7N(23-22) 25.9 GHz spectral lines in high-density molecular cores devoid of associatedIR sources. The results obtained are as follow.

1. In order to test the reproducibility of themeasurements of the relative radial veloc-ities between the NH3(1,1) and HC3N(2-1)transitions observed towards dark molec-ular cores in 2009-2010 at the Effelsberg100-m telescope, we re-observed twoclouds L1512 and L1498 and revealeddiscrepancy between the Vlsr(HC3N)

Vlsr(NH3) values which is as high as thechannel width, V


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Sonderforschungsbereich SFB 676 Teilprojekt C4,and in part by Research Program OFN-17 of theDivision of Physics, Russian Academy of Sciences.

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Limits on the Space-time Variations of Fundamental Constants 1307.8266

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