Robust Constraint on a Drifting Proton-to-Electron Mass Ratio at z=0.89 from Methanol Observation at Three Radio Telescopes
Julija Bagdonaite, Mario Daprà, Paul Jansen, Hendrick L. Bethlem, Wim Ubachs, Sébastien Muller, Christian Henkel, Karl M. Menten
RRobust Constraint on a Drifting Proton-to-Electron Mass Ratio at z = 0 . from Methanol Observation at Three Radio Telescopes J. Bagdonaite, M. Dapr`a, P. Jansen, H. L. Bethlem, W. Ubachs
Department of Physics and Astronomy, VU University Amsterdam,De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands
S. Muller
Onsala Space Observatory, Chalmers University of Technology, SE 439-92, Onsala, Sweden
C. Henkel
Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany andAstronony Department, King Abdulaziz University,Post Office Box 80203, Jeddah 21589, Saudi Arabia
K. M. Menten
Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany
A limit on a possible cosmological variation of the proton-to-electron mass ratio µ is derived frommethanol (CH OH) absorption lines in the benchmark PKS1830 −
211 lensing galaxy at redshift z = 0 .
89 observed with the Effelsberg 100-m radio telescope, the Institute de Radio AstronomieMillim´etrique 30-m telescope, and the Atacama Large Millimeter/submillimeter Array. Ten differentabsorption lines of CH OH covering a wide range of sensitivity coefficients K µ are used to derive apurely statistical 1- σ constraint of ∆ µ/µ = (1 . ± . × − for a lookback time of 7.5 billion years.Systematic effects of chemical segregation, excitation temperature, frequency dependence and timevariability of the background source are quantified. A multi-dimensional linear regression analysisleads to a robust constraint of ∆ µ/µ = ( − . ± . stat ± . sys ) × − . The fact that the strengths of the fundamental forcesof nature are not fixed by the Standard Model of physicsleaves space for the hypothesis of coupling constantsvarying over time and space. Such a constant is the di-mensionless proton-to-electron mass ratio µ = m p /m e ,representing the ratio of the strong force to the elec-troweak scale [1]. Effects of a time-varying µ may beprobed through the measurement of molecular line spec-tra in various cosmological epochs. The spectrum ofmolecular hydrogen, H , the most abundant molecule inthe Universe, can be investigated with large optical tele-scopes [2–5]. The sensitivity coefficient K µ , defined via∆ νν = K µ ∆ µµ (1)for the H spectral lines is only of the order of 0 .
05 [6].For this reason the µ constraint resulting from H datais not better than ∆ µ/µ < − .Transitions of some other molecules in the radio part ofthe electromagnetic spectrum exhibit larger sensitivitiesto a varying µ . Inversion transitions of ammonia (NH ),with K µ = − .
46, have been applied to produce 1- σ con-straints at the level of ∆ µ/µ = (1 . ± . × − in the ob-ject PKS1830 −
211 at z = 0 .
89 [7] and ( − . ± . × − in the object B0218+357 at z = 0 .
68 [8]. In the µ -variation analysis the strongly shifting NH lines mustbe compared with non-shifting anchor lines belonging todifferent species, such as HCO + and HC N. This maygive rise to systematic effects on the result for ∆ µ/µ due to chemical segregation, i.e. to a non-homogeneous spa-tial distribution of the various molecular species alongthe line-of-sight.It was recently pointed out that the interplay betweenthe internal and overall rotation in the methanol molecule(CH OH) results in specific transitions having an en-hanced sensitivity for a possible drift in µ [9, 10]. Some ofthese transitions involve low lying rotational energy lev-els populated at the low temperatures characterizing thebulk of the interstellar molecular gas. The spread in K µ coefficients for methanol lines provides the unique oppor-tunity of deriving a tight constraint on µ from a singlemolecular species, therewith avoiding chemical segrega-tion issues. Methanol has recently been observed in agravitationally lensing galaxy (at z = 0 .
89, correspond-ing to a lookback time of 7.5 billion years [11]) towardthe south-western (SW) image of the background blazarPKS1830 −
211 [12, 13]. In a preliminary investigationbased on a small sample of four methanol transitions a1- σ limit of ∆ µ/µ at 1 × − was derived [14], with an in-dication of a spatial differentiation of the E - and A -typesymmetry species. Here, we present an extended studyof µ variation based on 17 measurements of ten differentabsorption lines of CH OH allowing for a quantitativeanalysis of previously unaddressed underlying systematiceffects. This analysis leads to a similar constraint as theone found in [14], but the robustness of this constraint isgreatly improved.Methanol absorption spectra were recorded using three a r X i v : . [ a s t r o - ph . C O ] D ec different radio telescopes covering a range of 6–261 GHz.The CH OH lines in the low-frequency range (detectedfrequencies <
35 GHz), previously observed in the timeslot Dec. 2011–Apr. 2012 [14], were reobserved withthe 100-m single-dish Effelsberg radio telescope of theMax-Planck-Institute f¨ur Radioastronomie (see Table I).Spectra of the new observations in fall 2012 and spring2013 are shown in Fig. 1(a). The absorption profiles ofindividual transitions were fitted to single Gaussians, andthe line positions and widths were determined on a LocalStandard of Rest (LSR) velocity scale, which was cen-tered at z = 0 . − −
27 August 2012. Fig. 1(b) shows the overlappingcomponents of the 1 − − E , 2 − − E and 3 − − E transitions at a detection frequency of 83.3 GHz. A fitwas performed assuming that relative intensities betweenthe three components are proportional to their expectedoptical depths. The RADEX radiative transfer model[20] was used to estimate the relative intensities. Alsothe relative positions of the components were fixed basedon the laboratory measurements, and the widths wereassumed to be the same. The uncertainty of the com-bined line position is estimated by varying the relativestrengths of the three lines by 10-20% with regard to theRADEX prediction. Also shown in Fig. 1 is a recordingof the 1 − A + / − line at a detection frequency of 160GHz. In addition the weak 3 − A + line at ν obs ∼ . − A + CH OH transitionat a frequency of 261 GHz was conducted in June 2012with the Atacama Large Millimeter/submillimeter Array[ALMA, 20 dishes, 12 m in diameter each; see Fig. 1(c)].The angular resolution of the ALMA observations ( ∼ K µ coefficients [9]. The quoted optical depths τ are re-lated to the measured absorption line intensities I ν via τ = − ln(1 − I ν /f c I bg ) where I bg is the total continuumintensity and f c is the continuum source covering fac-tor. For unresolved single-dish observations, we adopt f c = 0 . − × cm − anda kinetic temperature of 80 K (values discussed in [7],[21],and [22]), FWHM linewidths and optical depths as fittedto observations, and a T CMB = 2 . z ) = 5 .
145 Kfor the temperature of the cosmic microwave backgroundradiation at z = 0 . . × cm − (adding E and A type methanolcolumn densities).All the detected methanol transitions have been in-cluded in the analysis. In addition, Table I includes twodata points resulting from observations with the Aus-tralia Telescope Compact Array (ATCA), presented inliterature: the 2 − − E transition in [12] observed inSeptember 2009, and the 3 − − E transition in [13] ob-served in November 2011. We adopt line positions fromthe latter work.The velocities between different transitions are inter-related via V /c = − K µ ∆ µ/µ , where c is the speed oflight (also see Eq. 1). The error bars in the velocity po-sitions reflect the statistical uncertainties from Gaussianprofile fitting to the observed spectra. The uncertainty inthe laboratory frequencies, expressed on a velocity scalein Table I with ∆ v D , is small ( < − or less [23, 24]. Theresult of the statistical analysis deducing ∆ µ/µ is shownin Fig. 2. A fit to the 17 data points delivers a constraintof ∆ µ/µ = (1 . ± . × − with a reduced χ ν = 10 . ν , is 15. Thelarge value of the goodness-of-fit measure χ ν indicatesthat the spread of the data is larger than expected fromtheir errors. As a consequence, the addition of new datato our previous set [14] did not lead to an expected im-provement of the constraint. Assuming we do not un-derestimate the errors from the observations, the ratherlarge value of χ ν suggests an underlying systematic ef-fect that is not taken into account. In the following weaddress possible candidates. Chemical segregation.
Spatial segregation of molecularspecies within an absorbing galaxy may mimic or hide avariation of µ . Since we rely on a single molecular specieschemical segregation cannot be an issue, however, it maybe possible that E and A type methanol are displacedspatially as suggested in [14]. In panel (a) of Fig. 3, thedata are grouped by their symmetry. The averages ofthe A and E transitions agree within their uncertain-ties. Furthermore, a two-dimensional linear regression(LR) analysis with K µ and E / A symmetry as indepen-dent variables results in an increase of χ ν , if comparedto a fit with K µ alone, thereby ruling out a possible E / A segregation. This new result of the extended study im-plies that all data pertaining to methanol can be includedin a µ variation analysis. Temperature dependence.
The spread in the line po-sitions might be ascribed to an inhomogeneous temper-ature distribution in the absorbing cloud. In panel (b)of Fig. 3, the V LSR /c values are plotted as a function ofthe excitation energy of the lower level. The solid lineshows a linear fit to the data, indicating a correlationbetween the measured line positions and the excitation � obs ~ 6 GHz3 -1 E Nov 2012, K μ = -32.8 � obs ~ 25 GHz0 E , 0 A + Apr 2013, K μ = -1 dv = 1.1 km s -1 dv = 1.1 km s -1 V LSR [km s -1 , relative to z =0.88582] + � – � + � – � L i n e - t o - c o n t i n uu m r a t i o [ % ] – – – (a) Effelsberg - - - � obs ~ 83 GHz1 -1 E , 2 -1 E , 3 -1 E Aug 2012, K μ = -3.5 dv =0.7 km s -1 � obs ~ 160 GHz1 A +/- Aug 2012, K μ = -1.9 L i n e - t o - c o n t i n uu m r a t i o [ % ] dv =1.4 km s -1 V LSR [km s -1 , relative to z =0.88582] + � + � – � – � – – – – – – – (b) IRAM 30-m V LSR [km s -1 , relative to z =0.88582] L i n e - t o - c o n t i n uu m r a t i o [ % ] + � – � � obs ~ 261 GHz3 A + Jun 2012, K μ = -1.6 dv = 0.6 km s -1 (c) ALMA FIG. 1. Some of the observed methanol transitions toward PKS1830 −
211 with their approximate observed frequencies ν obs ,observation epoch, sensitivity coefficients K µ , and channel spacings dv indicated in each panel for recordings at (a) Effelsbergradio telescope, (b) IRAM 30-m telescope, (c) ALMA array. The intensity is normalized to the total continuum flux, exceptfor (c) where the SW image could be observed exclusively. Gaussian fits to the absorption profiles are displayed in light greenwith residuals shown at the top of each panel.TABLE I. A summary of the observed methanol lines in PKS1830 − ν Lab and corresponding uncertainties, fractional uncertainties ∆ ν/ν , uncertainties interms of Doppler shift, ∆ v D , and corresponding frequencies at redshift z = 0 . K µ refers to the sensitivity coefficients(see Eq. 1). Fitted line positions V LSR are stated with respect to the Local Standard of Rest (centered at z = 0 . σ ). Optical depths τ are fitted from the spectra.In the last column the instrument and the observation period is mentioned. Eff. refers to the Effelsberg 100-m, IRAM to the30-m radio telescope at the Pico Veleta.Transition ν Lab ∆ ν/ν ∆ v D ν z=0 . K µ V LSR
Width τ Observationlower − upper (GHz) (km s − ) (GHz) (km s − ) (km s − )3 − − E a × − . . ± . . ± . h . ± . . ± . . ± . . ± . . ± . f . ± . f f ATCA Nov. 20110 − A + b × − . . ± . . ± . h . ± . . ± . h . ± . . ± . . ± . . ± . − E c × − . . ± . . ± . h . ± . . ± . h . ± . . ± . − − E c × − . . ± . . ± . h . ± . f . ± . f f ATCA Sep. 20093 − A + c × − . . ± . . ± . − − E c × − . . ± . g . ± . g − − E c × − . − − E c × − . − A + / − d × − . . ± . . ± . − A + e × − . . ± . . ± . a Breckenridge and Kukolich (1995) [15]. b Heuvel and Dynamus (1973) [16]. c M¨uller et al. [17]. d Sastry et al. [18]. e Herbst et al. [19]. f Values from [13], V HEL is converted to V LSR via V LSR − V HEL = 12 .
432 km s − . g Three components fittedjointly (see text). h Data used in [14] where the values of the widths were stated as FWHM/ (cid:112) (2 ln ∆µ/µ ( )× V L S R / c [ x10 - ] K µ FIG. 2. The positions of the ten observed methanol lines (rep-resented by V LSR /c with respect to z = 0 . K µ . Note that some tran-sitions were observed multiple times, hence, 17 data points aredisplayed. The slope of a straight line fitted to the datasetrepresents − ∆ µ/µ . The A transitions observed at Effelsbergare offset from K µ = −
0 5 10 15 20 1/ � obs [GHz -1 ]Epoch of observation[month, starting 2011 Nov] 0 0.05 0.10 0.15 0.20 V L S R / c [ ×10 - ] V L S R / c [ ×10 - ] (a) (b)(c) Symmetry (d) E A
0 5 10 15 T ex [K] a = (6.8±1.2)×10 -7 � � = 3.6 a = (1.86±0.44)×10 -6 a = (-1.06±0.25)×10 -7 � � = 5.8 a = (-3.0±3.9)×10 -5 � � = 11.1( V LSR / c ) E = (3.11±0.11)×10 -5 ( V LSR / c ) A = (2.88±0.12)×10 -5 FIG. 3. The positions of 16 observed methanol absorptions(leaving out the data point measured in 2009) as a functionof various parameters: (a) symmetry, (b) excitation tempera-ture of the lower level, (c) epoch of observation, (d) observedfrequency. The color coding is the same as in Fig. 2. Thesolid lines show a fit using a linear or quadratic function ofform y = a + a x + a x . energy. When we include the excitation energy as an in-dependent variable in a two-dimensional LR analysis, wefind a constraint of ∆ µ/µ = ( − . ± . × − with χ ν = 3 . ν = 14. The obtained limit of a timevariation of ∆ µ/µ changes only marginally when effectsof the excitation energy are included, i.e., the ∆ µ/µ isnot strongly correlated to the excitation energy in ourdata set, however, the χ ν is significantly reduced. Time variability of the background source.
Thestrength of radio absorption lines towards the SW im-age was found to vary by a factor of ∼ + transition have shown an absorption profile, composedof several components, evolving with time. This phe-nomenon was explained by morphological changes in thebackground blazar. Thus, comparing line profiles fromvarious time periods may lead to potential errors in linepositions, especially if the velocity structure is underrep-resented by the fitting [26]. In panel (c) of Fig. 3 weshow V LSR /c as a function of observation epoch. An in-dication of an oscillating behaviour can be found but aswe observe (less than) one period of this oscillation wechoose to fit a quadratic time dependence instead of asinusoidal one. A two-dimensional LR analysis with theobservation epoch and K µ as independent variables re-sults in ∆ µ/µ = (0 . ± . × − with χ ν = 5 . ν = 12. Again, although our data show a dependenceon observation epoch, this does not change the result-ing limit on a time variation of ∆ µ/µ if compared tothe one from a K µ -only fit. In a three-dimensional anal-ysis where both the time variability and the tempera-ture dependence are taken into account, a constraint of∆ µ/µ = ( − . ± . × − is delivered with χ ν = 2 . ν = 11. Frequency dependence.
Previous studies have shownthat the size of the south western image of thePKS1830 −
211 background blazar changes with fre-quency [27] and it exhibits a chromatic substructure, i.e.a different apparent position of the core at different fre-quencies, known as a core-shift effect. In particular, theangular separation ∆ θ of two sightlines at observed fre-quencies ν and ν is estimated to be ∆ θ = Ω(1 /ν − /ν )where Ω ∼ . V LSR /c and 1/ ν (Fig. 3(d)) but note that thesensitivity of the lines used in our study follow a 1/ ν dependence [9], hence, K µ and 1/ ν are correlated andcannot be fitted simultaneously. According to [28], thecore-shift effect in the PKS1830 −
211 system may intro-duce a shift of ∼ − between lines at ν obs ∼ µ/µ of 1 × − . As it is not possible toestimate the size of this effect based on the current dataset, we adopt the latter value as a systematic uncertaintyof ∆ µ/µ . In order to constrain the core-shift effect basedon methanol only it would be desirable to add low fre-quency methanol absorption that have positive or small K µ . Attempts to observe the 3 − − E transition at ν obs ∼ . K µ = +9 . µ at more than half of the age of the Uni-verse using methanol absorption lines detected in a fore-ground galaxy towards the PKS1830 −
211 blazar. Themethanol method, being the most sensitive probe fortime-variations of µ , can only be applied to this objectas it is the only place in the far distant Universe wherethe methanol molecule has been detected so far. Forthis reason we focused all efforts on observing this ob-ject and used different telescopes to collect a total of 17data points for ten different absorption lines from whicha statistical constraint of ∆ µ/µ = (1 . ± . × − is derived. The large data set greatly enhances theunderstanding of previously unaddressed systematic ef-fects and allows for a robust analysis. The suggestedsystematic on E/A chemical segregation [14] has nowbeen discarded. The analysis reveals that effects per-taining to temperature inhomogeneity of the absorbingcloud and time variability of the background source re-sult in a larger scatter than expected from the errorof the individual transitions. By including the under-lying systematic effects as independent variables in amulti-dimensional linear regression analysis, we obtain∆ µ/µ = ( − . ± . stat ± . sys ) × − . Translated intoa rate of change this corresponds to ˙ µ/µ < × − yr − , which is equally constraining as the bound on avarying constant obtained with the best optical clocks inlaboratory experiments [29].This work is supported by the FOM-program “Bro-ken Mirrors & Drifting Constants” and by FOM-projects10PR2793 and 12PR2972. W.U. and P.J. acknowledgesupport from the Templeton Foundation, and H.L.B.acknowledges support from NWO via a VIDI grant.The research leading to these results has received fund-ing from the European Commission Seventh FrameworkProgramme (FP/2007-2013) under grant agreement No283393 (RadioNet3). This paper makes use of the fol-lowing ALMA data: ADS/JAO.ALMA [1] V. V. Flambaum, D. B. Leinweber, A. W. Thomas, andR. D. Young, Phys. Rev. D , 115006 (2004).[2] J. A. King, J. K. Webb, M. T. Murphy, and R. F. Car-swell, Phys. Rev. Lett. , 251304 (2008).[3] A. L. Malec, R. Buning, M. T. Murphy, N. Milutinovic,S. L. Ellison, J. X. Prochaska, L. Kaper, J. Tumlinson, R.F. Carswell, and W. Ubachs, Month. Not. Roy. Astron.Soc. , 1541 (2010). [4] F. van Weerdenburg, M. T. Murphy, A. L. Malec, L.Kaper, and W. Ubachs, Phys. Rev. Lett. , 180802(2011).[5] M. Wendt and P. Molaro, Astron. Astroph. , A69(2012).[6] W. Ubachs, R. Buning, K. S. E. Eikema, and E. Reinhold,J. Mol. Spectrosc. , 155 (2007).[7] C. Henkel, K. M. Menten, M. T. Murphy, N. Jethava, V.V. Flambaum, J. A. Braatz, S. Muller, J. Ott, and R. Q.Mao, Astron. Astroph. , 725 (2009).[8] N. Kanekar, Astrophys. J. Lett. , L12 (2011).[9] P. Jansen, L. H. Xu, I. Kleiner, W. Ubachs, and H. L.Bethlem, Phys. Rev. Lett. , 100801 (2011).[10] S. A. Levshakov, M. G. Kozlov, and D. Reimers, Astro-phys. J. , 26 (2011).[11] Based on a standard Λ cosmology with H = 67.3 kms − Mpc − , Ω m = 0.315 and Ω Λ = 0.685; Planck Collab-oration: P. A. R. Ade et al., arXiv:1303.5076 (2013).[12] S. Muller, A. Beelen, M. Gu´elin, S. Aalto, J. H. Black, F.Combes, S. J. Curran, P. Theule, and S. N. Longmore,Astron. Astroph. , A103 (2011).[13] S. P. Ellingsen, M. A. Voronkov, S. L. Breen, and J. E.J. Lovell, Astrophys. J. Lett. , L7 (2012).[14] J. Bagdonaite, P. Jansen, C. Henkel, H. L. Bethlem, K.M. Menten, W. Ubachs, Science , 46 (2013).[15] S. M. Breckenridge and S. G. Kukolich, Astrophys. J. , 504 (1995).[16] J. E. M. Heuvel and A. Dymanus, J. Mol. Spectrosc. ,282 (1973).[17] H. S. P. M¨uller, K. M. Menten, and H. M¨ader, Astron.Astroph. , 1019 (2004).[18] K. V. L. N. Sastry, R. M. Lees, and F. C. De Lucia, J.Mol. Spectrosc. , 486 (1984).[19] E. Herbst, J. K. Messer, F. C. De Lucia, and P.Helminger, J. Mol. Spectrosc. , 42 (1984).[20] F. F. S. Van der Tak, J. H. Black, F. L. Sch¨oier, D. J.Jansen, and E. F. van Dishoeck, Astron. Astroph. ,627 (2007).[21] K. M. Menten, R. G¨usten, S. Leurini, S. Thorwirth, C.Henkel, B. Klein, C. L. Carilli, and M. J. Reid, Astron.Astroph. , 725 (2008).[22] S. Muller, A. Beelen, J. H. Black, S. J. Curran, C. Horel-lou, S. Aalto, F. Combes, M. Gu´elin, and C. Henkel,Astron. Astroph. , A109 (2013).[23] S. A. Levshakov, A. V. Lapinov, C. Henkel, P. Molaro,D. Reimers, M. G. Kozlov, and I. I. Agafonova, Astron.Astroph. , A32 (2010).[24] F. F. S. Van der Tak, H. S. P. M¨uller, M. E. Harding,and J. Gauss, Astron. Astroph. , 347 (2009).[25] S. Muller and M. Gu´elin, Astron. Astroph. , 739(2008).[26] M. T. Murphy, V. V. Flambaum, S. Muller, and C.Henkel, Science , 1611 (2008).[27] J. C. Guirado, D. L. Jones, L. Lara, J. M. Marcaide, R.A. Preston, A. P. Rao, and W. A. Sherwood, Astron.Astroph. , 392 (1999).[28] I. Mart´ı-Vidal, S. Muller, F. Combes, S. Aalto, A. Bee-len, J. Darling, M. Gu´elin, C. Henkel, C. Horellou, J. M.Marcaide, S. Mart´ın, K. M. Menten, D. V-Trung, and M.Zwaan, Astron. Astroph. 558, A123 (2013).[29] T. Rosenband, D. B. Hume, P. O. Schmidt, C. W. Chou,A. Brusch, L. Lorini, W. H. Oskay, R. E. Drullinger,T. M. Fortier, J. E. Stalnaker et al., Science,319