Constraining changes in the proton-electron mass ratio with inversion and rotational lines

0.29 MB·English

by  Nissim Kanekar

DRAFTVERSIONJANUARY24,2011
PreprinttypesetusingLATEXstyleemulateapjv.11/10/09
CONSTRAININGCHANGESINTHEPROTON-ELECTRONMASSRATIOWITHINVERSIONANDROTATIONAL
LINES
NISSIMKANEKAR1
DraftversionJanuary24,2011
ABSTRACT
We report deep Green Bank Telescope (GBT) spectroscopy in the redshifted NH (1,1), CS 1-0 and
3
1
1 H2CO 000-101 lines from the z ∼ 0.685 absorber towards B0218+357. The inversion(NH3) and rotational
0 (CS,H2CO)linefrequencieshavedifferentdependencesontheproton-electronmassratioµ,implyingthata
2 acnodmpHa2rCisOonlibneetswyeieenldtshe[∆liµn/eµr]ed=sh(if−ts3i.s5s±en1s.i2ti)ve×to10c−h7a,ngfreosminzµ∼. A0.6jo8i5ntto3-tcoodmayp,ownehnetrefitthteoethrreorNiHnc3l,uCdeSs,
n systematiceffectsfromcomparinglinesfromdifferentspeciesandpossiblefrequency-dependentsourcemor-
a phology. Twoadditionalsourcesofsystematicerrorremain,duetotimevariabilityinthesourcemorphology
J
andvelocityoffsetsbetweennitrogen-bearingandcarbon-bearingspecies. Wefindnostatistically-significant

0 (≥3σ)evidenceforchangesinµ,andobtainthestringent3σconstraint,[∆µ/µ]<3.6×10−7,over6.2Gyrs;
2 this is the best present limit on temporalchanges in µ from any technique, and for any lookbacktime, by a
factor&5.
]
O Subjectheadings:atomicprocesses—galaxies:high-redshift—quasars:absorptionlines
C
h. 1. INTRODUCTION oneobtains[∆α/α]=(−3.1±1.2)×10−6,consistentwith
theresultofMurphyetal.(2004),albeitatalowerredshift.
p A generic prediction of theories that attempt to unify the
Forthreedecades,ro-vibrationalmolecularhydrogen(H )
- standard model of particle physics with general relativity is 2
o lines provided the sole method to directly probe changes in
that particle masses and low-energycoupling constants vary
r the proton-electron mass ratio (Thompson 1975). Unfortu-
t withspaceandtime. Adetectionofsuchchangeswouldim-
s plynewphysicsbeyondthestandardmodel.Testsofchanges nately, few redshifted H2 absorbers have been detected so
a far (e.g. Ledouxetal. 2003), and, of these, only four have
[ infundamental“constants”suchasthefinestructureconstant
α, the proton-electronmassratio µ orthe protong-factorg beenfoundsuitabletostudychangesinµ(e.g.Ivanchiketal.
1 arehenceofmuchinterest(e.g.Uzan2003). p 2005;Reinholdetal.2006;Kingetal.2008;Thompsonetal.
v Redshiftedatomicand molecularspectrallinesprovidean 2009; Malecetal. 2010; Wendt&Molaro 2011). These re-
9 interesting avenue to probe the possibility of fundamental sultshavealsobeencontroversial: Reinholdetal.(2006)ob-
2 tained [∆µ/µ] = (+2.0±0.6)×10−5 from two absorbers
constant evolution over cosmological timescales (Savedoff
0 at z ∼ 2.6 − 3.0, i.e. evidence for a larger value of µ
1956). Comparisons between the redshifts of lines whose
4 at high redshift (see also Ivanchiketal. 2005). However,
rest frequencies have different dependences on a con-
. independent re-analyses of these data by Kingetal. (2008)
1 stant like α are sensitive to changes in the constant [see
andThompsonetal.(2009),usingimprovedwavelengthcal-
0 Kanekar (2008) for a recent review]. There are a num-
1 ber of such techniques, using comparisons between differ- ibration techniques, found no evidence for changes in µ.
1 ent transitions (e.g. Thompson 1975; Wolfeetal. 1976; Kingetal.(2008)obtain[∆µ/µ]=(+2.6±3.0)×10−6from
: Dzubaetal.1999;Darling2003;Chengalur&Kanekar2003; threeabsorbersatz ∼ 2.6−3.0(includingthetwo systems
v
ofReinholdetal.2006);note,however,thatWendt&Molaro
i Kanekar&Chengalur2004;Flambaum&Kozlov2007). In-
X deed, one of these techniques, the many-multiplet method, (2011)arguethatsystematicerrorshavebeenunder-estimated
inthelatteranalysis.
r hasyieldedevidenceforchangesin α: Murphyetal. (2004)
a obtained [∆α/α] = (−5.4 ± 1.2) × 10−6 from 143 ab- Anewlaboratorytechniquetoprobechangesinµwaspro-
posed by vanVeldhovenetal. (2004), using inversion tran-
sorbers with hzi = 1.75 (see also Murphyetal. 2003).
sitions of deuterated ammonia (ND ). Flambaum&Kozlov
This result has as yet been neither confirmed nor ruled out 3
(2007)adaptedthistechniquetoastrophysicalcircumstances,
(e.g. Srianandetal. 2007; Molaroetal. 2008; Murphyetal.
using ammonia (NH ) inversion lines and rotational lines.
2008b; Kanekaretal. 2010b), but evidence has now been 3
Rotational and inversion line frequencies have different de-
foundforadditionalsystematiceffectsinthedata, duetoer-
pendences on µ, and a comparison between the redshifts of
rors in the wavelength calibration (Griestetal. 2010). Re-
NH inversionlinesandrotational(e.g. CO,HCO+,CS,etc)
cently, an independent technique, using radio “conjugate” 3
lines from a single cosmologically-distant absorber is thus
satelliteOHlines(Kanekaretal.2004;Kanekaretal.2005),
found weak evidence (at ∼ 99.1% confidence level) for sensitivetochangesinµ. OnlytworedshiftedNH3absorbers
are currently known, at z ∼ 0.685 towards B0218+357
changes in a combination of α, µ and g : Kanekaretal.
(2010a)obtained[∆G/G]=(−1.18±0.46p)×10−5between (Henkeletal. 2005) and z ∼ 0.886 towards B1830−210
(Henkeletal. 2008). In both cases, the NH detectionspec-
z ∼ 0.247andthepresentepoch,whereG ≡ g [µα2]1.85. If 3
p trahavebeenusedtoobtaininitialconstraintsonchangesinµ
changesinαareassumedtodominateoverthoseinµandg ,
p (Murphyetal.2008a;Henkeletal.2009).Finally,theammo-
niatechniquehasalsobeenusedtosearchforspatialchanges
1Ramanujan Fellow, National Centre for Radio Astrophysics, TIFR, inµ:Levshakovetal.(2010)obtainedthe(conservative)con-
Ganeshkhind,Pune-411007,India
2 Kanekar
straint[∆µ/µ]<3×10−8fromstudiesofmultiplemolecular be the same, in both the number of absorbing “clouds” and
cloudsintheGalaxy. their redshifts. Turbulencewas assumed to be the dominant
The z ∼ 0.685 absorber towards B0218+357 has a far contributortothelinewidths,whichwerehencetiedtogether
smaller velocity spread than the z ∼ 0.886 system to- in the fit (Murphyetal. 2008a). The NH3 hyperfine struc-
wards B1830−210(Wiklind&Combes 1995, 1996b), mak- ture was included by assuming local thermodynamic equi-
ing it a better candidate for accurate redshift measure- librium(LTE),withthehyperfineratiostakenfromTableS1
ments.Thecarbonmonosulfide(CS)1-0line[restfrequency: of(Murphyetal.2008a). Finally,the fitalsoincludedasin-
48.990957(2)GHz; Kim&Yamamoto2003] is a goodrota- glevelocityoffsetbetweenthespectralcomponentsinthein-
tional transition for the comparison with the NH inversion version and rotational transitions, to account for a possible
3
linesbecauseitisknowntobeunsaturatedinthez ∼ 0.685 changeintheproton-electronmassratio.
absorber(Combesetal.1997)anditliesatafrequencyrela- Asimultaneousmulti-componentVoigtprofilefitwascar-
tivelyclosetothatoftheNH (1,1)lines. Theformaldehyde riedouttothethreespectraofFig.1withtheaboveassump-
3
(H2CO) 000-101 line [rest frequency: 72.837948(10) GHz; tions, aiming to minimize χ2ν by varying the fit parameters.
Cornet&Winnewisser 1980] was chosen as a second rota- A3-componentfitwasfoundtoyieldχ2 = 1.05andnoev-
ν
tional transition, to obtain an estimate of systematic effects idence for structure in the residuals after subtracting out the
intheabovecomparison;thistooisknowntobeunsaturated fitstoeachspectrum(seethelowerpanelsofFig.1). Specif-
in the z ∼ 0.685 absorber(Jethavaetal. 2007). This Letter ically,aKolmogorov-Smirnovrank-1testfoundthefitresid-
reportsGreenBankTelescope(GBT)spectroscopyinthered- uals for all lines to be consistent with a normal distribution
shiftedNH3(1,1),CS1-0andH2CO000-101lines,thatyield within∼ 1σ confidence. One-andtwo-componentfits were
thebestpresentconstraintsonchangesintheproton-electron foundtoyieldbothalargerχ2 andclearnon-Gaussianstruc-
ν
massratio. ture in the residualspectra. While increasing the numberof
spectralcomponentstofourdidyielda marginally-lowerχ2
2. OBSERVATIONS,DATAANALYSISANDRESULTS ν
(∼1.02),theadditionalspectralcomponentwasonlyweakly
The GBT observationsof the NH3 (1,1) and CS 1-0 lines detected in the H2CO spectrum (at . 3σ significance) and
atz ∼0.685towardsB0218+357werecarriedoutinJanuary wasnotvisibleintheNH orCStransitions. A3-component
3
andAugust2008(proposalsAGBT07C-016andAGBT07C- modelthusappearstoprovideagoodfittothedata;however,
054), using the Ku- and Ka-band receivers, respectively. for completeness, results from the 4-componentfit will also
A spectrum in the redshifted H2CO 000-101 line was ob- bementionedbelow.
tained in July 2008 with the GBT Q-band receiver, as part Forthecoupled3-componentmodel,thenumberoffitpa-
of an absorption survey of the z ∼ 0.685 galaxy (pro- rametersis16,threeredshifts,threelinewidths,nineoptical
posalAGBT07C-054). Bandpasscalibrationwascarriedout depthsintheNH ,CS,andH COlines,andthevelocityoff-
3 2
viabeam-switchingfortheNH3 observations,andwithsub- set betweenthe inversionandrotationaltransitions. The pa-
reflectornoddingforthehigher-frequencyCSandH2COob- rametersofthebest3-componentfitarelistedinTable1;the
servations. Twopolarizationswereusedfortheobservations best-fitvelocityoffsetis∆V =(−0.36±0.10)km/s,withthe
of the NH3 (Ku-band)and H2CO (Q-band)lines, and a sin- NH3 linesblueshiftedrelativeto therotationallines. A sim-
gle Ka-band polarization for the CS line. The total observ- ilar result is obtained from the best-fit 4-component model,
ing times were 6 hours (NH3), 1.5 hours (CS) and 3 hours ∆V =(−0.39±0.11)km/s.Similarresultsarealsoobtained
(H2CO),with the NH3 observationssplitintotwo observing fromcarryingout3-componentfits to theNH3 andCS lines
sessions, in January and August 2008. Standard procedures (i.e. without including the H CO line), and to the NH and
2 3
inthepackagesDISH(fortheNH3 lines)andGBTIDL(for H2COlines(i.e. withouttheCSline).
the CS andH2CO lines) were used to analyse the data. The To obtain an estimate of systematic effects, a similar 3-
final NH3, CS, and H2CO spectra are shown in Figs. 1[A], componentfit was also carried out to the CS and H2CO ro-
[B] and [C]; these have velocityresolutionsof ∼ 0.26, 0.12 tational lines alone (i.e. without including the NH inver-
3
and2.8km/s, respectively(afterHanning-smoothingandre- sionlines). ThisyieldedavelocityoffsetofδV = (0.029±
sampling),androot-mean-squarenoisevaluesof∼ 0.00082, 0.068)km/s, betweentheCSandH2CO lines. The1σ error
0.0097 and 0.0026, in optical depth units, per independent obtained here, when comparingtwo rotational lines, will be
velocitychannel. usedasanestimateofthesystematicerrorduetolocalveloc-
AGBTKu-bandsearchwasalsocarriedoutfortheCCS1- ityoffsetsbetweendifferentspeciesintheabsorber.
0 transition at z ∼ 0.685; no absorptionwas detected at the The fractional change in the proton-electron mass
redshiftedCCS line frequency,with a 3σ opticaldepthlimit ratio µ is related to the measured velocity offset
of ∼ 0.0016per4.2 km/schannel. The K- and Ku-bandre- between inversion and rotational lines ∆V by the
ceivers were further used to search for redshifted NH3 (1,1) expression (Flambaum&Kozlov 2007) [∆µ/µ] =
absorptionfromtwootherredshiftedmolecularabsorbers,at 0.289[(z −z )/(1+z¯)] ≈ 0.289[∆V/c], where
inv rot
z ∼ 0.247 towards B1413+135 (Wiklind&Combes 1997) z and z are, respectively, the inversion and rotational
inv rot
and z ∼ 0.674 towards B1504+377 (Wiklind&Combes redshifts, and z¯is their average. Our final velocity offset is
1996a), with no detected absorption in either case. The ∆V =[−0.36±0.10(stat.)±0.068(syst.)]km/s;thisyields
3σ optical depth limits were 0.00068 per 4 km/s channel [∆µ/µ] = [−3.47 ± 0.96(stat.) ± 0.66(syst.)] × 10−7.
(B1413+135)and0.00061per4km/schannel(B1504+377). Addingthestatisticalandsystematicerrorsinquadrature,we
Thetestforchangesintheproton-electronmassratioµwas obtain[∆µ/µ] = (−3.5±1.2)×10−7, betweenz ∼ 0.685
carriedoutthroughasimultaneousfittotheNH (1,1),CS1-
3 andthepresentepoch.
0andH CO0 -1 spectra,usingthepackageVPFIT2.The
2 00 01
velocity structure in all optically-thin lines was assumed to 3. DISCUSSION
An excellent summary of the systematic effects inherent
2http://www.ast.cam.ac.uk/˜rfc/vpfit.html in the comparison between rotational and inversion lines in
Constrainingchangesintheproton-electronmassratio 3
FIG.1.—GBTspectraintheredshifted[A]NH3(1,1),[B]CS1-0and[C]H2CO000-101transitionsfromthez∼0.685absorbertowardsB0218+357.The
upperpanelsshownormalizedlinedepthineachtransitionplottedagainstvelocity,inkm/s,relativetoaheliocentricredshiftofz=0.684676;the3-component
fitisoverlaidoneachspectrum. Thelowerpanelsshowtheresidualsfromthespectraaftersubtractingoutthejoint3-componentfit;theseareconsistentwith
noise.
the z ∼ 0.685 absorber is given by Murphyetal. (2008a). (2008a) were at very different frequencies, ∼ 14 GHz and
These include the following: (1) the assumption that dif- ∼ 106 GHz; changesin the backgroundsource morphology
ferent transitions have the same number of spectral compo- could thus result in different sightlines in the different tran-
nents, and at the same redshifts, (2) the background source sitions. The NH and HCO+/HCN observationswere sepa-
3
morphologyis frequency-dependent,implying that the NH ratedbyafewyears,implyingthattemporalvariabilityinthe
3
and rotationaltransitionsmightarise along slightly different source morphology could also be an issue, especially given
sightlines,(3)thebackgroundsourcefluxdensity(andhence that saturated transitions were used in the analysis. Finally,
morphology) varies with time, so observations at different the NH spectra were of too low signal-to-noise ratio (S/N)
3
epochsmightprobedifferentsightlines,(4)theassumptionof todetecttheNH hyperfinestructureandtotestfornon-LTE
3
LTEfortheNH hyperfinestructure,(5)saturationeffectsif effects.
3
highly-saturatedlines[e.g.theHCO+andHCNlinesusedby Most of the above issues have been directly addressed in
Murphyetal.(2008a)]areused,and(6)localvelocityoffsets the present work. All three transitions used in the analy-
between the species giving rise to the transitions. As noted sis are unsaturatedand havebeen observedat highS/N, and
byMurphyetal.(2008a),alltheseeffectscouldyieldsignif- with the same telescope. The two outlying NH hyperfine
3
icant contributions to their systematic errors. For example, components(at ±19.5km/srelative to the strongestcompo-
theinversionandrotationaltransitionsusedbyMurphyetal. nent) in the NH (1,1) line have also been clearly detected
3
4 Kanekar
Component Velocityoffset Redshift FWHM Linedepth×100
km/s km/s NH3 CS H2CO
1 0.6846935(2) 3.99±0.13 0.496±0.060 13.83±0.78 15.61±0.84
2 (−0.36±0.10) 0.6846858(10) 10.60±0.45 0.734±0.026 4.39±0.33 3.00±0.39
3 0.6846214(7) 3.53±0.33 0.128±0.032 2.84±0.28 5.17±0.37
TABLE1
PARAMETERSOFTHEBEST3-COMPONENTVOIGTPROFILEFITTOTHENH3(1,1),CS1-0ANDH2CO000-101SPECTRA.THESECONDCOLUMN
CONTAINSTHEBEST-FITVELOCITYOFFSETBETWEENTHEROTATIONALANDINVERSIONLINES;NOTETHATASINGLEVELOCITYOFFSETWAS
ASSUMEDFORALLSPECTRALCOMPONENTS.THEREDSHIFTSOFCOLUMN(3)AREINTHEHELIOCENTRICFRAME,WHILETHELINEDEPTHS(×100),
LISTEDINTHELASTTHREECOLUMNS,HAVEBEENNORMALIZEDBYTHESOURCECONTINUUMATEACHOBSERVINGFREQUENCY.
(seeFig.1[A]).AsnotedbyMurphyetal.(2008a),non-LTE addressed here is time variability in the background source
effects resulting in hyperfine “anomalies” should cause the morphology, which might yield different sightlines through
satellite hyperfine components (with ∆F1 6= 0, where F1 theabsorbingcloudsatdifferentepochs[Murphyetal.2008a;
is the quadrupolequantumnumber)to have differentoptical see Muller&Gue´lin (2008) for the z ∼ 0.886 lens towards
depths.Noevidenceforsuchnon-LTEconditionsisapparent B1830−210]. Unfortunately, the redshifted NH3, CS and
inthe±19.5km/ssatellitehyperfinecomponentsinFig.1[A]; H2COtransitionstowardsB0218+357requiredifferentGBT
theopticaldepthsarefoundtoagreewithinthenoise. receiversandcannotbeobservedsimultaneously.Thepresent
We note, finally, that the systematic error of 7.6 × 10−7 NH3, CS and H2CO observations were carried out between
in the result of Murphyetal. (2008a) containstwo contribu- JanuaryandAugust2008;thepossibilitythattheweakoffset
tions: (1)7×10−7 becausespectralcomponentsdetectedin betweentheinversionandrotationallinesarisesduetosmall
theHCO+ andHCNspectramaynotbedetectedintheNH changesinthesightlinethuscannotberuledout. Further,the
3
spectra,dueeithertothe largefrequencydifferencebetween agreementbetweenCSandH COvelocitiesdoesnotruleout
2
the inversionandrotationlinesor to the factthatthe HCO+ thepossibilitythatnitrogen-bearingspecieslikeNH ariseat
3
and HCN lines are optically thick, and (2) 3×10−7 due to different velocities than carbon-bearing species like CS and
the possibility of non-LTE effects in the NH spectra. Our H CO.Thiscanonlybetestedbyusingrotationaltransitions
3 2
choiceofrotationallinesandthehighersensitivityofourNH ofothernitrogen-bearingspecies(e.g. HC N,CH CN,etc).
3 3 3
spectraimpliesthatneitherofthesearesignificantsourcesof While there are two possible sources of systematic error
systematicerrorinthepresentanalysis. that we are as yet unable to quantify, the present data show
Lisztetal.(2006)findthatNH3 columndensitiescorrelate nostatistically-significant(≥3σ)evidenceforchangesinthe
bestwithCSandH2COcolumndensitiesinGalacticdiffuse proton-electronmassratio. Our3σupperlimitonchangesin
clouds;CSandH2COarethuslikelytobethebestrotational µ is [∆µ/µ] < 3.6×10−7, between z ∼ 0.685and z = 0
transitionsfortheinversion/rotationcomparison,asthecorre- (alookbacktimeof6.2Gyrs).Forcomparison,Murphyetal.
lationin columndensitiessuggeststhatthe three speciesare (2008a)obtained[∆µ/µ]<1.8×10−6(2σ)inthez ∼0.685
likelytoariseinthesamepartofagascloud.Galacticabsorp- absorbertowardsB0218+357,whileHenkeletal.(2009)ob-
tion has also been detected in all three species towards two tained [∆µ/µ] < 1.4 × 10−6 (3σ) in the z ∼ 0.886 ab-
quasars, B0355+508 and B0415+379 (Liszt&Lucas 1995; sorbertowardsB1830−210,withbothresultsbasedoninver-
Lucas&Liszt 1998; Lisztetal. 2006); both sightlines show sion/rotationcomparisons. Note, however, that Henkeletal.
two componentsin all species, with line velocities agreeing (2009)usedsingle-GaussianfitsfortheNH andHC Nlines
3 3
within0.2km/s[seeTable1ofLiszt&Lucas1995,Table6of towardsB1830−210,althoughitisclearfromtheprofilesof
Lucas&Liszt1998andTableA1ofLisztetal.2006]; local other unsaturated lines (e.g. CS) that at least three absorb-
velocityoffsetsbetween thespecies thusappearto besmall. ing“clouds”arepresentalongthesightline.Further,theGBT
Further,therotationalandinversionlinefrequenciesaremuch spectrain the strongest[(1,1), (2,2)and(3,3)]NH lines to-
3
closerherethanin the comparisonof Murphyetal. (2008a), wardsB1830−210wereseverelyaffectedbyradiofrequency
withthe redshiftedNH3, CS, andH2CO linesat∼ 14GHz, interference (see Fig. 1 of Henkeletal. 2008). The effect
∼ 29 GHz and ∼ 43 GHz, respectively. Changes in source of these issues on the results of Henkeletal. (2009) is un-
morphology with frequency are thus a less important issue clear, but the error budget is likely to increase. At higher
here than in the analysis of Murphyetal. (2008a). A direct redshifts, the best published constraint on changes in µ is
test comes from the comparison between the two rotational that of Kingetal. (2008): [∆µ/µ] < 6.0×10−6, using H2
lines, whosefrequenciesdifferbya factorof∼ 1.5, compa- lines (but see Wendt&Molaro 2011). The present result,
rabletotheratiooftheCSandNH3 frequencies(∼ 2). The [∆µ/µ] < 3.6×10−7 (3σ) at z ∼ 0.685, is thus the most
CS-H2CO comparison also provides an estimate of the sys- sensitiveconstraintontemporalchangesinµatanyredshift,
tematic error due to local velocity offsets between different byafactor&5.
speciesintheclouds. ThistestfoundtheCSandH CO line To compare this result with those from laboratory stud-
2
redshiftsto agreewithin the noise; the 1σ errorin thiscom- ies, it is necessary to assume a model for the variation of
parisonhasbeenusedtoquantifythesystematicerrordueto µ with time. For linear variation, the present result yields
both local velocity offsets and differing background source µ˙/µ < 5.6×10−17 per year, morethan an orderof magni-
morphologyatthedifferentlinefrequencies. Finally,similar tude better than the best (model-dependent)laboratory con-
velocityoffsets(consistentwithintheerrors)wereobtainedin straintonchangesinµ(Rosenbandetal.2008).
theindependentcomparisonsbetweentheNH andCSlines, In conclusion, we have used the GBT to obtain high
3
andtheNH andH COlines. S/N spectra in the NH (1,1), CS 1-0 and H CO 0 -
3 2 3 2 00
A source of systematic effects that could not be directly 101 transitions from the z ∼ 0.685 absorber towards
Constrainingchangesintheproton-electronmassratio 5
B0218+357. A comparison between the redshifts of the in- I thankBob Carswelland MichaelMurphyfor muchhelp
versionandrotationallinesyieldsavelocityoffsetof∆V = with using VPFIT for the Voigt-profile fitting, Carl Bignell
[−0.36±0.10(stat.)±0.068(syst.)]km/s,withtheNH3lines andBobGarwoodforhelpintheschedulingoftheGBTob-
blueshiftedrelativetotherotationalones.Twosourcesofsys- servations and the GBT data analysis, and Dave Meier for
tematicerrorremaintobequantified,arisingfrom(1)velocity permission to use the H CO line detected in our survey of
2
offsetsbetweennitrogen-bearingandcarbon-bearingspecies, B0218+357forthisproject.Ialsoacknowledgesupportfrom
and(2)timevariabilityinthebackgroundsourcemorphology, the Departmentof Science and Technology,India, via a Ra-
whichmightyielddifferentsightlinesatdifferentepochs.We manujanFellowship. TheNationalRadioAstronomyObser-
findnostatistically-significant(≥3σ)evidenceforchangesin vatoryisoperatedbyAssociatedUniversities,Inc,underco-
µ,withthe3σ constraint[∆µ/µ] < 3.6×10−7overalook- operativeagreementwiththeNSF.
backtimeof6.2Gyrs. Thisisthestrongestpresentconstraint
ontemporalchangesintheproton-electronmassratio.
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