Results from a High-Sensitivity Search for Cosmic Axions

VOLUME 80, NUMBER 10 P H Y S I C A L R E V I E W L E T T E R S 9 MARCH 1998

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Results from a High-Sensitivity Search for Cosmic Axions

C. Hagmann, D. Kinion, W. Stoeffl, and K. van BibberLawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550

E. Daw, H. Peng, and Leslie J RosenbergDepartment of Physics and Laboratory for Nuclear Science, Massachusetts Institute of Technology, 77 Massachusetts

Cambridge, Massachusetts 02139

J. LaVeigne, P. Sikivie, N. S. Sullivan, and D. B. TannerDepartment of Physics, University of Florida, Gainesville, Florida 32611

F. NezrickFermi National Accelerator Laboratory, Batavia, Illinois 60510-0500

Michael S. TurnerTheoretical Astrophysics, Fermi National Accelerator Laboratory, Batavia, Illinois 60510-0500

Departments of Astronomy & Astrophysics and Physics, Enrico Fermi Institute, The University of Chicago,Chicago, Illinois 60637-1433

D. M. Moltz and J. PowellLawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720

N. A. GolubevInstitute for Nuclear Research of the Russian Academy of Sciences, 60th October Anniversary Prospekt 7a,

117 312 Moscow, Russia(Received 5 November 1997)

We report the first results of a high-sensitivitys,10223 Wd search for light halo axions through theirconversion to microwave photons. At the 90% confidence level, we exclude a Kim-Shifman-Vainshtein-Zakharov axion of mass2.9 3 1026 to 3.3 3 1026 eV as the dark matter in the halo of our galaxy.[S0031-9007(98)05494-5]

PACS numbers: 95.35.+d, 14.80.Mz, 98.35.Gi

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The dynamics of galaxies and of clusters of galaxieas well as their peculiar motions, imply that most of thmass of the Universe is in an unseen form, called “damatter.” The amount of dark matter inferred is at leas20% of the critical density, and likely much more [1].Because the synthesis of the light elements in the big barestricts baryons to contribute no more than 10% of thcritical density, a large nonbaryonic component is requireThe development of structure in the Universe—galaxieclusters, and superclusters—and the anisotropies ofcosmic background radiation also support this conclusio

The axion is a well-motivated particle dark matter candidate, arising in models where the strong-CP problemsolved by the Peccei-Quinn mechanism [2]. The axiomass is constrained by laboratory experiments and astphysical limits to lie between1026 and 1023 eV, withlower masses preferred if axions provide the bulk of thcritical density [3].

If the dark matter is “cold” (small velocity dispersion),as is indicated by studies of structure formation, galatic halos are comprised primarily of cold dark matteparticles. Because dark matter axions were produceda coherent process in the early universe, they are co

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[4]. Modeling of the Milky Way Galaxy indicates a local halo densityrhalo of 0.45 GeV cm23 (about 7.5 3

10225 g cm23) [5], which implies an enormous local density O s1014 cm23d of axions if they are the dark matter. The velocity distribution of dark matter particlesexpected to be approximately Maxwellian, with a dispesion of kb2l1y2 . 270 kmysec [6]. There could also benarrow peaks in the velocity distribution from dark mater particles that have recently fallen into the Galaxy ahave yet to thermalize [7]. Because of its two-photcoupling Lagg 2gagga $E ? $B, an axion can converto a single photon in the presence of a magnetic fi[8]. Here,gagg ggaypfa, fa is the axion decay con-stant, the axion massma . 6 meV s1012 GeVyfad, andgg is a model-dependent coefficient of order unity. In twpopular models of the axion,gg 20.97 [Kim-Shifman-Vainshtein-Zakharov (KSVZ)] and 0.36 [Dine-FischleSrednicki-Zhitnitskii (DFSZ)] [2].

In a static magnetic field, the energy of the photequals that of the converted axion:Eg Ea ma 1

mab2y2 maf1 1 O s1026dg. The conversion procesis resonantly enhanced in a high-Q cavity with resonfrequencyf0 tuned toEg, with power given by [8]

© 1998 The American Physical Society 2043


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where V is the volume of the cavity,QL is the loadedquality factor of the cavity,B0 is the central magnitudefield strength,ra is the local axion density, and1yQa ,1026 is the width of the axion energy distribution. Themode-dependent form factorC is of order unity for theTM010 mode used in our search and falls off rapidly fohigher order modes. For the parameters of this experimand the KSVZ model,P , 5 3 10222 W .

Because the axion mass is unknown, the cavity resnant frequency must be tuned. When the TM010 resonantfrequency is close to the axion mass, the conversionaxions to photons produces a narrow peak of fractionwidth ,1026 in the cavity power spectrum. The noisbackground is characterized by an effective system teperatureTs Tc 1 Ta, whereTc is the cavity physicaltemperature andTa is the amplifier noise temperature.

Figure 1 is a schematic diagram of the axion detectwhich is located at LLNL [9]. The magnet is a superconducting solenoid of 7.6 T central field. The cylindricacavity (50 cm i.d., 100 cm long) is constructed of stainlesteel plated with copper and subsequently annealed. Ttemperature of the cavity isTc , 1.3 K. The reso-nant frequencyf0 of the empty cavity is 460 MHz.The unloadedQ, including losses in the tuning rods, is,200 000, the limit set by the anomalous skin depth ocopper. Two copper tuning rods, each 8 cm in diametrun the full length of the cavity. The cavity is tuned bmoving the rods radially between the wall and the centThe cavity is normally evacuated, but can be filled witliquid helium to shift the frequency from the vicinity ofmode crossings. There are two coupling ports in the tof the cavity, one weakly coupled and the other of variabcoupling strength. Power is extracted from the variabport through a50 V transmission line, which is 50 cmlong, to a directional coupler and amplifier chain. Thweakly coupled port and the 30 dB directional coupleprovide for transmission and reflection measurementscavity parameters. The coupling at the variable portadjusted to near critical.

The first- and second-stage amplifiers are balancGaAs high-electron-mobility transistor devices built bthe National Radio Astronomy Observatory (NRAOThey are cooled to the cavity temperature and are chacterized by noise temperatureTa , 4.5 K, power gainof G , 17 dB, and power reflection coefficient from theinput of ,30 dB [10]. The amplifier noise temperatureis measured by varying the physical temperature of tcavity and extrapolating the amplifier output to zerphysical temperature.

After 35 dB of further amplification at room temperature, the signal is down-converted to 10.7 MHz by aimage-rejection mixer. An eight-pole crystal filter setthe 30 kHz measurement bandwidth and prevents imapower from entering the second mixing stage. The sign

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is then down-converted a second time, in effect shifting thcavity resonant frequency to 35 kHz.

A commercial fast Fourier transform spectrum analyzethen generates the “medium-resolution” power spectrumDuring each 80-sec run, 10 000 subspectra are measuand averaged, resulting in a 400 point, 125 Hzypointpower spectrum. This is well matched to a search fothe Maxwellian component of the halo, which should beabout six channels wide.

The analog output is also applied to a six-pole filtefollowed by a third mixing stage centering the cavityresonant frequency at 5 kHz. This signal is processed ba commercial ADC/DSP PC board, yielding the “high-resolution” power spectrum. There is no averaging, burather one 250 000 point, 0.02 Hzypoint power spectrumis generated. This is well matched to a search for finstructure having fractional width,O s10211d or less in thepower spectrum. If any appreciable fraction of the axionare in a narrow-velocity line, it would be detected withhigh signal-to-noise ratio. A cesium clock serves as thfrequency reference for both receivers.

After each 80-sec run, the cavity frequencyf0 is tunedupwards by 2 kHz, the loaded cavity quality factorQL

is measured, and another run initiated. The dead timassociated with tuning and measuring cavity parameteis about 4 sec per run. The form factorC is calculatedby a computer simulation of the cavity at each frequencyEach frequency range is swept out, then the proceduis repeated at least twice more. Regions in frequencwhere TE or TEM modes cross the TM010 mode areexamined by filling the cavity with liquid helium, thusshifting the mode-crossing frequency down by 3%. Thoverall live time of the experiment has been well over 90%since the beginning of data taking. Of the approximatel4.2 3 105 spectra recorded for this analysis, 6058 wereliminated due to anomalously large cavity frequencshifts or pressure jumps, typically related to cryogen fillor other disturbances.

During off-line data processing, the middle 200 fre-quency bins of each 400 point spectrum are divided bthe eight-pole crystal filter response. The resulting powespectrum varies slowly with frequency by,1 dB acrossthe spectrum due to noise from sources in the amplifiepropagating backwards along the transmission line and rflecting from the cavity coupling. To obtain a flat, cor-rected power spectrum, we remove this slow variatiousing a five-parameter equivalent circuit model.

Because the typical 2 kHz tuning step is smaller thathe 30 kHz crystal filter bandwidth, and because threor more sweeps are made over the whole frequencrange, each 125 Hz bin appears in at least 45 spectThese spectra are linearly combined with a weightinthat accounts for theB0, Ts, C, Q, f 2 f0 appropriate foreach. The result is a single spectrum of nearly106 pointsbetween 701–800 MHz. Figure 2 shows (a) the expectedsignal from KSVZ axions, (b) the noise backgroundwere the axion signal to be distributed over six channel


FIG. 1. Schematic diagram of the axion detector.

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and (c) the noise background were the axion signal toconfined to one channel. Figure 3 shows the deviatof the single channel power from the thermal meanall of the data taken. The distribution is consistent wthermal (Gaussian) noise out to5s. This is an importantvalidation of our understanding of the experiment.

Candidates for further examination are those sin125 Hz channels with a3.3s power excess (538 candidates), or the sum of any six adjacent 125 Hz channwith a 2.25

p6s power excess (6535 candidates). The

candidates were then rescanned to the same power senity as the first spectrum. Of the six-channel (one-channcandidates, 23 (6) persisted, i.e., appeared independein the rescan. Of those, 8 (4) were at the same frequeas known external rf sources. The remainder developower in the tails of the cavity Lorentzian instead of nethe peak as would the axion. This behavior is expecfor external interference introduced through the calibratports and reflecting off of the cavity input back into th

FIG. 2. (a) The expected signal from KSVZ axions. (b) Thenoise background for an axion signal distributed overchannels. (c) The noise background for an axion signconfined to one channel.

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amplifier. The few persistent candidates were rescanafter terminating calibration lines leading into the cavitno candidates survived all scans.

Figure 4 shows the axion couplings and massescluded at the 90% confidence level by this analysis forions with the expected Maxwellian velocity distributionAt the 95% (68%) confidence level, the value ofg2

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excluded is approximately1.6s1.0d 3 10219 GeV22yeV2.Also shown are KSVZ and DFSZ model predictions. Idicated on the inset are the regions excluded by earmicrowave cavity experiments [11,12]. The present eperiment is more than 2 orders of magnitude more ssitive, and is the first to exclude a well-developed aximodel (KSVZ) at a realistic density over any mass ranThe significance of this result, however, is not just t

FIG. 3. The distribution of the deviation of single channnoise power from the thermal mean (in units of standadeviation s), in each 0.1s interval, for all of the datataken. The curve shows the theoretical expectation (therGaussian noise treated as input to the analysis chain).slight deviation from Gaussian shape is introduced by the firesponse.

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FIG. 4. Axion couplings and masses excluded at the 90% confidence level by this experiment. Also shown are KSVDFSZ model predictions. Indicated on the inset are the regions excluded by earlier microwave cavity experiments: RBF inRochester-BNL-Fermilab [11]; UF indicates University of Florida [12]. All results are scaled tora rhalo.

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exclusion of a given axion model over a narrow marange at the most probable local cold dark matter dens[within the full width at half maximum likelihood rangeof s4.5 12d 3 10225 g cm23 [5] ]. Equally important,the sensitivity of the microwave cavity scheme has bebrought into the region of interest, i.e., where the axiomight plausibly be discovered.

The high-resolution channel is analyzed similarly. Thpower spectra are binned on-line at resolutions 0.00.16, and 1.3 Hz, for which candidates were defineas those peaks with more than15s, 8s, and 5s ex-cess power, respectively. After rescanning candidapeaks and eliminating external noise peaks, no cadidates remained. This procedure resulted in upppower limits near 3.3 3 10223 W (0.02 Hzychannel),5.0 3 10223 W (0.16 Hzychannel), and8.8 3 10223 W(1.3 Hzychannel). We further searched for coincidencbetween medium-and high-resolution candidates, aafter excluding obvious rf sources, found none.

In conclusion, for the first time, sufficient sensitivity habeen achieved to detect KSVZ axions if they compristhe dark matter of our own galactic halo. Based upoour first results, we exclude at 90% confidence a KSVaxion of mass between 2.9 and3.3 meV, assuming haloaxions have a Maxwellian velocity distribution. If asignificant fraction of halo axions are distributed infew narrow peaks, weaker axion two-photon couplingare excluded. Promising developments in amplifier amagnet technologies may soon extend the sensitivity ofexperiment by more than an order of magnitude, permittia search for axions that couple more weakly (e.g., DFSat lower halo densities.

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The authors thank R. Bradley of NRAO for sharing hamplifier expertise. This research is supported by the UDepartment of Energy under Contracts No. W-7405-EN-048, No. DE-AC03-76SF00098, No. DE-AC0276CH03000, No. DE-FC02-94ER40818, No. DE-FG097ER41029, and No. DE-FG02–90ER40560, andNational Science Foundation Grant No. PHY-9501959

[1] See, e.g., A. Dekel, D. Burstein, and S. D. M. White,Critical Dialogs in Cosmology,edited by N. Turok (WorldScientific, Singapore, 1997); J. Willick, M. A. StrausA. Dekel, and T. Kolatt, Astrophys. J.46, 629 (1997).

[2] See, e.g., J. E. Kim, Phys. Rep.150, 1 (1997); H.-Y.Cheng,ibid. 158, 1 (1988).

[3] See, e.g., M. S. Turner, Phys. Rep.197, 67 (1990).[4] J. Preskill, M. Wise, and F. Wilczek, Phys. Lett. B120,

127 (1983); L. Abbott and P. Sikivie,ibid. 120 133(1983); M. Dine and W. Fischler,ibid. 120, 137 (1983).

[5] E. I. Gates, G. Gyuk, and M. S. Turner, Astrophys. J.449,123 (1995).

[6] M. S. Turner, Phys. Rev. D.42, 3572 (1990).[7] P. Sikivie, I. I. Tkachev, and Y. Wang, Phys. Rev. Le

75, 2911 (1995).[8] P. Sikivie, Phys. Rev. Lett.51, 1415 (1983); L. Krauss

et al., ibid. 55, 1797 (1985); P. Sikivie, Phys. Rev. D32,2988 (1985).

[9] More details may be found in C. Hagmannet al., Nucl.Phys.B51, 209 (1996).

[10] E. Daw and R. F. Bradley, J. Appl. Phys.82, 1925 (1997).[11] S. DePanfiliset al.,Phys. Rev. Lett.59, 839 (1987); W. U.

Wuensch et al., Phys. Rev. D40, 3153 (1989). Wechanged these limits to 90% confidence.

[12] C. Hagmannet al., Phys. Rev. D42, 1297 (1990).

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Results from a High-Sensitivity Search for Cosmic Axions