Mhz Gravitational Wave Constraints with Decameter Michelson Interferometers

Home , Holometer

arXiv:1611.05560v2 [astro-ph.IM] 9 Jun 2017 aaaqiiinsse n aaaayi ieie Next, pipeline. analysis data and system acquisition data holes black primordial for [15]. ranges mass constrained least pt 10 to up rqec ad h asrneo lc oebinaries hole black of this is search range in this mass in lie probed The non-chirping frequencies orbital resolved, band. whose frequency individually binaries on hole black constraint then and on a constraint background, a as stochastic as first isotropic the ways: statistically two a Therefore, in here analyzed [14]. will is and radiation data today Addition- gravitational exist emitting still [13]. may be universe relics black individual early those primordial the ally, in relics as other produced and such possibly [12] loops sources (super)-string cosmic individual holes[11], super-position many a of from background stochastic unresolved 10]. [9, magnitude frequency of high orders on by waves using results gravitational MHz, earlier [8]. gravitational 13 Holometer exceeds for Fermilab to sensitivity the search up Our instrument, MHz new a 1 a report from from band data we broad [1– paper, a frequencies in at this waves these operating In at sources either for 7]. are search a to experiments that designed Current or less frequencies kHz. at few radiate strongest The sources sources. of astrophysical of range variety a broad probe a can from experiments measurements direct and quencies ∗ orsodn uhr:[email protected] : author Corresponding hspprbgn ihadsrpino h instrument, the of description a with begins paper This oeta ore tteehg rqece nld an include frequencies high these at sources Potential fre- all at exist to predicted are waves Gravitational H rvttoa aeCntanswt eaee Michels Decameter with Constraints Wave Gravitational MHz 26 hyn Kwon Ohkyung ihtesm aae.Ti soeo the of one is This dataset. same the with g nasohsi akruda 8 zrslto.Te3 The resolution. Hz 382 at background orde stochastic many a a by on experiments sensitivity wave the gravitational exceeds frequency high measurement This dataset. 130-hr nefrmtr.Sri estvt civdi etrth better is achieved sensitivity Strain interferometers. nrydniynraie otecouedniy agsfr ranges density, closure the to normalized density energy PH) hr r odtcal oohoai BB ntem the in PBHBs ne monochromatic for search detectable a is no dataset are same the There from (PBHB). result Another MHz. 13 ewe h at n h on rjcin o hr searc chirp a for 0 Projections to range moon. the mass and earth the between ytmsace o BB lc iiso hi contributio their prim on of limits range place mass PBHBs constrained for poorly searches a system on limits placing for e eetr h emlbHlmtr ossso separat of consists Holometer, Fermilab the detector, new A 1 .INTRODUCTION I. em ainlAclrtrLaboratory; Accelerator National Fermi 6 ascuet nttt fTechnology; of Institute Massachusetts ao .Chou S. Aaron oahnRichardson Jonathan 4 adritUniversity; Vanderbilt ∼ 10 3 , . 5 59 21 oetLanza Robert , ihteptnilt test to potential the with g − 2 . 5 1 ihr Gustafson Richard , × 10 25 2 hi Stoughton Chris , n itne u oJptr hsrsl rsnsanwmet new a presents result This Jupiter. to out distances and g TeHlmtrCollaboration) Holometer (The 5 3 oe dacdIsiueo cec n Technology; and Science of Institute Advanced Korea , 6 hn .Larson L. Shane , 2 7 nvriyo Michigan; of University otwsenUniversity; Northwestern 2 ri Hogan Craig , 1 edn lr-ihvcu ytm.Dtiso h setup the inde- of Details in enclosed systems. vacuum mirrors) ultra-high end pendent two power- and (beamsplitter, mirror, optics recycling core and separate electronics, with lasers, equipped is elec- interferometer and inter- Each mechanically, the tronically. optically, cross-talk, isolated or- from are In outputs, ferometers backgrounds minimize signal to achieved. their der is cross-correlating performance and sub-shot-noise-limited m 0.635 by fasnl nefrmtrb nodro antd to magnitude of order an by interferometer ∼ single a sensitivity which of displacement kW, 2 shot-noise-limited aproximately to the 1W improves of power laser input the rudadtenro-ie erhfrpioda black back- presented. primordial wave are for binaries gravitational search holes narrow-lined stochastic the the and ground for results the mtrweeteamlnt ieec smaue as measured interfer- is the difference of length output arm ∆ the the where at light ometer interferometer destructive the returning the at The exits mirror power-recycling input. res- the interferometer’s is by beam- light enhanced interfering the onantly constructively at the interferes returning where coherently Light splitter, mirrors end arms. the 39-meter-long from the beamsplitter, down the input by sent paths the and orthogonal at two inter- into laser each divided 1064nm is In wave continuous space. in a a orientation ferometer, same half the by with separated meter, interferometers, Michelson recycled amn Tomlin Raymond , L yoeaigtoietclitreoeesseparated interferometers identical two operating By h ooee scmrsdo w dnia power- identical two of comprised is Holometer The σ 2 n10 an × ≡ pe ii nΩ on limit upper 7 , 8 m5 om 10 L e McCuller Lee , dfeunyrnemd rmprevious from made range frequency nd so antd.Cntansaeplaced are Constraints magnitude. of rs otettldr atrfraction. matter dark total the to n − x − rilbakhls diinly solar Additionally, holes. black ordial ihtesm aae nrae the increases dataset same the with h 21 − 18 . / 1 e dnia 9mtrMichelson 39-meter identical yet e 6 rypioda lc oebinaries hole black primordial arby L √ , meters 3 × y rtayKamai Brittany , zbten1t 3Mzfo a from MHz 13 to 1 between Hz h oe-eyln ehiu increases technique power-recycling The . I H HOLOMETER THE II. 10 s ag 0 range ass .TeInstrument The A. 12 3 / GW nvriyo Chicago; of University t1Mzt 8 to MHz 1 at 1 8 √ anrWeiss Rainer , de Planetarium Adler 3 Hz. h rvttoa wave gravitational the , , 6 tpa .Meyer S. Stephan , nInterferometers on . 3-3 - 83 1 , 3 . 4 , . 4 5 × , 6 ∗ × 10 10 15 hod 21 at g 3 , 2 appear in PhD theses [27–30] and the Holometer instru- 34,079, which has a frequency resolution of 382 Hz. After ment paper [? ]. 1.4 seconds, 1,400 milli-second power- and cross-spectra At MHz frequencies, photon shot noise is the domi- are averaged together, GPS-time-stamped and recorded nant noise source, which is uncorrelated between the two in the final hierarchical data formatted (hdf5) file. interferometers. Therefore, cross-correlating the output Data vetoes were implemented to ensure that contami- of the interferometers increases the sensitivity as 1/√N, nated data (i.e. from large RFI spikes) were not included for N samples. This allows us to surpass the shot noise in the averaging. This procedure repeats until the end limited sensitivity of a single interferometer and hunt for of data acquisition. The 1-second averaged spectra were signals far below the baseline shot noise level. Conversely, calibrated against a 1kHz length dither to establish the when a correlated signal is present in both detectors, the conversion from V/Hz to m/Hz. averaged cross-spectrum will converge to the level of the signal after a sufficient number of averages have been recorded. Extensive campaigns were conducted to verify III. STOCHASTIC GRAVITATIONAL WAVE that there are no unknown correlated noise sources above BACKGROUND 1 MHz. Unknown correlated noise sources were characterized through extensive measurements before and after A. Data Analysis pipeline data taking campaigns. Additionally, laser phase and in- tensity noise was bounded using dedicated monitors dur- To place constraints on the energy density of the ing the runs. stochastic gravitational wave background in the MHz frequency range, the entire 130-hour dataset was averaged to increase the strain sensitivity. The fully aver- B. Dataset aged strain spectral density is in Figure 1. Each interferometer’s PSD is shown by the green traces, the CSD The 130-hour dataset used in this analysis was col- between both interferometers is shown by the blue trace, lected from 15 July 2015 to 15 August 2015 at Fermi the error on the CSD is shown by the black trace. The National Accelerator Laboratory. First, this dataset is 2 orders of magnitude gain in sensitivity between the analyzed to place constraints on the energy density of power- and cross- spectral density are from averaging to- stochastic gravitational wave backgrounds. Then utiliz- gether complex numbers. The CSD error has the scaling ing the same dataset, a different analysis is done to place as pPSD1PSD2/N where N is the number of milli- constraints on primordial black hole pairs. second≃ spectra used in the averaging. In practice, this The design of the Holometer data acquisition sys- was independently calculated from the sample variance tem differs from other gravitational wave experiments of millisecond CSDs in 5-min averaged batches. The final such as Pulsar Timing Arrays (PTAs), Laser Interfer- CSD error averages together the 5-min CSD errors, which ometeric Gravitational-Wave Observatory (LIGO), and was verified to directly follow the prediction of where the Laser Interferometric Space Antenna (LISA) [1–7]. These CSD should be given two Gaussian noise source (such as other experiments continuously store time domain data photon shot noise from each interferometer as measured to search for a range of sources from bursts to stochastic by the PSDs) and the integration time (130 hours). Any backgrounds. The Holometer was initially designed to excess measured by the blue trace above the black trace look for a stationary noise source where storage of time (i.e. what is shown below 1 MHz) is correlated noise domain data was unnecessary [8]. Therefore, the data between the two interferometers whereas greater than 1 acquisition pipeline was written to retain only frequency MHz the noise that is consistent with the statistical error domain data in the form of power- and cross- spectral for uncorrelated noise. densities for each channel. All of the features above 500kHz in the individual A total of 8 channels corresponding to the output of traces of Figure 1 are well understood. From 500kHz to the interferometers along with environmental monitors 1 MHz, the dominant source of noise is laser phase and are digitized at 100MHz sampling rate. To reduce the amplitude noise. From 1 MHz to 13 MHz, the dominant data rate per channel, two neighboring time-series mea- source of noise is photon shot noise. The large spikes surements are averaged together to result in an effective at 3.75 MHz and its harmonics are due to laser noise 50 MHz sampling rate. Each 3-millisecond, a Fast- leaking into each interferometer due to a lack of filtering Fourier Transform (FFT) is calculated∼ for each channel. from the Fabry-Perot cavity. Another type of noise is Additionally, real-valued, power spectral density (PSD) the clusters of spikes that begin in the low frequency end is calculated for each channel and the complex-valued, (most noticeable at 1 MHz) and have repeated decay- cross-spectral density (CSD) is computed for each com- ing harmonics that are∼ barely noticeable above 13 MHz. bination of channels (i.e 1x2, 1x3, 1x4, etc). Explicitly, These are due to the drumhead modes of the optics in 2 i(θ1−θ2) the PSD is A1 and the CSD is A1A2e where A is each interferometer. Studies have verified that each clus- the amplitude| | of the Fourier transform, θ is the angle of ter of spikes actually consists of three spikes from the the vector in the complex plane for channels 1 and 2. The beamsplitter and two end mirrors. This noise source is total number of frequency bins between 0 and 13 MHz is independent for each interferometer and does not show 3

To compute the energy density from the strain measurements, Ωˆ gw(f), the following relation is used

[h (f)] Ωˆ (f) ℜ 1,2 (2) gw ≡ S(f)

where are the real components, h1,2(f) is the strain cross spectralℜ density in [1/Hz] units and S(f) is the conversion factor that is sky and polarization averaged, which is deﬁned as 3H2 1 S(f)= 0 (3) 10π2 f 3

where H0 is the Hubble parameter (the expansion rate of the universe H0 = 69 [km/s/Mpc]) [17]. The noise on the measurement is calculated as σ2 (f) σ2 (f) 1,2 (4) Ωˆ ≈ S2(f)

FIG. 1. Strain amplitude spectral density as a function of fre- PSD1PSD2 that has a scaling relationship N though it is quency for the 130-hour dataset from 0.5-13 MHz. The green calculated directly from the averaged≈ CSDs as discussed traces are the power spectral densities for each of the interfer- in Section. III A. ometers (Interferometer 1 = dark green, Interferometermeter The measurement of the gravitational wave energy 2 = light green). The blue trace is the magnitude of the cross spectral density between Interferometer 1 and Interferometer density, Ωgw, is plotted in Figure 2. Each individual 2. The black trace is the statistical uncertainty in the cross- point represents the value of the energy density for each spectral density. The spectral features above 500 kHz are well 382 Hz frequency bin where the shaded region illustrates understood and described in Section III A. the corresponding 3σ values. The 3σ value of the energy density at 1 MHz is 5.6 1012 and goes up to 8.4 1015 at 13 MHz. This result× has an additional 15% system-× up in the cross-correlated measurement. atic error from calibration uncertainties. It is should be The Holometer strain spectral density result surpasses noted that each frequency bin has a 50% overlap frac- the only other measurement previously made in this tion with the neighboring bin from the Hanning-Window frequency range as shown by the red star in Figure 1 function used in the FFT computation, which is impor- [9]. Their measurement was performed using super- tant for the direct interpretation of the Ωgw value for conducting microwave cavities with a narrow-line strain each frequency bin. Additionally, this result does not ac- sensitivity of 3.3 10−20 Hz1/2 centered at 1.38 MHz with count for the degradation in sensitivity beyond the long a bandwidth of 100× Hz. wavelength approximation [18], which is applicable to frequencies above 1.92 MHz, and would need to be properly accounted for as done for space-based gravitational wave B. Result 1 : MHz Constraints on SGWB missions. [19] This is the only direct measurement at MHz frequen- The energy density of a stochastic gravitational wave cies of the energy density of a stochastic gravitational background is characterized by how the energy is dis- wave background. This result is much higher than the closure density that would have a value of 1 in these tributed in frequency [16]. This is parametrized by Ωgw which relates the gravitational wave energy density in a units. Additionally, it is higher than indirect measure- bandwidth of ∆f to the total energy density to close the ments at these frequencies from integrated limits placed universe deﬁned as [16] by the Cosmic Microwave Background [20] and Big Bang Nucleosynthesis[21] that have limits of 10−5 in these units. At the current sensitivity, continuous∼ integration 24 1 dρgw would not be the right solution because it would take 10 Ωgw(f)= (1) ρc dln(f) times longer than the current age of the universe to reach the closure density. In order to improve this measure- where f is the frequency, ρc is the closure (critical) en- ment, a major overhaul to the instrument design must ergy density of the universe and dρc is the gravitational be done to increase its sensitivity. Since the Holometer radiation energy density contained in the range from f is shot noise limited at these frequencies, the eﬀorts must to df. be invested in increasing each interferometer’s power. 4

age of power- and cross- spectral densities is calculated per RA bin, which results in a total of 24 RA binned spectra.

FIG. 2. Experimental constraints on the energy density of the gravitational wave backgrounds, ΩGW, as function of frequency. Each dot represents the measurement for a single 382 Hz frequency bin and the shaded region represents the 3σ upper limit on one of the frequency bins. This is the first direct measurement of the stochastic gravitational backgrounds at these frequencies. This measurement is higher than both the FIG. 3. The exposure as a function of RA for the Holome- closure density of the universe (ΩGW=1) and indirect limits set by the cosmic microwave background and the big bang ter zenith and anti-zenith for a declination of +41.85. The −5 130-hour dataset was split up into 24 RA bins and each dot nucleosynthesis which are at ΩGW 10 . In order to be competitive with these other probes,≈ a major overhaul to represents the exposure time in each RA bin. The modulation the Holometer’s sensitivity of the individual interferometers in the exposure time is only representative of the amount of would need to be achieved. available operators. The minimum of 3 hours at RA 260 corresponded to midnight while the maximum∼ at 8.75∼ hours corresponded to 4pm CST. ∼ IV. PRIMORDIAL BLACK HOLE BINARIES The frequency range used in this narrow-lined search was limited to 1 - 1.92 MHz. The low frequency cut-off A. Data analysis pipeline avoids correlated laser noise and high frequency cut-off is the valid limit for the long wavelength approximation, Using the same 130-hour dataset, a different analysis which other large scale interferometers such as aLIGO was performed to search for stationary, monochromatic use [1, 22, 23]. Additionally, this search is for monochro- gravitational wave sources. This search evaluated indi- matic gravitational wave sources, which means the grav- vidual frequency bins as a function of position on the sky itational wave frequency must not change by more than over the duration of data acquisition. If a real monochro- 382 Hz (frequency bin width) during the course of a matic source exists, the strain signal will be the highest month of observation taking. at some RA then as the earth rotates away the signal will In the design and implementation of the Holometer, decay to become consistent with the noise. If there is no the interferometers have been verified to be perfectly in amplitude decay pattern, then the excess strain power phase across this frequency range [8? ]. Therefore, the identified in some RA bin is excluded as a gravitational real component of the cross-spectral density for each fre- wave candidate. Time domain template matching is not quency bin was used to search for a gravitational wave possible since the Holometer data acquisition system only signal. The imaginary component was used as an inde- retains spectral density measurements. pendent measure of the noise distribution. First, the 130-hour dataset was sorted into 24 RA bins A signal-to-noise was computed using the real com- as shown in Figure 3. Each blue point represents the ponent of the CSD to the error for each of the 2,396 amount of exposure for each RA bin of the Holometer’s frequency bins between 1-1.92 MHz. This signal-to-noise zenith and anti-zenith. The variation in exposure time ratio was computed for each of the 24 RA binned spectra. was dependent on operator availability. Next, the aver- The 57,504 signal-to-noise ratios were verified to be con- 5 sistent with a Gaussian distribution. For comparison, the same signal-to-noise ratio was calculated using the imaginary component rather than the real component. This was also consistent with a Gaussian distribution, which verifies that the noise model is well understood. A gravitational wave candidate could still exist that would be consistent with a Gaussian distribution. Any frequency bins with a signal-to-noise value higher than 4 were flagged as potential candidates and a total of two potential candidates were followed up individually. For each of the potential candidates, the real component of the CSD was plotted as a function of RA. These potential candidates had some high CSD value at only a single RA bin but were consistent with zero in the neighboring ones, which is consistent with noise. The behavior was the same when compared to the imaginary component of the CSD as a function of RA. Using this method, the existence of a stationary astrophysical, narrow-lined source is ruled-out.

B. Result 2 : PBH Constraints FIG. 4. Primordial black hole distance as a function of chirp In the data analysis pipeline described above, no mass. This is a comparison of the distance for this monochro- narrow-lined sources were found. This result is used matic frequency analysis (blue) and a projection for merging frequency stacked analysis (green). For reference, the dashed to place constraints on primordial black hole binaries. black line shows the distance to the moon, the solid black line Chirp masses and distances are computed based on the shows the distance to Jupiter. frequency range and strain sensitivity. This search was deﬁned to look for monochromatic sources, meaning that if there were an inspiralling binary pair there would be the sky and the RA bin with the longest exposure was no detectable change in frequency during the duration of used to calculate the distance. data acquisition. Figure 4 is the distance as a function of chirp mass The chirp mass, Mc, of the binary system can be calcu- where ρ = 4, hdet =5 10−21 [1/√Hz] and N 1.6 105 lated given this constraint on the change in gravitational fgw × ≈ × for 8 hrs of integration. The blue trace corresponds wave frequency (∆f = 382 Hz), the observing time gw to the∼ distance and the chirp masses calculated in this (∆t = 1 month) and the individual frequency bin (f ) gw analysis. For reference, the distance to the moon (dashed [24, 25]: trace) is shown. We report a null result of primordial black hole binaries 20 21 − ∆f with masses 8.3 10 3.48 10 g between the earth M = (αf 11/3 gw )3/5 (5) × − × c gw ∆t and the moon. This is the ﬁrst constraint of primordial black hole binaries in this distance range. This is the 5 1 c 5 most conservative estimate for PBH pairs that can be where α is 96 π8/3 ( G1/3 ) , c is the speed of light and G is the Newtonian gravitational constant. Given the fre- tested with this dataset and an alternative analysis path quency range of 1 - 1.92 MHz, the range of chirp masses will be presented below. are 8.3 1020 3.5 1021 g. The distance to these binary pairs is× computed− in× the following way [24, 25]: V. ANALYSIS OPPORTUNITIES

β 2/3 1 D = Mc(πfgwMc) √N (6) The analysis above for MHz gravitational wave sources SNR hdet fgw is far from exhaustive. Searches for more massive pri-

5 3 2 mordial black holes binaries, individual cosmic strings, or G / π 1/3 where β is the combination of constants c4 ( 2 ) , c is the collision of vacuum bubbles from early universe phase the speed of light, G is the Newtonian gravitational con- transitions or inﬂation is possible. New analysis with this stant, SNR is the signal-to-noise ratio, N is the number of dataset and/or data from identical operating conditions det cross spectral densities used in the averaging and hfgw is and storing the time series data (rather than on the av- the instantaneous strain of the detector at the frequency eraged power- and cross- spectral densities) would make fgw. Measurements were repeatedly taken on all parts of additional tests of these ideas possible. 6

A search for more massive primordial black hole bi- we exclude the existence of monochromatic PBHBs be- nary pairs is possible with this same dataset. The dif- tween the earth to the moon as shown by the blue trace ference would be a frequency stacked search for chirping in Figure 4. black hole binaries rather than the monochromatic black Projections are given for doing a chirp search with the hole binaries searched for in this paper. The new analysis would use the 1-second averaged (1,400 millisecond) same dataset, which can extend the PBHB mass range search up to 0.59 2.5 1025g. This new mass range spectra, the shortest time averaged spectra stored to disk − × from this observing run. New chirp masses are calcu- increases the distance range out to Jupiter as shown by the green trace in Figure 4. Solar system searches lated from equation 5 using the instantaneous sensitivity of 5 10−21 /√Hz and the chirp condition of ∆f/∆t > can eﬀectively constrain the dark matter contribution from light PBHs. These measurements are a new way 382 Hz× /1 s (rather than ∆f/∆t > 382 Hz/1 month used in the monochromatic search). This would increase the to search for primordial black holes in one of the least constrained mass ranges (1020 to 1026g) [15]. The chirp masses by 4 orders of magnitude and the increase the distance out to Jupiter as shown by the green trace Holometer or a Holometer-like experiment opens up a new opportunity to improve measurements in this mass in Figure 4. Further details of all the above mentioned analysis can be found in Kamai Ph.D. dissertation [29]. range.

VI. CONCLUSIONS This work was supported by the Department of Energy at Fermilab under Contract No. DE-AC02-07CH11359 In this paper, we have demonstrated how decameter and the Early Career Research Program (FNAL FWP scale Michelson interferometers can be used for MHz 11-03), and by grants from the John Templeton Foun- gravitational wave searches. Employing the Fermilab dation, the National Science Foundation (Grants No. Holometer, dual power-recycled 39 m Michelson Inter- PHY-1205254 and No. DGE-1144082), NASA (Grant ferometers, strain sensitivities better than 10−21 [1/√Hz] No. NNX09AR38G), the Fermi Research Alliance, are achieved with a 130-hr dataset obtained between July the Kavli Institute for Cosmological Physics, Univer- to August, 2015. This sensitivity spans from 1 to 13 MHz sity of Chicago/Fermilab Strategic Collaborative Initia- with a frequency resolution of 382 Hz, which surpasses tives, Science Support Consortium, and the Universities previous measurements both in strain sensitivity and fre- Research Association Visiting Scholars Program. B.K. quency range as shown in Figure 1. was supported by National Science Foundation Gradu- The first gravitational wave measurement with this ate Research Fellowship Program (DGE-0909667), Uni- dataset is a constraint on the energy density of gravi- versities Research Association Visiting Scholars Program tational waves from a statistically, isotropic stochastic and the Ford Foundation. O.K. was supported by the gravitational wave background. The 3σ upper limit on Basic Science Research Program (Grant No. NRF- 12 the energy density, Ωgw, is 5.6 10 at 1 MHz and goes 2016R1D1A1B03934333) of the National Research Foun- up to 8.4 1015 at13 MHz as shownin× Figure 2. This con- dation of Korea (NRF) funded by the Ministry of Edu- straint places× a direct upper bound on the contribution cation. L.M. was supported by National Science Foun- of gravitational waves to the total energy budget in each dation Graduate Research Fellowship Program (DGE- 382 Hz frequency bin. This limit is much higher than the 0638477). The Holometer team gratefully acknowledges closure density in a λ-CDM universe and indirect mea- the extensive support and contributions of Bradford surements (such as CMB and BBN), however this is the Boonstra, Benjamin Brubaker, Andrea Bryant, Marcin first direct measurement in this frequency range. Burdzy, Herman Cease, Tim Cunneen, Steve Dixon, The second gravitational wave measurement with this Bill Dymond, Valera Frolov, Jose Gallegos, Hank Glass, dataset is a constraint on 0.85 to 3.5 1021g primordial Emily Griffith, Hartmut Grote, Gaston Gutierrez, Evan black holes binaries (PBHB). The search× was defined to Hall, Sten Hansen, Young-Kee Kim, Mark Kozlovsky, look for stationary, monochromatic sources (i.e. no de- Dan Lambert, Scott McCormick, Erik Ramberg, Doug tectable change in frequency over the range of data acqui- Rudd, Geoffrey Schmit, Alex Sippel, Jason Steffen, Sali sition). No frequency bins between 1 to 1.92 MHz with Sylejmani, David Tanner, Jim Volk, Sam Waldman, a signal-to-noise threshold of 4 exhibited a modulation William Wester, and James Williams for the design and pattern consistent with an antenna pattern. Therefore, construction of the apparatus.

[1] D.V. Martynov et al. (LIGO Scientiﬁc Collaboration), GEO 600,’ Class. Quantum Gravity, 22, 10, (2004). arXiv:1604.00439. [4] G. Hobbs et al. (IPTA Collaboration), Class. Quantum [2] F. Acernese et al. (Virgo Collaboration), Class. Quantum Gravity 27, 27, (2010). Gravity, 32, 2, (2015). [5] M. Kramer and D. J. Champion, Class. Quantum Grav- [3] H. Grote et al. (GEO 600 Collaboration), “The status of ity, 30, 22, (2013). 7

[6] F. Jenet, et al. (NanoGrav Collaboration), [18] B. F. Schutz, Class. Quantum Gravity, 28, 12, (2011). arXiv:0909.1058 [19] S. L. Larson, W. Hiscock, and R. Hellings, Phys. Rev. D, [7] S. Vitale, Gen. Relativ. Gravit., 46, (2014). 62, 6, (2000). [8] A. S. Chou, et al. (Holometer Collaboration) Phys. Rev. [20] I. Sendra and T. L. Smith, Phys. Rev. D , 85, 12, Lett., 117, 111102 (2016). (2012). [9] P. Bernard, G. Gemme, R. Parodi, and E. Picasso, Rev. [21] R. H. Cyburt, B. D. Fields, K. A. Olive, and E. Skillman, Sci. Instrum., 72, 5, (2001). Astropart. Phys., 23, 3, (2005). [10] A. M. Cruise and R. M. J. Ingley, Class. Quantum Grav- [22] R. Weiss, Quarterly Report of the Research Laboratory ity, 23, 22, 2006. for Electronics, MIT, 1972. [11] B. J. Carr and S. Hawking, Mon. Not. R. Astron. Soc., [23] B.P. Abbott et al. (LIGO Scientiﬁc Collaboration) and 168, (1974). (Virgo Collaboration), arxiv:1602.03838 [12] X. Siemens, V. Mandic, and J. Creighton, Phys. Rev. [24] P. Peters and J. Mathews,Phys. Rev.,131, 1, (1963). Lett., 98, 11, (2007). [25] S. L. Larson, 2001, (unpublished) [13] A. M. Cruise, Class. Quantum Gravity, 29, 9, (2012). [26] G. Battaglia, A. Helmi, H. Morrison, P. Harding, E. W. [14] B. J. Carr, Astrophys. J., 201, (1975). Olszewski, M. Mateo, K. C. Freeman, J. Norris, and S. A. [15] B. J. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, Shectman, Mon. Not. R. Astron Soc., 364, 2, (2005). Phys. Rev. D, 81, 10, (2010). [27] R. K. Lanza, Ph.D. thesis, University of Chicago, 2015. [16] B. Allen and J. D. Romano, Phys. Rev. D, 59, 10, [28] L. McCuller, Ph.D. thesis, University of Chicago, 2015. (1999). [29] B. Kamai, Ph.D. thesis, Vanderbilt University, 2016. [17] C. L. Bennett, et al., Astrophys. J. Suppl. Ser., 208, 2, [30] J. Richardson, Ph.D. thesis, University of Chicago, 2016. (2013).