Gravitational-Wave Lunar Observatory for Cosmology
GGravitational-Wave Lunar Observatory for Cosmology
Karan Jani and Abraham Loeb Department Physics & Astronomy, Vanderbilt University,2301 Vanderbilt Place, Nashville, TN, 37235, USA Department of Astronomy, Harvard University, 60 Garden Street, Cambridge, MA 02138, USA
Several large-scale experimental facilities and space-missions are being suggested to probe theuniverse across the gravitational-wave (GW) spectrum. Here we propose Gravitational-wave LunarObservatory for Cosmology (GLOC) - the first concept design in the NASA Artemis era for a GWobservatory on the Moon. We find that a lunar-based observatory is ideal for probing GW frequenciesin the range between deci-Hz to 5 Hz, an astrophysically rich regime that is very challenging forboth Earth- and space-based detectors. GLOC can survey (cid:38)
70% of the observable volume of ouruniverse without significant background contamination. Its unprecedented sensitivity would tracethe Hubble expansion rate up to redshift z ∼ z ∼ Introduction .— Observations from the first set ofsuccessful gravitational-wave (GW) experiments - LIGOand Virgo - have shown the far reaching impact of theGW spectrum from 10 ∼ ∼ Letter , we propose a GW detector on theMoon whose primary goal is to access the deci-Hz range.With the advent of NASA’s Artemis and CommercialCrew programs, the time is ripe to consider fundamentalphysics experiments from the surface of the Moon.We find that the Moon offers an ideal environmentfor pursuing uninterrupted deci-Hz GW astronomy for decades and will strongly complement with the Earth-and space-based network of telescopes. We suggest theacronym GLOC - Gravitational-wave Lunar Observatoryfor Cosmology, for a detector that would survey 30 − Gravitational-Wave Setup on the Moon .— The Moonoffers a natural environment for constructing a large-scaleinterferometer as a GW detector, and such a scenariohave been mentioned in the literature [11, 12]. Theatmospheric pressure on the surface of the Moon duringsunrise is comparable to the currently implemented 8km ultra high vacuum (10 − torr) at each of the LIGOfacilities [13]. After sunset, the atmospheric pressure onMoon scales down to 10 − torr [14]. The presence ofvacuum just above Moon’s solid terrain provides a greatbenefit in extending the LIGO interferometer length atminimal cost.The seismometers left from the Apollo missionssuggests that the Moon is much quieter than Earth(see [15] and the references within). At low-frequencies(0 . ∼ (cid:46)
10 Hz. The next generationEarth-based experiments are intended to push the limitto ∼ ∼ . a r X i v : . [ g r- q c ] J u l
40 kmEnd Stations
GLOC
10 km
Space
LISA op ti m a l aLIGOETCE Moon Earth
GLOC c on s e r v a ti ve FIG. 1.
Concept design for GLOC and predicted sensitivity.
Left: Three end stations on the surface of the Moonforming the full triangular-shape GW detector. The end stations are separated by 40 km. Each end station will contain a testmirror and a laser, making GLOC equivalent of three interferoemters. Right: GW sensitivity (as characteristic strain √ fS n )of space-based (LISA), Earth-based (aLIGO, ET, CE) and lunar-based (GLOC-optimal and conservative) detectors. Image ofMoon’s surface was adapted from Lunar Reconnaissance Orbiter (NASA/GSFC/ASU) and Earthrise from the Apollo archives. as winds or lightening, and it is very mildly sensitiveto the gravitational pull from the Earth’s ocean waves.This would ensure continuous operation of GLOC (a near100% duty-cycle). The Moon-quakes occur at much lowerfrequencies [16] and thus should not impact the GWsensitivity at the deci-Hz range. Bombardment by cosmicrays and solar flares can be a source of non-Gaussiannoise. To reduce this noise, the end stations securing thetest mass and the optics can be coated with a magneticshield to keep the excess charge grounded. In addition,a cooling source can maintain a steady temperature andmitigate thermal expansion, as the temperature on thesurface of the Moon changes from − ◦ C to 120 ◦ C ina day [21].An additional advantage (thus far) is that the Moonis not corrupted by any unpredictable noise from humanactivities. The site selection for the detector should avoidterrain favorable for potential launches. In case of alock-loss in the interferometer, a lunar-based detector canbe brought back online from a control center on Earth.In the event of a serious hardware failure, parts of thedetector can be replaced and repaired by astronauts.The benefit of performing on-request maintenance isnot available for space-based GW detectors, makingthe Moon a better long-term investment. In addition,future space-missions to access the deci-Hz range arelimited in their lifetime (typically a few years), afterwhich the gravitational perturbation from solar system objects will disrupt their geometry. In contrast, a lunar-based detector can operate and be steadily improved fordecades.
GLOC Concept Design .— We adopt a design schematicsimilar to that in next-generation Earth-based detectorsCosmic Explorer (CE) and Einstein Telescope (ET). Asshown in the left panel of Fig. 1 (left), the arm-lengthof the interferometer is set at 40 km and the L-shapedadvanced LIGO (aLIGO) type intereferoemter is replacedby a triangular geometry. Each end station formingthe triangle will consists of a laser and two test masses.Therefore, the full GLOC would be equivalent of threeindependent detectors. The end stations can be designedas dorm shaped compartments that are temperaturecontrolled and isolated from the rest of the detector. Thecurvature of the Moon leads to a ∼
450 m vertical offsetfor the light path between 40 km separation. An ideal sitefor GLOC would be within a bigger craters ( (cid:38)
20 km),providing a flat land for at least two end stations and ahigher elevation to place to the third station.The right panel of Fig. 1 shows the target sensitivity ofGLOC versus GW frequencies and compare it with otherproposed detectors [20, 24]. We consider two projectionsfor GLOC - a moderately ambitious approach to havedetection sensitivity down to f low = 0 .
25 Hz (GLOC-optimal), and a more conservative approach that reaches f low = 1 Hz (GLOC-conservative). The sensitivity curve FIG. 2.
Cosmological reach of GLOC in comovingcoordinates.
The concentric circles represents thepercentage fraction of the comoving volume of the observableuniverse ( V obs = 1 . × Gpc ) out to a given cosmologicalredshift, with the outermost being the CMB [22]. Thehighlighted slices refer to the horizon redshifts in GLOC(optimal) for the corresponding GW sources at their detectionthreshold (SNR ≥ for the optimal and conservative cases of GLOC can bedownloaded from https://doi.org/10.5281/zenodo.3948466 .In both the stated cases of GLOC, we assume that theprimary limiting noise in the mid to higher frequencies(2 − pygwinc [25]. Below ∼ ∼
3. Further improvements in the thermalnoise can be achieved by implementing mirror coating being planned for the cryogenic detector [26]. Withthese improvements, GLOC would achieve the projectedconservative sensitivity. To reach the optimal sensitivitywill require an unconventional suspension setup. Apossible mechanism it to let the test masses be in a freefall with a so-called juggled interferometer [27]. Such asetup is more favorable to implement on the Moon dueto the design freedom with the atmospheric vacuum.
Science Case of GLOC .— As showcased with fig. 2, thedetector would have a rare advantage of accessing GWsat cosmological distances across five orders of magnitudein mass - from sub-solar dark matter candidates( ∼ − M (cid:12) ) [28] to stellar mass binaries ( ∼ − M (cid:12) )to intermediate-mass black holes (IMBHs, ∼ − M (cid:12) )[29]. Across this entire mass-range, GLOC’s optimalsensitivity would outperform that of the upcoming GWexperiments on Earth (CE, ET) and space (LISA).Furthermore, the sensitivity band of GLOC is notexpected to have any astrophysical foregrounds from thewhite dwarf binaries [24]. Thus, any GWs with redshiftedfrequency f det = (1 + z ) f src (cid:38) . IMRPhenomPHM [30]. The integration is started from f low = 0 . ≥ z (cid:46) z ∼
70 [32], even one suchdetection will violate ΛCDM cosmology [33]. Themeasurements of stellar binaries at such high redshiftswould also constrain the earliest stellar population [34].With the low-frequency limit up to ∼ . L of GLOCwould become comparable to the Moon’s orbital diameteraround the Earth. The typical SNRs in GLOC for stellar IMBH ~hours~day~month
Light BBH
GLOC + Ground NetworkGLOC only
Heavy BBH BNS
FIG. 3.
Sky-localization with GLOC.
Each colored codedcurve represents a face-on binary at different redshifts. Thehighlighted masses are in the source frame of the binary. Theshaded region refers to the potential improvement for a 10 +10 M (cid:12) binary with multiband network on GLOC (optimal)and next-generation Earth-based detectors. binaries from high redshifts would be ∼ σ t , could be as good as ∼ . ∼ σ θ ∼ σ t ( c/L ) ∼ − deg [37]. As a result, the sky-localization, ∆Ω ∼ πσ θ , of stellar binaries from GLOCalone can be ∼ − deg . In Fig. 3, we show thisapproximate constraint on sky-localization for coalescingbinaries at different redshifts.A binary neutron star (BNS) at z ∼ (cid:46) − arcmin . The sky-localizationalert for BNSs can be sent days in advance, allowingreadiness of high-latency electromagnetic followups withreach up to high redshifts. Even in the case of GLOC-conservative, the effective baseline for a BNS would be aquarter of the Moon’s orbit, leading to tight constraints.For a relatively light binary black hole (BBH) likeGW151226 [39], GLOC would start measuring its inspirala day before the merger. These could constrain thesources at redshifts ∼ . . Nextgeneration Earth-based detectors CE and ET have their peak sensitivity for BBHs of these total masses [31].A combined network between these enhanced detectorson Earth and a geocentric detector like GLOC canfurther reduce the sky-location error by two ordersof magnitude (see calculations in [40]). As shownin Fig. 3 (dotted line), these combined network canconstrain mergers of light BBHs to 1 arcsec , namely theangular scale of a single galaxy. These are the tightestconstraints on the source location in GW astronomy,allowing to identify the potential host galaxy withoutelectromagnetic counterparts. The strongest sciencecase of GLOC is opening such high redshift dark sirensto independently measure the evolution of the Hubbleparameter as a function of redshift [41].For heavy stellar BBHs like GW170729 [42] or 170502[43], GLOC would measure their inspiral a few hoursbefore their mergers. These are the brightest sourcesin GLOC, registering SNR ∼ (cid:46)
2. Inconjunction with the detectors on Earth, the distance andsky-location constraints ( ∼ ) would be ideal fortesting the association of Active Galactic Nuclei (AGN)flares with heavy binaries [44]. While a space-missionlike LISA can measure the early-inspiral of these heavybinaries years in advance [45], it can only do so for sourcestypically within a Gpc [31] and retrospective after adetection from Earth [46].The enhanced low-frequency sensitivity permits GLOCto survey binaries with IMBHs in the lower (10 − M (cid:12) )to medium range (10 − M (cid:12) ), practically across theentire universe. Such cosmological reach is crucial forconnecting IMBHs with the Pop-III remnants [47] andthe seeds of super-massive black holes [48, 49]. Thetheoretical estimates on their populations are fairly weak,but the upper-limits from LIGO and Virgo detectors [50]suggests that the mergers of lower-range IMBH binariesare much rarer ( (cid:46) − yr − ) compared to stellarbinaries. Unlike GLOC, space-missions have just a fewyears of lifetime (4 −
10 years for LISA), allowing thedetection of only a handful of such rare sources.In the case of potential IMBH detection, the advent ofGLOC opens a new possibility of multi-band observationsacross three frequency bands - from early inspiral atmilli-Hz (space), to late-inspiral at deci-Hz (Moon)and mergers/ringdown at ∼
10 Hz (Earth). Such jointmeasurements of a source across three bands of frequencyspectrum would provide the strongest tests of generalrelativity [7, 51]. Furthermore, the intermediate-mass-ratio inspirals (IMRIs) [52], which are relatively weaksources in both LISA and the next-generation Earthdetectors, can be surveyed in GLOC to z ∼
10. ForIMRIs within redshift (cid:46)
1, GLOC would measure themwith SNR ∼ . − M (cid:12) ) [28]. Thereare no known astrophysical phenomena that can createdetectable GWs at such low-masses, however, primordialblack holes or dark matter within neutron star cores offerpossible scenarios (see [53] and references within). Thelow-frequency sensitivity of GLOC allows us to measurethe dark matter density of such exotic objects to 30% ofthe entire observable volume of the universe ( z ∼ Acknowledgements .— We are grateful to Rainer Weiss,Scott Hughes, Mathew Evans, Bob Eisenstein, KevinKuns, Brian O’Reilly, Stefan Hild and Kelly Holley-Bockelmann for insightful comments. K.Js researchwas supported by the GRAVITY program at VanderbiltUniversity. A. L.’s work was supported in part by theBlack Hole Initiative at Harvard University, which isfunded by grants from the John Templeton Foundationand the Gordon and Betty Moore Foundation. [1] B. Abbott, R. Abbott, T. Abbott, S. Abraham,F. Acernese, K. Ackley, C. Adams, R. Adhikari, V. Adya,C. Affeldt, and et al., Physical Review X (2019),10.1103/physrevx.9.031040.[2] M. Punturo et al. , Proceedings, 14th Workshop onGravitational wave data analysis (GWDAW-14): Rome,Italy, January 26-29, 2010 , Class. Quant. Grav. ,194002 (2010).[3] D. Reitze et al. , arXiv e-prints , arXiv:1907.04833 (2019),arXiv:1907.04833 [astro-ph.IM].[4] P. Amaro-Seoane et al. , arXiv e-prints , arXiv:1702.00786(2017), arXiv:1702.00786 [astro-ph.IM].[5] R. N. Manchester, Class. Quant. Grav. , 224010(2013), arXiv:1309.7392 [astro-ph.IM].[6] I. Mandel, A. Sesana, and A. Vecchio, Classical andQuantum Gravity , 054004 (2018).[7] M. A. Sedda, C. P. L. Berry, K. Jani, et al. , “The missinglink in gravitational-wave astronomy: Discoveries waitingin the decihertz range,” (2019), arXiv:1908.11375 [gr-qc].[8] S. Lacour, F. H. Vincent, M. Nowak, A. Le Tiec,V. Lapeyrere, L. David, P. Bourget, A. Kellerer, K. Jani,J. Martino, and et al., Classical and Quantum Gravity , 195005 (2019).[9] S. Kawamura et al. , Laser interferometer space antenna.Proceedings, 8th International LISA Symposium,Stanford, USA, June 28-July 2, 2010 , Class. Quant.Grav. , 094011 (2011).[10] J. Crowder and N. J. Cornish, Physical Review D (2005), 10.1103/physrevd.72.083005.[11] K. S. Thorne, Black holes and time warps : Einstein’soutrageous legacy (W.W. Norton).[12] N. Lafave and T. L. Wilson, in
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