KAGRA: wandering through a gravitational wave observatory

Before I start writing a new blog entry, let me wish you all a very happy 2019! I hope the coming year brings you as many exciting experiences and new realisations as the ones I’ve had the opportunity to gather here in Japan over the course of the last few months. Coming weeks I will be writing a few short stories on the various locations and areas I’ve visited in Tokyo and Kyoto during the new year period. Before we set out on this recounting of my journey, however, I feel obliged to write about one more event that took place prior to the holiday season and which I haven’t been able to fully put on paper yet (or chisel into this website’s pixels for that matter). In a way it seems fitting that I explain about it now, taking into account that the story requires us to revisit the small mountain village of Kamioka and considering that I was invited to go back there to help with some onsite work recently. Thus, without further ado, let us transport ourselves back to the area of the mine, where I had the opportunity to join Stefano and Ishidoshiro-san on a small tour through the KAGRA facilities.

My previous stories on the Kamioka mine, might have suggested that KamLAND and Super-Kamiokande are the only experiments housed within its tunnels. What a grave misconception that would be! The subterranean corridors of Ikenoyama are filled with a variety of different experiments, tackling research topics which vary from the direct detection of dark matter1 to the observation of gravitational waves. Explaining about each and every one of them unfortunately goes far beyond the scope of this website. However, I would like to highlight one of them in relation to a visit I was fortunate enough to pay its facilities during my first stay at the mine: the KAmioka GRAvitational wave observatory (or KAGRA for short).
Hearing that I was allowed to come along on a small trip towards the tunnels of the detector, formed both a big surprise and tremendous reason for excitement:  for one reason, because some people I know at RCNS had not even had the chance to see it yet, but first and foremost, because it would give me a rare glimpse of a detector type that recently sparked momentous breakthroughs in the astrophysics community2.

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After finishing up our regular duties — checking the purification areas and mopping up water spillages using diapers — my fellow shifter and I were picked up at the control room by Ishidoshiro-san. As a former KAGRA collaborator, he had been able to contact some of his old colleagues to arrange for a tour.
We arrived at the entrance of the experiment around noon. Reminiscent of the calligraphy that marks majestic wooden gates of buddhist temple halls, a black- and gold-lacquered Japanese name tag could be seen hanging above the main access-way: かぐらトネル (“ka-gu-ra to-ne-ru”). Underneath it, a set of sturdy concrete walls demarcated the start of a tunnel that led to the main experimental site. Compared to the tunnels one would drive through to reach Super-Kamiokande or KamLAND, this driveway looked incredibly spacious and modern: not much of a surprise, considering it had been built only a few years ago, simultaneously with the cavities that would house KAGRA’s principal technology (a so-called Fabry-Pérot-Michelson interferometer3). A small black golf cart approached us from within, its headlights growing brighter as the vehicle moved towards us. I chuckled a little at the sight. Even though a vehicle such as this one, ferrying scientists to and fro, seemed appropriate for a state-of-the-art detector like KAGRA, there was a comedic side to the situation which struck me funny. Perhaps it was the extreme contrast between the experiment’s grandeur on the one hand and the golf cart’s tiny size on the other. Whatever the reason, our transport was welcomed with smiles and open arms. We climbed on the back as Tomaru-san, a senior member of the collaboration who could tell us all about the ins and outs of the experiment, re-started the engine and drove us back in.

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Explaining about the rest of what we saw and experienced that day, would be hard without elaborating a little on the experiment itself. I should warn you beforehand, however, that my knowledge on gravitational waves is fairly limited. So don’t fret if many questions remain by the end of this text. I have just as many. And so do the experts! If anything, I hope it will form an invitation to try and learn more.
But I think I’m getting ahead of myself. Before we explore what KAGRA looks like, we need to establish what is actually meant when people speak of ‘gravitational waves’. I’m sure that most of you will have heard and read plenty about them during the recent media hypes surrounding the 2017 physics Nobel Prize4 and the first confirmed detections by LIGO and VIRGO5. In their most basic form, gravitational waves can be thought of as ripples in the fabric of spacetime. Propagating through the universe at the constant speed of light — a dazzling 1.08 billion kilometers per hour (or, if you’re willing to entertain the notion, 7.5 tours around the world within a single second) — they contract space in one direction orthogonal to the wave’s motion, whilst stretching it in the other simultaneously. As such, objects standing in its path (the Moon, the Earth, that tree around the corner and, yes, you and me as well) will be bended and warped accordingly. This is not unlike a rubber ducky bobbing on the waves in your bathtub. Only this time, the bobbing is caused by the deformation of space itself (instead of the up-and-down motion of the water), whilst the waves arise from extremely violent cosmic events (instead of the undoubtedly equally explosive motions of your arms).

If the thought of shrinking and expanding on the passing of a gravitational wave unnerves you, rest assured. Variations induced in the physical dimensions of your body are so small, that not even a hair’s width laid on top of the distance to Proxima Centauri, our stellar neighbour some 40 trillion kilometers away, can compare! In fact, accompanying energies are so astronomically small, that Albert Einstein deemed it necessary to comment on the impracticality of gravitational waves from an experimental point of view,  when he first conceptualized the implications of his Theory of General Relativity for gravity-induced transport of information. Adopting a down-to-Earth and almost drily pragmatic tone, he writes down the following, regarding the total emitted power (A) of a gravitationally interacting system in his 1916 paper on the integration of field equations6:

(…), so sieht man, daß A in allen nur denkbaren Fällen einen praktisch verschwindenden Wert haben muß.

The fact that scientists were not only able to pick up on these energies, but characterize the underlying signals and retrace their origins as well, falls nothing short of jaw-dropping. What sparked the change in perspective that motivated scientists to attempt their observation? And what allows present-day physicists to announce gravitational wave detections with such certainty? To answer these questions, we need to transport ourselves back in time to the seventies.

In 1972, astronomers Russel Hulse and Joseph Taylor stumbled upon what, in hindsight, can be considered a scientific goldmine, when they first looked at the brightness variations of a neutron star in the Aquila constellation with the Puerto-Rican Arecibo radio telescope. Although similar periodic changes had been observed in other stars (nowadays categorized as pulsars), the system immediately stood out to them, because of observable modulations on top of the original pulsation frequency: whereas the main signal could be seen rising and falling at a rate of 17 Hz, there seemed to be an additional variation peaking every 8 hours. This could be no coincidence. Diving into the peculiar feature and taking great pains in establishing that no other pulsating stars in the vicinity could be responsible, Hulse and Taylor soon realized that the system consisted of a pair of neutron stars, orbiting around each other. Moreover, the scientists were able to establish that the gravitational forces exerted by one star on the other were more than sufficient to serve as a testing ground for general relativity. One of the remarkable features of the two bodies’ mutual inspiral, turned out to be the emission of gravitational waves. Although not directly observable, the effect could be inferred from temporal variations in the stars’ orbital periods (see the figure below).

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Comparison of observed and predicted orbital period decays as inferred from GR, for the binary pulsar system PSR B1913+16 (from Weisberg, J.M.; Nice, D.J. and Taylor, J.H. (2010)7). A horizontal line indicates the expectation for a non-decaying orbit.

With this first ever establishment of the existence of gravitational waves, Hulse and Taylor not only assured themselves of the 1993 Nobel Prize, but also spurred on the development of direct detection methods. Various technologies had been under consideration from as early as the 1950’s, with simultaneous measurements on cylindric resonance chambers having constituted perhaps one of the most debated options. However, it would take several more decades, up until the early 1980’s, before the precursors to modern gravitational wave detectors properly came off the ground. Their general working principle has remained largely the same up until today, although many additions and adjustments, large and small, have been made over the years and decades (and are still being made) to enhance their sensitivity.

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The fundamental working principle of Michelson-type GW interferometers, as presented by Rainer Weiss in his 2018 Nobel Lecture.

Rainer Weiss summarizes it very comprehensively in his Nobel Lecture. When you’d strip a modern gravitational wave detector of all added components, laying bare its very core, you would retrieve something like the figure above. This Michelson-type interferometer set-up forms the common ancestor of all current gravitational wave detectors. Its main component is formed by a laser which shoots pulses of light unto a beam-splitter. As the name suggests, the latter element splits the incident beam in two, allowing some of the light to pass through, whilst reflecting the rest in the perpendicular direction. Mirrors situated at both ends of the split beam (officially referred to as test masses) subsequently redirect all light back to the beam splitter, where the same happens as before: some of the light is reflected, whilst the rest passes through. This causes a fraction of the original light to move back towards the laser. Another portion, however, will veer off in a different direction, ending up at a photo-detector which registers the final signal.
So how do gravitational waves fit into this picture? I haven’t said a single word about them up until now! We can only form a proper understanding of the influence of gravitational waves on the laser beam, if we take into consideration the laserlight’s wave-character. Similar to the diffraction patterns which arise due to interference when light shines through a narrow slit (e.g. a small crack in the door), the laser pulses which combine at different stages of the detector, will enhance each other or cancel out, depending on their frequency and relative phase. In the absence of any gravitational wave, all detector components are aligned such that no light comes through to the photo-detector at all (the reflected and the through-going beam in the direction of the photo-detector cancel each other out perfectly in this case). But when a gravitational wave comes in, causing space to alternately contract and expand in the directions perpendicular to its motion, variations in the distances between each mirror and the beam-splitter will cause the formation of sidebands, i.e. laserlight converted to frequencies fc+fm and fc-fm slightly above and below the original carrier frequency fc. Whilst the original laser pulses cancel as before, the sidebands double at the detector, passing through the information of their progenitor gravitational wave.

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A schematical overview of the main components in present-day gravitational wave detectors (from Rainer Weiss’s Nobel Lecture). Additional test masses have been added, to constitute a so-called Fabry-Perot-Michelson interferometer. Additionally two mirrors near the laser and photo-detector, allow for more efficient use of input laser power and, respectively, for tuning the interferometer’s spectral response to the sought-after gravitational wave signals.

Present-day gravitational wave detectors work on the basis of a very similar principle, albeit with the addition of three major components. One of them is constituted by the inclusion of two additional test masses, right behind the beam-splitter. Together with the original two mirrors, they form a pair of Fabry-Pérot cavities. Light will scatter back and forth several hundred times within them, in order to enhance the sidebands induced by gravitational waves.
The second addition is formed by the power recycling mirror. Placed in between the laser and the beam splitter, this component allows part of the laserlight which travels backwards in the direction of the laser source to be reflected back into the interferometer, which in turn allows for input power enhancements by several hundred times. The final added component is the signal recycling mirror, which partially reflects the sidebands back into the interferometer, thereby providing the opportunity to tune the detector to different gravitational wave sources of potential interest.

KAGRA contains all of the detector elements above. However, it also differs from its older counterparts, LIGO and VIRGO, in a number of ways. The most obvious difference is its position underground. Why go to the lengths of constructing an underground labyrinth when your top-side cousins are able to detect gravitational waves as well? As with most things concerning gravitational wave astronomy, this has everything to do with enhanced sensitivity. Although surface detectors are arguably more cost-efficient, they come with the downside of being much more prone to seismic noise. Consider standing on top of a plate of jelly pudding versus living inside of it: it’s perhaps not the most savoury of scenarios, but in case of a tremor, I’d rather find myself within the latter region of the gelatine.
Seismic noise reduction in underground gravitational wave detectors comes at a cost however. Aside from the already mentioned financial and constructional challenge, there is also the issue of reaching various detector compartments. Out in the open one can easily get to different segments by driving a car up to the desired point on a sideways road. Doing so inside the narrow cavities of the KAGRA mine would only result in angry car insurance companies. Always innovative, however, scientists working on the site came up with a clever solution: bicycles! As our golf cart approached the end of the entrance tunnel and veered off towards what looked like a large storage-room, we suddenly encountered several dozen of them lined up along the wall. A Dutch physicist couldn’t feel more at home. Realizing our initial surprise, our tourguide laughed, commenting how the bikes not only offered greater mobility, but kept all researchers in shape too: not at all unwelcome, considering the amount of time we sometimes spend behind our desks.

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Having parked our golf cart around the corner, we tagged along behind the expert and entered an antechamber that offered access to one of the main experimental sites. At the other side of the room, behind a glass pane, several scientists seemed busy monitoring  displays. A large sign next to it, glorified the sponsors of the project. Some of them must have contributed considerable amounts, considering the large fonts that projected their names into the hall.
After changing into a pair of laboratory slippers, we walked along towards one of the room’s corners and entered what might be considered to be a cathedral of experimental physics. The number of different experimental towers around us was staggering, not to mention the sheer height of the cavity which housed them all.
Having passed along a section of one of the outer walls, we halted as soon as we reached the front of KAGRA’s power recycling installation. The benefit of this compartment is not to be taken lightly. At an input power of 78 W, the laserlight within the Fabry-Pérot cavities of the interferometer can reach powers up to a value 400 kW8: an augmentation of a few thousand, just like the theory contends.

Perhaps even more interesting to note, however, is the addition of an additional element, wedged in between the power recycler and the laser source. Among other applications, this so-called input mode cleaner allows for the rejection of unwanted sideband frequencies in the input beam. A similar system (called the output mode cleaner) mounted on the other side of the interferometer, allows for the converse process for the output beam which is measured by the photo-detector. It’s interesting to note the various geometrical considerations which have come into play whilst designing these compartments. Whereas the input mode cleaner consists of three mirrors, arranged in a triangular fashion, the output mode cleaner has been set out in a bow-tie pattern with four mirrors reflecting light diagonally towards each other. I presume this has to do with their different design purposes and the various path length considerations (among many other influencing factors) that came with it.

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As we moved along the various segments of the detector, we soon approached an impressive structure guarding the entrance to one of the Fabry-Pérot cavities. Inside it, suspended via a complex assemblage of interlocked mechanical dampers and spring-systems, was one of the test masses. At least, so we were told by our guide. Tomaru-san explained to us the remarkable noise reduction achieved by the suspension system. A total of eight interconnected pendulums had been strung up from a filter on the top of the tower, which in turn rested on top of a separate, inverted pendulum. The set-up’s purpose: getting rid of every source of vibrational noise conceivable, to the maximum possible extent, such that variations in the Fabry-Pérot cavity’s mirror-to-mirror distance could be safely traced back to gravitational waves. Explaining how each of the different stages of the pendulum-contraption pushes towards greater sensitivity in detail, would be quite impossible for me at this point9. But I hope I can at least illuminate some of the basic notions behind the system in order for you to understand the general mechanisms.

Vibrational isolation systems can be broadly categorized into two different classes. The first, called passive isolation, attempts to reduce motions by means of unaided, mechanical damping. This is the group to which the eight-stage pendulum system belongs. Although the full mathematical description which characterizes the motion of the system is fairly complex, grasping the general idea behind it is easy. You can even try it at home! Simply tie two different pendulums to each other and swing them, whilst holding the top: depending upon the speed at which you move your hand back and forth, the lower pendulum will either move along with the upper one or, as is the intention when applying them in vibrational isolation systems, move slower and to a much lesser degree. A chain of them forms an excellent first line of defense against incoming horizontal and vertical vibrations. However, the system does not account for intrinsic motion. On a microscopic level, the atoms and molecules which comprise the chain itself, will oscillate and migrate as a consequence of thermal motion. Canceling out these movements is hard, but it can be achieved by taking away the source: heat. In KAGRA, the four pendulums comprising the bottom part of the vibrational isolation system, are cooled down to cryogenic temperatures of around -250 degrees Celsius (around 20 Kelvin). This takes care of most thermal motion, rendering the type of noise subdominant at low-level frequency regions (below 1 or 2 Hz).
Additionally, however, a system has been put to work which cools the test mass mirror itself. Reaching similarly low temperatures as in the case of the eight-stage pendulum poses a considerable challenge. After all, the mirror is continuously reheated by the incident laser beam. Facilitating the best degree of cooling requires the mirror to be crafted out of a material which easily conducts heat, without compromising its reflectivity. Taking this issue to heart, the KAGRA collaboration opted to use sapphire for their design10  in an attempt to strike the best deal on both fronts.

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KAGRA’s cryogenic system can be considered somewhat of a class of its own, when it comes to distinguishing passive from active vibration isolation mechanisms. Although it constantly extracts energy from the set-up in order to facilitate effective cooling, it does not come with the kind of feedback mechanism which is characteristic of real active damping systems. KAGRA contains a few of the latter category in the form of seismic sensors and actuators which measure and counteract any leftover vibrational motions at the end of the eight-stage pendulum. Typically they achieve a noise reduction of at least an order of magnitude towards lower vibrational frequencies (below ~0.3 Hz)11.

Having entered on the back of a golf cart and having passed a bicycle shed, tall cooling towers, intricate damping mechanisms and a pristine sapphire mirror, I started to think I had seen it all. But it seemed the detector grounds had one more surprise for us in store. Staring at the cooling towers from ground level, I had already felt somewhat overwhelmed by its enormous size. But, as it turned out, the contraptions full proportions could only be appreciated in their entirety if you went to the top. To reach the upper part of the tower, we spiraled up along a narrow and seemingly never-ending staircase. It reminded me of scaling the towers of a church back in Europe, only with a much more even stepping and no awkward circumvention of the occasional passer-by. At the end, we reached a small side-chamber, where a tent had been set up to shelter the top section of the entire suspension system. Not all active elements were immediately visible. But we knew from a model set-up downstairs what the general design looked like. Perhaps some of the most fascinating elements we were told about were the so-called Geometric Anti-Spring filters12. With a collection of six blades hanging over the suspension point in a manner reminiscent of bent fishing rods, these structures dampen any vertical motions induced by seismic noise. Horizontal vibrations are, on the other hand, countered via three inverted pendulum legs, which support the entire structure and, in turn, rest upon a table surface which is fixed unto the the second floor.
Had I not seen the various interdependent systems of the pendulum suspension with my own eyes, both on the ground level and at the top, I think it would have been hard to comprehend the tremendous odds which needed to be overcome, in order to keep the mirror at a vibrational still-stand. I therefore feel extremely lucky, for having had the opportunity to take a peek inside. Hopefully this article has allowed you to take a small glance at some of the detector-systems as well (albeit over my shoulders).

Since I’m aware that my introductory comments and personal remarks on the various elements and physical theories behind the compartments hardly paint a fully descriptive picture of the gravitational wave facility, I’ve tried my best to accumulate a selection of interesting sources for further reading, if anyone is interested. These can be accessed via the different links in the footnotes below. With that, let me end this blog entry with a little encouragement to do some (literature) research of your own. Gravitational wave physics and astronomy form two extremely rapidly developing disciplines in modern science. And I’m confident that it’s not a question if, but rather when new discoveries and revolutions sparked by the accumulating statistics within the field will take place. So stay curious! Who knows what the coming years will bring…

Footnotes

1. See the website of the XMASS collaboration and the NEWAGE experiment

2. The first paper published on the detection of a gravitational wave back in 2015, can be found here

3. Both Michelson interferometers and their Fabry-Pérot counterparts have played an unmistakable role in the development of modern physics, their applications ranging from the original Michelson-Morley experiment at the end of the 19th century (which formed one of the principal inspirations for Einstein’s theory of Special Relativity) to bio-medical research in the present-day. A very brief summary of the technologies and their applications can be found at here and here.

4. Rainer Weiss, Kip Thorne and Barry Barish, the three scientists who received the prize, have written an excellent introduction to the physics of gravitational waves and their detection through their Nobel Lecture series. A lot of what I’m telling here, has been inspired by these texts, so I cordially invite you to read up on them yourselves for better judgement.

5. The original scientific papers on all detected gravitational waves thus far can be found here

6. Your trusty blogwriter’s take on a translation of this sentence (pardon my German), would be: “(…) and thus we see that the totally emitted power of the gravitational system, A, would assume a naught but negligible value in all conceivable cases.” Have a look at this website for the original text. (Really, by all means do! It’s a delight to see some of the man’s work in its original form.)

7. See this arxiv article for the original pre-print.

8. These are the numbers presented by the KAGRA collaboration in their 2017 paper. Have a look at the interferometer schematics and surrounding discussions.

9. I refer the interested reader to this article

10. Have a look at this paper for the various considerations and complications which arose when opting for this remarkable material.

11. See for example the figures in chapter 5 of Takanori Sekiguchi’s 2016 Ph.D. thesis on low frequency vibrational isolation systems

12. A small drawing of the system (and other interconnected components) can be found in Yoshinori Fujii et al. (2016)

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