Virgo interferometer

In the 2000s, the Virgo detector was built, commissioned and operated. The instrument reached its design sensitivity to gravitational wave signals. This initial endeavour was used to validate the Virgo technical design choices; and it also demonstrated that giant interferometers are promising devices to detect gravitational waves in a wide frequency band.[3][4] The construction of the Initial Virgo detector was completed in June 2003[5] and several data taking periods followed between 2007 and 2011.[6] Some of these runs were done in coincidence with the two LIGO detectors. The initial Virgo detector recorded scientific data from 2007 to 2011 during four science runs.[7] There was a shut-down of a few months in 2010 to allow for a major upgrade of the Virgo suspension system: the original suspension steel wires were replaced by glass fibers in order to reduce the thermal noise.[8] After several months of data taking with this final configuration, the initial Virgo detector was shut down in September 2011 to begin the installation of Advanced Virgo.[9]

The first direct detection of gravitational wave of Virgo, GW170814.

However, the initial Virgo detector was not sensitive enough to detect such gravitational waves. Therefore, it was decommissioned in 2011 and replaced by the Advanced Virgo detector which aims at increasing its sensitivity by a factor of 10, allowing it to probe a volume of the Universe 1,000 times larger, making detections of gravitational waves more likely. The original detector is generally referred to as the "initial Virgo" or "original Virgo". The Advanced Virgo detector benefits from the experience gained on the initial detector and from technological advances since it was made.

Advanced Virgo started the commissioning process in 2016, joining the two advanced LIGO detectors ("aLIGO") for a first "engineering" observing period in May and June 2017.[10] On 14 August 2017, LIGO and Virgo detected a signal, GW170814, which was reported on 27 September 2017. It was the first binary black hole merger detected by both LIGO and Virgo.[11]

The Advanced Virgo is 10 times more sensitive than the initial Virgo.[12] According to the Advanced Virgo Technical Design Report VIR–0128A–12 of 2012, advanced Virgo keeps the same vacuum infrastructure as Virgo, with four additional cryotraps located at both ends of both three-kilometre-long arms to trap residual particles coming from the mirror towers, but the remainder of the interferometer has been significantly upgraded. The new mirrors are larger (350 mm in diameter, with a weight of 40 kg), and their optical performances have been improved.[13] The critical optical elements used to control the interferometer are under vacuum on suspended benches. A system of adaptive optics was to be installed to correct the mirror aberrations in-situ.[13] In the final Advanced Virgo configuration, the laser power will be 200 W.

A milestone for the Advanced Virgo was reached in 2017 with the installation of the new detector. A first joint science run with LIGO, in the second half of 2017, started following a commissioning period of a few months.

The first detection of gravitational waves by Virgo is known as GW170814, which was announced on 27 September 2017 in a G7 science meeting conference in Turin, Italy.[14][11]

Just few days later, GW170817 was detected by the LIGO and Virgo on 17 August 2017. The GW was produced by the last minutes of two neutron stars spiralling closer to each other and finally merging, and is the first GW observation which has been confirmed by non-gravitational means.

After further upgrades Virgo started the "O3" observation run in April 2019, it is planned to last one year, followed by further upgrades.[15]

Numerical simulations of the gravitational waves emitted by the inspiral and merger of two black holes.

When two massive and compact objects such as black holes and neutron stars start spinning one around the other during the inspiral fase, they emit gravitational radiation and, therefore, lose energy. Hence, they begin to get closer to each other, increasing the frequency and the amplitude of the gravitational waves: it is the coalescence phenomenon and can last for millions of years. The final stage is the merger of the two objects, eventually forming a black hole. The part of the waveform corresponding to the merger has the largest amplitude and highest frequency. It can only be modeled by performing numerical relativity simulations of these systems. The interferometer is designed to be sensitive to the late phase of the coalescence of black hole and neutron star binaries: only between several milliseconds and a seconds of the whole process can be observed. All detections so far have been of black hole or neutron star mergers.

Neutron stars are the second most compact known object in the Universe, right after black holes. They have approximately one and a half masses as our Sun, but contained within a sphere of approximately 10-km of radius. Pulsars are special cases of neutron stars that emit light pulses periodically: they can spin up to 1000 times per second. Any small deviation from axial symmetry (a tiny "mountain" on the surface) will generate continuous gravitational waves. Advanced Virgo has not detected any signal from known pulsar, which concludes that the deviation from perfect spinning balls is less than 1 mm.

Any signal lasting from a few milliseconds to a few seconds is considered a gravitational wave burst. Supernovae explosions, the gravitational collapse of massive stars at the end of their lives, emit gravitational radiation that can be seen by the Advanced Virgo interferometer. A multi-messenger detection (electromagnetic and gravitational radiation, and neutrinos) would help to better understand the supernovae process and the formation of black holes.

The Cosmic Microwave Background (CMB) is the earliest time of the Universe that can be observed in the electromagnetic spectrum. However, cosmological models predict the emission of gravitational waves generated instants after the Big Bang. Because gravitational waves interact very weakly with matter, detecting such background would give more insight in the cosmological evolution of our Universe.

Moreover, an astrophysical background must result from the superposition of all faint and distant sources emitting gravitational waves at all times, that would help to study the evolution of astrophysical sources and star formation.

Non conventional, alternative models of compact objects have been proposed by physicists. Some examples of these models can be described within General Relativity (quark and strange stars, boson and Proca stars, Kerr black holes with scalar and Proca hair), arise from some approaches to quantum gravity (cosmic strings, fuzzballs, gravastars), and also come from alternative theories of gravity (scalarised neutron stars or black holes, wormholes). Theoretically predicted exotic compact objects could now be detected and would help to elucidate the true nature of gravity or discover new forms of matter. Besides, completely unexpected phenomena may be observed, unveiling new physics.

Plus polarization of a gravitational wave.

Cross polarization of a gravitational wave.

Gravitational waves have two polarization: "plus" and "cross" polarization. The polarization depends on the nature of the source (for instance, precessing spins in a black hole binary merger generate gravitational waves with "cross" polarization). Therefore, detecting the polarization of the gravitational radiation would give more insight in the physical properties of the system.

In general relativity, a gravitational wave is a space-time perturbation which propagates at the speed of light. It then curves slightly the space-time, which changes locally the light path. Mathematically speaking, if ${\displaystyle h}$ is the amplitude (assumed to be small) of the incoming gravitational wave and ${\displaystyle L}$ the length of the optical cavity in which the light is in circulation, the change ${\displaystyle \delta L}$ of the optical path due to the gravitational wave is given by the formula:[18]

${\displaystyle {\frac {\delta L}{L}}=C\times h}$

with ${\displaystyle C\leq 1}$ being a geometrical factor which depends on the relative orientation between the cavity and the direction of propagation of the incoming gravitational wave.

Basic scheme of a gravitational wave suspended interferometric detector like Virgo (labels are in French)

Virgo is a Michelson interferometer whose mirrors are suspended. A laser is divided into two beams by a beam splitter tilted by 45 degrees. The two beams propagate in the two perpendicular arms of the interferometer, are reflected by mirrors located at the end of the arms and recombine on the beam splitter, generating interferences which are detected by a photodiode. An incoming gravitational wave changes the optical path of the laser beams in the arms, which then changes the interference pattern recorded by the photodiode.

The signal induced by a potential gravitational wave is thus "embedded" in the light intensity variations detected at the interferometer output.[19] Yet, several external causes—globally denoted as noise—change the interference pattern perpetually and significantly. Should nothing be done to remove or mitigate them, the expected physical signals would be buried in noise and would then remain undetectable. The design of detectors like Virgo and LIGO thus requires a detailed inventory of all noise sources which could impact the measurement, allowing a strong and continuing effort to reduce them as much as possible.[20][21] During the data taking periods, dedicated software monitors in real time the noise levels in the interferometer, and deep studies are carried out to identify the loudest noises and mitigate them. Each period during which a detector is found to be "too noisy" is excluded from the data analysis: these dead times need to be reduced as much as possible.

A sensitivity curve from the Virgo detector in the frequency band [10 Hz; 10 kHz], computed in August 2011"Virgo Sensitivity Curves". 2011. Archived from the original on 1 December 2015. Retrieved 15 December 2015.. Its shape is typical: the thermal noise of the mirror suspension pendulum mode dominates at low frequency while the increase at high frequency is due to the laser shot noise. In between these two frequency bands and superimposed to these fundamental noises, one can see resonances (for instance the suspension wire violin modes) such as contributions from various instrumental noises (among which the 50 Hz frequency from the power grid and its harmonics) which one is trying to reduce continuously.

A detector like Virgo is characterized by its sensitivity, a figure of merit providing information about the tiniest signal the instrument could detect—the smaller the value of the sensitivity, the better the detector. The sensitivity varies with frequency as each noise has its own frequency range. For instance, it is foreseen that the sensitivity of the advanced Virgo detector be ultimately limited by:[21]

• seismic noise (any ground motion whose sources are numerous: waves in the Mediterranean sea, wind, human activity for instance the traffic during daytime, etc.) in the low frequencies up to about 10 Hertz (Hz);
• the thermal noise of the mirrors and their suspension wires, from a few tens of Hz up to a few hundreds;
• the laser shot noise above a few hundreds of Hz.

Virgo is a wide band detector whose sensitivity ranges from a few Hz up to 10 kHz. Mathematically speaking, its sensitivity is characterized by its power spectrum which is computed in real time using the data recorded by the detector. The curve opposite shows an example of a Virgo amplitude spectrum density (the square root of the power spectrum) from 2011, plotted using log-log scale.

Using an interferometer rather than a single optical cavity allows one to enhance significantly the sensitivity of the detector to gravitational waves.[22] Indeed, in this configuration based on an interference measurement, the contributions from some experimental noises are strongly reduced: instead of being proportional to the length of the single cavity, they depend in that case on the length difference between the arms (so equal arm length cancels the noise). In addition, the interferometer configuration benefits from the differential effect induced by a gravitational wave in the plane transverse to its direction of propagation: when the length of an optical path ${\displaystyle L}$ changes by a quantity ${\displaystyle \delta L}$, the perpendicular optical path of same length changes by ${\displaystyle -\delta L}$ (same magnitude but opposite sign). And the interference at the output port of a Michelson interferometer depends on the difference of length between the two arms: the measured effect is hence amplified by a factor 2 with respect to a simple cavity.

Then, one has to "freeze" the various mirrors of the interferometer: when they move, the optical cavity length changes and so does the interference signal read at the instrument output port. The mirror positions relative to a reference and their alignment are monitored accurately in real time[23] with a precision better than the tenth of a nanometre for the lengths;[21] at the level of a few nanoradians for the angles. The more sensitive the detector, the narrower its optimal working point.

Reaching that working point from an initial configuration in which the various mirrors are moving freely is a control system challenge.[24] In a first step, each mirror is controlled locally to damp its residual motion; then, an automated sequence of steps, usually long and complex, allows one to make the transition between a series of independent local controls to a unique global control steering the interferometer as a whole. Once this working point is reached, it is simpler to keep it as error signals read in real time provide a measurement of the deviation between the actual state of the interferometer and its optimal condition. From the measured differences, mechanical corrections are applied on the various mirrors to bring the system closer to its best working point.

The optimal working point of an interferometric detector of gravitational waves is slightly detuned from the "dark fringe", a configuration in which the two laser beams recombined on the beam splitter interfere in a destructive way: almost no light is detected at the output port. Calculations show that the detector sensitivity scales as[21] ${\displaystyle {\frac {1}{L\times {\sqrt {P}}}}}$, where ${\displaystyle L}$ is the arm cavity length and ${\displaystyle P}$ the laser power on the beam splitter. To improve it, these two quantities must be increased.

• The arms of the Virgo detector are thus 3-km long.
• To increase even more (by a factor 50) the length of the laser optical paths, highly reflecting mirrors are installed at the entry of the kilometric arms to create Fabry-Perot cavities.
• Finally, as the interferometer is tuned on the dark fringe and that the mirrors located at the end of the arms are highly reflecting as well, almost all the laser power is sent back to the laser source from the beam splitter. Therefore, an additional highly reflecting mirror is located in this area to recycle the light and store it inside the instrument.

Optical configuration of the first generation Virgo detector. On the schematics one can read the level of magnitude of the power stored in the various cavities.