Gravitational Wave Fiesta : course material

Following our Gravitational Wave Fiesta, below are the slides shown in the various presentations and a record of the last session, the ultimate quizz proposed by Pierre Binétruy to the learners of the Gravity!

Thanks to all for these fruitful and friendly couple of days!

fiesta16 001

Pierre Binétruy (Paris Centre for Cosmological Physics/APC)

Introduction to the Fiesta: physicists dreamed about them for 100 years English/French

Introducing the Fiesta

Eric Chassande-Mottin (Laboratoire APC)

The story of GW150914 discovery (English)

GW150914_DiscoveryStory_Chassande-Mottin

Matteo Barsuglia (APC)

The LIGO and Virgo detectors (English)

InterferometricGW_Detector_Barsuglia

Eric Plagnol (APC)

LISAPathfinder news (English)

LPF_Mission_Plagnol

LPF_inSpaceCommunic_plagnol

Antoine Petiteau (APC)

How will we analyze the LISAPathfinder data? (French)

LPF_MissionAnalyse_Petiteau

Joël Bergé (ONERA)

The Microscope mission and the equivalence principle (English)

Microscope_JBerge

Pierre Binétruy and all the participants

A last quiz: questions and answers during the last session of the “Fiesta”

The teaser:

The full recording:

https://www.apc.univ-paris7.fr/Downloads/com-apc/Fiesta/FiestaG_II2.mov

 

Feb 29 at 16.30 UTC: hangout on the discovery of gravitational waves

On February 11th, 2016 was announced the discovery of gravitational waves by the LIGO and Virgo collaborations. We organize the Gravitational Wave Fiesta in Paris for this historical occasion. In order to allow everyone to participate, we hold a special hangout on February 29 at 16:30 GMT.

Ask your questions!

You will have the opportunity to ask your questions about this exceptional discovery.

This Google Hangout will be streamed live on YouTube and Google+ Hangouts for approximately 60 minutes, where you can follow the questions and answers live.

If you are not among our 80 lucky guests who will be present in Paris for the Fiesta, we encourage you to ask your questions and we will select the most popular ones to ask our guests during the Hangout.

There are three ways you can do this:

  • You will be able to send questions and comments before and during the event by submitting them in the Google Hangout Q&A chat window (if you have a Google account).
  • You can send us questions to our Twitter account @Gravity_Paris, using the hashtag #FLGravity.
  • If you are registered to the first session of the Gravity! course on Futurelearn,  you can leave your questions or comments in advance on the discussion of step 5.12 of the course .

What happens if I can’t watch the live Hangout?

Don’t worry!  A recording of the discussion will be made available after the live event finishes. You will be able to access the recorded video after the event right below.

Will loading the Hangout mean I appear on camera?

No, you will just watch the live stream like any other video (though Google users can submit comments via the interface).

Is a Google account required to view the Hangout?

No, you can watch the Hangout without logging in to Google.

Gravitational wave fiesta 29Feb/01Mar

This is the first of the Gravity! workshops for the learners of Gravity!, all their friends and all those interesting in getting a better understanding of the mysteries of our Universe.

The workshop will of course focus on the topic of gravitational waves, with the historic event of their discovery.
What is a gravitational wave? How were they observed? What have we learnt about black holes from their discovery? What comes next? What is the present status of  LISAPathfinder? So many questions to cover with specialists of the field, with a programme of lab visits in small groups, a social event and a hangout live with the rest of the world.

images-3

To reserve your participation, please go to this website  (we ask for a modest participation of 10€ in order not to cover the expenses but to have a better idea of the number of participants).

The event takes place from Monday February 29 at 9.30am till Tuesday March 1 at 4pm.

Language: English and French
Venue: University Paris Diderot, Amphitheater Buffon, 15, rue Hélène Brion (13th arrondissement)

Metro and RER stop: Bibliothèque François Mitterrand

Programme: see below

affiche_GW Fiesta_V3

A questionnaire has been distributed to all participants to stimulate their curiosity. You may have access to it here.

Monday 29 February/Lundi 29 février

Amphitéâtre Buffon

9h30-11h00 : Gravitational waves and their discovery, an overview/Les ondes gravitationnelles et leur découverte, une introduction (P. Binétruy)

11h00-11h30 : Coffee break/Pause café

11h30-12h30 : What do you expect from MOOCs, a discussion led by P. Binétruy

12h30-14h00 : Buffet lunch/Déjeuner buffet

  • Amphithéâtre Buffon (en français)

14h00-14h30 L’histoire de la découverte de GW150914 (E. Chassande-Mottin)

14h45-15h15 Les détecteurs LIGO et Virgo (M. Barsuglia)

15h30-15h50 Les nouvelles de LISAPathfinder (E. Plagnol)

16h00-16h20 Comment va-t-on analyser les données de LISAPathfinder (A. Petiteau)

  • Bâtiment Condorcet, Salle Luc Valentin (4th floor, 454A) (in English)

14h00-14h30 The LIGO and Virgo detectors (M. Barsuglia)

14h45-15h15 Story of GW150914 discovery (E. Chassande-Mottin)

15h30-15h50 How to analyze the LISAPathfinder data (A. Petiteau)

16h00-16h20 LISAPathfinder news (E. Plagnol)

  • Amphitéâtre Buffon

16h30-17h30 Coffee break/Pause café

17h30-18h30 Hangout with the whole Gravity! community (in English)

 

Tuesday 1 March/Mardi 1er mars

  • Bâtiment Condorcet

9h00-10h30 : Group visits/Visites par groupe

10h30-11h00 : Coffee break/Pause café (4th floor/4ème étage)

11h00-12h30 : Group visits/Visites par groupe

12h30-14h00 : Free time for lunch/Temps libre pour déjeuner

  • Amphithéâtre Buffon

14h00-14h40 : The Microscope mission and the equivalence principle/La mission Microscope et le principe d’équivalence (J. Bergé)

14h40-16h00 : Discussion session, future actions, wrap up/Session de discussion, actions futures, conclusions (P. Binétruy)

What is a gravitational wave?

According to Einstein’s theory of general relativity, a mass deforms space-time. This was spectacularly observed in 1919, only four years after the publication of the theory: thanks to a Sun eclipse, one could observe that light rays passing close to the Sun are following slightly curved trajectories.

 

Since mass induces curvature of space-time, mass in motion will induce propagation of curvature. If you throw a stone into a pond, you induce, on the water surface, wavelets that originate from the place where the stone fell. Similarly, if a mass suddenly moves in the Universe, this will induce waves of curvature, called gravitational waves, that propagate through space-time.

GWimage

 

Which sources generate gravitational waves? Every mass in motion does generate such waves. But we will see that the effects of a passing gravitational wave are extremely tiny. We thus have to ask which are the most powerful sources of gravitational waves. They are energetic events like the rapid rotational motion of two nearby compact stars (like neutron stars or black holes) or explosions (for example supernova explosions, or even the Big Bang itself).

 

How do I know that a gravitational wave is passing through the lab? Because distances between objects vary in a periodic way (remember that a wave is a periodic phenomenon). Imagine masses which are arranged in a circle as on the left-hand side of the following Figure.

 

The two types of gravitational wave polarizations

The two types of gravitational wave polarizations

If a gravitational wave propagates perpendicularly to the screen, the distances between the masses will change and the circle will be deformed periodically into an ellipse. There are actually two different types of deformation, which correspond to what one calls the two polarizations of the gravitational waves.

 

The relative motion of the masses is largely exaggerated in the Figure above. It turns out that, for the most significant cosmic events, the relative variation of distance is smaller than 10-21, in other words 1/1000000000000000000000 meter for a circle of one meter diameter. It is thus not surprising that discovering gravitational waves is such a difficult task!

 

Why are gravitational waves so interesting?

 

The effect of gravitational waves is so tiny because gravity is a very weak force. But conversely, this means that gravitational waves are interacting very little with the environment, and are thus very little disturbed by the objects they encounter on their way: they keep intact all the information of the sources that produced them. They are thus ideal messengers of very distant cosmic events.

 

Moreover, we have known since Newton that the Universe in its largest dimensions is moved by gravity. With the discovery of gravitational waves, we will thus have the possibility to get first-hand information on gravity, through gravity itself turned into waves!

Detecting gravitational waves with interferometry

In order to detect gravitational waves, one must be able to measure exquisitely small (and periodic) variations of distances. There is no use to take the prototype metre bar out of the Bureau International des Poids et Mesures in Sèvres. One has known for a long time that precise metrology requires a more refined type of prototype, the wavelength of light.

Diapositive1

 

 

Light is an electromagnetic wave. As any wave, it is an oscillation characterized by its wavelength, the distance between two crests. The wavelength of visible light is a fraction (0.4 to 0.7) of a micron (one millionth of a metre).

 

Diapositive2But how to turn light into a measuring device? It is the physicist Albert A. Michelson who taught us how to do this at the end of the XIXth century. He used the phenomenon of interference: when you shed coherent light (nowadays laser light) onto a board pierced with two slits, the light beams reemitted by the two slits on the other side of the board interfere. One observes on a screen placed further away zones (called “fringes”) which are alternatively luminous and dark. They are forming an interference pattern. The thickness of the fringes is directly related to the wavelength of the light.

Diapositive4

Albert Michelson (1852-1931) counting interference fringes

Albert Michelson used this phenomenon to measure distances in a set up called an interferometer. In its modern version, a laser beam falls onto a beamsplitter which splits into two: each beam is then reflected on distant mirrors to return to the beamsplitter where they are recombined to interfere on a screen some distance away. The two arms of the interferometer are the trajectories of the two independent beams. The interference pattern on the final screen depends on the difference of length of the two arms.

A Michelson interferometer

A Michelson interferometer

If a gravitational wave goes through an interferometer, distances such as the arm lengths change periodically, which leads to a periodic change of the interference pattern. This allows to detect the gravitational wave.

Which kind of detectors for gravitational waves?

 

As for any wave, a gravitational wave is characterized by its velocity, its wavelength and its amplitude.

characteristics_EN

The velocity is predicted by general relativity to be the same as the velocity of light. This will have to be tested once gravitational waves are discovered.

The wavelength is directly related to the size of the cosmic site (binary system or explosion) which is the source. To understand this, note that, in the picture below, the size of the drop fixes the wavelength of the waves (the distance between crests). It is similar for gravitational waves. Now, the size of the detector has to be of the order of the wavelength, neither much larger, nor much smaller. Hence the size of the detector has to be of the order of the size of the cosmic site.

waterdrop

One thus have two main types of man-made detectors:

  • small cosmic sites i.e. wavelengths of a few thousand kilometres : ground interferometers
  • large cosmic sites i.e. wavelengths of a tens of million kilometres : space interferometers

 

Finally, the amplitude of the wave is related to the strength of the event, measured by the amount of mass that produces the propagating curvature. In large cosmic sites, there is usually much more mass available, hence the signals are much larger for space detectors. For ground detectors, they are much weaker and thus only events within a certain distance of the detector are accessible.

 

There are also two other ways of detecting gravitational waves.

One uses millisecond pulsars, that is cosmic sources in our own Galaxy that emit regularly electromagnetic pulses observed on Earth. When a gravitational wave passes between the source and us, this induces time distortions that can be measured. Using several of these sources, one obtains a detector of the size of our Galaxy (say tens of thousands of light-years).

 

One can also look at the effect of primordial gravitational waves, that is gravitational waves produced in the very early Universe, on the first light emitted 380 000 years after the Big Bang. They tend to polarize this cosmic background of light. In this case, because the background light fills the early Universe, one uses in a sense a detector of the size of the whole observable Universe at that early time. It is this polarisation that the BICEP2 experiment thought that they had detected some years ago.

 

To summarize, the following Figure shows the rich variety of scales over which one hopes to detect gravitational waves, and the science one would study with them:

The gravitational wave spectrum (NASA Goddard Space Flight Center)

The gravitational wave spectrum (NASA Goddard Space Flight Center)

A black hole pas de deux

A binary system of black holes merging into a single black hole provides one of the most interesting systems that can be probed by gravitational waves.

 

One traditionally distinguishes three phases in the phenomenon, often called black hole coalescence. They are depicted in the following diagram, drawn by the renowned black hole specialist, Kip Thorne.

The phases of black hole fusion

The phases of black hole fusion

 

The two black holes initially form a binary system in rotation. This is mass in motion: it thus loses energy in the form of gravitational waves (the frequency of the gravitational waves is directly related to the frequency of rotation). The two black holes thus get closer and rotate faster. This first phase is called the inspiral phase. The gravitational attraction between the black holes remains small and one can apply standard gravitational methods to compute the gravitational wave signal emitted.

 

At some point, the two black holes become so close that their horizons touch. The horizon of the black hole is the spherical surface that corresponds to the surface of no return: once crossed, impossible to go backward and tell what we have observed, one is fatally drawn to the centre of the black hole. Once the horizons have touched, one is left with a single black hole. This is the merger phase.

 

Because gravitational effects close to the horizon are strong, one needs to solve Einstein’s equation in the strong regime. This is done using numerical methods and was a major achievement of the field called numerical relativity in the last ten years (this computation of the form of the gravitational waves during merger was even called the “grand challenge” in the late 1990s). Probing this phase will lead to tests of general relativity in the strong regime (i.e. when gravity is strong), a real premiere.

 

The final phase is called ringdown. Once the new black hole has been formed, with a rather irregular sort of horizon (made of the two previous horizons), it will shake off its unwanted characteristics through a series of resonant oscillations and emission of gravitational waves. The oscillations are depending on the parameters of the black holes (the initial ones and the final one) and the gravitational waves emitted carry all this information away, encoded in their shape. Again, one will gain precious information on black holes and general relativity by studying the waves produced during ringdown.

 

The following video shows (credit: NASA/C. Henze) presents a simulation of the merger of two black holes and the resulting emission of gravitational radiation. The coloured fields represent a component of the curvature of space-time. The outer red sheets correspond directly to the outgoing gravitational radiation that may be detected by gravitational-wave observatories.

 

 

A final question : how long is a signal of black hole coalescence seen in a detector?

 

To answer this question, one must realize that detectors function in a given range of frequencies, typically between 10 and 1000 Hz for ground detectors, and between 1/10 000 and 1/10 Hz for space detectors. The gravitational wave signal is seen in the detector only if it falls in this range. But as the two black holes rotate around one another, their rotation frequency increases and thus the frequency of the emitted gravitational waves as well.

 

The binary system has been evolving for ages but the frequency enters the detector range only a short time before the final plunge (the black holes are then close to one another, the gravitational attraction is stronger and thus the amplitude of the gravitational waves is larger). Typically, ground detectors pick up the signal a few seconds before the merger, and space detectors a few months before.

GW150914

GW150914: this may not mean anything to you but I can assure you that any gravitational wave physicist is just melting when seeing this codename.

 

GW150914 is the name of the source observed by the LIGO experiment on 2015, September (09) 14. And, of course GW stands for Gravitational Wave. This is the first source ever discovered by gravitational waves, the first of hopefully a very long series. And their name will follow the same pattern, GW followed by the date of detection.

 

And what an amazing source: two black holes of respective masses 29 and 36 solar masses which merge into a single one, of 62 solar masses. Add things up: you are missing three solar masses. This corresponds to a release in a few hundredths of second of the corresponding mass-energy in the form of gravitational waves, close to 1050 Watts! This distorts space and time around, and this distortion propagates in all directions…

 

…1.3 billion years later, exactly on September 14, 2015, at 09:50:45 UTC, this distortion reached Earth and was detected in sequence by the two LIGO detectors, first in Livingston (Louisiana) then in Hanford (Washington state), separated by 7 milliseconds.

 

Here is the beautiful signal, as shown in the press conference of February 11, and in the article published in Physical Review Letters, and its comparison with the theoretical predictions:

fig1In the top panels, you can see the signals arrived first in Livingston (right), then in Hanford (left): see on the right how well they match! In the medium panel, you find the prediction from relativity for the mass parameters given above. Even with the eye, you see by comparing with the plots above how well observation and prediction match. In the bottom panels, you have the difference between signal and prediction i.e. what we physicists call the noise. Does it seem “noisy” to you? Well, look at the numbers on the vertical axis on the left: the signal is clearly dominating. This is in part because those were massive black holes: the event was a very powerful one.

 

Note also the horizontal time axis: everything happened in less than half a second. Isn’t that an awfully short time for a cosmic event? Well, you have to remember that the LIGO detector is sensitive to waves in a certain frequency range, basically 10 Hz to a few thousand Hz. The frequency of gravitational waves are directly related to the frequency of rotation of the two black holes. As they get closer over centuries and years, their frequency increases until it is picked up by the detector (when the frequency reaches 10 Hz) but that is only a fraction of a second before the final plunge.

 

You can see this on the next plot, again provided by the authors of the discovery paper:

fig2

You see here the three phases (see post A black hole pas de deux) and to which oscillations in the detector they correspond to. On the bottom panel, you see the evolution with time of the distance between the black hole, in units of the so-called Schwarzschild radius. The Schwarzschild radius is basically the radius of the horizon of the final black hole, approximately 200 km. You also see their relative velocity in units of the velocity of light: it evolves from 1/3 the velocity of light to 2/3 the velocity of light at touchdown! Really an amazing event!

 

The LIGO collaboration has shown at the press conference the following video showing the collision of these two black holes. Enjoy!

Now, you are ready to get a closer look at the discovery paper. It is written for the scientific community, but the first part is rather accessible. If you have to read only one scientific paper in your lifetime, this may be the one.

And if you are a physics student, with at least some background in classical mechanics, here are a few notes for you to understand better this remarkable event. If you feel dizzy when you see a maths equation, stay away!

Understanding GW150914 notes

 

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