Deuxième Assemblée Générale du GdR Ondes Gravitationnelles

10 oct. 2019, 09:00 → 11 oct. 2019, 19:00 Europe/Paris

Amphithéâtre (INSTITUT DE PHYSIQUE NUCLEAIRE LYON)

Le GdR Ondes Gravitationnelles (http://gdrgw.in2p3.fr/) a été crée en 2017 avec le but de rassembler la communauté scientifique intéressée par l’exploration de l’Univers avec les ondes gravitationnelles, et de lui fournir des occasions de rencontres et de discussions communes. 

La deuxième assemblée générale du GdR Ondes Gravitationnelles aura lieu à Lyon, dans l'amphithéâtre de l'Institut de Physique des 2 Infinis de Lyon, et couvrira les thèmes d’intérêt du GdR, représentés par ses Groupes de Travail. 

L'inscription à cette réunion est obligatoire avant le 14 juillet 2019. Il faut, au préalable, devenir membre du GdR en s'inscrivant sur le site http://gdrgw.in2p3.fr/

La date limite pour envoyer une contribution est le 30 juin 2019.

        

       

      

 

 

jeudi 10 octobre

1 Welcome

2 Séminaire sur invitation: catalogue des sources LIGO/Virgo

Orateur: Edward Porter (APC/CNRS)

3 Séminaire sur invitation: utilisation des données ouvertes

Orateur: Frédérique MARION (LAPP)

Utilisation_données_ouvertes.pdf

4 Séminaire sur invitation: présentation de l'IPNL/LMA

• La théorie des fusions d'étoiles à neutrons (Jérôme Margueron)
• Le pôle analyse de données (Viola Sordini)
• L'activité sur les grands miroirs (Jérôme Degallaix et Laurent Pinard).

Orateurs: Jerome Degallaix (Laboratoire des Matéraux Avancés), Jérôme Margueron (IPN Lyon), Laurent PINARD (LMA), viola sordini (in2p3, infn)

GDR_GOLyonV4.pptx

12:30 Déjeuner au buffet

5 Séminaire sur invitation: multi-messager, présent et futur

Orateur: Mélanie Habouzit

6 Séminaire sur invitation: détecteur futurs et contribution française

Orateur: Matteo BARSUGLIA (AstroParticule et Cosmologie)

Groupe de travail: Tests de la relativité générale et théories alternatives

7 How-to: testing alternatives theories of gravity with gravitational waves

General relativity predicts Gravitational waves (GWs) to propagate through the Friedmann–Lemaître–Robertson–Walker (FLRW) metric as a spherical wave at the speed of light and with a friction term given by the expansion of the universe. However, several modified gravity theories (such as massive gravity or effective field theories in the dark energy sector), modify the friction term and the speed of a propagating GW in the FLRW metric, adding in some cases also a frequency dependent dispersion relation. In this talk we will present how to measure these modifications with observations of GWs from compact binary coalescences. Moreover we will review the current constrains by the LIGO and Virgo observations of gravitational waves.

Orateur: Dr Simone Mastrogiovanni (APC- Paris diderot)

GDR_presentation.pdf

8 BH and (neutron) stars in the minimal theory of massive gravity

The minimal theory of massive gravity (MTMG) is a theory of massive gravity that displays only the two canonical tensor degrees of freedom.Thus it provides a natural explanation for the late-time acceleration (via the graviton's mass) while passing with flying colors the bounds of GW170817 + GRB170817A, as the speed of GW is exactly 1. As this theory was constructed for cosmological purposes, it is natural to ask whether if it is also viable at astrophysical scales, and notably if its gravitational radiations match the observed ones. The first step in this direction is to investigate if black holes (BH) and neutron stars exist in such a theory.

After a rapid review of the peculiar properties of MTMG, we will show that neutron stars and static BH are natural solutions. This is the first construction of BH in a theory of massive gravity that agree with the corresponding solutions in GR and that are free from strong coupling issues. This result implies notably that the post-Newtonian parameters $\beta$ and $\gamma$ are 1. We will finally discuss the existence of realistic, spinning BH.

Orateur: François Larrouturou (IAP)

presentation_Larrouturou.pdf

9 LISA: a primordial black hole detector?

Orateur: Eric Gourgoulhon (LUTH, Observatoire de Paris)

LISA_primordialBH.pdf

16:00 pause café

Groupe de travail: Formes d'onde

10 Characterizing binary black hole signals with LISA

The future LISA detector will complement current ground-based observations of gravitational waves by targeting a lower-frequency band, enabling the detection of supermassive black hole mergers, as well as stellar mass black hole before they reach the LIGO/Virgo band. Much remains to be explored for LISA capabilities to characterize those signals. Using recently developed techniques enabling accelerated Bayesian parameter estimation simulations, we highlight the role of the merger, of higher harmonics and of the time and frequency-dependency in the LISA response. We also explore the impact of the latest instrument design updates on the length of the signals after passing the detection threshold.

Orateur: Dr Sylvain Marsat (APC, Paris)

gdr_marsat_2019-10-10_short.pdf

11 Bilan du premier atelier du groupe de travail «Formes d'onde» et recent progress in the computation of post-Newtonien waveforms for compact binaries

Post-Newtonian (PN) calculations constitute a crucial ingredient to build the
waveform models for compact binaries that are used in the data analysis of the
current (and future) gravitational-wave interferometers. For the resulting
templates to be faithful, the overlap of the PN polarisations with their
numerical counterparts must be made as high as possible. This requires to
obtain the orbital phase analytically at the 4PN order at least. We shall
describe the current status of this computation, focusing on the most recent
progress. We shall also discuss the implementation of the tidal effects at the
2PN order, relevant in the case where the companions are neutron stars.

Orateur: Guillaume Faye (Institut d'Astrophysique de Paris)

Lyon19.pdf

Groupe de travail: Cosmologie

12 Observations gravitationnelles et incertitudes dans la mesure de distance

Les ondes gravitationnelles issues de la coalescence de binaires compacts, ainsi qu'une contrepartie électromagnétique associée, sont des sondes idéales pour les modèles cosmologiques. Nous obtenons des expressions analytiques pour les erreurs statistiques sur la distance de luminosité déduite des observations des ondes gravitationnelles en fonction de la position du ciel et du réseau de détecteurs. En particulier, nous prenons en compte la dégénérescence dans l'espace des paramètres de la forme d'onde gravitationnelle montrant que, selon le réseau de détecteurs d'ondes gravitationnelles et la position du ciel source, il peut être impossible de bien estimer la distance de luminosité de la source. Nos approximations analytiques montrent un bon accord avec les incertitudes mesurées avec les échantillonneurs bayésiens à partir de données simulées. Nous présentons les implications pour l'erreur d'estimation sur la constante de Hubble.

Orateur: Eric Chassande-Mottin (CNRS AstroParticule et Cosmologie)

presentation.pdf

13 Résultats récents sur les modèles de cordes cosmiques

Les cordes cosmiques sont des défauts topologiques unidimensionnels formés à la suite d'une brisure spontanée de symétrie. Si des cordes cosmiques ont été formées dans l'Univers primordial, elles peuvent être à l'origine d'un fond stochastique d'ondes gravitationnelles détectable dans une large bande de fréquence. La détection d'un tel signal permettrait de contraindre les extensions du modèle standard des particules à très haute énergie.
Dans cette présentation, nous proposons de revenir sur quelques résultats théoriques récents concernant l'évolution temporelle d'un réseau de cordes cosmiques et les prédictions en termes d'ondes gravitationnelles. En particulier, nous souhaiterions présenter un nouveau modèle, basé sur les simulations récentes de Matsunami et al, prenant en compte conjointement l'émission d'ondes gravitationnelles et de particules.

Orateur: Pierre Auclair (Laboratoire APC)

seminar.pdf

14 LSST broker systems and follow-up strategy

The next decade will see the arrival of a new generation of instruments with a large increase of data flux at the 2020 horizon, and beyond. Among these, LSST will provide a unique information in the visible band and it will have the opportunity to perform deep follow-up of events detected by gravitational wave detectors. While LSST strategy for photometric follow-up of gravitational wave alerts is not yet fully determined, I will describe the main efforts carried on by the LSST community.

In a second part, I will focus on the LSST broker ecosystem whose main challenges are to process the large volume of data expected from LSST, correlate alerts from different telescopes (real-time and post-processing), extract the sources, and efficiently trigger repointing of LSST and other telescopes. A collaboration centred on several IN2P3 laboratories and led by LSST France is developing such a broker with a large part of the project dedicated to the multi-messenger astronomy. A close collaboration between the IN2P3 gravitational wave community and this effort is a unique opportunity to create a synergy that will enable an efficient cross-correlation and characterization of alerts, maximizing the scientific return on both LSST and collaborating experiments.

Orateur: Julien Peloton (CNRS-LAL)

GdR OG - LSST brokers.pdf

15 BNS Electromagnetic Counterparts: a population study

Following the historical observation of GW170817 and its electromagnetic follow-up, new multi-messenger observations of such events are expected during the present and future observing runs of Ligo-Virgo. The diversity of the observed population of afterglows of these future events is subject to various factors, which are (i) intrinsic, such as the energy of the ejecta, (ii) environmental, such as the ambient medium density or (iii) observational, such as the viewing angle and distance of the source. Through prescribing a population of mergers and modelling their kilonova and their afterglows, we study the diversity of those events to be observed jointly in gravitational waves and electromagnetic bands. We show that the distribution of observed properties of events with a joint detection (e.g. viewing angle, distance, afterglow peak flux, proper motion, etc.) will provide insight on neutron star mergers, their formation channels and their environments, as well as on the geometry of the relativistic ejection.

Orateur: Prof. Frédéric Daigne (Institut d'Astrophysique de Paris - Sorbonne Université)

20191010-Daigne.pdf

Discussion: Enstein Telescope et science du 3g

19:00 Diner au buffet

vendredi 11 octobre

Groupe de travail: Développement des détecteurs

16 Preparing LISA : Status of the mission and technical activities in France

LISA is presently undergoing many technical studies to assess its feasibility (Phase A), at ESA, but also in the different countries contributing to the instrument. In France, the foreseen contributions are on the Data Processing Center, the integration and tests (AIVT) of the Instrument and the maintenance of the scientific performance model.In this presentation, I’ll briefly summarise the status of LISA (at ESA, NASA and on the European Consortium) and focus mostly on the technical activities presently performed in France. In particular, I’ll describe the undergoing project of developing an ultra stable optical bench for demonstrating the feasibility and achievable performance of the instrument characterisation during the instrument AIVT. This experiment is also an opportunity to set up a large French collaboration around the LISa instrumentation, in view of the development of more ambitious optical bench for the LISA instrument models AIVT, which will start as early as 2021/2022.

Orateur: Hubert Halloin (APC / University Paris Diderot)

GDROGDetecteurs_Oct2019.pdf

17 Intercalibration of Advanced LIGO and Advanced Virgo for the third observing run O3

The astrophysical parameters estimation of the sources detected by Advanced LIGO and Advanced Virgo is biased by the uncertainty on the physical parameters of each detector of the network and thus the final uncertainty on the reconstruction of the gravitational waves signal h(t). Before the observing run O3, Advanced LIGO and Advanced Virgo had different absolute references for their calibration procedure to derive the uncertainty on h(t). We present the first results of the intercalibration between Advanced LIGO and Advanced Virgo photon calibrators with respect to the LIGO Gold Standard which has been chosen to be the absolute reference for the time being. This work should lead to a relative calibration of the interferometers network during O3 using the same absolute reference for Advanced LIGO and Advanced Virgo and thus better quantify the global uncertainty of the network. Future interferometers joining the network, for instance KAGRA which has worked for more than one year with LIGO on their Working Standard for calibration, will also be calibrated with respect to the LIGO Gold Standard to be on the same level of absolute uncertainty.

Orateur: Dimitri Estevez (CNRS)

GdR_OG_Lyon_Oct_2019.pdf

18 Reducing quantum noise for Advanced Virgo gravitational-wave detector by using frequency-dependent squeezing technique with Einstein-Podolsky-Rosen (EPR) entanglement

In order to increase the science reach of GW detectors, it is fundamental to reduce the quantum noise, composed of radiation pressure noise (RPN) at low frequencies (roughly < 100 Hz) and shot noise (SN) at high frequencies (roughly >100 Hz). Since the quantum noise is generated by vacuum fluctuations entering the interferometer, the injection of phase-squeezed vacuum states reduces the SN and increases the RPN. Frequency-independent squeezing (FIS) has been implemented in the Advanced Virgo for the current LIGO-Virgo observation run O3. As RPN does not limit the current sensitivity of Advanced Virgo, the increasing of RPN due to FIS is not a problem. However, for the next detector upgrade (Advanced Virgo+), RPN will limit the sensitivity at low frequencies. In order to reduce simultaneously SN and RPN, the injection of frequency-dependent squeezing (FDS) is needed. This can be obtained inserting an external filter cavity between the squeezing source and the interferometer, before the injection of the squeezed vacuum in the interferometer.
Alternatively, it has been recently proposed that a broadband reduction of quantum noise in gravitational-wave detectors can also be achieved using a pair of squeezed EPR-entangled beams. A frequency-dependent optimization of the injected squeezed light fields is possible with this technique, without the need of an external filter cavity.
After an introduction about the squeezing techniques in the context of GW detectors, we will introduce the EPR squeezing and we will describe the R&D on-going effort in Virgo about this technique.

Orateur: Catherine Nguyen

[GdROG]Nguyen_DevDet_11092019_v1.pdf

19 Squeezing independent de la fréquence pour O3

Le bruit quantique limite une part de plus en plus importante de la sensibilité de Virgo. L'injection d'états comprimés du vide, ou squeezing, par le port de détection permet de réduire le bruit quantique sans engendrer de changement drastique sur la configuration du détecteur.
Cela nécessite néanmoins de limiter les pertes optiques et le bruit de phase qui réduisent fortement le degré de squeezing.
Durant O3, l'injection de squeezing indépendant de la fréquence permet ainsi de réduire de 3dB le shot-noise et d'augmenter la BNS range de 2Mpc

Orateur: Marc Eisenmann (LAPP Virgo)

GdR_2019.pdf

20 Optical design of the Advanced Virgo + detector

Advanced Virgo+ (AdV+) will see the improvement of several aspects of the Advanced Virgo (AdV) detector. In this talk we will give an overview of the efforts on-going for the optical design of the detector. In particular, we will describe the activity related to the increase of the beam size on the test masses, in order to reduce the coating Brownian noise.

Orateur: Jonathon Baird (APC)

AdV_OpticsUpdate.pdf

Groupe de travail: Méthodes d'analyse des données

21 LISA Data Challenge

LISA is in the mission definition stage (phase A). The instrumental design defines the LISA operation and sensitivity which in turn affect the scientific outcome of the mission. We conduct a program of LISA data challenges where we simulate the LISA data and advertise it to the scientific community at large. The idea is to let people try to extract maximum information from the data (using their favorite data analysis methods) and return results back to LISA project. I will
describe the current LISA data sets and outline the future directions.

Orateur: Stanislav Babak (APC)

LDC_2019.pdf

22 Reconstruction et caractérisation non-paramétriques de la polarisation des ondes gravitationnelles des coalescences de trous noirs avec précession

Nous proposons une procédure d'analyse de données qui, à partir des signaux mesurés par un réseau d'au moins trois détecteurs, permet l'estimation de la direction de la source, et reconstruit les deux polarisations d'une onde gravitationnelle, sans avoir recours à un modèle spécifique pour la dynamique de la source. Nous calculons ensuite les paramètres de Stokes instantanés associés aux deux polarisations ainsi reconstruites, ce que fournit un ensemble d'observables "non-paramétriques" permettant la caractérisation du motif de polarisation de l'onde gravitationnelle et son évolution au cours du temps. Il est possible d'en déduire des propriétés de la source astrophysique comme une indication de la précession du plan orbital d'une binaire compacte coalescente de trous noirs.

Orateur: Cyril Cano (Gipsa-lab)

presentation_GDR_OG.pdf

23 GWOSC: Gravitational Wave Open Science Center

The LIGO Scientific Collaboration and Virgo Collaboration actively pursue an open science programme. Gravitational wave strain data are publicly released through the website http://www.gwopenscience.org along with the information and tools necessary to understand and use the data.
This contribution will give an overview of past and current activities related to this topic and will give a sense of its impact on science, teaching and other applications.

Orateur: Agata Trovato (APC-CNRS)

2019_10_11_Trovato.key

2019_10_11_Trovato.pdf

24 Single pulsar analysis on PSR J1909-3744 : Limits on the low-frequency stochastic gravitational wave background

Pulsar Timing Array (PTA) projects intend to detect low-frequency gravitational waves (GWs) by probing their imprints on times of arrival (TOAs) of pulsar radio signals. PTAs are sensitive to nanohertz GWs, corresponding for instance to the emission from super-massive black hole binaries (SMBHBs). One expects to measure the superposition of continuous GWs originating from the cosmic population of such objects as a stochastic signal. Individual nearby massive systems could also produce a detectable GW signal that rises above the gravitational wave background. Precise and high cadence pulsar timing observations are carried out over a long time span in order to obtain highly accurate (sub mu-s) pulsar TOA residuals. Observed with the Nançay Radio Telescope since 2004, PSR J1909-3744 is one of the most stable pulsar known today (timing precision < 100 ns). I will present some preliminary results on a gravitational wave background upper-limit study for this pulsar.

Orateur: Aurélien Chalumeau (APC - LPC2E)

Presentation_achalumeau_Lyon_GdR_1910.pdf

25 Recherche à faible latence de coalescences binaires avec MBTA et alertes publiques pendant O3

La période d'observation O3 a commencé en avril dernier.
Durant cette période, plusieurs pipelines d'analyse recherchent des coalescences d'objets compacts dans les données recueillies par les détecteurs LIGO et Virgo.
MBTA a ainsi pu participer à l'identification de nombreux candidats impliquant des trous noirs et des étoiles à neutrons.
De tels candidats sont rendus publics quelques minutes seulement après leur découverte, pour permettre un suivi multi-messagers et une meilleure compréhension des sources d'ondes gravitationnelles.
Après un récapitulatif des différents types de recherche et des alertes publiques qui ont été émises, je reviendrai sur les spécificités de MBTA et discuterai les perspectives concernant ce pipeline d'analyse.

Orateur: Florian Aubin (LAPP)

Recherche à faible latence de coalescences binaires avec MBTA et alertes publiques pendant O3.pdf

11:30 pause café

Groupe de Travail: Prédiction et suivi des signaux multi-messager

26 Prédiction et suivi des signaux multi-messager

TBA

Orateur: Susanna Vergani (CNRS-Observatoire de Paris)

GDRGW19_Vergani.pdf

27 Observations of Hard X-ray counterparts of multi-messenger transients with INTEGRAL

Recent years were marked by breakthrough observations of new multi-messenger and multi-wavelength transients, often unveiling unanticipated and puzzling phenomena. Likely almost universally associated with most energetic processes in the dense regions at the heart of the peculiar supernovae, mergers of compact objects, or tidal disruption events, these events expose unique signatures in hard X-ray and gamma-ray emission.

I will highlight recent pioneering observations of short energetic transients made with INTEGRAL, which is especially well-equipped to observe unpredictable, short-lived, and energetic hard X-ray and gamma-ray transients. It carries a collection of detectors that monitor the entire hard X-ray sky with over 80% duty cycle and are able to re-point to perform deep and sensitive hard X-ray observations of a large selected sky region.

Finally, I will review how the recent discoveries in the domain of multi-messenger transients were made possible by a global effort to achieve a new degree of automation and interoperability.

Orateur: Volodymyr Savchenko (University of Geneva)

INTEGRAL GW - 2019 O3a.pdf

28 SVOM et le suivi des alertes OG

Je présenterai le statut de satellite SVOM et la politique du consortium pour le suivi des alertes multi-messagers, en particulier pour les alertes ondes gravitationnelles

Orateur: Nicolas Leroy (LAL IN2P3/CNRS)

Leroy_GDROG2019_SVOM.pdf

13:00 Déjeuner au buffet + visite salle blanche LMA

Groupe de travail: Populations des sources

29 Binary population models of GW progenitors

The LIGO/Virgo detections of gravitational waves from merging massive black holes
suggest progenitor stars of low metallicity. In this talk I will provide constraints on the formation of the stellar progenitors based on advanced models of galaxy formation and evolution
combined with binary population synthesis models. First I will combine
estimates of galaxy properties (star-forming gas metallicity, star
formation rate and merger rate) across cosmic time to predict the low
redshift BBH merger rate as a function of present day host galaxy
mass, formation redshift of the progenitor system and different
progenitor metallicities. I will show that the signal is dominated by
binaries formed at the peak of star formation in massive galaxies with
and binaries formed recently in dwarf galaxies. Then, I will present
what very high resolution hydrodynamic simulations of different galaxy
types can learn us about their black hole populations.

Orateur: Astrid Lamberts (Observatoire de la Côte d'Azur)

30 Constraining galaxy and black hole binary mergers with pulsars

We have strong evidence that super massive black holes reside in most galaxies. Galaxies have also been observed to merge, consequently the central black holes should also form a binary and eventually merge. These super massive black hole binaries (SMBHBs) emit gravitational waves (GWs) as they spiral into each other. The superposition of all the GWs emitted by the cosmic population of SMBHBs form a gravitational wave background (GWB). This GWB affect the time of arrival (TOA) series of the radio signals from pulsars in a characteristic and correlated fashion. Pulsar Timing Arrays (PTAs) make use of this fact and aim to detect gravitational waves by precisely timing an array of pulsars.

One of the prime targets for PTAs is the GWB from a population of SMBHBs. SMBHBs have a strong relation with their host galaxies, in fact, we believe that SMBHBs are created via the merger of the host galaxies. Thus, the rate at which galaxies merge is related to the population of merging SMBHBs. The GWB frequency spectrum can be computed by integrating the emission of one single binary over the whole population. I will present a parametric model to compute the strength of the GWB from the population of SMBHBs in terms of astrophysical observables. These include the galaxy stellar mass function, pair fraction and merger time scale as well as the
galaxy mass - black hole mass relation with scattering. All of which are interesting quantities, that have already been measured and constrained. Using a PTA upper limit on the GWB, we can directly compare and combine the constraints on these astrophysical observables from electromagnetic observations with those from PTAs. I will present results with our nested sampling algorithm, showing how much (or little) PTAs can tell us about galaxy and black hole mergers.

Orateur: Siyuan Chen

Presentation_chen_gdrog.pdf

31 Merger rates of binary neutron stars and r-process element abundances in the Milky Way

The chemical abundance patterns of Milky Way stars allow to trace the nucleosynthetic processes that took place before these stars were born, and in particular, to study the sources of r-process elements. In this talk I will discuss the contribution of binary neutron star mergers to the production of r-process elements, focusing on the effect of the delay time distribution between the formation and merger of binary neutron stars. I will also discuss the dispersion in the observed abundances of r-process elements.

Orateur: Irina Dvorkin (Institut d'Astrophysique de Paris)

dvorkin_lyon_oct19.pdf

Groupe de travail: Etoiles à neutrons, supernovae et synthèse des éléments lourds

32 Peut on identifier une transition de phase dans une coalescence de binaire d'étoiles à neutrons via les ondes gravitationnelles ?

Les fréquences des oscillations dans l'objet massif issu de la coalescence de deux étoiles à neutrons portent les caractéristiques de la matière dense et chaude. Dans cette contribution je discuterai les perspectives d'identifier une potentielle transition de phase entre matière hadronique et plasma de quarks et gluons via la détection d'ondes gravitationnelles émis dans cette phase "post-merger".

Orateur: Micaela Oertel (LUTH, Observatoire de Paris)

oertel.pdf

oertel.pdf

33 Towards a better understanding of dense matter with gravitational waves

The observation of the tidal deformability extracted from GW170817 have been analyzed by many teams, leading to boundaries of the neutron star radius. In our analysis, we contrast continuous EoS with EoS with strong first order phase transitions showing that these two cases induce different constrain on global neutron star properties. We also explore the impact of low density neutron matter predictions from chiral EFT approach, and we show that our current nuclear physics knowledge is still a bit more constraining than GW170817 tidal deformability. We also analyze the required accuracy for the tidal deformability which can make it compete with nuclear knowledge and the one which could shed light on the presence of phase transition in the core of NS.

Orateur: Jérôme Margueron (IPN Lyon)

2019-10-GDR.pdf

34 Résumé de la réunion “Equations d’état dans Virgo”

Nous présenterons un résumé de la réunion commune avec le groupe de travail astrophysique du GdR RESANET qui a eu lieu le 13 mai à Paris. Cette réunion était focalisée sur la possible mise en place des résultats récents de physique nucléaire sur l’équation d’état de la matière dense dans l’analyse des données de Virgo.

Orateurs: Anthea Francesca FANTINA ({CNRS}UPR3266), Jérôme Novak (LUTH, CNRS - Observatoire de Paris)

35 Discussion sur "Equations d'état dans Virgo"

Discussion générale + goodbye