Astrophysical implication discussion of TAROT and GRANDMA observations

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Gamma-ray bursts

During the cold war era, the United States and the Soviet Union adopted the ”Nuclear Test Ban Treaty” in 1963 to limit nuclear bomb tests in the Earth atmosphere and in space. To check the respect of the treaty the United States launched eleven satellites, named Vela, equipped with scintillator sensors sen-sitive to high energy photons. The signal analysis revealed the existence of GRBs by chance. The first GRB was captured by Vela satellites on 2 July 1967 and its light curve is shown in Figure 2.12. Waiting the detection and analysis of 15 additional events, Klebesadel et al. (1973) published the dis-covery confirming their cosmic origin. A GRB is the observation of short duration and intense emissions of EM spectrum centered at about 100 keV (Cline et al., 1973). To explain such an amount of energy GRBs were linked to explosions of stars as soon as their discovery (Klebesadel et al., 1973; Woosley et al., 1999). Indeed, the short duration and milliseconds pulses imply a small dimension progenitor as NSs or BHs.
The high energy sensor technology of the years before 1980 did not allow to determine precisely the incident direction of gamma-rays. The question of the direction is important because, if the spatial provenance is concentrated to the direction of our Galaxy we can conclude the GRB progenitors are lo-cated in the Milky Way. Else, the GRBs will be located much more far and perhaps coming from elsewhere in the Universe.
The burst duration is not easy to define because the end of gamma emis-sion has often a shape of an exponential tail. The duration of a GRB is commonly defined by the T90 duration (Kouveliotou et al., 1993). Starting from the light curve, one can compute the instant t5% when 5% of the flux was emitted and t95% when 95% of the flux density was emitted. Then T90= t95% – t5%. Most of GRBs have T90 lying between few milli-seconds and some hundred of seconds.
Figure 2.12: The light curve of the first GRB detected by the Vela IVa satellite on 2 July 1967 (Klebesadel et al., 1973).
Note that the flounce, i.e integrated energy over the burst duration, is about 10−6 erg/cm2 (with variation of a few orders of magnitude from an event to the other). Converted to a typical galactic distance it corresponds to a source emitting an energy of EISO ≃ 1043 ergs (EISO stands for an isotropic emission of the energy). Converted to an extra-galactic distance of 1 giga-parsec EISO ≃ 1050 ergs. We must compare these energies with the Solar mass energy (E=mc2) of EISO ≃ 1054 ergs. The duration of gamma-rays being limited to few seconds, and considering that only a small fraction of the stellar mass can be converted in energy, privilege a galactic origin if the emission is isotropic. The great debate during the ’90 was to discuss about the galactic versus extra-galactic origins (Paczy´nski, 1991).
The CGRO in operation between 1991 and 2001 was equipped by the experi-ment BATSE consisting in eight detectors allowing to determine the angular position in sky of about 3000 GRBs (about 1 event per day during 10 years) with a precision of about 5 degrees (Fishman et al., 1982). Despite this low spatial resolution, as soon as 1996, the measures allowed to convince the community that the progenitors of GRBs have an origin outside our Milky Way (Briggs et al., 1996), see Figure 2.15.
From previously mentioned energetic reasons, it was not probable that an extra-galactic source was emitting its energy isotropically. Then the energy had to be emitted in a narrow beam. In such a beam one is then confronted with the problem of compactness. Indeed, the gamma photons emitted in a compact zone have the property of interacting rapidly by forming electron positron pairs. These electron positron pairs end up annihilating by radiating but no gamma ray emission above energy of 1 MeV should be detected. How-ever, gamma rays above this limit are detected during GRBs. The problem of compactness, however, is circumvented if we add the hypothesis that the ejection of the material into the beam is at ultra-relativistic speeds towards the Earth (Piran, 1999). Under these conditions, the speed (denoted v) is always greater than 99% of that of the light (denoted c) and it is preferable to use the notion of Lorentz factor defined by equation 2.4:
In this context, the gamma emission would come from the collision of lumps of matter that catch up in the ejected jet. To generate enough energy each lump must travel with a factor > 100 with small differences from one to the other to generate collisions. The collisions are weak shocks that cause an X-ray emission that does not suffers from the problem of compactness. The emission of gamma radiation, seen from the Earth, then comes from the Doppler-Fizeau shift by the factor > 100 towards the blue of the emission X due to shocks inside the jet (Meszaros and Rees, 1993). Finally, the problem of compactness is completely bypassed by the effect of relativistic aberration. Indeed, the light emitted by a particle moving with a relativistic velocity can be observed only in a cone whose principal axis is directed according to the direction of motion of the particle. The opening angle θ of the relativistic aberration cone is given by the relation 2.5:
For a value = 100, we have θ = 0.6 degrees. Thus, each emitted photon has no interaction with the space outside this narrow cone, which virtually eliminates any absorption of high energy photons.
The principle of the emission of high-energy photons from GRBs results in the synchrotron radiation of electrons in magnetic fields in the jet as large as 103 to 104 Gauss (Proga et al., 2003). The magnetic field would then be created during collisions in a relatively confined region around the progenitor star and usually referred to as internal shocks (Paczynski and Rhoads, 1993).
The spectral hardness of a burst corresponds to the ratio between the num-ber of photons at high and at low energy. The high / low energy limit is arbitrary and depends mainly on detector technology for each experiment. In the case of BATSE, hardness is defined as the ratio between 100 to 300 keV photons and those emitted between 50 and 100 keV. A hard burst has a spectrum richer in gamma rays than in X-rays. The representation of each burst in the form of a point in a duration / hardness diagram clearly shows two categories: The SGRBs (hard and T90<2s) and long gamma-ray bursts (LGRBs) (soft and T90>2s) (Kouveliotou et al., 1993), see Figure 2.16.
A major breakthrough came with the BeppoSAX satellite (1995-2002). This satellite was equipped with a wide field coded mask camera providing X-ray images with a resolution of a few arcmin (Scarsi, 1984). The satellite was repointed to the bursts detected by BATSE. The burst of February 28, 1997 was detected by BeppoSAX a few hours after the gamma flash in the form of an X-ray source whose brightness was decreasing rapidly (Costa et al., 1997). This event made it possible to distinguish the prompt emission, the gamma flash itself, and the afterglow which lasts for several days after the burst. From the precise position of BeppoSAX, it was possible to point the terres- trial telescopes towards the X-ray source. At this location, a point source of visible light was detected at the magnitude 20, whose brightness decreased in the same way as the X-ray source.
Figure 2.16: Distribution of GRB T90 durations in the 50-300keV energy range (top) and classification based on the hardness-duration diagram (bot-tom). Colors indicated their group membership (red: on average short/hard, blue: on average long/soft). Ellipses show the best fitting multivariate Gaus-sian models (Bhat et al., 2016).
The interpretation of the afterglow is that the material ejected by the jet meets the gas of the interstellar medium (Piran and Granot, 2001). An external shock occurs, consisting of the slowing of the ejecta that hits the in-terstellar medium. This shock is much more violent than the internal shocks because it is no longer two layers that catch up but a frontal collision with an initially immobile medium. During external shock, the factor decreases by a factor of 10 or more. The external shock accelerates the electrons of the interstellar medium and creates strong magnetic fields, which results in the generation of synchrotron radiation observable from X-rays to radiomet-ric waves. The common accepted model of the external shock is the fireball model (Goodman, 1986; Piran, 1999) which will be discussed later.
The afterglow optical emission is important because it acts as a lighthouse in front of which all properties of the matter located between the GRB and the Earth will be able to be measured by absorption spectrometry. The spectrum features are affected by the cosmological redshift which allow to estimate the distance of the GRB progenitor. The LGRBs have an average redshift of ∼ 2. Some very far GRBs have a redshift larger than 6.
The first X and optical light curves showed a decay for which the flux de-creases as t−α where t is the time that separates the moment of the measure from the beginning of the gamma emission. The light curve is therefore a line in a representation of the magnitude, as a function of the logarithm of t. Generally α is close to 1. This decay index value is important because it means that the afterglow looses a factor 10 in flux between t=2 minutes to t=20 minutes, another factor 10 in flux between t=20 minutes to t=3 hours and so on. The practical consequence is that optical telescopes must start observations as early as possible to maintain the afterglow brighter than the limiting magnitude of the sensors.
For some LGRBs for which the redshift z < 1, after the initial afterglow decay, one can find a faint bump of optical light peaked at around 30 days after the gamma-ray emission (Stanek et al., 2003). The spectral analysis of the light in this bump shows that this component is related to type Ib/c supernova (often called hypernova). This late event tends to prove that the progenitors of LGRBs are the end of life of isolated ≥35 solar mass stars.
SGRBs progenitors must have very small size expected by the short duration of the gamma-ray emission. The progenitor must be surrounded by matter to allow gamma emission. This excludes BHs that are believed to sweep all the surrounding mater. It remains NSs. However, to explain the reservoir of energy used to create the jet of a GRB, the model of the merging of two NSs is commonly accepted after the discovery and interpretation of GRB 050709 (Hjorth et al., 2005).
Figure 2.17: Schematic view of a GRB, from a collapsing massive stellar progenitor until the production of gamma-ray and EM waves (Piran, 1999).
Considering the very different progenitor natures of SGRBs and LGRBs one can be surprised by such a common phenomenological consequences that mix them in same designation: GRBs. Regarding the physics, both GRB types start with collapse of matter: External envelope for LGRBs or merging of stars for SGRBs. Then, one can consider a central engine constituted by a massive compact object transforming the falling matter into a beamed ultra-relativistic jet. Many questions remain to answer to explain the efficiency of such a transformation. The later phases, i.e. the evolution of the jet and the afterglow, are generally treated by the so-called fireball model.
The fireball model (Goodman, 1986) explains how the kinetic energy of the relativistic flow and some micro physic parameters can explain the spectral energy distribution and its evolution with time (see Figures 2.17 and 2.18). In this way it is possible to fit fireball model parameters to explain the light curve at different wavelengths (Turpin, 2016).
From bibliographic data provided by Damien Turpin (private communica-tion), we are able to plot a collection of optical light curves (Figure 2.19). From these plots we can derive parametric envelopes of light curves using a broken power law (Equation 2.6):
The a parameter characterizes the slope of the rise and b is the slope of the decay. The s parameter is the smoothing factor that shapes the break at the time t0. The Table 2.2 gives the fitted parameters.
Figure 2.19: Observed light curve of GRBs for which the redshift is known. Top panel: Optical light curves of 141 long GRBs (red lines). Bottom panel: Optical light curves of 6 short GRBs (black lines). We correct the distance to plot magnitude in absolute scale. The pink lines show the brightest and faintest of energy predicted by Equation 2.6

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Theories of EM emissions from BNSs and the relation between GWs and GRBs

A common object type is invoked for GW and GRB emissions: The BNS merger. The GW emission increases strongly few seconds before the merging and stops few tenths of seconds after. The GRB emission results from internal shocks in a polar jet ejected after the merging occurs. A rapid GW wave form analysis allows to determine the masses of the binary system and also its distance (see formula 2.2 and 2.3). Few minutes after the merging such an event can be classified as BNS, BBH or neutron star-black hole (NSBH).

Theory of kilonova

The merging of BNS or NSBH is expected to eject matter from the NS. Metzger et al. (2010) studied the process which was refined year after year (Metzger, 2017). A huge quantity of neutrons should be blown up in expand-ing shells and the energy will be released at optical wavelengths many hours later. The theory predicts also a luminosity reaching 1000 times that of a classical nova, giving the name of kilonova for the EM emission. The peak of luminosity depends strongly on the wavelength.
Metzger et al. (2010) predicted that the huge quantity of free neutrons injected in the expanding shells will be absorbed by atomic nuclei creating heavy unstable nuclei (i.e. r-process). Lanthanide nuclei are expected to be created. They induce a high opacity ejecta which gives a unique signature of optical light curves: A blue peak is expected less than one day after the merging followed by a near-infrared peak few days after. This behaviour is very different compared to supernovas associated to LGRB.
Until 2017 only one kilonova was tentatively identified by the late optical light curve of the short GRB 130603B (Tanvir et al., 2013). The discovery of GW170817/GRB170817A confirmed the concept of kilonova.

Table of contents :

1 Introduction 
2 Scientific background 
2.1 Gravitational waves
2.2 Gamma-ray bursts
2.3 Theories of EM emissions from BNSs and the relation between GWs and GRBs
2.4 Theories of EM emissions from BBHs
3 The TAROT telescopes 
3.1 Anatomy of the telescopes
3.2 Historical GRB observations with TAROT
3.2.1 GRB 050525A
3.2.2 GRB 050904
3.2.3 GRB 060111B
3.2.4 GRB 110205A
3.2.5 GRB 111209A
3.2.6 GRB 180418A
3.3 Conclusions on GRB observations with TAROT
4 Optical transient search during runs O1 and O2
4.1 GW detections by interferometers during runs O1 and O2
4.2 TAROT observations
4.3 The image analysis method
4.4 The transient search algorithm
4.5 Image analysis and results
5 Optical transient search during run O3 
5.1 GW detections by interferometers during run O3
5.2 GRANDMA-TAROT observations
5.3 The transient search pipeline
5.4 Detection results
6 Astrophysical implication discussion of TAROT and GRANDMA observations 
6.1 Summary of GW detections by LIGO/Virgo
6.2 Spatial completion of optical observations
6.3 Energy constraints from optical observations
6.4 Analysis of BBH events observed by TAROT during runs O1 and O2
6.5 Comparison of optical limits of GWevents observed by GRANDMA with GRB and kilonova light curves
7 Conclusions

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