A class of long gamma-ray bursts (GRBs) presenting light curves with an extended plateau phase in their X-ray afterglows obeys a correlation between the rest-frame end-time of the plateau, T _a , and its corresponding X-ray luminosity, L _a , (Dainotti et al). In this work we perform an analysis of a total sample of 176 Swift GRBs with known redshifts, exhibiting afterglow plateaus. By adding a third parameter that is the peak luminosity in the prompt emission, L _peak, we discover the existence of a new three-parameter correlation. The scatter of data about this plane becomes smaller when a class-specific GRB sample is defined. This sample of 122 GRBs is selected from the total sample by excluding GRBs with associated supernovae (SNe), X-ray flashes and short GRBs with extended emission. With this sample the three-parameter correlation identifies a GRB “fundamental plane.” Moreover, we further limit our analysis to GRBs with light curves with good data coverage and almost flat plateaus, 40 GRBs forming our “gold sample.” The intrinsic scatter, , for the three-parameter correlation for this last sub-class is more than two times smaller than the value for the one, making this the tightest three-parameter correlation that involves the afterglow plateau phase. Finally, we also show that a slightly less tight correlation is present between L _peak and a proxy for the total energy emitted during the plateau phase, , confirming the existence of an energy scaling between the prompt and afterglow phases.

The X-ray afterglow plateau emission observed in many gamma-ray bursts (GRBs) has been interpreted as being fueled either by fallback onto a newly formed black hole or by the spin-down luminosity of an ultra-magnetized millisecond neutron star. If the latter model is assumed, GRB X-ray afterglow light curves can be reproduced analytically. We fit a sample of GRB X-ray plateaus, interestingly yielding a distribution in the diagram of magnetic field versus spin period (B–P) consistent with B ∝ P ^7/6, which is consistent with GRB expectations of the well-established physics of the spin-up line for accreting Galactic X-ray pulsars. The normalization of the relation that we obtain perfectly matches spin-up line predictions for typical neutron star masses (∼1 M _⊙) and radii (∼10 km), and for mass accretion rates typically expected in GRBs, . Short GRBs with extended emission (SEEs) appear toward the long-period end of the distribution, and long GRBs (LGRBs) toward the short-period end. This result is consistent with expectations from the spin-up limit, where the total accreted mass determines the position of the neutron star in the B–P diagram. The B–P distributions for LGRBs and SEEs are statistically different, further supporting the idea that the fundamental plane relation—a tri-dimensional correlation between the X-ray luminosity at the end of the plateau, the end time of the plateau, and the 1 s peak luminosity in the prompt emission—is a powerful discriminant among those populations. Our conclusions are robust against suppositions regarding the collimation angle of the GRB and the magnetar braking index, which shift the resulting properties of the magnetar parallel to the spin-up line, and strongly support a magnetar origin for GRBs presenting X-ray plateaus.

Long gamma-ray bursts (GRBs) with a plateau phase in their X-ray afterglows obey a 3D relation, between the rest-frame time at the end of the plateau, T a , its corresponding X-ray luminosity, L a , and the peak luminosity in the prompt emission, L peak. This 3D relation identifies a GRB fundamental plane whose existence we here confirm. Here we include the most recent GRBs observed by Swift to define a "gold sample" (45 GRBs) and obtain an intrinsic scatter about the plane compatible within 1σ with the previous result. We compare GRB categories, such as short GRBs with extended emission (SEE), X-ray flashes, GRBs associated with supernovae, a sample of only long-duration GRBs (132), selected from the total sample by excluding GRBs of the previous categories, and the gold sample, composed by GRBs with light curves with good data coverage and relatively flat plateaus. We find that the relation planes for each of these categories are not statistically different from the gold fundamental plane, with the exception of the SSE, which are hence identified as a physically distinct class. The gold fundamental plane has an intrinsic scatter smaller than any plane derived from the other sample categories. Thus, the distance of any particular GRB category from this plane becomes a key parameter. We computed the several category planes with T a as a dependent parameter obtaining for each category smaller intrinsic scatters (reaching a reduction of 24% for the long GRBs). The fundamental plane is independent from several prompt and afterglow parameters.

Gamma-ray Bursts (GRBs) are the most explosive phenomena in the universe after the big bang. A large fraction of GRB lightcurves (LCs) shows X-ray plateaus. We perform the most comprehensive analysis of all GRBs (with known and unknown redshifts) with plateau emission observed by The Neil Gehrels Swift Observatory from its launch until 2019 August. We fit 455 LCs showing a plateau and explore whether these LCs follow closure relations, relations between the temporal and spectral indices of the afterglow, corresponding to two distinct astrophysical environments and cooling regimes within the external forward shock (ES) model, and find that the ES model works for the majority of cases. The most favored environments are a constant-density interstellar or wind medium with slow cooling. We also confirm the existence of the fundamental plane relation between the rest-frame time and luminosity at the end of the plateau emission and the peak prompt luminosity for this enlarged sample, and test this relation on groups corresponding to the astrophysical environments of our known redshift sample. The plane becomes a crucial discriminant corresponding to these environments in terms of the best-fitting parameters and dispersions. Most GRBs for which the closure relations are fulfilled with respect to astrophysical environments have an intrinsic scatter σ compatible within 1σ of that of the “Gold” GRBs, a subset of long GRBs with relatively flat plateaus. We also find that GRBs satisfying closure relations indicating a fast cooling regime have a lower σ than ever previously found in literature.

The Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope (Fermi) shows long-lasting high-energy emission in many gamma-ray bursts (GRBs), similar to X-ray afterglows observed by the Neil Gehrels Swift Observatory (Swift). Some LAT light curves (LCs) show a late-time flattening reminiscent of X-ray plateaus. We explore the presence of plateaus in LAT temporally extended emission analyzing GRBs from the second Fermi-LAT GRB Catalog from 2008 to 2016 May with known redshifts, and check whether they follow closure relations corresponding to four distinct astrophysical environments predicted by the external forward shock model. We find that three LCs can be fit by the same phenomenological model used to fit X-ray plateaus and show tentative evidence for the existence of plateaus in their high-energy extended emission. The most favorable scenario is a slow-cooling regime, whereas the preferred density profile for each GRBs varies from a constant-density interstellar medium to an r ⁻² wind environment. We also compare the end time of the plateaus in γ-rays and X-rays using a statistical comparison with 222 Swift GRBs with plateaus and known redshifts from 2005 January to 2019 August. Within this comparison, the case of GRB 090510 shows an indication of chromaticity at the end time of the plateau. Finally, we update the 3D fundamental plane relation among the rest-frame end time of the plateau, its correspondent luminosity, and the peak prompt luminosity for 222 GRBs observed by Swift. We find that these three LAT GRBs follow this relation.