## Periodic Report Summary 1 - COSMOLOGICAL CANDLES (New Cosmological Standard Candles from Gamma Ray Burst Correlations)

The study of cosmic Gamma-Ray Bursts (GRBs), the most powerful and distant phenomena ever observed so far, is of fundamental importance for modern astrophysics and cosmology, because of the extreme physics involved in their relativistic outflows, their connection with the formation of stellar mass black-holes and, in particular, their potential use for investigating the expansion rate and geometry of the Universe. Indeed, thanks to their huge luminosity, GRBs are observed at distances (redshift) much farther than Type Ia Supernovae (SNe Ia), which are the most robust probes of the accelerating Universe, a discovery that was awarded the Nobel Prize in 2011 and implies the existence of a “Dark Energy” or the need for modifying the Einstein’s field equation. Several proposed models for Dark energy, as well as alternative cosmological models, can be discriminated only with astrophysical probes with distances extending much beyond those of SNe-Ia, limited to redshift of 1.5 - 2. Thus, GRBs, which can be observed even beyond the epoch when the first stars start re-ionizing the intergalactic medium (i.e., up to redshift 10 or even more, that is a few hundred million years after the Big-Bang) are potentially a unique probe to test the evolution of Dark Energy and alternative cosmological models. To this end, it is crucial to understand if they can be considered standard candles (astronomical objects whose luminosity is known or can be derived from other distance-independent observables) as SNe Ia and thus can be used as precise distance indicators. Indeed, GRBs seem to be far from standard candles, with their luminosities spanning over eight orders of magnitude. Thus, discovering universal relations linking observable GRB properties and their luminosity or radiated energy is a basic step toward using them as precise distance indicators for cosmological applications. Moreover, investigating relations between important GRB characteristics will shed light not only on their use as possible standard candles, but can also provide new constraints for the physical models of the GRB explosion mechanism.

The project’s aim is to update in a multi-wavelength range, from 0.3 keV to 300 GeV, the luminosity-time correlation (Lx-Tx) for GRBs (known in the literature as the “Dainotti relation”) and identify a subclass of GRBs with well-defined properties and bias-free, namely corrected by redshift evolution and selection effects due to instrumental threshold through refined statistical methods. This subclass will be the candidate for GRB standard candles. The bias-free Lx-Tx correlation might be the basis for a new independent and powerful cosmological tool. Finally, the challenge is to use the Lx-Tx correlation together with other correlations, like the Ep – Eiso correlation (known in the literature as the “Amati relation”), both corrected for selection biases in order to discriminate among theoretical models, to use them as cosmological tools and valuable redshift estimators. The expected final results are to obtain a cosmological tool for GRBs derived through the combination of the Amati and Dainotti correlations after their corrections for selection biases and cosmological evolutions. The potential impact is to use these two correlations to improve significantly the accuracy in the determination of the cosmological parameters with GRBs and in perspective to use them for investigating property and evolution of dark energy and testing alternative cosmological models. In addition, the improved characterization of these correlations will provide a fundamental step forward in shedding light on the still poorly understood physics of GRB “prompt” (i.e., the burst of gamma-rays itself) and “afterglow emission” (i.e., the multi-wavelength fading and weaker emission which follows the burst).

The wider societal implications relies on a broader and deeper understanding of the geometry and expansion rate of our Universe, including the nature of newly discovered and still mysterious components like “Dark Energy” and/or modifications to the general relativity theory, the fundament of modern cosmology and of the “Big-bang” standard cosmological model. This progress in the Universe understanding will also provide an increasing awareness of the perspective offered by the investigation of very far away astrophysical phenomena like GRBs and their use to map the evolution and properties of the Cosmos, thus constituting a unique bridge between astrophysics, cosmology and fundamental physics.

The main results achieved so far have been featured in the 11 publications (refereed papers, conference proceedings, and additional papers in preparation) and are summarized in the points below.

1. Prompt-afterglow correlations. The discovery of a unique luminosity-time (hereafter LT) correlation which spans from prompt to afterglow is presented in [1]. Within this framework, the Researcher updated the Lx-Tx relation and the Lpeak-Tγ relation. With a sample, which is doubled compared to previous work it is possible to explain the presence of an offset between the two LT relations (those ones related to the prompt and the afterglow). The Researcher applied the Efron and Petrosian method and demonstrated that the Lpeak-Lx relation is not due to selection bias, but it is intrinsic to the physics of GRBs.

2. The discovery of the fundamental plane. This discovery opened the way to a new 3 parameter correlation, namely the Lx-Ta-Lpeak correlation [3] which is also intrinsic to the physics of GRBs because both Lx-T*a and Lpeak-Lx are intrinsic. The Lx-Ta-Lpeak correlation, which identifies a fundamental plane, has an intrinsic dispersion 54% smaller than the (LX, Ta) one, and therefore will result in an improved correlation that can allow the use of GRBs as standard candles. This result has been chosen as highlight from the American Astronomical Society and as a press conference at AAS [4].

3. The magnetar model and the Galactic magnetar population. Within the context of the magnetar model, a millisecond spinning neutron star with high magnetic field, [2] debated on the reliability of this model as the correct interpretation for the X-ray plateaus. The GRB-magnetar model in its present form is safe only if GRB magnetar progenitor should be different from Galactic magnetars and should be considered super-magnetars.

4. The study of the Lx-Ta relation and GRBs associated with SNe. The subsample of long GRBs associated with SNe (LONG-SNe) presents a very high correlation coefficient for the Lx-Tx correlation and a slope of roughly -2. This possibly suggests that this category might not require a standard energy reservoir in the plateau phase unlike the long GRBs for which no SNe has been observed (LONG-NO-SNe). Therefore, this analysis may open new perspectives in future theoretical investigations of the GRBs with plateau emission and associated with SNe. Namely, a different theoretical scenario from the magnetar and the accretion for which the energy reservoir of the plateau is not constant can be found (This replies the 8th bullet of clarifications in the summary. The project tasks has been fully achieved). The Researcher also discusses how much this difference can be due to the jet opening angle effect.

5. Review on GRB prompt-afterglow correlations. The mechanism responsible for the afterglow emission of GRBs and its connection to the prompt is still a debated issue. Thus, the Researcher presents an overview of the afterglow and prompt-afterglow two parameter correlations, their physical interpretations, and their use as redshift estimators, as possible cosmological tools and on how they are corrected for selection biases [10].

6. The Lx-Ta relation and the decay index in the afterglow emission. In the context of reducing the scatter of the Lx-Tx correlation, [5] investigated the indices α after the plateau phase for a sample of 176 GRBs detected by Swift. They concluded that the LT correlation for the low and high luminous GRBs seems to depend differently on the α parameter, thus implying a diverse density medium dominating the afterglow emission.

7. The Fermi-LAT analysis. The Fermi-Large Area Telescope (LAT, 20 MeV-30 GeV) shows long lasting high energy emission in many GRBs similar to the X-ray afterglows observed by Swift. Some of the lightcurves (LCs) show a late time flattening reminiscent of the X-ray plateaus. The Researcher investigates how many GRBs seen by LAT show a plateau similar to the observed X-ray and if the mechanism that powers the gamma- and X-ray plateaus is the same. The Researcher has pioneered a thorough analysis of LAT LCs present in all Fermi LAT sources observed so far using the new event data algorithm PASS 8; has found that among the 120 GRBs observed by the LAT in 4 cases it is possible to identify a secure plateau emission; has also investigated if the LAT GRBs are generated via synchrotron emission in the external shock (ES) and verified the so called closure relations α=(3*β-1)/2 between the temporal decay index α of the LCs and the energy spectral index β above 100 MeV. This relation serves as a rough indication that the observed radiation is being produced in the ES.

8. The Epeak-Eiso relation. Regarding the Epeak-Eiso or Epeak-Lpeak intrinsic correlation the Researcher has investigated so far the data which present a Band function and a cut-off power law in the spectrum of GRBs. The Researcher has preliminary approximated the Epeak distribution with a Gaussian. The intrinsic Epeak distribution peaks at higher energies than the observed one in the Swift data. The Researcher has computed the minimum and maximum Epeak for this distribution, written a code for the determination of the intrinsic distribution and make use of the R code publicly available in order to compare her code and the one available to the public in R.

9. GRBs as redshift estimators through a machine learning tools. The Researcher adopted several cutting edge methods of supervised machine learning to use different observables to build a GRB redshift estimator. Methods applied are the so called random trees, random forests and the generalized additive models, GAM. The first two methods are completely non-parametric thus allowing to identify the best predictors (the observed variables) of redshift as well as to determine groups of similar GRBs in terms of the values of the predictors and the redshift. GAM models builds a non-parametric relationship between the response variable (in our case the redshift) and the predictors in a relatively simple form and allows for an efficient extrapolation.

The project’s aim is to update in a multi-wavelength range, from 0.3 keV to 300 GeV, the luminosity-time correlation (Lx-Tx) for GRBs (known in the literature as the “Dainotti relation”) and identify a subclass of GRBs with well-defined properties and bias-free, namely corrected by redshift evolution and selection effects due to instrumental threshold through refined statistical methods. This subclass will be the candidate for GRB standard candles. The bias-free Lx-Tx correlation might be the basis for a new independent and powerful cosmological tool. Finally, the challenge is to use the Lx-Tx correlation together with other correlations, like the Ep – Eiso correlation (known in the literature as the “Amati relation”), both corrected for selection biases in order to discriminate among theoretical models, to use them as cosmological tools and valuable redshift estimators. The expected final results are to obtain a cosmological tool for GRBs derived through the combination of the Amati and Dainotti correlations after their corrections for selection biases and cosmological evolutions. The potential impact is to use these two correlations to improve significantly the accuracy in the determination of the cosmological parameters with GRBs and in perspective to use them for investigating property and evolution of dark energy and testing alternative cosmological models. In addition, the improved characterization of these correlations will provide a fundamental step forward in shedding light on the still poorly understood physics of GRB “prompt” (i.e., the burst of gamma-rays itself) and “afterglow emission” (i.e., the multi-wavelength fading and weaker emission which follows the burst).

The wider societal implications relies on a broader and deeper understanding of the geometry and expansion rate of our Universe, including the nature of newly discovered and still mysterious components like “Dark Energy” and/or modifications to the general relativity theory, the fundament of modern cosmology and of the “Big-bang” standard cosmological model. This progress in the Universe understanding will also provide an increasing awareness of the perspective offered by the investigation of very far away astrophysical phenomena like GRBs and their use to map the evolution and properties of the Cosmos, thus constituting a unique bridge between astrophysics, cosmology and fundamental physics.

The main results achieved so far have been featured in the 11 publications (refereed papers, conference proceedings, and additional papers in preparation) and are summarized in the points below.

1. Prompt-afterglow correlations. The discovery of a unique luminosity-time (hereafter LT) correlation which spans from prompt to afterglow is presented in [1]. Within this framework, the Researcher updated the Lx-Tx relation and the Lpeak-Tγ relation. With a sample, which is doubled compared to previous work it is possible to explain the presence of an offset between the two LT relations (those ones related to the prompt and the afterglow). The Researcher applied the Efron and Petrosian method and demonstrated that the Lpeak-Lx relation is not due to selection bias, but it is intrinsic to the physics of GRBs.

2. The discovery of the fundamental plane. This discovery opened the way to a new 3 parameter correlation, namely the Lx-Ta-Lpeak correlation [3] which is also intrinsic to the physics of GRBs because both Lx-T*a and Lpeak-Lx are intrinsic. The Lx-Ta-Lpeak correlation, which identifies a fundamental plane, has an intrinsic dispersion 54% smaller than the (LX, Ta) one, and therefore will result in an improved correlation that can allow the use of GRBs as standard candles. This result has been chosen as highlight from the American Astronomical Society and as a press conference at AAS [4].

3. The magnetar model and the Galactic magnetar population. Within the context of the magnetar model, a millisecond spinning neutron star with high magnetic field, [2] debated on the reliability of this model as the correct interpretation for the X-ray plateaus. The GRB-magnetar model in its present form is safe only if GRB magnetar progenitor should be different from Galactic magnetars and should be considered super-magnetars.

4. The study of the Lx-Ta relation and GRBs associated with SNe. The subsample of long GRBs associated with SNe (LONG-SNe) presents a very high correlation coefficient for the Lx-Tx correlation and a slope of roughly -2. This possibly suggests that this category might not require a standard energy reservoir in the plateau phase unlike the long GRBs for which no SNe has been observed (LONG-NO-SNe). Therefore, this analysis may open new perspectives in future theoretical investigations of the GRBs with plateau emission and associated with SNe. Namely, a different theoretical scenario from the magnetar and the accretion for which the energy reservoir of the plateau is not constant can be found (This replies the 8th bullet of clarifications in the summary. The project tasks has been fully achieved). The Researcher also discusses how much this difference can be due to the jet opening angle effect.

5. Review on GRB prompt-afterglow correlations. The mechanism responsible for the afterglow emission of GRBs and its connection to the prompt is still a debated issue. Thus, the Researcher presents an overview of the afterglow and prompt-afterglow two parameter correlations, their physical interpretations, and their use as redshift estimators, as possible cosmological tools and on how they are corrected for selection biases [10].

6. The Lx-Ta relation and the decay index in the afterglow emission. In the context of reducing the scatter of the Lx-Tx correlation, [5] investigated the indices α after the plateau phase for a sample of 176 GRBs detected by Swift. They concluded that the LT correlation for the low and high luminous GRBs seems to depend differently on the α parameter, thus implying a diverse density medium dominating the afterglow emission.

7. The Fermi-LAT analysis. The Fermi-Large Area Telescope (LAT, 20 MeV-30 GeV) shows long lasting high energy emission in many GRBs similar to the X-ray afterglows observed by Swift. Some of the lightcurves (LCs) show a late time flattening reminiscent of the X-ray plateaus. The Researcher investigates how many GRBs seen by LAT show a plateau similar to the observed X-ray and if the mechanism that powers the gamma- and X-ray plateaus is the same. The Researcher has pioneered a thorough analysis of LAT LCs present in all Fermi LAT sources observed so far using the new event data algorithm PASS 8; has found that among the 120 GRBs observed by the LAT in 4 cases it is possible to identify a secure plateau emission; has also investigated if the LAT GRBs are generated via synchrotron emission in the external shock (ES) and verified the so called closure relations α=(3*β-1)/2 between the temporal decay index α of the LCs and the energy spectral index β above 100 MeV. This relation serves as a rough indication that the observed radiation is being produced in the ES.

8. The Epeak-Eiso relation. Regarding the Epeak-Eiso or Epeak-Lpeak intrinsic correlation the Researcher has investigated so far the data which present a Band function and a cut-off power law in the spectrum of GRBs. The Researcher has preliminary approximated the Epeak distribution with a Gaussian. The intrinsic Epeak distribution peaks at higher energies than the observed one in the Swift data. The Researcher has computed the minimum and maximum Epeak for this distribution, written a code for the determination of the intrinsic distribution and make use of the R code publicly available in order to compare her code and the one available to the public in R.

9. GRBs as redshift estimators through a machine learning tools. The Researcher adopted several cutting edge methods of supervised machine learning to use different observables to build a GRB redshift estimator. Methods applied are the so called random trees, random forests and the generalized additive models, GAM. The first two methods are completely non-parametric thus allowing to identify the best predictors (the observed variables) of redshift as well as to determine groups of similar GRBs in terms of the values of the predictors and the redshift. GAM models builds a non-parametric relationship between the response variable (in our case the redshift) and the predictors in a relatively simple form and allows for an efficient extrapolation.