The duration-luminosity phase space of optical transients is used, mostly heuristically, to compare various classes of transient events, to explore the origin of new transients, and to influence optical survey observing strategies. For example, several observational searches have been guided by intriguing voids and gaps in this phase space. However we should ask: Do we expect to find transients in these voids given our understanding of the various heating sources operating in astrophysical transients? In this work, we explore a broad range of theoretical models and empirical relations to generate optical light curves and to populate the duration-luminosity phase space (DLPS). We explore transients powered by adiabatic expansion, radioactive decay, magnetar spin-down, and circumstellar interaction. For each heating source, we provide a concise summary of the basic physical processes, a physically motivated choice of model parameter ranges, an overall summary of the resulting light curves and their the occupied range in the DLPS, and how the various model input parameters affect the light curves. We specifically explore the key voids discussed in the literature: the intermediate luminosity gap between classical novae and supernovae, and short-duration transients ( -15 mag). Finally, we explore the detection potential of optical surveys (e.g., LSST) in the DLPS and quantify the notion that short-duration and dim transients are exponentially more difficult to discover in untargeted surveys.

Theoretical Models of Optical Transients. I. A Broad Exploration of the Duration–Luminosity Phase Space

Knowledge of the bulk Lorentz factor $\Gamma_{0}$ of GRBs allows us to compute their comoving frame properties shedding light on their physics. Upon collisions with the circumburst matter, the fireball of a GRB starts to decelerate, producing a peak or a break (depending on the circumburst density profile) in the light curve of the afterglow. Considering all bursts with known redshift and with an early coverage of their emission, we find 67 GRBs with a peak in their optical or GeV light curves at a time $t_{\rm p}$. For another 106 GRBs we set an upper limit $t_{\rm p}^{\rm UL}$. We show that $t_{\rm p}$ is due to the dynamics of the fireball deceleration and not to the passage of a characteristic frequency of the synchrotron spectrum across the optical band. Considering the $t_{\rm p}$ of 66 long GRBs and the 85 most constraining upper limits, using censored data analysis methods, we reconstruct the most likely distribution of $t_{\rm p}$. All $t_{\rm p}$ are larger than the time $t_{\rm p,g}$ when the prompt emission peaks, and are much larger than the time $t_{\rm ph}$ when the fireball becomes transparent. The reconstructed distribution of $\Gamma_0$ has median value $\sim$300 (150) for a uniform (wind) circumburst density profile. In the comoving frame, long GRBs have typical isotropic energy, luminosity, and peak energy $\langle E_{\rm iso}\rangle=3(8)\times 10^{50}$ erg, $\langle L_{\rm iso}\rangle=3(15) \times 10^{47}$ erg s$^{-1}$ , and $\langle E_{\rm peak}\rangle =1(2)$ keV in the homogeneous (wind) case. We confirm that the significant correlations between $\Gamma$ and the rest frame isotropic energy ($E_{\rm iso}$), luminosity ($L_{\rm iso}$) and peak energy ($E_{\rm peak}$) are not due to selection effects. Assuming a typical opening angle of 5 degrees, we derive the distribution of the jet baryon loading which is centered around a few $10^{-6} {\rm M_{\odot}}$.

/pdf/bulk-lorentz-factors-of-gamma-ray-bursts-36puaoja8v.pdf

Bulk Lorentz factors of Gamma-Ray Bursts

We derive, adopting a direct method, the luminosity function and the formation rate of long Gamma Ray Bursts through a complete, flux-limited, sample of Swift bursts which has a high level of completeness in redshift z (~82%). We parametrise the redshift evolution of the GRB luminosity as L = L_0(1+ z)^k and we derive k = 2.5, consistently with recent estimates. The de-evolved luminosity function of GRBs can be represented by a broken power law with slopes a = -1.32 +- 0.21 and b = -1.84 +- 0.24 below and above, respectively, a characteristic break luminosity L_0,b = 10^51.45+-0.15 erg/s. Under the hypothesis of luminosity evolution we find that the GRB formation rate increases with redshift up to z~2, where it peaks, and then decreases in agreement with the shape of the cosmic star formation rate. We test the direct method through numerical simulations and we show that if it is applied to incomplete (both in redshift and/or flux) GRB samples it can misleadingly result in an excess of the GRB formation rate at low redshifts.

The rate and luminosity function of long Gamma Ray Bursts

Long duration gamma-ray bursts (GRBs) and broad-line, type Ic supernovae (SNe) are strongly connected. We aim at characterizing SN 2013dx, associated with GRB\,130702A, through sensitive and extensive ground-based observational campaigns in the optical-IR band. 
We monitored the field of the Swift GRB 130702A (redshift z = 0.145) using the 8.2-m VLT, the 3.6-m TNG and the 0.6-m REM telescopes during the time interval between 4 and 40 days after the burst. Photometric and spectroscopic observations revealed the presence of the associated Type Ic SN 2013dx. Our multi-band photometry allowed the construction of a bolometric light curve.} 
The bolometric light curve of SN 2013dx resembles that of 2003dh (associated with GRB 030329), but is ~10% faster and ~25% dimmer. From this we infer a synthesized 56Ni mass of ~0.2 solar masses. The multi-epoch optical spectroscopy shows that the SN 2013dx behavior is best matched by SN 1998bw, among the other well-known low-redshift SNe associated with GRBs and XRFs, and by SN 2010ah, an energetic Type Ic SN not associated with any GRB. The photospheric velocity of the ejected material declines from ~2.7X10^4 km/s at 8 rest frame days from the explosion, to ~3.5X10^3 km/s at 40 days. These values are extremely close to those of SN1998bw and 2010ah. We deduce for SN 2013dx a kinetic energy of ~35X10^51 erg, and an ejected mass of ~7 solar masses. This suggests that the progenitor of SN2013dx had a mass of ~25 solar masses, i.e., 15-20% less massive than that of SN 1998bw. 
Finally, we performed a study of the SN 2013dx environment, through spectroscopy of the closeby galaxies. 9 out of the 14 inspected galaxies lie within 0.03 in redshift from z=0.145, indicating that the host of GRB 130702A/SN 2013dx belongs to a group of galaxies, an unprecedented finding for a GRB-associated SN and, to our knowledge, for long GRBs in general.

/pdf/sn-2013dx-associated-with-grb-130702a-a-detailed-photometric-epebsgucaj.pdf

SN 2013dx associated with GRB 130702A: a detailed photometric and spectroscopic monitoring and a study of the environment

Long duration gamma-ray bursts (GRBs) and broad-line, type Ic supernovae (SNe) are strongly connected. We aim at characterizing SN 2013dx, associated with GRB\,130702A, through sensitive and extensive ground-based observational campaigns in the optical-IR band. We monitored the field of the Swift GRB 130702A (redshift z = 0.145) using the 8.2-m VLT, the 3.6-m TNG and the 0.6-m REM telescopes during the time interval between 4 and 40 days after the burst. Photometric and spectroscopic observations revealed the presence of the associated Type Ic SN 2013dx. Our multi-band photometry allowed the construction of a bolometric light curve.} The bolometric light curve of SN 2013dx resembles that of 2003dh (associated with GRB 030329), but is ~10% faster and ~25% dimmer. From this we infer a synthesized 56Ni mass of ~0.2 solar masses. The multi-epoch optical spectroscopy shows that the SN 2013dx behavior is best matched by SN 1998bw, among the other well-known low-redshift SNe associated with GRBs and XRFs, and by SN 2010ah, an energetic Type Ic SN not associated with any GRB. The photospheric velocity of the ejected material declines from ~2.7X10^4 km/s at 8 rest frame days from the explosion, to ~3.5X10^3 km/s at 40 days. These values are extremely close to those of SN1998bw and 2010ah. We deduce for SN 2013dx a kinetic energy of ~35X10^51 erg, and an ejected mass of ~7 solar masses. This suggests that the progenitor of SN2013dx had a mass of ~25 solar masses, i.e., 15-20% less massive than that of SN 1998bw. Finally, we performed a study of the SN 2013dx environment, through spectroscopy of the closeby galaxies. 9 out of the 14 inspected galaxies lie within 0.03 in redshift from z=0.145, indicating that the host of GRB 130702A/SN 2013dx belongs to a group of galaxies, an unprecedented finding for a GRB-associated SN and, to our knowledge, for long GRBs in general.

/pdf/sn-2013dx-associated-with-grb-130702a-a-detailed-photometric-g5a7o9qtwl.pdf

We present the rest-frame light curves in the optical and X-ray bands of an unbiased and complete sample of Swift long Gamma-Ray Bursts (GRBs), namely the BAT6 sample. The unbiased BAT6 sample (consisting of 58 events) has the highest level of completeness in redshift ($\sim$ 95%), allowing us to compute the rest-frame X-ray and optical light curves for 55 and 47 objects, respectively. We compute the X-ray and optical luminosities accounting for any possible source of absorption (Galactic and intrinsic) that could affect the observed fluxes in these two bands. We compare the behaviour observed in the X-ray and in the optical bands to assess the relative contribution of the emission during the prompt and afterglow phases. We unarguably demonstrate that the GRBs rest-frame optical luminosity distribution is not bimodal, being rather clustered around the mean value Log(L$_{R}$) = 29.9 $\pm$ 0.8 when estimated at a rest frame time of 12 hr. This is in contrast with what found in previous works and confirms that the GRB population has an intrinsic unimodal luminosity distribution. For more than 70% of the events the rest-frame light curves in the X-ray and optical bands have a different evolution, indicating distinct emitting regions and/or mechanisms. The X-ray light curves normalised to the GRB isotropic energy (E$_{\rm iso}$), provide evidence for X-ray emission still powered by the prompt emission until late times ($\sim$ hours after the burst event). On the other hand, the same test performed for the E$_{\rm iso}$-normalised optical light curves shows that the optical emission is a better proxy of the afterglow emission from early to late times.

/pdf/optical-and-x-ray-rest-frame-light-curves-of-the-bat6-sample-fsvx2uxv3o.pdf

Optical and X-ray Rest-frame Light Curves of the BAT6 sample

Aims. We present the rest-frame light curves in the optical and X-ray bands of an unbiased and complete sample of the Swift long gamma-ray bursts (GRBs), namely, the BAT6 sample.Methods. The unbiased BAT6 sample (consisting of 58 events) has the highest level of completeness in redshift (~95%), allowing us to compute the rest-frame X-ray and optical light curves for 55 and 47 objects, respectively. We compute the X-ray and optical luminosities, which accounte for any possible source of absorption (Galactic and intrinsic) that could affect the observed fluxes in these two bands.Results. We compare the behaviour observed in the X-ray to that in the optical bands to assess the relative contribution of the emission during the prompt and afterglow phases. We unarguably demonstrate that rest-frame optical luminosity distribution of the GRBs is not bimodal and is clustered around the mean value Log(LR) = 29.9 ± 0.8 when estimated at a rest-frame time of 12 h. This is in contrast to what is found in previous works and confirms that the GRB population has an intrinsic unimodal luminosity distribution. For more than 70% of the events, the rest-frame light curves in the X-ray and optical bands have a different evolution, indicating distinct emitting regions and/or mechanisms. The X-ray light curves, which are normalised to the GRB isotropic energy (Eiso), provide evidence for X-ray emission that is still powered by the prompt emission until late times (~hours after the burst event). On the other hand, the same test performed for the Eiso-normalised optical light curves shows that the optical emission is a better proxy of the afterglow emission from early to late times.

/pdf/optical-and-x-ray-rest-frame-light-curves-of-the-bat6-sample-4pthwxx7bw.pdf

Optical and X-ray rest-frame light curves of the BAT6 sample

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Optical and X-ray Rest-frame Light Curves of the BAT6 sample

Optical and X-ray rest-frame light curves of the BAT6 sample