text:
\section{Introduction}
\label{sec_intro}

Gamma-ray bursts (GRBs) are cataclysmic explosions resulting from the collapse of massive stars or the merging of two compact objects (see \cite{Kumar2014} and references therein). During these events, an ultra relativistic jet is produced that is accompanied by an intense gamma-ray flash which can be seen at very high redshifts (up to $z=9$ for GRB090429B; see \cite{Cucchiara2011a}. The gamma-ray emission is produced in a few seconds (prompt emission) with a total energy release of up to E$\sim10^{54}$ erg assuming an isotropic emission. This prompt emission is followed by a long-lasting and fading multi-wavelength emission from X-rays to radio (afterglow emission) which can be attributed to the external shock between the relativistic ejecta and the interstellar medium (ISM). The prompt $\gamma$-ray emission has been suggested as being due to internal shocks between shells moving at different Lorentz factors, $\Gamma$, inside the jet (see \citep[][]{Rees1994,Paczynski1994,Piran1999,Kumar2014}). However, the physical processes at work in these shocks are still not well understood due to strong uncertainties on the physical conditions (baryon loading, energy dissipation in the jet, acceleration mechanism; see the review by \cite{Kumar2014}). On the contrary, the afterglow emission is better understood and can be explained by the synchrotron emission from accelerated electrons in the shock between the relativistic ejecta and the ISM (forward shock; (see \cite{Sari1998} $\&$ \cite{Granot2002}). An optical/radio flash is also expected and is sometimes observed from a reverse shock propagating into the relativistic ejecta (see \citep[][]{Meszaros1993, Kobayashi2000}). Studying the optical flash radiation from the reverse shock provides us with the opportunity to constrain the magnetization parameter of the ejecta \citep[][]{Zhang2005, Narayan2011}, the Lorentz factor of the jet, and also on the jet composition \citep[][]{McMahon2006, Nakar2004}. In this framework, the dynamics of the afterglow is determined by the microphysics of the shocked material, the ISM properties, and the kinetic energy of the blast wave, $E_k$, which depends on the prompt emission properties (the isotropic gamma-ray energy released, $E_{iso}$, and the gamma-ray radiative efficiency, $\eta$). Understanding the connection between the prompt and afterglow properties would help us to better constrain the physics of GRBs and relativistic jets.

\smallskip

Many authors have discussed correlations between the afterglow luminosity and the prompt GRB energetics. Correlations between the afterglow optical luminosity and prompt isotropic energy have been found by \cite{Kann2010} and \cite{Nysewander2009}, and between the afterglow X-ray emission and the isotropic energy by \cite{Kaneko2007} and \cite{Margutti2013}. However, it is difficult to assess whether or not these relations have their origin in the physics of the GRB because some studies have shown that they could result from selection effects. Indeed, \cite{Coward2014} recently detected a strong Malmquist bias in the correlation $E_{iso}-L_{opt,X}$ as we preferentialy detect the brightest GRBs. While it is clear that gamma-ray selection effects can bias statistical studies of prompt GRB properties, the impact of optical selection effects is rarely assessed. This paper is dedicated to the study of potential selection effects in the distribution of rest-frame prompt properties due to the need of measuring the redshift.
We construct a sample of GRBs with good optical and gamma-ray data in section \ref{sec_sample}. The potential parameters (extrinsic and intrinsic) that could bias our sample are also investigated in section \ref{sec_analyse_opt}. The main conclusion of this section is that the distribution of the afterglow optical flux is mainly driven by their optical luminosities as opposed to redshift distribution. Thus, in section \ref{sec:sel_effect}, we show how the need to detect the optical afterglow can act against the measurement of the rest-frame properties of some GRBs. Then, in section \ref{sec_prompt} we compare the afterglow optical flux of GRBs with their typical rest-frame prompt properties as $E_{iso}$ or $L_{iso}$ to estimate the impact of the optical selection effect. We also investigate optical selection effects on GRB rest-frame correlations in section \ref{sec_correlation}. In section \ref{discussion}, we briefly discuss the consequences of our findings.

\section{GRB sample and data}
\label{sec_sample}

\subsection{Gamma-ray data}
\label{sub_HE}

Our gamma-ray selection criteria followed a procedure similar to that of \cite{Heussaff2013}.
We selected a large sample of GRBs with well-measured spectral parameters available in the literature, i.e GCN Circulars\footnote{http://gcn.gsfc.nasa.gov}. This covers GRB observations from 1997 to 2014. GRB spectra are parametrized with the Band function, \cite{Band1993}, which consists of two smoothly connected power laws :

\begin{equation}
\begin{array}{clllll}
F_\gamma(E_\gamma) =\\
\\
 f_\gamma \left\lbrace
\begin{array}{ll}
(\frac{E_\gamma}{\rm{100~keV}})^{\alpha_\gamma} ~ \rm{exp}(-\frac{E_\gamma(\alpha_\gamma-\beta_\gamma)}{E_b}), ~ if~E_\gamma < E_b\\
\\
(\frac{E_b}{\rm{100~keV}})^{\alpha_\gamma-\beta_\gamma} ~ \rm{exp}(\beta_\gamma-\alpha_\gamma)~ (\frac{E_\gamma}{\rm{100~keV}})^{\beta_\gamma},\\
\\
\rm{ if~E_\gamma \ge E_b}\\
\end{array}
\right.
\end{array}\\
\end{equation}
where $E_b = \frac{\alpha_\gamma-\beta_\gamma}{2+\alpha_\gamma}\times E_{po}$. $\alpha$ ($\alpha >-2$) and $\beta$ ($\beta < -2$) are the low- and high-energy photon spectral indexes of the power law, respectively. $E_{po}$ is the break energy of the observed $\nu F_{\nu}$ gamma-ray spectrum.

The selection was performed by applying the following cuts.

\begin{enumerate}
\item First, we selected GRBs with $T_{90}$, the time for which 90\% of the energy is released, between 2 and 1000 s. This criterion excludes short GRBs ($T_{90}<2s$), and very long GRBs that are superimposed on a varying background and whose $E_{po}$ is difficult to measure accurately.
\item Second, we required reliable spectral parameters. We excluded GRBs with one or more spectral parameters missing. We excluded GRBs with an error on $\alpha$ (the low-energy index of the Band function) larger than 0.5. We excluded a few GRBs with $\alpha <-2.0$ and GRBs with $\beta>\alpha$ because such values suggest a confusion between fitting parameters. We excluded GRBs with large errors on $E_{po}$, which are defined by a ratio of the $90\%$ upper limit to the $90\%$ lower limit larger than 3.5. When the error on $\beta$ in the catalog is lacking or larger than 1.0, we assigned a typical value of –2.3\footnote{This typical value of beta corresponds to the mean values for GRB spectra according to BATSE results, e.g. \cite{Preece2000} and \cite{ Kaneko2006}. It is also very close to the median value beta=-2.26 measured for the {\it Fermi} GRBs , see \cite{Gruber2014}} to $\beta$ and we give no error. In a few cases, the high-energy spectral index in the GRB catalogs ({\it HETE}-2, {\it Fermi}) is incompatible with being $<$-2.0 at the 2 $\sigma$ level, and the catalog gives the energy of a spectral break that is not $E_{po}$. In these cases, we look for $E_{po}$ in the GCN Circulars, and if we cannot find it, then we simply remove the burst from the sample.
\end{enumerate}

Finally, our analysis required GRBs with both well-measured $\gamma$-ray spectral parameters and an optical afterglow light curve. Consequently, we removed GRBs inaccurately localized (typically GRBs not localized by the {\it Swift}-XRT instrument)  because most of the time it prevents ground-based telescope from detecting their optical afterglows.

At the completion of the high-energy selection process, we ended with 126\ GRBs with a redshift and 42\ GRBs without a redshift.  Then, in a second step, we extracted the short list of GRBs with exploitable optical afterglow light curves.

\subsection{Optical data}
\label{sub_opt}
We collected the afterglow R-band light curves of the pre-selected 126\ GRBs with a redshift and 42\ GRBs without a redshift. We specifically choose the R-band because it concentrates the largest number of optical measurements. These R-band photometric measurements are issued from published articles and GCN Circulars. References are given in table \ref{tab_refz}.

Then, we used the apparent R magnitude measured 2 hr after the burst uncorrected for extinction as a proxy for the optical flux of the afterglow. The R magnitude is directly interpolated from the available measurements.
To do so, we required GRBs with good optical follow-up during the first hours after the burst to accurately measure the optical flux of the afterglow.

The choice of the time (2 hr after the trigger) at which we measure the R magnitude results from various constraints.
\begin{enumerate}
\item We want the afterglow to be in its classical slow cooling and decaying regime, yet to be bright enough to permit reliable measurements of the magnitude.
\item We want to measure the optical flux at a time comparable to the time at which the majority of GRB redshifts are measured (in the first few hours after the trigger), so that the optical flux measurement provides a good indicator of our ability to measure the redshift of the GRBs.
\end{enumerate}

We decided to exclude few GRBs with high visual extinction such that $\rm{A_V^{tot}=A_V^{Gal}+A_V^{Host}>1.2}$, which corresponds to a total extinction in the R-band of about 1 mag. Indeed, GRB afterglows which are strongly absorbed by dust do not provide information on their true optical brightness. This cut is a good trade-off to optimize the number of GRBs for which the afterglow flux is not as polluted by external effects (dust absorption). The galactic extinction $\rm{A_V^{Gal}}$ has been calculated from the dust map of \cite{Schlegel1998} and the host extinctions $\rm{A_V^{Host}}$ are issued from various sources. For some bursts we did not have access to the host extinction. In order to have a rough estimate of the host extinction, we performed a simple linear fit between $\rm{A_V^{Host}}$ and the intrinsic X-ray absorption $\rm{NH_{X,i}}$ derived from the {\it Swift}-XRT catalog. We had 114 GRBs available for this fit. The best-fit gives us the following relation : $\rm{A_V^{Host} = 3.9\times 10^{-23}\times NH_{X,i} + 0.06}$ with a standard deviation of $\sigma\sim~0.34$ mag which we considered to be an acceptable uncertainty in our $\rm{A_V^{Host}}$ estimates.

We also removed those GRBs located at very high redshift since at such redshifts the Ly-$\alpha$ break prevents the observation of the optical afterglow in the R band. The redshift cut was fixed at $z=5.5$ where the Lyman absorption starts to significantly attenuate the R band.

Finally, for GRB afterglows with only an upper limit of detection, we required that they have R magnitudes that are deeply constrained by large telescopes (at least one 2.0 m telescope). Moreover, these upper limits must be estimated from images taken close to 2 hr after the burst.

After passing the optical selection criteria, we finally ended with 76\ GRBs with a redshift (75 detections and 1 upper limit) and 14\ GRBs without a redshift (3 detections and 11 upper limits). These 90 GRBs constitute our full sample, which is summarized in table \ref{tab_GRB} for GRBs with a redshift and table \ref{tab_GRB_sansz} for GRBs without a redshift. This sample covers about 15 years of pre-{\it Swift} and {\it Swift} GRB observations (from 1999 to 2014). The afterglow light curves of our complete sample of GRBs can be seen in figure \ref{fig_afterglow}.

\begin{figure}[t!]
\hspace*{-0.4cm}
\includegraphics[trim = 0 150 0 200,clip=true,width=0.54\textwidth]{Afterglow_LCs.pdf}
\caption{R-band optical light curves in the observer frame of the afterglows of 76\ GRBs with a redshift (gray solid line) and 14\ GRBs without a redshift (blue dashed line with triangle for upper limits) considered in this study. The magnitudes are not corrected for galactic and host extinctions. The vertical solid line represents the time (2 hr) at which we estimate the uncorrected R magnitude.
}
\label{fig_afterglow}
\end{figure}

\section{Afterglow optical flux and potential biases}
\label{sec_analyse_opt}

The afterglows of our 90\ GRBs span a large range of optical flux from mag R$^{2h}$ = 13.02 to mag R$^{2h}$ = 23.9 (see figure \ref{Rmag_dist}). We noted that GRBs without a redshift have faint optical counterparts, which is not due to high visual extinction since they pass our optical selection criteria. These GRBs may be high-z GRBs or GRBs with sub-luminous afterglows. Our GRBs with a redshift are also distributed over a wide range of redshift from $z=0.168$ to $z=4.11$ and we need to understand whether or not the distribution of the R magnitudes is dominated by the redshift distribution. To verify this hypothesis, we divided our 76\ GRBs with a redshift into three equally populated classes of optical flux.

\begin{enumerate}
\item The class of {\it bright} GRBs is composed of 26 GRBs with an afterglow R magnitude brighter than $\rm{R=17.9}$.
\item The class of {\it intermediate flux} GRBs is composed of 25 GRBs with an afterglow  R magnitude in the range $\rm{17.9<R\leq19.1}$.
\item The class of {\it faint} GRBs is composed of 25 GRBs with an afterglow  R magnitude weaker than $\rm{R=19.1}$.
\end{enumerate}

We will refer to these classes throughout this paper.

\begin{figure}[t!]
\includegraphics[trim = 40 192 0 200,clip=true,width=0.535\textwidth]{Rmag_dist.pdf}
\caption{Distribution of the afterglow optical flux measured 2 hr after the burst (uncorrected R magnitude). The 76\ GRBs with a redshift are shown in black and the 14 GRBs without a redshift are in red.
}
\label{Rmag_dist}
\end{figure}

\subsection{Impact of the redshift on the afterglow optical flux distribution}
\label{redshift_dist}

We compared the redshift distribution of our three GRB classes with a Kolomogorov-Smirnov statistical test (KS test; see figure \ref{z_dist}). The KS test clearly reveals that the redshift distributions of the three classes are similar. The results of the statistical tests are summarized in table \ref{tab_stat1}. We conclude that the redshift is not the main driver of our optical flux distribution. This observation is explained in figure \ref{z_vs_LR}, which shows a shift in the GRB population to higher luminosities with the redshift. At large redshifts, the combination of the increased volume and the GRB density evolution allow us to see very luminous GRBs, which are too rare to be visible below $z\sim$1. This luminosity shift nearly compensates for the effect of distance, leading to similar fractions of bright and faint GRBs at all redshifts.

\begin{figure}[h]
\centering
\includegraphics[trim = 40 200 30 190,clip=true,width=0.5\textwidth]{CDFhisto_z.pdf}
\caption{Cumulative distribution function (bottom) and histogram (top) of the redshift for the three classes of GRBs. The bright, intermediate, and faint GRB afterglows are indicated by solid red, dashed black, and dotted blue lines, respectively.
}
\label{z_dist}
\end{figure}

\subsection{Impact of the visual extinction on the afterglow optical flux}
\label{Av_dist}
Although we have selected GRBs with relatively low total visual extinction ($\rm{A_V^{tot}<1.2}$), we checked if this parameter could bias our afterglow flux distribution, i.e, whether afterglows with faint optical flux are more obscured by dust. We again performed a KS test to compare the $\rm{A_V^{tot}}$ distributions of our three classes of GRB afterglow flux. We found that the three populations of GRBs are drawn from the same underlying distribution (see figure \ref{AV_dist} and table \ref{tab_stat1}). We conclude that GRBs with faint afterglow optical fluxes are not more obscured than the bright ones, and thus visual extinction does not bias our afterglow optical distribution.

\begin{figure}[t]
\centering
\includegraphics[trim = 40 190 30 200,clip=true,width=0.50\textwidth]{CDFhisto_AV.pdf}
\caption{Cumulative distribution function (bottom) and histogram (top) of $\rm{A_V^{tot}}$ for the three classes of GRBs. The bright, intermediate, and faint GRB afterglows are indicated by solid red, dashed black, and dotted blue lines, respectively.
}
\label{AV_dist}
\end{figure}

\subsection{Afterglow optical luminosity}
\label{Lopt_dist}
As the extrinsic factors (redshift, visual extinction) do not seem to play a major role in the observed optical flux distribution, we investigated the impact of the intrinsic optical luminosity of the afterglow.
We calculated the optical luminosity density (in units of $\rm{erg.s^{-1}.Hz^{-1}}$) two hours after the burst using the following formula:

\begin{equation}
L_R(t_{rest})=\frac{4\pi D_L(z)^2}{(1+z)^{1-\beta_o+\alpha_o}}\times F_{R}(t_{obs})(\frac{\nu_R}{\nu_{obs}})^{-\beta_o}
\end{equation}

where $F_R$ is the optical flux density corrected from the Galactic and host extinction measured at $\rm{t_{obs}=2h}$ after the burst, z is the GRB redshift, $D_L(z)$ is the luminosity distance, $\beta_o$ is the optical spectral index and $\alpha_o$ the optical temporal index, $\nu_R$ is the typical frequency of the R-band (Vega system), and $\nu_{obs}$ is the observed frequency (here $\nu_{obs}=\nu_R$).
For GRBs with no optical detection, we used their optical upper limits to compute $F_R$ and the median values of the $\alpha_o$ ($|\alpha_o^{med}| = 0.975$) and $\beta_o$ ($|\beta_o^{med}| = 0.65$) distributions to estimate an upper limit on their optical luminosity density.
Finally, for GRBs without a redshift, we also calculated their optical luminosity density as function of the redshift, (considering $0.168<z<6.0$) using the method decribed above. Since their derived  luminosity (or upper limit) depends on the redshift, they produce tracks in the $z-L_R$ plane as shown in figure \ref{z_vs_LR}.

Then, we compared the optical luminosity densities of the three classes of GRB afterglow fluxes ({\it bright}, {\it intermediate}, and {\it faint}; see figure \ref{CDF_LR}). The KS test clearly reveals that GRBs with low optical flux are also less luminous in the optical domain.

\begin{figure}[t!]
\includegraphics[trim = 40 195 30 200,clip=true,width=0.5\textwidth]{CDFhisto_LR.pdf}
\caption{Cumulative distribution function (bottom) and histogram (top) of the optical luminosity density (taken 2hr after the burst in the rest-frame) for the three classes of GRBs. The bright, intermediate, and faint GRB afterglows are indicated by solid red, dashed black, and dotted blue lines, respectively.
}
\label{CDF_LR}
\end{figure}

We conclude that our afterglow optical flux distribution is strongly shaped by the optical luminosity densities of the GRB afterglows. This result is valid for GRBs with a redshift but, interestingly, GRBs without a redshift also follow this trend. Indeed, they have the afterglows with the lowest optical fluxes (figure \ref{Rmag_dist}), and at any redshift most of them would have had sub-luminous afterglows, see figure \ref{z_vs_LR}. Thus, we conclude that the aferglow optical flux of the GRBs in our sample is very likely dominated by their optical luminosity. As a consequence, a large population of GRBs with sub-luminous afterglows may escape detection in the optical domain, creating a strong bias in the observed afterglow luminosity distribution. In particular, we note that GRBs with $\rm{L_{R}<10^{30}~erg.s^{-1}.Hz^{-1}}$ have no redshift measurement beyond $z\sim1$ (see figure  \ref{z_vs_LR}), except for GRB090519 which is discussed in more details in the Appendix.

\begin{figure*}[t!]
\begin{minipage}{1.0\textwidth}
\centering
\includegraphics[trim =20 175 70 210,clip=true,width=0.8\textwidth]{z_vs_LR.pdf}
\end{minipage}
\caption{Intrinsic optical luminosity density as a function of redshift for 76\ GRBs with a redshift and 14\ GRBs without a redshift (dashed-dotted lines). Upper limits are plotted as downward triangles. The red dashed lines indicates the iso-magnitude of the optical afterglow as a function of the redshift (up to $z=6.0$). They define our three classes of optical afterglow flux ({\it bright} are GRBs with R$\le$17.9, {\it intermediate} are GRBs with $17.9 < R\le19.1$, and {\it faint} are GRBs with $R>19.1$). As discussed in section \ref{sec_correlation}, the green circles represent GRBs below the best-fit \epi\ -- \eiso\ {\rm relation}\ while black squares represent GRBs located above the best-fit \epi\ -- \eiso\ {\rm relation}. For GRBs without a redshift, the color of the dashed-dotted line indicates whether the GRB is located below the best-fit \epi\ -- \eiso\ {\rm relation}\ (green) or above it (black).
}
\label{z_vs_LR}
\end{figure*}

\begin{deluxetable}{cccccccccc}
\tablecolumns{10}
\tablewidth{0pc}
\tablecaption{Results of the different KS tests of section \ref{sec_analyse_opt}.}
\tablecomments{The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refers to the three classes of afterglow optical flux : Faint, Intermediate, and Bright, respectively.
}
\tablehead{
\colhead{Parameter}    &  \multicolumn{3}{c}{$z$}&  \multicolumn{3}{c}{$A_V$}&  \multicolumn{3}{c}{$L_R$}
}
\startdata
{GRB samples} & F/I & F/B & I/B&  F/I& F/B & I/B & {\bf F/I}& {\bf F/B} &I/B\\[0.5pc]
P-value&  0.30 &   0.47 & 0.88&  0.88 &  0.33 &0.30&  $\mathbf{1.28\times 10^{-3}}$ & $\mathbf{8.06\times 10^{-7}}$ & 0.02 \\
\enddata
\label{tab_stat1}
\end{deluxetable}

\section{Selection effects in the observed GRB population}
\label{sec:sel_effect}

\subsection{The physical picture}
The population of GRBs with a redshift suffers from two different selection effects. The "$\gamma$-ray selection effect" prevents the detection of GRBs with low peak flux while the "optical selection effect" prevents measuring the rest-frame properties of GRBs with faint optical afterglows. In both cases, the final result is that we lose a significant fraction of GRBs for statistical studies dealing with their rest-frame prompt properties. The relative influence of the two selection effects is difficult to assess, but we try to quantify it by comparing the two quantities related to the two selection effects in figure \ref{fig:Rmagvspflux} :
\begin{enumerate}
\item the observed peak flux (${\rm erg.cm^{-2}.s^{-1}}$) in the {\it Swift} band (15-150 keV) connected to the detectability of a GRB in $\gamma$-rays; and
\item the uncorrected R magnitude of the afterglow related to our ability to measure the redshift of a GRB via the spectroscopy of the optical afterglow.
\end{enumerate}

For each GRB, we simulated the evolution with the redshift of its peak flux and optical afterglow flux. In particular, we checked whether a given GRB located at higher redshift would first disappear from our sample because it becomes undetectable in $\gamma$-rays or because its afterglow is becoming too faint to allow measuring its redshift. Thus, for each GRB, we define $z_\gamma^{max}$ and $z_{opt}^{max}$ as the maximum redshifts that the GRB could have before being limited by the $\gamma$-ray detection threshold ($z_\gamma^{max}$) or the optical threshold related to the redshift measurement ($z_\gamma^{max}$).
To do so, we define a peak flux limit below which the GRB is supposed to be undetectable in $\gamma$-rays at $z = z_{\gamma}^{max}$. We decided to choose the faintest peak flux of our sample (except for GRB090519, which is an exceptional burst), i.e. that of GRB140626A with $P_{15-150{\rm keV}} = 0.7~{\rm ph.cm^{-2}.s^{-1}}$. For the R magnitude limit that defines $z_{opt}^{max}$  we choose the weakest measured R magnitude of our GRB sample with redshift (again we remove GRB090519 from the list), i.e that of GRB090812 with R mag. = 21.15.

\smallskip

For instance,  GRB080605, with $z_{opt}^{max}\sim2.85$ and $z_\gamma^{max}\sim 6.45$ would be limited by its optical afterglow flux, as shown in figure \ref{fig:Rmagvspflux}. On the contrary, a GRB like GRB 050820A would be limited by the $\gamma$-ray detection with $z_{opt}^{max}>10~$ much\footnote{Note that here we do not take into account the effect of the Lyman break in the R band which appears at $z\sim 5.5-6$. For very high-z GRB ($z>6$), the optical threshold for a redshift measurement has to be preferentially defined based on the infrared afterglow flux (IJHK band).} larger than $z_\gamma^{max}\sim 4.55$ . In the end, we find that about 20$\%$ of our GRBs with redshift would predominantly suffer from optical selection effects if they were located at higher redshift ($z_{opt}^{max}<z_\gamma^{max}$ ), while about 80$\%$ of GRBs would definitely disappear because the GRBs themselves becomes too faint to be detected ($z_{opt}^{max}>z_\gamma^{max}$).

Clearly, the computation of $V/V_{max}$ or other measures of the detectability of GRBs with a redshift have to take into account that some GRBs will be effectively limited by their $\gamma$-ray visibility ($z_\gamma^{max}$), while others ($\sim$ 20 $\%$ of the GRBs with a redshift in our sample) will be firstly limited by their optical afterglow flux  ($z_{opt}^{max}$) and our ability to determine their redshift. In addition, as suggested by figure \ref{Rmag_dist}, we confirm that most of the GRBs in our sample without a redshift are dominated by optical selection effects ($\sim 85\%$ of them) since their peak flux does not prevent them from a $\gamma$-ray detection (see figure \ref{fig:Rmagvspflux}).

We conclude that optical selection effects play a significant role in shaping the observed population of GRBs with a redshift. The next question is as follows : do these optical selection effects create a significant bias in the observed distribution of the rest-frame properties of GRBs?  Below, we discuss the method used to assess the significance of the selection effects associated with the measure of the redshift.

\begin{figure*}[t!]
\centering
\includegraphics[trim = 20 180 60 220,clip=true,width=0.6\textwidth]{RmagvsPflux2.pdf}
\caption{Our GRB sample in the Peak flux-R mag plane. GRBs with a redshift measurement are represented in blue (circles for GRBs afterglows with a well-measured R magnitude, downward triangles for optical upper limits). GRBs without a redshift measurement are represented in black (stars for GRBs afterglows with a well-measured R magnitude, downward triangles for optical upper limits). The red dashed lines represent the limiting peak flux and the limiting R magnitude for GRB detection and redshift measurement, respectively. The black dashed line divides the population of GRBs that would undergo the $\gamma$-ray selection effect before the optical one (above this line) from those that firstly suffer from the optical selection effect (below this line).
}
\label{fig:Rmagvspflux}
\end{figure*}

\subsection{A method to assess the significance of optical selection effects}
The impact of measuring the redshift is assessed by comparing the properties of GRBs with different optical fluxes (R magnitudes measured 2 hr after the trigger).
If GRBs with different optical fluxes show no difference in the distribution of a given parameter, then it is expected that the measure of the redshift, which depends strongly on the optical flux of the afterglow, will not impact the distribution of this parameter.
If, on the other hand, GRBs with different optical fluxes show significant differences in the distribution of a given parameter, then the measure of the redshift will impact the distribution of this parameter.

Of course, one limitation of this method is that it cannot be used to measure the biases between the population of GRBs with a redshift and GRBs without one, that is, it can only be used to measure differences between subpopulations of GRBs with a redshift.
The scope of this paper is thus restricted to an evaluation of the prompt GRB properties which may be biased by the measure of the redshift.
A detailed evaluation of the biases between GRBs with and without a redshift would require the construction of a GRB "world model" which takes into account many parameters of the GRBs and their afterglows and their correlations, a task which is beyond the scope of this paper (see, however, \cite{Shahmoradi2013, Kocevski2012}).

\section{Optical selection effects on the rest-frame prompt properties of GRBs}
\label{sec_prompt}

We compare the distributions of various parameters of the prompt emission for the three classes of afterglow flux. The four parameters discussed here are the isotropic $\gamma$-ray energy, $E_{iso}$, the isotropic $\gamma$-ray luminosity, $L_{iso}$, the intrinsic peak energy of the $\nu F_\nu$ $\gamma$-ray spectrum, $E_{pi} = E_{po}\times(1+z)$, and the duration of the burst, $T_{90}^{rest}=T_{90}/(1+z)$.

We performed KS tests to compare the distributions of the four parameters listed above for GRBs in the three classes of afterglow flux (see figure \ref{prompt_par}). These tests are based on the population of 76 GRBs with a redshift when comparing the $E_{iso}$, $E_{pi}$ and $T_{90}^{rest}$ distributions, and only 73 GRBs for the $L_{iso}$ distributions because three GRBs had unsecured peak flux measurements. The results of the KS test are summarized in table \ref{tableprompt}. We found no significant differences between the $L_{iso}$ and $E_{pi}$ distributions. Nevertheless, we noted that the $T_{90}^{rest}$ distributions differ by more than 2.5$\sigma$  between GRBs with faint and bright afterglows. This marginal discrepancy highlights the fact that GRBs with low afterglow fluxes could be shorter on average than GRBs with high afterglow fluxes. Finally, we note that GRBs with faint afterglow fluxes seem to have slightly lower $E_{iso}$ than the rest of the GRB population (intermediate and bright GRB afterglows). This difference is not significant, and so no conclusive statement can be made. The low significance of the KS test applied to $E_{iso}$ can be explained by two reasons. First, the afterglow dynamics are driven by both the kinetic energy of the jet ($E_k = E_{iso}\times\frac{1-\eta}{\eta}$, where $\eta$ is the $\gamma$-ray radiative efficiency) and the density of the shocked ISM. Thus it is not straightforward to connect $E_{iso}$ with the afterglow optical flux. Second to the first order, $E_{iso}$ can be roughly estimated from the averaged $\gamma$-ray luminosity $<L_{iso}>$ integrated over the $T_{90}^{rest}$ duration, $E_{iso}\sim<L_{iso}>\times T_{90}^{rest}$. Since we observed no bias in the $L_{iso}$ distribution but a marginal one in the $T_{90}^{rest}$ distribution, the combination of the two distributions leads to a similar but lower bias in the $E_{iso}$ distribution compared to what we observed for $T_{90}^{rest}$. In the end, no clear trend emerges from these statistical tests and we conclude that the rest-frame prompt properties of GRBs are not significantly biased by optical selection effects

\begin{figure*}[t!]
\hspace{-1.9cm}
\begin{minipage}{0.5\linewidth}
\centering
\includegraphics[trim = 0 175 0 200,clip=true,width=1.2\textwidth]{CDFhisto_Eiso.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\centering
\includegraphics[trim = 0 175 0 200,clip=true,width=1.2\textwidth]{CDFhisto_Liso.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\hspace{-1.0cm}
\includegraphics[trim = 0 175 0 190,clip=true,width=1.17\textwidth]{CDFhisto_Epi.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\includegraphics[trim = 0 175 0 190,clip=true,width=1.17\textwidth]{CDFhisto_T90.pdf}
\end{minipage}
\caption{Top left: cumulative distribution function (bottom) and histograms (top) of the isotropic $\gamma$-ray energy ($E_{iso}$) for the three classes of afterglow optical flux and based on a population of 76 GRBs with a redshift. Top right: same caption for the isotropic $\gamma$-ray luminosity ($L_{iso}$) based on a population of 73 GRBs with a redshift. Bottom left: same caption for the intrinsic peak energy ($E_{pi}$) based on a population of 76 GRBs with a redshift. Bottom right: same caption for the rest-frame burst duration ($T_{90}^{rest}$) based on a population of 76 GRBs with a redshift. All panels: the faint GRBs  are represented with a blue dotted line, the intermediate GRBs with a black dashed line, and the bright GRBs with a red solid line.
}
\label{prompt_par}
\end{figure*}

\begin{deluxetable}{ccccccccccccc}
\tablecolumns{13}
\tablewidth{0pc}
\tablecaption{Results of the different KS tests of section \ref{sec_prompt}.}
\tablecomments{The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refer to the three classes of afterglow optical flux, Faint, Intermediate, and Bright, respectively.}
\tablehead{
\colhead {Parameter } &  \multicolumn{3}{c}{$E_{iso}$}&  \multicolumn{3}{c}{$L_{iso}$}&  \multicolumn{3}{c}{$E_{pi}$} &  \multicolumn{3}{c}{$T_{90}^{rest}$}
}
\startdata
{GRB samples}& F/I& F/B &I/B& F/I &  F/B&I/B &  F/I & F/B & I/B &  F/I &  F/B& I/B\\[0.5pc]
P-value&  0.41 & 0.17 & 0.77& 0.62 &  0.73 & 0.99& 0.12&  0.56& 0.99 &  0.12 &  0.02 & 0.53\\
\enddata
\label{tableprompt}
\end{deluxetable}

\section{Optical selection effects on rest-frame prompt correlation}
\label{sec_correlation}
The study of biases in GRB spectral energy correlations has led to many studies concerning $\gamma$-ray selection effects. However, the role of optical selection effects on these correlations has not been explored as much. If such an optical bias exists, then we expect to find a link between the afterglow flux and the positions of GRBs in the corresponding  parameter space of the correlation. We decided to study such a connection using the $\rm{E_{pi}-E_{iso}}$ and $\rm{E_{pi}-L_{iso}}$ relations (respectively reported for the first time by \cite{Amati2002} and \cite{Yonetoku2004}) as they are among the most robust GRB correlations, yet are highly debated in the GRB community.

\subsection{Our GRB sample in the \epi\ -- \eiso\ {\rm plane}}
As shown in figure \ref{fig_amati}, the 76\ selected GRBs with a redshift follow a standard \epi\ -- \eiso\ {\rm relation}.
The best-fit \epi\ -- \eiso\ {\rm relation}\ for this sample is ${\rm E}_{\rm pi} = 145~{\rm E}_{52}^{0.463}~ {\rm keV}$, where E$_{52}$ is the GRB isotropic energy in units of $10^{52}$ erg.
This best-fit relation is consistent with the \epi\ -- \eiso\ {\rm relation}\ found by other authors \citep[e.g.][]{Nava2012,Gruber2012}, showing that our sample is not significantly biased for what concerns the distribution of GRBs with a redshift  in the \epi\ -- \eiso\ {\rm plane} . The dispersion of the points around the best-fit relation along the vertical axis, $\sigma = 0.31$, is also comparable to the values found by \cite{Nava2012} and \cite{Gruber2012} ($\sigma = 0.34$). In the following, we compare the positions of our three classes of GRBs in the \epi\ -- \eiso\ {\rm plane}\ using the mean distance to best-fit the Amati relation as a criterion for this comparison.

\begin{figure*}[t!]
\begin{minipage}{0.5\linewidth}

\includegraphics[trim = 0 175 0 200,clip=true,width=1.0\textwidth]{Amati_relation.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}

\includegraphics[trim = 0 175 0 200,clip=true,width=1.0\textwidth]{Amati_relation_sansz.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\hspace*{-0.5cm}
\includegraphics[trim = 0 175 0 200,clip=true,width=1.1\textwidth]{dist_amati.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\hspace*{-0.4cm}
\includegraphics[trim = 0 175 0 190,clip=true,width=1.04\textwidth]{R_ab.pdf}
\end{minipage}
\caption{Top left: distribution of the 76\ GRBs with a redshift in the \epi\ -- \eiso\ {\rm plane}\ with its 2$\sigma$ limit (dashed line). The red circles corresponds to the population of GRBs with bright afterglows, the black diamonds corresponds to the GRB afterglow with intermediate flux, and the blue squares corresponds to the faint GRB afterglows. Top right: distribution of the 14\ GRBs without a redshift in the \epi\ -- \eiso\ {\rm plane}\ with its 2$\sigma$ limit (dashed line). They all appear in the class of GRBs with faint afterglows (blue solid line). Bottom left: Distribution of the uncorrected R magnitude as a function of the vertical distance to the best-fit to the \epi\ -- \eiso\ {\rm relation}\ for our global sample of GRBs (90 GRBs). Bottom right: cumulative distribution function of the uncorrected R magnitude between GRBs located above the best-fit \epi\ -- \eiso\ {\rm relation}\ (dashed line) and those located below the best-fit \epi\ -- \eiso\ {\rm relation}\ (solid line). This analysis used a sample of 76 GRBs with a redshift and 8 GRBs without one.
}
\label{fig_amati}
\end{figure*}

\subsubsection{Comparing the vertical distances with respect to the \epi\ -- \eiso\ {\rm relation}}
\label{brightness_eep}
The vertical distance is defined as $\rm{log_{10}(E_{pi})} - \rm{log_{10}[best~fit~(E_{pi})]}$, where best-fit ($E_{pi}$) is the value measured on the best-fit relation. In figure \ref {fig_amati}, we show the complete GRB sample (90 GRBs) in a plane displaying the vertical distances to the best-fit \epi\ -- \eiso\ {\rm relation}\ as a function of the afterglow optical flux. We performed a KS test to compare the vertical distance distributions for our three classes of GRBs with a redshift. The KS tests reveal that GRBs with intermediate and bright afterglow fluxes follow similar distributions, while GRBs with low afterglow fluxes differ by more than $\sim3\sigma$ from GRBs with high afterglow fluxes and by $\sim2.6\sigma$ from GRBs with intermediate afterglow fluxes. Because the faint GRBs seem to behave unlike intermediate and bright GRBs, we compared the vertical distance distributions of these two groups of GRBs (faint versus intermediate+bright). The KS test reveals that the distribution of faint GRBs in the \epi\ -- \eiso\ {\rm plane}\ is not compatible with that of the intermediate and bright GRBs with a probability of 99.96$\%$ ($\sim 3.7\sigma$). The results of the different statistical tests are summarized in table \ref{tabledist}. This table shows that GRBs with faint afterglows are mostly located in the upper part of the \epi\ -- \eiso\ {\rm plane}\, compared to the other GRBs. This suggests that an extended population of GRBs with low afterglow fluxes may fill the upper part of the \epi\ -- \eiso\ {\rm plane}\, even above the 2$\sigma$ limit of the \epi\ -- \eiso\ {\rm relation}\, but cannot be seen due to optical selection effects that prevent us from measuring their redshift.

\subsubsection{Comparing the afterglow optical flux above and below the best-fit \epi\ -- \eiso\ {\rm relation}}
In order to confirm the suggestion that GRBs located above the best-fit Amati relation have fainter afterglows than GRBs located below the best-fit Amati relation, we compared the optical flux of the GRBs located above and below the best-fit \epi\ -- \eiso\ {\rm relation}. In order to include GRBs without a redshift, we calculated their minimum and maximum vertical distances to the best-fit \epi\ -- \eiso\ {\rm relation}\, which depends on the redshifts (considered here between $0.168<z<6.0$). Then, we only kept those which are strictly located above the best-fit \epi\ -- \eiso\ {\rm relation}\ (i.e, those for which the minimum and the maximum distances to the best-fit \epi\ -- \eiso\ {\rm relation}\ are always positive) or strictly below it at any possible redshift. Eight GRBs without a redshift were selected, all of which were located strictly above the best-fit \epi\ -- \eiso\ {\rm relation}. Therefore, we finally used 84 GRBs in this analysis.

Figure \ref{fig_amati} compares the afterglow optical flux of GRBs located above and below the best-fit \epi\ -- \eiso\ {\rm relation}. A KS test shows that the two distributions strongly differ with a p-value of $4.77\times 10^{-6}$  ($\sim$ 4.5$\sigma$). The high significance of this test confirms that GRBs located below the best-fit \epi\ -- \eiso\ {\rm relation}\ have, on average, brighter afterglows than GRBs located above it. The average difference in magnitude between the two groups of GRBs is 1.76. We also noted that this result becomes less significant when we only consider GRBs with a redshift. Thus, GRBs without a redshift seem to confirm the trend that GRBs with low afterglow fluxes are mainly located above the \epi\ -- \eiso\ {\rm relation}\ and that they can suffer from a lack of redshift measurement.

\subsection{Our GRB sample in the \epi\ -- \liso\ {\rm plane}}

To compute the standard \epi\ -- \liso\ {\rm relation}\ we removed 3 GRBs from our sample of 76 GRBs with a redshift because of unsecured peak flux measurements. The best-fit \epi\ -- \liso\ {\rm relation}\ for this sample (73 GRBs) is ${\rm E}_{\rm pi} = 304~{\rm L}_{52}^{0.428}~ {\rm keV}$, where L$_{52}$ is the GRB isotropic luminosity in units of $\rm{10^{52}~erg.s^{-1}}$.
This best-fit relation is consistent with the \epi\ -- \liso\ {\rm relation}\ found by other authors \cite[e.g.][] {Nava2009,Nava2012}. The dispersion of the points around the best-fit relation along the vertical axis, $\sigma = 0.34$, is also comparable with the values found by \cite{Nava2012}, ($\sigma = 0.30$). We then produced the same analysis and the similar figures than for the \epi\ -- \eiso\ {\rm relation}\ (see figure \ref{fig_yonetoku} and table \ref{tabledist}).

\subsubsection{Comparing the vertical distances to the \epi\ -- \liso\ {\rm relation}}

For this analysis, our complete GRB sample is now composed of 87 GRBs since 3 GRBs have unsecured measured peak fluxes. The KS test that compares the vertical distances to the \epi\ -- \liso\ {\rm relation} s of our classes of afterglow optical flux reveals that the three populations of GRBs follow nearly the same statistical distribution. Contrary to the \epi\ -- \eiso\ {\rm relation}\, no clear connection can be determined between the afterglow optical flux and the positions of the GRBs in the \epi\ -- \liso\ {\rm plane}.

\begin{figure*}[t!]
\begin{minipage}{0.5\linewidth}

\includegraphics[trim = 0 175 0 200,clip=true,width=1.0\textwidth]{Yonetoku_relation.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}

\includegraphics[trim = 0 175 0 200,clip=true,width=1.0\textwidth]{Yonetoku_relation_sansz.pdf}
\end{minipage}

\begin{minipage}{0.5\linewidth}
\hspace*{-0.5cm}
\includegraphics[trim = 0 175 0 200,clip=true,width=1.1\textwidth]{dist_yonetoku.pdf}
\end{minipage}
\begin{minipage}{0.5\linewidth}
\hspace*{-0.5cm}
\includegraphics[trim = 0 190 0 190,clip=true,width=1.07\textwidth]{Yonetoku_80GRB.pdf}
\end{minipage}
\caption{Same caption as figure \ref{fig_amati}, except E$_{iso}$ changed to L$_{iso}$. Top left: 73 GRBs with a redshift are shown here. Bottom left: the 14 GRBs without a redshift are shown here. Bottom left: our sample of 87 GRBs is shown here. Bottom right: this analysis used a sample of 73 GRBs with a redshift and 6 GRBs without a one.
}
\label{fig_yonetoku}
\end{figure*}
\subsubsection{Comparing the afterglow optical brightness above and below the best-fit \epi\ -- \liso\ {\rm relation}}
In this analysis, we could use 73 GRBs with a redshift and add 6 GRBs without a redshift which are all located above the best-fit \epi\ -- \liso\ {\rm relation}, so that we used a total of 79 GRBs.

The KS test reveals that the two distributions of afterglow optical flux marginally differ with a p-value of $5.0\times 10^{-3}$ ($\sim2.8\sigma$). The significance of this test cannot strictly confirm that GRBs located below the best-fit \epi\ -- \liso\ {\rm relation}\ have, on average, brighter afterglows than those of GRBs located above it. The average difference in magnitude between the two groups of GRBs is 0.97.
In conclusion, while we find a clear segregation of GRBs with different optical fluxes in the \epi\ -- \eiso\ {\rm plane}\, the situation is much less clear in the \epi\ -- \liso\ {\rm plane}. The possible origin of this difference is discussed in section \ref{discussion}.

\begin{deluxetable}{ccccccc}
\tablecolumns{7}
\tablewidth{0pc}
\tablecaption{Results of the different KS tests of section \ref{sec_correlation}.}
\tablecomments{The indicated probabilities correspond to the p-values, i.e, the probability of observing a test statistic as extreme as, or more extreme than, the observed value under the null hypothesis. "F", "I" and "B" refer to the three classes of afterglow optical flux, Faint, Intermediate, and Bright, respectively.}
\tablehead{
\colhead{Parameter}&  \multicolumn{3}{c}{distance to \epi\ -- \eiso\ {\rm relation}} &  \multicolumn{3}{c}{distance to \epi\ -- \liso\ {\rm relation}}
}
\startdata
{GRB samples}&  F/I & {\bf F/B} & I/B& F/I &  F/B &I/B  \\
 &   &  & & &  & \\[0.5pc]
P-value& $0.01$ & $\mathbf{8.57\times 10^{-4}}$ &0.21& 0.11& 0.28 &0.98 \\
\cline{1-7}\\[-0.80pc]
\cline{1-7}
\\
 Parameter & \multicolumn{6}{c}{Uncorrected R magnitude}\\[0.5pc]
\cline{1-7}\\
 {GRB samples}&  \multicolumn{3}{c}{\bf Above/Below} &\multicolumn{3}{c}{\bf Above/Below}\\
 &  \multicolumn{3}{c}{\bf the \epi\ -- \eiso\ {\rm relation}} & \multicolumn{3}{c}{\bf the \epi\ -- \liso\ {\rm relation}}  \\[0.5pc]
P-value& \multicolumn{3}{c}{$\mathbf{4.77\times 10^{-6}}$} & \multicolumn{3}{c}{$\mathbf{5.0\times 10^{-3}}$}\\
\enddata
\label{tabledist}
\end{deluxetable}

\section{Discussion and conclusion}
\label{discussion}

GRBs with a redshift undergo two types of selection effects: those connected with the detection of the burst in $\gamma$-rays and those connected with the measure of the redshift.
About 30\% of the GRBs detected with {\it Swift}/BAT have their redshift measured; this small fraction is partly due to a lack of early optical observations (which can nevertheless be compensated for at later times with large observing resources, as in the TOUGH program; \cite{Hjorth2012}) and partly due to the faintness of the optical afterglows, which prevents us from obtaining useful spectra.
Our study based on a population of 90 GRBs shows that the redshift measure selects the most luminous GRBs.
When the luminosity dominates over the impact of distance, as is the case for the majority of GRB afterglows, the difficulty to detect faint afterglows biases the GRB optical luminosity function in favor of luminous events. According to our GRB sample, most of the time, the redshifts of GRBs with afterglows less luminous than $\rm{10^{30}~erg.s^{-1}.Hz^{-1}}$ are not measured beyond $z=1$.

In addition to biasing the distribution of GRB optical luminosities, the measure of the redshift may also impact the observed distribution of prompt GRB parameters if there is a connection between the prompt properties and the optical flux of the afterglow.

\subsection{Redshift and duration}
Our results show that the distributions of E$_{\rm iso}$\, L$_{\rm iso}$\, and E$_{\rm pi}$\ do not differ much between GRBs with faint and bright optical afterglows.
Consequently, optical selection effects are not expected to bias these distributions, beyond the biases resulting from the GRB detection in hard X-rays.

On the contrary, the distribution of $T_{90}^{rest}$ looks different for those GRBs with strong and faint optical afterglows, and thus, this parameter may undergo additional biases due to the measure of redshift.
According to figure \ref{prompt_par}, the measure of the redshift may select GRBs which are about two times longer than average (i.e. with a larger $T_{90}^{rest}$). This bias is in addition to, and may partially compensate for, the biases resulting from the $\gamma$-ray selection effects discussed by \cite{Kocevski2013}. A detailed analysis of the $\gamma$-ray light curves would be helpful to assess more precisely the differences between the light curve of GRBs with bright and faint optical afterglows.

\subsection{Redshift and GRB correlations}
We have found a significant correlation between the optical magnitudes of GRBs and their locations in the \epi\ -- \eiso\ {\rm plane}.
In our sample, GRBs with a large optical flux concentrate in the region located below the best-fit \epi\ -- \eiso\ {\rm relation}, while GRBs with low optical flux preferentially fill in the region located above the best-fit \epi\ -- \eiso\ {\rm relation} , like a majority of GRBs without a redshift, which have very faint optical afterglows.
This optical bias could explain the apparent contradictory results obtained between GRBs with a redshift, which seem to follow the \epi\ -- \eiso\ {\rm relation}\ relation quite well, and the whole GRB population, which seems to contain a significant fraction of outliers.
Our observations also show that GRBs with a redshift underestimate the true width of the \epi\ -- \eiso\ {\rm relation}\ correlation.
We propose an explanation for this observation in the next section.

On the contrary, we  observe no clear correlation between the afterglow optical brightness and the positions of GRBs in the \epi\ -- \liso\ {\rm plane}.
This means that the \epi\ -- \liso\ {\rm relation}\ does not suffer as much from optical selection effects.
If biases affect the observed \epi\ -- \liso\ {\rm relation}\, then they should mostly come from the $\gamma$-ray detections.

\subsubsection{Why Do GRBs below and above the Best-fit \epi\ -- \eiso\ {\rm relation}\ have different R magnitudes?}
Figure \ref{z_vs_LR} clearly shows that the excess of bright optical afterglows among GRBs located below the best-fit \epi\ -- \eiso\ {\rm relation}\ is due to a bunch of GRBs with $\rm R < 17.9$ and $\rm z < 1.5$ ($\rm log(1+z) < 0.4$).
Above $z=1.5$, on the other hand, the bright GRBs are equally distributed with respect to the \epi\ -- \eiso\ {\rm relation} .
This led us to study the \epi\ -- \eiso\ {\rm relation}\ below and above redshift $z=1.5$.
We find that the best-fit moves from ${\rm E}_{\rm pi} = 128~{\rm E}_{52}^{0.397}~ {\rm keV}$ for GRBs with  $\rm z < 1.5$ to ${\rm E}_{\rm pi} = 211~{\rm E}_{52}^{0.400}~ {\rm keV}$ for GRBs with  $\rm z \geq 1.5$.
Assuming that GRBs below and above $z=1.5$ follow different \epi\ -- \eiso\ {\rm relation} s,  the bright GRBs are now distributed equally above and below the best-fit \epi\ -- \eiso\ {\rm relation}\ for GRBs with $\rm z < 1.5$. Using the same method as in section \ref{sec_correlation}, we compared the R magnitudes of GRBs with a redshift located below their best-fit \epi\ -- \eiso\ {\rm relation}\ to those located above it and now found an insignificant result with a KS test p-value = 0.0329. Thus, we observe that the correlation between optical brightness and the location of GRBs in the \epi\ -- \eiso\ {\rm plane}\ disappears.

We conclude that there is no real difference between GRBs located below and above the \epi\ -- \eiso\ {\rm relation}. Instead, the \epi\ -- \eiso\ {\rm relation}\ evolves with redshift or changes with GRB luminosity, leading to the observed correlation between the location of GRBs in the \epi\ -- \eiso\ {\rm plane}\ and the magnitude of their afterglows when a single \epi\ -- \eiso\ {\rm relation}\ is considered in the full redshift range.
A similar conclusion was proposed by \cite{Li2007} and  \cite{Lin2015}.

Based on the present statistics, it is not possible to determine whether the change of the \epi\ -- \eiso\ {\rm relation}\ below and above  $\rm z = 1.5$ is due to an evolution of the \epi\ -- \eiso\ {\rm relation}\ with the redshift or to different relations for GRBs with small and large E$_{\rm iso}$ . Considering that the location of GRBs in the \epi\ -- \eiso\ {\rm plane}\ is an intrinsic property, like their energy E$_{\rm iso}$\, we tend to favor the second possibility.

\subsubsection{Using the \epi\ -- \eiso\ {\rm relation}\ for cosmological purposes}

The simplest way to use the \epi\ -- \eiso\ {\rm relation}\ for GRB standardization is to consider that it as an intrinsic GRB property that does not evolve with redshift or with the properties of the GRBs.
However, this simple view is being challenged by growing evidence that the \epi\ -- \eiso\ {\rm relation}\ is a boundary in the \epi\ -- \eiso\ {\rm plane}\ and not a true correlation (e.g. \cite{Heussaff2013}), and by the possibility that the \epi\ -- \eiso\ {\rm relation}\ evolves with redshift (\cite{Li2007,Lin2015}; see, however, \cite{Ghirlanda2008}).

We have shown here that the selection effects due to the measure of the redshift cannot be neglected when discussing the \epi\ -- \eiso\ {\rm relation}\ as a genuine rest-frame prompt property of long GRBs or when attempting to use it for cosmology.
In addition, our study suggests that GRBs which can be calibrated with Type Ia supernobvae (at redshifts $z < 1.5$) are not representative of the GRB population at higher redshift, which raises important concerns for GRB cosmology based on the \epi\ -- \eiso\ {\rm relation} (see for example \cite{Liang2008}).

We conclude that GRB standardization is a complex issue that cannot rely on the construction of a GRB Hubble diagram simply based on the measure of E$_{\rm pi}$\, and the redshift and an "ideal" \epi\ -- \eiso\ {\rm relation} .
It requires a better understanding of the nature of the \epi\ -- \eiso\ {\rm relation}\ (boundary or true correlation), of its dependence on GRB parameters, of its possible evolution with redshift, and of the biases resulting from current observations.

\subsection{Conclusion}

Large samples of GRBs with a redshift are required in order to obtain a correct understanding of the intrinsic properties of GRBs and their afterglows.
Such samples suffer from combined selection effects due to the need to detect the GRBs and the need to measure their redshift.
The connections that exist between the prompt emission and the afterglow imply that these selection effects will impact both the observed properties of the prompt emission and those of the afterglow.

Here, we have studied the potential impact of measuring the redshift on the observed properties of the prompt emission.
According to our results, the redshift measurement slightly alters the observed distribution of GRB durations, leading to a longer-than-average selection of GRBs.
A stronger effect is observed for the \epi\ -- \eiso\ {\rm relation} .
We have found a correlation between the location of a GRB in the \epi\ -- \eiso\ {\rm plane}\ and the optical R magnitude of its afterglow, we interpret this observation as being due to the dependence of the \epi\ -- \eiso\ {\rm relation}\ on the GRB energy or its evolution with redshift.

\begin{deluxetable}{ccccccccccc}
\tablecolumns{10}
\tablewidth{0pc}
\tablecaption{Parameters of the GRB Sample with a redshift}
\tablecomments{(1) GRB name; (2) redshift; (3) rest-frame peak energy of the gamma-ray spectral energy distribution; (4) isotropic gamma-ray energy; (5) isotropic gamma-ray luminosity; (6) duration, in seconds, during which 90$\%$ of the burst fluence was accumulated starting by the time at which 5$\%$ of the total fluence has been detected; (7) $R_{mag}$ is the apparent R magnitude 2 hr after the burst not corrected from the galactic and host extinctions ($\blacktriangledown$ indicates it is an upper limit on R mag); (8) $L_R^{rest}$ is the optical luminosity density taken 2 hr after the burst (in the rest-frame); (9) galactic extinction from \cite{Schlegel1998}; (10) host extinction (*) indicates that the host extinction is estimated from the $\rm{NH_{X,i}}$ measurement), otherwise the references for the host extinction are listed in table \ref{tab_refz}; (11) the references are listed in table \ref{tab_refz}.
}
\tablehead{
\colhead{GRB }& \colhead{ z} & \colhead{ $E_{pi}$}&\colhead{ $E_{iso}$}&\colhead{ $L_{iso}$}&\colhead{ $T_{90}$} & \colhead{ $R_{mag}$}&\colhead{ $log_{10}(L_R^{rest})$} &\colhead{ $\rm{A_V^{gal}}$}& \colhead{ $\rm{A_V^{host}}$}& {Ref. z}\\
\colhead{ } & \colhead{ }& \colhead{(keV)}&\colhead{ ($10^{52} erg$) }& \colhead{ ($10^{52} erg.s^{-1}$)}& \colhead{ (s)}&\colhead{ (mag)}& \colhead{($\rm{erg.s^{-1}.Hz^{-1}})$}&\colhead{ (mag)}& \colhead{ (mag)}& \colhead{ }\\
\colhead{ (1)}& \colhead{ (2)} & \colhead{ (3)} & \colhead{ (4)}& \colhead{ (5)} &\colhead{ (6)}&\colhead{ (7) }& \colhead{ (8)}& \colhead{ (9)}&\colhead{ (10)} &\colhead{ (11)}}
\startdata
 990123 &  1.60 &  $2030.0^{+161.0}_{-161.0}$ & $278.0^{+31.5}_{-31.5}$ & $57.56^{+16.9}_{-16.9}$ & 63.3 & $17.90$ & 31.03&0.05&$\sim 0$$~^{a)}$& A.\\[0.5pc]
 990510&  1.619&  $423.0^{+42.0}_{-42.0}$ & $20.6^{+2.9}_{-2.9}$ & $6.68^{+0.56}_{-0.56}$ & 67.6 & $17.40$ & 31.58&0.66&0.22$~^{a)}$& B.\\[0.5pc]
 990712&  0.434&  $93.0^{+15.0}_{-15.0}$ & $0.78^{+0.15}_{-0.15}$ & $0.24^{+0.02}_{-0.02}$ & 30 & $18.64$ & 29.78&0.11&0.15$~^{b)}$& C.\\[0.5pc]
 020124&  3.198&  $339.6^{+44.0}_{-44.0}$ & $99.8^{+21.0}_{-21.0}$ & $2.01$ & 51.2 & $18.29$ & 31.29&0.16&0.28$~^{a)}$& D.\\[0.5pc]
 020813&  1.25&  $592.9^{+60.2}_{-60.2}$ & $95.9^{+3.6}_{-3.6}$ & $5.79$ & 87.9 & $17.91$ & 30.99&0.36&0.12$~^{a)}$& E.\\[0.5pc]
 021004&  2.33&  $310.5^{+84.0}_{-84.0}$ & $5.68^{+1.26}_{-1.26}$ & \nodata & 48.9 & $16.40$ & 32.01&0.20&0.26$~^{a)}$& F.\\[0.5pc]
 021211&  1.01&  $94.8^{+6.8}_{-6.8}$ & $2.23^{+0.23}_{-0.23}$ & \nodata & 4.2 & $20.19$ & 29.81&0.09&$\sim 0$$~^{a)}$& G.\\[0.5pc]
 030328&  1.52&  $327.3^{+22.6}_{-22.6}$ & $24.0^{+0.73}_{-0.73}$ &$2.28$  & 138.3 & $18.79$ & 30.66&0.15&$\sim 0$$~^{a)}$& H.\\[0.5pc]
 030329&  0.168&  $82.2^{+1.5}_{-1.5}$ & $1.07^{+0.02}_{-0.02}$ &$0.25$& 25.9 & $13.02$ & 31.29&0.08&0.54$~^{a)}$& I.\\[0.5pc]
 040924&  0.859&  $75.9^{+2.5}_{-2.5}$ & $1.96^{+0.14}_{-0.14}$ & $5.71$ & 3.4 & $20.12$ & 29.78&0.19&0.16$~^{a)}$& J.\\[0.5pc]
 041006&  0.716&  $82.2^{+3.1}_{-3.1}$ & $1.66^{+0.05}_{-0.05}$ & \nodata & 22.1 & $18.68$ & 30.35&0.71&0.11$~^{a)}$& K.\\[0.5pc]
 050416A&  0.6535&  $24.8^{+3.8}_{-4.5}$ & $0.10^{+0.01}_{-0.01}$ & $0.09^{+0.01}_{-0.01}$ & 2.4 & $20.87$ & 29.22&0.10&0.19$~^{a)}$& L.\\[0.5pc]
 050525A&  0.606&  $135.1^{+2.7}_{-2.7}$ & $2.41^{+0.04}_{-0.04}$ & $0.75^{+0.42}_{-0.42}$ & 8.8 & $17.40$ &  30.60&0.32&0.26$~^{c)}$& M.\\[0.5pc]
 050820A&  2.612&  $1326.7^{+343.4}_{-224.1}$ & $20.3^{+1.43}_{-1.43}$ & $4.42^{+0.17}_{-0.17}$ & 26 & $17.51$ & 31.61&0.15&0.065$~^{d)}$& N.\\[0.5pc]
 050922C&  2.198&  $417.5^{+162.8}_{-85.7}$ & $4.56^{+0.15}_{-0.15}$ & $5.35^{+0.24}_{-0.24}$ & 5 & $17.87$ & 31.36&0.34&0.07$~^{e)}$& O.\\[0.5pc]
 060115&  3.53&  $280.9^{+86.1}_{-27.2}$ & $8.87^{+0.78}_{-0.78}$ & $1.38^{+0.19}_{-0.19}$ & 139.6 & $19.97$ & 30.88&0.44&$\sim 0^*$& P.\\[0.5pc]
 060908&  1.1884&  $425.3^{+264.1}_{-130.3}$ & $9.48^{+0.38}_{-0.38}$ & $2.81^{+0.23}_{-0.23}$ & 19.3 & $19.85$ & 30.08&0.12&0.09$~^{a)}$& Q.\\[0.5pc]
 061007&  1.261&  $1065.4^{+81.4}_{-81.4}$ & $91.41^{+1.16}_{-1.16}$ & $6.23^{+0.16}_{-0.16}$ & 75.3 & $17.44$ & 31.21&0.07&0.66$~^{f)}$& R.\\[0.5pc]
 061121&  1.314&  $1402.3^{+208.3}_{-166.6}$ & $28.21^{+0.41}_{-0.41}$ & $8.04^{+0.18}_{-0.18}$ & 81.3 & $18.63$ & 30.72&0.15&0.28$~^{a)}$& S.\\[0.5pc]
 070612A&  0.617&  $305.6^{+95.4}_{-95.4}$ & $3.0^{+0.17}_{-0.17}$ & $0.06^{+0.02}_{-0.02}$ & 368.8 & $17.45$ & 30.67&0.17&0.46$^*$& T.\\[0.5pc]
 071010B&  0.947&  $87.6^{+7.8}_{-1.4}$ & $2.35^{+0.05}_{-0.05}$ & $0.49^{+0.02}_{-0.02}$ & 35.7 & $18.28$ & 30.61 &0.03&$0.18^*$& U.\\[0.5pc]
 071020&  2.145&  $1014.3^{+252.0}_{-167.0}$ & $14.06^{+0.61}_{-0.61}$ & $15.81^{+0.56}_{-0.56}$ & 4.2 & $19.81$ & 30.61&0.21&0.28$~^{a)}$& V.\\[0.5pc]
 080319B&  0.937&  $1261.0^{+27.1}_{-25.2}$ & $120.36^{+1.49}_{-1.49}$ & $6.90^{+0.14}_{-0.14}$ & 66 & $16.89$ & 31.03&0.04&0.07$~^{a)}$& W.\\[0.5pc]
 080411&  1.03&  $525.8^{+71.1}_{-54.8}$ & $23.24^{+0.09}_{-0.09}$ & $5.59^{+0.12}_{-0.12}$ & 56 & $16.54$ & 31.36&0.11&$0.28^*$& X.\\[0.5pc]
 080413A&  2.433&  $432.6^{+449.7}_{-144.2}$ & $12.97^{+0.37}_{-0.37}$ & $5.38^{+0.19}_{-0.19}$& 19 & $18.43$ & 31.19&0.51&$\sim 0$$~^{d)}$& Y.\\[0.5pc]
 080413B&  1.10&  $140.7^{+27.3}_{-16.8}$ & $1.85^{+0.06}_{-0.06}$ & $1.51^{+0.06}_{-0.06}$ & 8 & $17.39$ & 31.00&0.12&$\sim 0$$~^{a)}$& Z.\\[0.5pc]
 080605&  1.64&  $768.2^{+198.0}_{-198.0}$ & $27.60^{+0.41}_{-0.41}$ & $8.53^{+0.26}_{-0.26}$ & 20 & $20.20$ & 30.40&0.44&0.47$~^{g)}$& AA.\\[0.5pc]
 080721&  2.591&  $1747.0^{+241.3}_{-212.5}$ & $91.00^{+7.58}_{-7.58}$ & $52.31^{+4.51}_{-4.51}$ & 16.2 & $18.24$ & 31.34&0.34&0.35$~^{d)}$& AB.\\[0.5pc]
 080804&  2.2045&  $697.2^{+78.4}_{-78.4}$ & $19.80^{+1.01}_{-1.01}$ & $5.28^{+0.68}_{-0.68}$ & 34 & $20.03$ & 30.43&0.05&0.06$~^{g)}$& AC.\\[0.5pc]
 080810&  3.355&  $3957.3^{+801.7}_{-801.7}$ & $58.58^{+2.55}_{-2.55}$ & $9.42^{+0.94}_{-0.94}$ & 106 & $17.25$ & 31.79&0.09&0.16$~^{d)}$& AD.\\[0.5pc]
 081007&  0.5295&  $61.2^{+15.3}_{-15.3}$ & $0.12^{+0.01}_{-0.01}$ & $0.04^{+0.01}_{-0.01}$ & 12 & $19.45$ & 29.56&0.05&$\sim 0$$~^{a)}$& AE.\\[0.5pc]
 081008&  1.9685&  $493.3^{+107.7}_{-107.7}$ & $12.70^{+0.59}_{-0.59}$ & $0.93^{+0.07}_{-0.07}$ & 185.5 & $17.62$ & 31.59&0.31&0.46$~^{a)}$& AF.\\[0.5pc]
 081121&  2.512&  $564.6^{+58.1}_{-58.1}$ & $19.57^{+1.43}_{-1.43}$ & $6.92^{+1.57}_{-1.57}$ & 42 & $17.65$ & 31.52&0.17&$0.13^*$& AG.\\[0.5pc]
 081222&  2.77&  $538.1^{+36.1}_{-36.1}$ & $20.28^{+0.42}_{-0.42}$ & $10.13^{+0.26}_{-0.26}$ & 24 & $18.45$ & 31.21&0.07&$\sim 0$$~^{a)}$& AH.\\[0.5pc]
 090102&  1.543&  $1073.8^{+45.9}_{-45.9}$ & $15.96^{+0.70}_{-0.70}$ & $2.98^{+0.43}_{-0.43}$ & 27 & $20.17$ & 30.22&0.15&0.45$~^{a)}$& AI.\\[0.5pc]
 090418A&  1.608&  $1567.4^{+1444.8}_{-560.7}$ & $13.75^{+0.60}_{-0.60}$ & $1.19^{+0.19}_{-0.19}$ & 56 & $20.03$ & 30.54&0.15&$0.67^*$& AJ.\\[0.5pc]
 090424&  0.544&  $237.1^{+5.9}_{-5.9}$ & $3.54^{+0.35}_{-0.35}$ & $1.47^{+0.04}_{-0.04}$ & 52 & $18.33$ & 30.15&0.08&0.50$~^{d)}$& AK.\\[0.5pc]
 090516A&  4.11&  $725.9^{+135.2}_{-135.2}$ & $73.95^{+4.93}_{-4.93}$ & $4.69^{+0.59}_{-0.59}$ & 10.3 & $20.88^{\blacktriangledown}$ & $30.24^\blacktriangledown$&0.17&$0.84^*$& AL.\\[0.5pc]
 090519&  3.85&  $7848.2^{+4282.6}_{-4282.6}$ & $34.30^{+2.86}_{-2.86}$ & $7.86^{+2.62}_{-2.62}$ & 74.2 & $23.14$ & 29.77&0.13&0.01$~^{g)}$& AM.\\[0.5pc]
 090618&  0.54&  $226.2^{+5.6}_{-5.6}$ & $22.95^{+0.22}_{-0.22}$ & $1.02^{+0.02}_{-0.02}$ & 105 & $16.65$ & 30.83&0.28&0.25$~^{a)}$& AN.\\[0.5pc]
 090812&  2.452&  $2022.9^{+838.8}_{-524.7}$ & $43.26^{+1.49}_{-1.49}$ & $8.27^{+0.46}_{-0.46}$ & 66.7 & $21.15$ & 30.18&0.08&0.41$~^{g)}$& AO.\\[0.5pc]
 091020&  1.71&  $661.9^{+99.5}_{-99.5}$ & $6.81^{+0.18}_{-0.18}$ & $1.65^{+0.12}_{-0.12}$ & 34.6 & $18.31$ & 31.01&0.06&$0.36^*$& AP.\\[0.5pc]
 091029&  2.752&  $229.7^{+33.8}_{-94.5}$ & $9.46^{+0.39}_{-0.39}$ & $1.71^{+0.10}_{-0.10}$ & 39.2 & $17.85$ & 31.44&0.06&$\sim 0$$~^{g)}$& AQ.\\[0.5pc]
 091127&  0.49&  $52.9^{+2.3}_{-2.3}$ & $1.39^{+0.05}_{-0.05}$ & $0.65^{+0.04}_{-0.04}$ & 7.1 & $16.77$ & 30.60&0.13&0.11$~^{a)}$& AR.\\[0.5pc]
 091208B&  1.063&  $255.4^{+41.4}_{-40.0}$ & $2.50^{+0.15}_{-0.15}$ & $1.67^{+0.11}_{-0.11}$ & 14.9 & $19.59$ & 30.24&0.18&0.40$~^{a)}$& AS.\\[0.5pc]
 100728B&  2.106&  $341.2^{+68.5}_{-68.5}$ & $5.66^{+0.33}_{-0.33}$ & $2.90^{+0.41}_{-0.41}$ & 10.2 & $20.11$ & 30.53&0.22&$0.35^*$& AT.\\[0.5pc]
 100814A&  1.44&  $330.9^{+25.5}_{-25.5}$ & $11.65^{+0.26}_{-0.26}$ & $0.72^{+0.06}_{-0.06}$ & 110 & $19.02$ & 30.59&0.07&$0.11^*$& AU.\\[0.5pc]
 110205A&  2.22&  $714.8^{+238.3}_{-238.3}$ & $57.82^{+5.78}_{-5.78}$ & $2.83^{+0.16}_{-0.16}$ & 257 & $17.33$ &  31.49&0.05&0.20$~^{a)}$& AV.\\[0.5pc]
 110213A&  1.46&  $223.9^{+76.3}_{-64.0}$ & $8.57^{+0.58}_{-0.58}$ & $0.37^{+0.14}_{-0.14}$ & 48 & $16.02$ &  32.14&1.06&$0.07^*$& AW.\\[0.5pc]
 110422A&  1.77&  $421.0^{+13.9}_{-13.9}$ & $66.04^{+1.61}_{-1.61}$ & $12.06^{+0.39}_{-0.39}$ & 40 & $19.04$ &  30.89&0.09&$0.65^*$& AX.\\[0.5pc]
 110503A&  1.613&  $572.3^{+52.3}_{-49.3}$ & $17.84^{+0.71}_{-0.71}$ & $0.53^{+0.02}_{-0.02}$ & 10 & $18.89$ &  30.68&0.08&$0.15^*$& AY.\\[0.5pc]
 110731A&  2.83&  $1223.0^{+73.4}_{-73.4}$ & $39.84^{+0.66}_{-0.66}$ & $25.49^{+0.70}_{-0.70}$ & 6.6 & $20.36$ &  30.72&0.57&0.24$~^{a)}$& AZ.\\[0.5pc]
 120326A&  1.798&  $122.9^{+10.8}_{-10.8}$ & $4.08^{+0.47}_{-0.47}$ & $1.28^{+0.06}_{-0.06}$ & 69.6 & $18.91$ &  30.90&0.17&$0.23^*$& BA.\\[0.5pc]
 120811C&  2.671&  $204.0^{+19.6}_{-19.6}$ & $7.42^{+0.74}_{-0.74}$ & $2.44^{+0.12}_{-0.12}$ & 26.8 & $19.42$ &  30.94&0.11&$0.53^*$& BB.\\[0.5pc]
 120907A&  0.97&  $241.2^{+67.3}_{-67.3}$ & $0.27^{+0.04}_{-0.04}$ & $0.19^{+0.03}_{-0.03}$ & 5.8 & $20.17$ &  29.88&0.31&$0.13^*$& BC.\\[0.5pc]
 121211A&  1.023&  $202.8^{+32.0}_{-32.0}$ & $0.49^{+0.10}_{-0.10}$ & $0.06^{+0.02}_{-0.02}$ & 182 & $19.65$ &  30.09&0.03&$0.37^*$& BD.\\[0.5pc]
 130408A&  3.758&  $1003.9^{+138.0}_{-138.0}$ & $21.39^{+3.72}_{-3.72}$ & $21.58^{+4.40}_{-4.40}$ & 7 & $19.13$ &  31.30&0.84&$0.06^*$& BE.\\[0.5pc]
 130420A&  1.297&  $131.6^{+7.2}_{-7.2}$ & $4.61^{+0.19}_{-0.19}$ & $0.33^{+0.02}_{-0.02}$ & 123.5 & $19.06$ &  30.51&0.04&$0.21^*$& BF.\\[0.5pc]
 130427A&  0.3399&  $1112.1^{+6.7}_{-6.7}$ & $81.93^{+0.79}_{-0.79}$ & $11.57^{+0.16}_{-0.16}$ & 138.2 & $15.08$ &  30.96&0.07&$0.11^*$& BG.\\[0.5pc]
 130505A&  2.27&  $2063.4^{+101.4}_{-101.4}$ & $220.26^{+10.49}_{-10.49}$ & $104.01^{+10.75}_{-10.75}$ & 88 & $17.89$ & 31.42&0.13&$0.35^*$& BH.\\[0.5pc]
 130610A&  2.092&  $911.8^{+132.7}_{-132.7}$ & $9.59^{+0.38}_{-0.38}$ & $1.75^{+0.21}_{-0.21}$ & 46.4 & $19.88$ &  30.53&0.07&$0.23^*$& BI.\\[0.5pc]
 130701A&  1.155&  $191.8^{+8.6}_{-8.6}$ & $3.52^{+0.08}_{-0.08}$ & $2.12^{+0.09}_{-0.09}$ & 4.4 & $19.08$ &  30.43&0.28&$0.09^*$& BJ.\\[0.5pc]
 130831A&  0.4791&  $81.4^{+5.9}_{-5.9}$ & $0.775^{+0.002}_{-0.002}$ & $0.15^{+0.01}_{-0.01}$ & 32.5 & $17.23$ &  30.39&0.15&$0.07^*$& BK.\\[0.5pc]
 131030A&  1.293&  $405.9^{+22.9}_{-22.9}$ & $28.91^{+2.89}_{-2.89}$ & $5.72^{+0.14}_{-0.14}$ & 41.1 & $17.70$ &  31.04&0.19&$0.21^*$& BL.\\[0.5pc]
 131231A&  0.6419&  $291^{+6}_{-6}$ & $23.02^{+0.28}_{-0.28}$ & $2.16^{+0.02}_{-0.02}$ & 31.2 & 16.15 &  31.26 &0.07&$0.23^*$& BM.\\[0.5pc]
 140213A&  1.2076&  $191.2^{+7.8}_{-7.8}$ & $10.75^{+1.07}_{-1.07}$& $3.31^{+0.11}_{-0.11}$ & 18.6 & $18.32$ &  30.83&0.49&$0.06^*$& BN.\\[0.5pc]
 140419A&  3.956&  $1452.1^{+416.3}_{-416.3}$ & $191.66^{+19.17}_{-19.17}$ & $28.35^{+1.16}_{-1.16}$ & 94.7 & $18.17$ &  31.67&0.10&$0.47^*$& BO.\\[0.5pc]
 140423A&  3.26&  $532.5^{+38.3}_{-38.3}$ & $67.97^{+2.17}_{-2.17}$ & $5.93^{+0.56}_{-0.56}$ & 134 & $19.08$ &  31.12&0.04&$0.32^*$& BP.\\[0.5pc]
 140506A&  0.889&  $373.2^{+61.5}_{-61.5}$ & $1.28^{+0.14}_{-0.14}$ & $0.74^{+0.06}_{-0.06}$ & 64.13 & $19.60$ &  30.11&0.31&$0.32^*$& BQ.\\[0.5pc]
 140508A&  1.03&  $534^{+28}_{-28}$ & $24.53^{+0.86}_{-0.86}$ & $6.79^{+0.10}_{-0.10}$ & 44.3 & 16.78 &  31.28 &0.08&$0.20^*$& BR.\\[0.5pc]
 140512A&  0.725&  $1177.8^{+121.3}_{-121.3}$ & $9.44^{+0.20}_{-0.20}$ & $0.66^{+0.03}_{-0.03}$ & 154.8 & $18.44$ &  30.41&0.53&$0.10^*$& BS.\\[0.5pc]
 140606B&  0.384&  $801^{+182}_{-182}$ & $0.468^{+0.04}_{-0.04}$ & $0.19^{+0.01}_{-0.01}$ & 22.8 & 19.25 &  29.65 &0.32&$0.34^*$& BT.\\[0.5pc]
 140620A&  2.04&  $387^{+34}_{-34}$ & $7.28^{+0.37}_{-0.37}$ & $3.02^{+0.17}_{-0.17}$ & 45.8 & 19.08 &  31.11 &0.15&$0.16^*$& BU.\\[0.5pc]
 140623A&  1.92&  $834^{+317}_{-317}$ & $3.58^{+0.40}_{-0.40}$ & $0.69^{+0.08}_{-0.08}$ & 114.7 & 20.07 &  30.64 &0.10&$\sim0^*$& BV.\\[0.5pc]
 140703A&  3.14&  $861.3^{+148.3}_{-148.3}$ & $20.96^{+1.61}_{-1.61}$ & $4.82^{+1.03}_{-1.03}$ &84.2 & $19.10$ &  31.28&0.34&$0.27^*$& BW.\\[0.5pc]
 140808A&  3.29&  $503^{+35}_{-35}$ & $8.71^{+0.60}_{-0.60}$ & $10.69^{+0.37}_{-0.37}$ & 4.5 & 18.23 &  32.16 &0.07&$1.1^*$& BX.\\[0.5pc]
\enddata
\label{tab_GRB}
\end{deluxetable}

\begin{deluxetable}{ccccccc}
\tablecolumns{7}
\tablewidth{0pc}
\tablecaption{Parameters of the GRB Sample without a Redshift.}
\tablecomments{(1) GRB name where ($^\bigstar$) indicates that for this GRB a strong constraint on the redshift was determined by \cite{Volnova2014f}; (2) observed peak energy of the $\rm{\nu F_\nu}$ spectrum; (3) observed $\gamma$-ray fluence in the 15-150 keV energy band; (4) Observed 1s-peak photon flux in the 15-150 keV energy band; (5) and (6) galactic and host visual extinctions, respectively, where (*) indicates that the host extinction is estimated from the $NH_{X,i}$ measurement); (7) apparent R magnitude measured 2 hr after the burst not corrected for the galactic and host extinctions ($\blacktriangledown$ : upper limit on R mag. $\dagger$ : calibrated with the V-band magnitude).
}
\tablehead{
\colhead{GRB }& \colhead{ $E_{po}$} & \colhead{ $S_\gamma$}&\colhead{ $P_\gamma$}&\colhead{ $A_V^{gal}$}& \colhead{ $A_V^{host}$} & \colhead{ $R_{mag}$} \\
\colhead{ } &\colhead{(keV)}&\colhead{ $(\rm{10^{-7}~erg.cm^{-2}})$ }& \colhead{ $(\rm{photon.cm^{-2}.s^{-1}})$}& \colhead{ (mag)}& \colhead{ (mag)}& \colhead{ (t$_{\rm obs}$=2h)} \\
\colhead{ (1)}& \colhead{ (2)} & \colhead{ (3)} & \colhead{ (4)}& \colhead{ (5)} &\colhead{ (6)}&\colhead{ (7) }}
\startdata
051008$^\bigstar$ & $307^{+178}_{-136}$ &  $50.90^{+1.45}_{-1.45}$ & $5.44^{+0.35}_{-0.35}$ &0.04 &  0.21$^*$ & $23.30^{\blacktriangledown}$\\[0.5pc]
060105 & $327^{+40}_{-46}$ & $176.00^{+3.04}_{-3.04}$ & $7.44^{+0.36}_{-0.36}$ &  0.56 & 0.13$^*$& $20.20^{\blacktriangledown}$ \\[0.5pc]
060117 & $184^{+30}_{-30}$ & $202.00^{+3.71}_{-3.71}$ & $48.30^{+1.56}_{-1.56}$ & 0.12 &0.45$^*$& $20.15^{\blacktriangledown}$ \\[0.5pc]
060904 & $163^{+31}_{-31}$ & $77.20^{+1.51}_{-1.51}$ & $4.87^{+0.20}_{-0.20}$ &  0.06 & 0.05$^*$& $21.51^{\blacktriangledown}$ \\[0.5pc]
090813 & $95^{+30}_{-30}$ & $13^{+1}_{-1}$ &$8.5^{+0.6}_{-0.6}$ & 0.56 &0.12$^*$& $20.21^{\blacktriangledown}$ \\[0.5pc]
091221 & $207^{+22}_{-17}$ & $57^{+2}_{-2}$ & $3.0^{+0.2}_{-0.2}$ & 0.70 &0.07$^*$& 21.44 \\[0.5pc]
100413A & $446^{+123}_{-123}$ & $62^{+2}_{-2}$ & $0.7^{+0.1}_{-0.1}$ &  0.37 & 0.15$^*$& 23.20 \\[0.5pc]
101011A & $296.6^{+49.4}_{-49.4}$ & $14^{+1}_{-1}$ &$1.3^{+0.2}_{-0.2}$ & 0.10 &0.11$^*$& $20.80^{\blacktriangledown\dagger}$ \\[0.5pc]
140102A & $186^{+5}_{-5}$ & $77^{+2}_{-2}$ & $29.8^{+0.6}_{-0.6}$ & 0.11 &0.10$^*$& 19.34 \\[0.5pc]
140626A & $44.7^{+9.5}_{-9.5}$&  $3.6^{+0.5}_{-0.5}$ & $0.7^{+0.1}_{-0.1}$ & 0.47 &0.07$^*$&$20.84^{\blacktriangledown}$\\[0.5pc]
140709B & $530^{+232}_{-232}$ &  $42^{+2}_{-2}$ &$0.9^{+0.1}_{-0.1}$ &  0.13 &0.12$^*$& $20.50^{\blacktriangledown}$\\[0.5pc]
140713A & $96^{+24}_{-24}$ & $3.7^{+0.3}_{-0.3}$ & $1.9^{+0.2}_{-0.2}$ &  0.16 &0.27$^*$& $23.90^{\blacktriangledown}$\\[0.5pc]
141005A & $119^{+10}_{-10}$ & $11^{+1}_{-1}$ &$4.2^{+0.8}_{-0.8}$ & 0.56 &0.13$^*$& $21.44^{\blacktriangledown}$\\[0.5pc]
141017A & $97^{+12}_{-10}$ & $31^{+1}_{-1}$ & $6.7^{+0.3}_{-0.3}$ & 0.13 &0.12$^*$&$22.40^{\blacktriangledown}$\\
\enddata
\label{tab_GRB_sansz}
\end{deluxetable}

\newpage

\begin{deluxetable}{ll}
\tablecolumns{2}
\tablewidth{0pc}
\tablecaption{References for the afterglow optical light curve}
\tablehead{
\colhead{GRB }& \colhead{ Reference R mag} \\
}
\startdata
\cutinhead{GRBs with a Redshift}
990123 & \cite{Kulkarni1999}\\
990510 & \cite{Harrison1999}\\
990712 &\cite{Sahu2000}\\
020124 & \cite{Berger2002} \cite{Hjorth2003}\\
020813 & \cite{Urata2003}, \cite{Laursen2003}, \cite{Li2002a} ,\cite{Li2002b}, \cite{Williams2002}\\
       & \cite{Beskin2002},\cite{Kiziloglu2002}, \cite{Fiore2002}, \cite{Gorosabel2002}\\
021004 &\cite{Pandey2003a},  \cite{Holland2003},\cite{Bersier2003}\\
       & \cite{deUgartePostigo2005}, \cite{Garnavich2002}\\
021211 & \cite{Fox2003}, \cite{Li2003}, \cite{Holland2004}\\
       & \cite{Pandey2003b}, \cite{Testa2003}, \cite{Price2002a}\\
030328 & \cite{Maiorano2006}, \cite{Burenin2003}, \cite{Rumyantsev2003}\\
       & \cite{Fugazza2003}, \cite{Ibrahimov2003}, \cite{Martini2003}\\
030329 &\cite{Gorosabel2006}, \cite{Lipkin2004}\\
040924 &\cite{Huang2005}, \cite{Soderberg2006},  \cite{Wiersema2008}\\
041006 &\cite{Stanek2005}, \cite{Urata2007}, \cite{Misra2005}\\
050416A &\cite{Kann2010}\\
050525A &\cite{Resmi2012}, \cite{Klotz2005}, \cite{Rykoff2005}, \cite{Torii2005}\\
        & \cite{Malesani2005}, \cite{Mirabal2005},  \cite{Cobb2005}, \cite{Durig2005}\\
        & \cite{Haislip2005}, \cite{Yanagisawa2005},  \cite{Kann2010}\\
050820A &\cite{Cenko2006a}, \cite{Kann2010}\\
050922C &\cite{Kann2010}\\
060115 & \cite{Yanagisawa2006}, \cite{Distefano2006}, \cite{Nysewander2006a}\\
060908 &\cite{Covino2010}\\
061007 &\cite{Mundell2007}\\
061121 &\cite{Kann2010}, \cite{Halpern2006a}, \cite{Halpern2006b}, \cite{Halpern2006c}\\
       & \cite{Yost2006}, \cite{Melandri2006},  \cite{Uemura2006}\\
070612A & \cite{Updike2007a}, \cite{Updike2007b}, \cite{Updike2007c},  \cite{Mirabal2007}, \cite{Malesani2007}\\
071010B & \cite{Lee2010}, \cite{Oksanen2008}, \cite{Wang2008}, \cite{Kann2007}, \cite{Kocevski2007}\\
071020 &\cite{Kann2010}, \cite{Schaefer2007}, \cite{Ishimura2007}, \cite{Hentunen2007}, \cite{Im2007}\\
080319B & \cite{Bloom2009}, \cite{Wozniak2009}\\
080411 & \cite{Kruehler2008a}, \cite{Thoene2008a}\\
080413A & \cite{Kann2010}, \cite{Rykoff2008}, \cite{Gomboc2008a}, \cite{Cobb2008a}, \cite{Klotz2008}\\
080413B & \cite{Brennan2008}, \cite{Gomboc2008b}\\
080605 & \cite{Zafar2012}, \cite{Kuvshinov2008}, \cite{Rumyantsev2008}, \cite{Gomboc2008c}\\
       & \cite{Kann2008}, \cite{Jakobsson2008a}, \cite{Yoshida2008a}\\
080721 & \cite{Starling2009}, \cite{Chen2008}, \cite{Huang2008}\\
080804 & \cite{Rujopakarn2008}, \cite{Kruehler2008b}, \cite{Guidorzi2008}\\
080810 & \cite{Page2009}, \cite{Kann2010}, \cite{Yoshida2008b}\\
081007 &\cite{Jin2013}\\
081008 & \cite{Yuan2010}, \cite{Cobb2008b}, \cite{Kann2010}, \cite{Cucchiara2008b}\\
081121 & \cite{Yuan2008}, \cite{Loew2008}, \cite{Cobb2008c}\\
081222 & \cite{Covino2013}, \cite{Cwiok2008},  \cite{Sonoda2008}\\
       & \cite{Kuroda2008}, \cite{Melandri2008}, \cite{Roy2008}\\
090102 & \cite{Gendre2010}\\
090418A& \cite{Yuan2009a}, \cite{Henden2009a}, \cite{Chornock2009a}\\
       & \cite{Bikmaev2009}, \cite{Pavlenko2009}\\
090424 & \cite{Kann2010},  \cite{Jin2013}, \cite{Urata2009},  \cite{Yuan2009b},  \cite{Mao2009}\\
       & \cite{Roy2009}, \cite{Rumyantsev2009a}, \cite{Oksanen2009}\\
       & \cite{Gorosabel2009a}, \cite{Olivares2009}, \cite{Im2009a}\\
090516A & \cite{Guidorzi2009}, \cite{Christie2009a}, \cite{Vaalsta2009a}, \cite{Gorosabel2009b}\\
        & \cite{deUgartePostigo2009a}, \cite{Rossi2009b}\\
090519 & \cite{Klotz2009a}, \cite{Klotz2009b}, \cite{Jelinek2009}, \cite{Rossi2009a}\\
              & \cite{Thoene2009a}, \cite{Thoene2009b}\\
090618 &\cite{Rujopakarn2009}, \cite{Li2009}, \cite{Cenko2009b}\\
       &\cite{Im2009b}, \cite{Updike2009a}, \cite{Melandri2009}, \cite{Klunko2009}\\
       &\cite{Anumapa2009}, \cite{Rumyantsev2009b}, \cite{Cano2009a}, \cite{Fernandez-soto2009}\\
       & \cite{Fatkhullin2009}, \cite{Galeev2009}, \cite{Khamitov2009}\\
090812 & \cite{Wren2009}, \cite{Smith2009a}, \cite{Haislip2009a}, \cite{Updike2009b}\\
091020 & \cite{Gorbovskoy2009}, \cite{Kann2009a}, \cite{Kann2009b}, \cite{Xu2009a} \\
       & \cite{Perley2009a}, \cite{Perley2009b}, \cite{Xin2009a}\\
091029 & \cite{Filgas2009a}, \cite{Chornock2009c}, \cite{Christie2009b}, \cite{deUgartePostigo2009c} \\
091127 & \cite{Troja2012}, \cite{Filgas2011}, \cite{Xu2009b}, \cite{Klotz2009c}, \cite{Cobb2010} \\
       & \cite{Kinugasa2009a}, \cite{Vaalsta2009b}, \cite{Andreev2009a}, \cite{Haislip2009b}\\
       & \cite{Haislip2009c}, \cite{Thoene2009c}\\
091208B & \cite{Nakajima2009}, \cite{Cano2009b}, \cite{Yoshida2009}, \cite{Xin2009b}\\
        & \cite{Kinugasa2009b},  \cite{Andreev2009b}, \cite{Xu2009c}, \cite{Updike2009c}\\
100728B & \cite{Perley2010a}, \cite{Perley2010b}, \cite{Elenin2010},\cite{Decia2010}, \cite{Olivares2010} \\
100814A & \cite{Nardini2014}\\
110205A & \cite{Zheng2012},\cite{Gendre2012}, \cite{Cucchiara2011b}\\
110213A & \cite{Cucchiara2011b}, \cite{Rujopakarn2011}, \cite{Wren2011}, \cite{Ukwatta2011}\\
        & \cite{Hentunen2011a}, \cite{Kuroda2011a}, \cite{Volnova2011}\\
        & \cite{Zhao2011}, \cite{Hentunen2011b}\\
110422A & \cite{Elunko2011}, \cite{Moskvitin2011a}, \cite{Rumyantsev2011a}\\
               & \cite{Hentunen2011c}, \cite{Xu2011a},  \cite{Melandri2011}\\
        & \cite{Jeon2011}, \cite{Kuroda2011b}, \cite{Xu2011b}, \cite{Rumyantsev2011b}\\
110503A & \cite{Klotz2011}, \cite{Kann2011}, \cite{Leloudas2011}, \cite{Tasselli2011}, \cite{Broens2011} \\
        & \cite{Davanzo2011}, \cite{Pavlenko2011}, \cite{Im2011},  \cite{Updike2011}\\
110731A & \cite{Bersier2011}, \cite{Kuroda2011c}, \cite{Moskvitin2011b}, \cite{Malesani2011b}\\
        & \cite{Tanvir2011}, \cite{Ackermann2013}\\
120326A & \cite{Melandri2014}, \cite{Klotz2012}, \cite{Hentunen2012},  \cite{Jang2012}\\
        & \cite{Zhao2012},  \cite{Xin2012a}, (254) \cite{Xin2012b}, \cite{Soulier2012}\\
        & \cite{Quadri2012},  \cite{Sahu2012}\\
120811C & \cite{Elenin2012},  \cite{Litvinenko2012}, \cite{Galeev2012a},  \cite{Galeev2012b}\\
120907A & \cite{Nevski2012} \\
121211A & \cite{Japelj2012},\cite{Kuroda2012},  \cite{Butler2012a}, \cite{Butler2012b}\\
130408A & \cite{Melandri2013a},\cite{Sudilovsky2013}, \cite{Trotter2013a},  \cite{Dereli2013} \\
130420A & \cite{Guver2013},\cite{Elenin2013a}, \cite{Guidorzi2013a},  \cite{Trotter2013b},  \cite{Hentunen2013a}\\
        & \cite{Butler2013a}, \cite{Watson2013a},  \cite{Butler2013b},  \cite{Zhao2013}\\
130427A & \cite{Vestrand2014}, \cite{Maselli2014}\\
130505A & \cite{Hentunen2013b},  \cite{Kuroda2013}, \cite{Xu2013a}\\
        & \cite{Xin2013a},  \cite{Kann2013}, \cite{Krugly2013},\cite{Watson2013b}\\
130610A & \cite{Klotz2013},  \cite{Melandri2013b}, \cite{Hentunen2013c}\\
        & \cite{Elenin2013b}, \cite{Cenko2013a},  \cite{Im2013a},  \cite{Rumyantsev2013}\\
130701A & \cite{Leloudas2013}, \cite{Cenko2013b}, \cite{Xu2013b}\\
130831A & \cite{Cano2014a}, \cite{Yoshii2013}, \cite{Guidorzi2013b},  \cite{Volnova2013a}, \cite{Xu2013c}\\
        & \cite{Izzo2013}, \cite{Xin2013b}, \cite{Sonbas2013}, \cite{Volnova2013b}\\
        & \cite{Volnova2013c}, \cite{Hentunen2013d}, \cite{Leonini2013}, \cite{Khorunzhev2013}\\
        & \cite{Masi2013}, \cite{Butler2013c}, \cite{Watson2013c}, \cite{Lee2013}\\
131030A & \cite{Moskvitin2013},  \cite{Xu2013d},  \cite{Virgili2013},  \cite{Gorbovskoy2013}, \cite{Terron2013}\\
        & \cite{Im2013b},  \cite{Perley2013}, \cite{Littlejohns2013a}\\
        & \cite{Littlejohns2013b},  \cite{Littlejohns2013c}, \cite{Littlejohns2013d}, \cite{Littlejohns2013e}\\
        & \cite{Hentunen2013e}, \cite{Tanigawa2013},  \cite{Xin2013c}, \cite{Pandey2013}\\
131231A & \cite{Singer2015}\\
140213A & \cite{Trotter2014}, \cite{Elliott2014}\\
140419A & \cite{Guver2014},  \cite{Zheng2014}, \cite{Butler2014a}, \cite{Littlejohns2014a} \\
        & \cite{Littlejohns2014b}, \cite{Cenko2014a}, \cite{Hentunen2014}, \cite{Choi2014b}\\
        & \cite{Kuroda2014a}, \cite{Kuroda2014b}, \cite{Volnova2014a}, \cite{Pandey2014b}, \cite{Xu2014b}\\
140423A & \cite{Ferrante2014}, \cite{Elenin2014}, \cite{Cenko2014b}, \cite{Harbeck2014a}\\
               & \cite{Harbeck2014b}, \cite{Akitaya2014},  \cite{Kuroda2014c}\\
        & \cite{Fujiwara2014}, \cite{Volnova2014b},  \cite{Sahu2014}\\
        & \cite{Cano2014b},  \cite{Volnova2014c}, \cite{Bikmaev2014}\\
        & \cite{Littlejohns2014c},  \cite{Butler2014b},  \cite{Volnova2014d}\\
140506A & \cite{Fynbo2014}\\
140508A & \cite{Singer2015}\\
140512A & \cite{Gorbovskoy2014}, \cite{Klunko2014}, \cite{deUgartePostigo2014a},  \cite{Graham2014}\\
140606B & \cite{Singer2015}\\
140620A & \cite{Singer2015}\\
140623A & \cite{Singer2015}\\
140703A & \cite{Ciabattari2014}, \cite{Perley2014b}, \cite{Butler2014c},  \cite{Volnova2014e} \\
140808A & \cite{Singer2015}\\
\cutinhead{GRBs without a Redshift}
051008 & \cite{Rumyantsev2005},  \cite{Pozanenko2005},  \cite{Volnova2014f}\\
060105 & \cite{Urata2006a}, \cite{Zimmerman2006}, \cite{Kann2006}\\
060117 & \cite{Nysewander2006b}\\
060904 & \cite{Klotz2006}, \cite{Cenko2006b}, \cite{Urata2006b} \\
090813 & \cite{Smith2009b}, \cite{Volnova2009}\\
091221 & \cite{Zheng2009}, \cite{Filgas2009b}, \cite{Haislip2009d}\\
100413A & \cite{Ivanov2010}, \cite{Guidorzi2010}, \cite{Xin2010},  \cite{Filgas2010}\\
101011A & \cite{Laas-Bourez2010}, \cite{Nardini2010}, \cite{dePasquale2010}, \cite{Tello2010}\\
140102A & \cite{Yoshii2014}, \cite{Guziy2014}, \cite{Chen2014}, \cite{Xu2014a}, \cite{Pandey2014a}\\
        & \cite{Tanga2014a}, \cite{Perley2014a}, \cite{Choi2014a}, \cite{Volnova2014g} \\
140626A & \cite{Klotz2014a}, \cite{Tanga2014b}\\
140709B & \cite{Ivanov2014}, \cite{Volnova2014i}, \cite{Volnova2014j} \\
140713A & \cite{Xin2014}, \cite{Cano2014b}\\
141005A & \cite{Perley2014c}, \cite{Schmidl2014} \\
141017A &  \cite{Klotz2014b}, \cite{Kann2014}\\
\enddata
\end{deluxetable}

\begin{deluxetable}{l}
\tablecolumns{1}
\tablewidth{0pc}
\tablecaption{References for the redshifts and Host extinctions}
\tablehead{References for the redshift}
\startdata
{{\bf A.} \cite{Kulkarni1999}, {\bf B.} \cite{Vreeswijk1999}, {\bf C.} \cite{Galama1999}, {\bf D.} \cite{Hjorth2003}}\\
{{\bf E.} \cite{Price2002b}, {\bf F.} \cite{Castro-Tirado2010}, {\bf G.} \cite{DellaValle2003}, {\bf H.} \cite{Rol2003}}\\
{{\bf I.} \cite{Thoene2007}, {\bf J.} \cite{Wiersema2008}, {\bf K.} \cite{Price2004}, {\bf L.} \cite{Cenko2005}}\\
{{\bf M.} \cite{Foley2005}, {\bf N.} \cite{Prochaska2005}, {\bf O.} \cite{Jakobsson2005},{\bf P.} \cite{Piranomonte2006}}\\
{{\bf Q.} \cite{Fynbo2009}, {\bf R.} \cite{Osip2006}, {\bf S.} \cite{Bloom2006}, {\bf T.} \cite{Cenko2007a}}\\
{{\bf U.} \cite{Cenko2007b}, {\bf V.} \cite{Jakobsson2007}, {\bf W.} \cite{Vreeswijk2008a}, {\bf X.} \cite{Thoene2008a}}\\
{{\bf Y.} \cite{Thoene2008b}, {\bf Z.} \cite{Vreeswijk2008b}, {\bf AA.} \cite{Jakobsson2008a}, {\bf AB.} \cite{Jakobsson2008b}}\\
{{\bf AC.} \cite{Cucchiara2008a}, {\bf AD.} \cite{Prochaska2008}, {\bf AE.} \cite{Berger2008a}, {\bf AF.} \cite{Cucchiara2008c}}\\
{{\bf AG.} \cite{Berger2008b}, {\bf AH.} \cite{Cucchiara2008d}, {\bf AI.} \cite{Cucchiara2009a}, {\bf AJ.} \cite{Chornock2009b}}\\
{{\bf AK.} \cite{Chornock2009d}, {\bf AL.} \cite{deUgartePostigo2009b}, {\bf AM.} \cite{Thoene2009b}}\\
{{\bf AN.} \cite{Cenko2009c}, {\bf AO.} \cite{deUgartePostigo2009d}, {\bf AP.} \cite{Xu2009a}, {\bf AQ.} \cite{Chornock2009c}}\\
{{\bf AR.} \cite{Cucchiara2009b}, {\bf AS.} \cite{Wiersema2009a}, {\bf AT.} \cite{Flores2010}, {\bf AU.} \cite{Omeara2010}}\\
{{\bf AV.} \cite{Cenko2011a}, {\bf AW.} \cite{Milne2011}, {\bf AX.} \cite{Malesani2011a}, {\bf AY.} \cite{deUgartePostigo2011a}}\\
{{\bf AZ.} \cite{Tanvir2011}, {\bf BA.} \cite{Tello2012}, {\bf BB.} \cite{Thoene2012}, {\bf BC.} \cite{SanchezRamirez2012}}\\
{{\bf BD.} \cite{Perley2012}, {\bf BE.} \cite{Hjorth2013}, {\bf BF.} \cite{deUgartepostigo2013}, {\bf BG.} \cite{Flores2013}}\\
{{\bf BH.} \cite{Tanvir2013}, {\bf BI.} \cite{Smette2013}, {\bf BJ.} \cite{Xu2013b}, {\bf BK.} \cite{Cucchiara2013}}\\
{{\bf BL.} \cite{Xu2013d}, {\bf BM.} \cite{Singer2015},{\bf BN.} \cite{Schulze2014}, {\bf BO.} \cite{Tanvir2014a}}\\
{{\bf BP.} \cite{Tanvir2014b},{\bf BQ.} \cite{Fynbo2014}, {\bf BR.} \cite{Singer2015},{\bf BS.} \cite{deUgartePostigo2014b}}\\
{{\bf BT./BU./BV.} \cite{Singer2015}, {\bf BW.} \cite{CastroTirado2014}, {\bf BX.} \cite{Singer2015}}\\
\cutinhead{References for the Host extinction}
{a) \cite{Japelj2014}, b) \cite{Christensen2004}, c) \cite{Schady2007a}, d) \cite{Kann2010}}\\
{e) \cite{Schady2010}, f) \cite{Schady2007b}, g) \cite{Greiner2011}}\\
\enddata
\label{tab_refz}
\end{deluxetable}

redpajama_set_name: RedPajamaArXiv


As a Catholic moral theologian, I find Baker's perspective problematic from a just war standpoint. In the Catholic just war tradition, just cause is indeed an important criterion, but so are all of the other jus ad bellum and jus in bello criteria (and, of course, I would add jus post bellum). Simply put, just cause is a necessary but not a sufficient criterion. Each and every criterion should be taken into account to govern a just war, if a war is indeed to be considered just. Whether or not the use of drones is congruent with just war theory is a question I'll continue to ponder, and I welcome your thoughts here.


text:
Q: fire onload event when open a DIV page inside android phonegap application i am trying to activate a alert message inside my android application which will open when i open a specific div called page2 , however all my tries went unsuccessful , each time the application run , it display the message without opening the div itself.
here is my code
My Div code

Page Two2

        Content

Page Footer

i tried to Jquery to onload the alert message , here is the code :
$('#page2').load('', function() {
  alert('Load was performed.');
});

i put the jQuery script inside the div, did not work , then on the header but the same problem remains
any suggestions ?

A: If your listening for page changes:
$('page2').live('pageinit', function(event) {
    alert('Load was performed.');
});

redpajama_set_name: RedPajamaStackExchange


text:
in Music News
Songs By Billie Eilish, Travis Scott, Jennifer Lopez Enter Top 50 At Pop Radio
"bad guy," "Wake Up," and "Medicine" are on the rise at pop radio.
Billie Eilish in Bad Guy | Darkroom/Interscope
by Brian Cantor Apr 21, 2019, 11:10 pm
Headline Planet recently noted that Billie Eilish's "bad guy" had begun to receive pop radio airplay — even as official single "when the party's over" continues to climb the chart.
This week, it received enough airplay to secure a Top 50 position. Travi$ Scott's "Wake Up" and Jennifer Lopez's "Medicine (featuring French Montana)" also grab Top 50 positions.
Played 891 times during the April 14-20 tracking period (+544), "bad guy" ranks as the Mediabase pop panel's #42 song. It was #56 last week.
Up eleven places, "Wake Up" grabs #44 with 738 spins (+355).
"Medicine" concurrently rises sixteen places to #47 with 669 spins (+413).
bad guybillie eilishfrench montanaJennifer Lopezmedicinetravi$ scottwake up
Written by Brian Cantor
Brian Cantor is the editor-in-chief for Headline Planet. He has been a leading reporter in the music, movie, television and sporting spaces since 2002.
Brian's reporting has been cited by major websites like BuzzFeed, Billboard, the New Yorker and The Fader -- and shared by celebrities like Taylor Swift, Justin Bieber and Nicki Minaj.
Contact Brian at brian.cantor[at]headlineplanet.com.
Jennifer Lopez's "Medicine" Makes Top 40 At Pop Radio; Bazzi, MAX, More Enter Top 50
Billie Eilish's "Bad Guy," Travis Scott's "Wake Up" Enter Top 40 At Pop Radio
Daddy Yankee, Katy Perry & Snow's "Con Calma" Ranks As Pop Radio's Most Added Song
Jonas Brothers' "Cool" Erupts As Pop Radio's Most Added Song
Diplo, French Montana, Lil Pump & Zhavia's "Welcome To The Party" Ranks As Rhythmic Radio's Most Added Song
Khalid's "Talk" Enjoys 2nd Week As Pop Radio's #1 Song
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Ed Sheeran, Chris Stapleton & Bruno Mars' "BLOW" Makes Billboard Hot 100 Chart
Hot 100: Lil Nas X & Billy Ray Cyrus' "Old Town Road" Holds At #1; Now One Week Away From Tying Record
Denzel Curry Performed On "The Tonight Show Starring Jimmy Fallon" (Watch Now)
Sierra Skye Flaunts Mesmerizing Bikini Body In New Pictures, Video On Instagram
Megan Rapinoe Appears On Monday's "Late Night With Seth Meyers" (Watch Now)
nbc the tonight show jimmy fallon Taylor Swift Drake abc featured cbs ariana grande Justin Bieber ed sheeran fox nicki minaj the weeknd Selena Gomez Rihanna halsey camila cabello the chainsmokers meghan trainor cardi b shawn mendes the voice maroon 5 imagine dragons
Songs By Twenty One Pilots, Lizzo, Daddy Yankee & Katy Perry Join Top 40 At Pop Radio
Pink Chats, Performs "Walk Me Home" on Monday's "Ellen DeGeneres Show" (Watch)

redpajama_set_name: RedPajamaCommonCrawl


This will lead to a campsite and then shortly after to Zu, a family crow-like beast. Make sure to get the bounty for him from the nearby settlement! Make sure to get the bounty for him from the how to get rid of shits In the Final Fantasy XV, the Limit Break spells are of Flare, Freeze and Electon. These are tier of four spells of Fire, Thunder and Blizzard.
Guide Final Fantasy 15 Royal Edition how to get the new Armiger Unleashed 0. By Michael on March 8, 2018 Last Guides Video Games, Microsoft, PlayStation. If you possess the Royal Edition of Final Fantasy XV and you have collected the thirteen Royal arms, Noctis can get the ultimate power called the " Armiger Unleashed ". This power is activated with the accessory " Founder King's Sigil final fantasy xiv how to get materia Final Fantasy XV released for PS4 and Xbox One in Nov 2016. It is an open world environment and a battle system similar to the Kingdom Hearts series. It is an open world environment and a battle system similar to the Kingdom Hearts series.
7/12/2016 · There has never been a difficult Final Fantasy main story campaign lol. Very seldom did you get difficulty spikes or hard bosses (most relatable to most people probably being Yunalesca in FFX). The challenging content is reserved for optional side bosses and post-game content like Vio Purifico. Not sure why suddenly people are expecting FF to be Dark Souls.
Zu Beak is a Treasure. Acquired By See also: [[Fast and Easy Way to Make 17 Use 999 Potency Maxicast Spells (Freeze, Flare, Electon)]] Obtained by killing Zu (Level 67) during the hunt Feathered Giant of the Firesmoke.
5/12/2016 · Final Fantasy XV is an open world action role-playing video game that is now available on PlayStation 4 and Xbox One. The game was released worldwide on Nov. 29 and is the fifteenth main installment of the Final Fantasy series.


I have a confession to make. I love those apple pies that come in a cardboard tube with a 'Caution! Filling is hot!' warning, from a certain fast food chain. Sadly, though not for my waistline, since my coeliac diagnosis 6 years ago, those little crisp beauties have become but a distant memory.
OK, so the pastry, being gluten free, isn't flaky like the original, but the filling! Oh, Sweet Heaven, the filling! With one bite I was transported. My real inspiration for this gluten free apple pie however, was from the most gorgeous piece of cooking equipment I own; a wooden, engraved rolling pin given to me by my best friend this Christmas.
Isn't she beautiful? I INSTANTLY had the urge to make pastry. So I did. On my first attempt I didn't press hard enough and the imprint kind of baked out, but, look what gorgeousness you can create!
Fancy rolling pin or not, if you love apple pie, you'll love this homemade gluten free version.
Makes one approx 20cm pie.
6 apples – peeled, cored and diced.
1 egg beaten with a little water to glaze.
In a medium saucepan, melt the butter and cinnamon, stirring to combine.
Stir in the apples, sugar and 3 tablespoons of water.
Lower the heat and cover, stirring occasionally, cooking for about 5 minutes.
In a small bowl, whisk the cornflour into 2 tablespoons of water and pour into the apple mix.
Simmer until the juice thickens and the apples are soft and tender.
Grease well a 20cm pie dish with removable base.
Place the flour, xantham gum, baking powder and salt in the bowl of a food processor and pulse to combine.
Take the chilled butter cubes from the fridge and add them to the flour, pulsing to create a 'crumble' like mixture (some lumps are OK).
Slowly pour the iced water in, while pulsing the blade of the processor, until the mix just comes together.
Turn out ont0 a well floured board and knead to form a dough.
Divide into 2 equal halves.
Wrap one half in cling film and place in the freezer.
Gently roll out the other half in between 2 pieces of baking paper until you have a disc big enough to cover the base and sides of your pie tin.
Carefully lift the pastry to cover the dish and press it into the base and sides. Prick with a fork.
Return to the freezer for 10 minutes.
After 10 minutes, blind bake the base in the pre-heated oven until golden.
While the base is blind baking, remove the second batch of pastry from the freezer and roll out to become the lid.
Remove the base, fill with the cooled apple mix and gently place the pastry lid on top.
Using a pastry brush, cover generously with egg wash and return to the oven.
Bake for around an hour, or until the pastry is golden brown.
Allow to cool a little before removing from the tin.
Slice and serve hot with whipped cream or ice cream.


Born in Japan. Lives and works in London.
2015 Art residency, artFix gallery, London.
2014 CGP LONDON ANNUAL OPEN, CGP gallery, London.
2013 27th Interim Exhibition : Slice, Hanmi gallery, London.
2012 Recent Graduates' Exhibition at Affordable Art Fair Battersea, London.
2012 MA Fine Art Final Show, Chelsea College of Art and Design, London.
2012 Painting in Conversation, Peckham, London.
2012 MA Fine Art Interim Show, Chelsea College of Art and Design, London.
2010 Art goes around by Cheap Arts Parades, Soho, London.


Discovery: Colby Symphony Orchestra directed by Jinwook Park (Presence of the Past Humanities Theme Event) | Waterville Creates!
In its second concert of the season, the orchestra explores The Presence of the Past theme as it performs Mozart's timeless "Jupiter" symphony, and, in celebration of Leonard Bernstein's 100th birthday, the "Symphonic Dances" from West Side Story. Minji Ko '21 will also be featured in the first movement of William Walton's Violin Concerto.