text:
\section{Introduction}

The interplay between the production/recycling of metals and the formation/evolution of cosmic dust is strongly connected with star formation \citep[e.g.,][]{Gall11,Cortese12} and plays a fundamental role in the chemical enrichment of the interstellar medium (ISM). One way of estimating the dust content along the line of sight is through the optical dust extinction $A_V$ \citep[e.g.,][]{Pei92}. The low-ionization gas content is typically traced by the neutral hydrogen $N$(\hi{}), while a possible probe of the metals is the soft X-ray absorption $N(H)_{\rm{X}}${} \citep[e.g.][]{Morrison83,Wilms00}. $A_V/N$(\hi{}) can then be used to infer the dust-to-\textit{gas} ratio. However, this ratio does not provide a natural way to quantify the amount of dust in a galaxy's interstellar medium as it does not include the metals in the gas. On the other hand, the dust-to-metal ratio, i.e. the fraction of metals in dust, represents the ability of a system to produce or destroy dust grains. Besides, it can be derived regardless of the \hi{} constraint, which is often not available (see Sect \ref{sample}). We refer to $\mathcal{{DT\!\!M}}${} to indicate the dust-to-metal ratios normalized by the Galactic value.

The dust-to-metal ratio in the Galaxy is $A_V$/$N(H)_{\rm{X}}${}[Gal] $ \sim5.6\times 10^{-22}$ mag cm$^2$ \citep[][the latter two providing a 20\% lower value]{Predehl95,Guver09,Watson11}, in agreement with the measurements based on UV absorption lines \citep{Bohlin78}. The SMC and LMC have $A_V$/$N(H)_{\rm{X}}${}[SMC]\footnote{This value is derived from the observed $E(B-V)/N({\rm H})$ from \citet{Martin89} and \citet{Draine03} and converting it to $N(H)_{\rm{X}}${}/$A_V$ assuming $R_V=2.9,3.2$ \citep{Pei92,Draine03} and a mean [Zn/H] $=-0.64,-0.55$ for the SMC and LMC respectively \citep{Welty97,Welty99}.} $ \sim2.8\times 10^{-22}$ mag cm$^2$ and $A_V$/$N(H)_{\rm{X}}${}[LMC]\footnotemark[1] $\sim5.3\times 10^{-22}$ mag cm$^2$, corresponding to $\sim50$\% and $\sim~95$\% of the Galactic value, respectively. Such measurements are typically difficult to carry out for distant galaxies. \citet{Dai09} studied the ratio in gravitationally lensed galaxies at $z<1$ by comparing the extinction curve and the X-ray absorption in the spectra of multiply-imaged quasars (QSOs) in the background. They find the dust-to-metal ratio to range from $\sim10$\% to a few times the Galactic value, but with large uncertainties. \citet{Brinchmann13} recently derived dust-to-metal ratios increasing with metallicity for super-solar metallicity galaxies based on observed CO absorption and the theoretical expectations of \citet{Charlot01}.

Long-duration ($>2$~s) GRBs can offer the unique possibility of directly probing the gas, dust, and metal content in their star-forming host galaxy, out to very high redshifts. Their afterglows are often bright enough to allow absorption-line spectroscopy that can reveal the \hi{} gas and metal column densities in the ISM \citep[e.g.,][]{Savaglio03,Vreeswijk04,Berger06,Prochaska07,Ledoux09,Fynbo09}. In addition, the well-understood power-law continuum \citep[e.g.,][]{Sari98,Piran99} facilitates the determination of the intrinsic $A_V$ and $N(H)_{\rm{X}}${} \citep[e.g.,][]{Campana06,Kruehler11,Zafar11,Schady12}. The latter is measured for most \textit{Swift} bursts \citep{Evans09} and $A_V$  can be studied out to $z>6$ \citep{Schady10,Zafar11b}. In contrast, the same measurements are more difficult to make towards QSOs, due to the presence of broad emission lines contaminating a large fraction of their optical/ultraviolet continuum. The samples of GRB absorbers that are typically followed up for spectroscopic studies are biased against the most dusty systems that have been dimmed by large $A_V$'s or faint GRBs. A fraction of GRB host galaxies is massive and dusty \citep{ Kruehler11, Hunt11, Rossi12, Perley13}. Nevertheless, the current (biased) samples are still representative of the majority of the GRB host population, i.e., low-mass, low-metallicity and actively star-forming galaxies \citep[e.g.][]{Savaglio09}.

\citet{Zafar11} and \citet{Schady10} investigated the dust-to-metal ratios for a large sample of distant GRB-selected galaxies using $A_V/N(H)_{\rm{X}}${}. They found $A_V/N(H)_{\rm{X}}${} in GRBs that were up to two orders of magnitude lower than what had been observed in the Local Group, confirming the results of \citet{Galama01}. This implies that either GRB-DLAs have a different dust-to-metal ratios or that $A_V$ and $N(H)_{\rm{X}}${} probe different regions along the line of sight. While the dust is expected to lie in the cold low-ionization medium, the X-ray absorption traces the metals regardless of their ionization state. The evidence of ionization induced by the GRB on the surrounding medium, in the immediate environment of the GRB for most bursts and out to hundreds of pc for absorbing systems with low $N$(\hi{}) \citep{DeCia12,Vreeswijk13}, confirms that indeed the line of sight analysis can be affected by ionization and dust destruction. Thus, the $A_V/N(H)_{\rm{X}}${} may not provide the best estimate of the dust-to-metal ratio for GRB host galaxies. Recent estimates based on line of sight $A_V$, $N$(\hi{}) and the metallicity suggest that the dust-to-metal ratios in GRB and QSO absorbers are roughly constant around the Galactic value \citep{Zafar13}.

An alternative approach to calculate the extragalactic dust-to-metal ratios is based on the dust-depletion pattern revealed by UV/optical absorption-line spectroscopy. Using such methods, the dust-to-metal ratios in QSO-DLAs and a few GRB-DLAs were found to be consistent with or slightly lower than the Galactic value \citep[][]{Vladilo98, Savaglio01, Savaglio03,Savaglio04,Vladilo04}. One of the advantages of using optical absorption lines rather than dust extinction to determine the dust content is that the absorption lines refer to a particular redshift and thus they are not integrated along the whole line of sight. This is particularly crucial for low-metallicity systems with an intrinsically low dust content and for high-$z$ targets, whose lines of sight likely cross intervening galaxies, each contributing to $A_V$.

In this paper, we develop a new dust-depletion-based method to derive the dust-to-metal ratios, cross-checked with the \citet[][S01 hereafter]{Savaglio01} method, and apply it to a sample of 20 GRB absorbers (observed at medium to high spectral resolution) and 72 QSO-DLAs (all with high-resolution spectroscopy). This approach solely relies on the observation of optical/UV low-ionization absorption lines associated with DLAs and therefore there is little or no ambiguity on the location or ionization state of the absorbing gas/dust: we purely focus on the bulk of the ISM in the host galaxies, which is mostly faraway from the GRB \citep[e.g., hundreds of parsecs from the burst][]{Vreeswijk07, Vreeswijk11} and therefore not affected by ionization due to the GRB or the progenitor.

The paper is organized as follows. Our sample is defined in Sect. \ref{sample} and the methods of our analysis are explained in Sect. \ref{method}. The results are presented in Sect. \ref{results} and discussed in Sect. \ref{discussions}. Finally, we summarize our conclusions in Sect. \ref{conclusions}. Throughout the paper we adopt ions cm$^{-2}$ as the linear unit of column densities N. We refer to relative abundances of two chemical elements $X$ and $Y$ defined as $\left[X/Y\right] \equiv \log{\frac{N(X)}{N(Y)}} - \log{\frac{N(X)_\odot}{N(Y)_\odot}}$. For the reference solar abundances appearing in the second term of this formula, we use the values of \citet{Asplund09} and follow the recommendations of \citet{Lodders09} by adopting the photospheric estimates for the more volatile elements, the meteoritic estimates for the less refractory elements, or the average between them \citep[see details in][]{DeCia12}. The quoted errors and limits correspond to $1\,\sigma$ and $3\,\sigma$ significance levels, respectively, unless otherwise stated.

\section{The GRB-DLA sample}
\label{sample}

We select all GRB absorbers with a constrained estimate of the column density of \feii{}, and of at least one ion among \znii{} and \siii{}, from the largest sample to date of GRB absorber column densities collected by \citet{Schady11}. The resulting sample is composed of 20 GRB absorbers in the redshift range $1.2<z<4.0$ and spans a wide range of metallicities (from $Z\sim2\,Z_\odot$ down to $Z\sim0.005\,Z_\odot$), listed in Table \ref{tab dtm}. Most absorbers have an \hi{} estimate from Lyman-$\alpha${}, all but one with $\log N$(\hi{}) $>20.3$ and therefore classified as DLAs \citep{Wolfe86}. One exception is GRB\,090323 with $\log N$(\hi{}) $=19.6$ for one of the two absorbing systems that composes its line profile. The column density estimates of the GRB sample are derived from absorption-line spectroscopy, using curve-of-growth analysis for the spectra with low or medium resolution \citep[see details in][and references therein]{Schady11} and Voigt profile fitting for a handful of high-resolution spectra \citep{Vreeswijk07,Ledoux09}.

\section{Revisiting the dust-to-metal ratio for GRB-DLAs: the \citet{Savaglio01} recipe and a new method.}
\label{method}

It is possible to estimate the dust-to-metal ratio from the depletion in dust of different elements, observed with optical/UV absorption-line spectroscopy, in particular from \feii{} and \znii{} lines. While \hi{} is fundamental to deriving the overall metallicity, it is not necessary to derive this ratio. \feii{} and \znii{} are two elements that have a similar nucleosynthetic history, but very different depletion properties. Fe is typically heavily depleted onto dust grains, while Zn is only mildly depleted \citep[e.g.,][]{Savage96,Ledoux02} and is therefore a metallicity indicator. Thus, we use [Fe/Zn] as a dust indicator, where the reliability of iron as a tracer of the bulk of the dust is explained in Appendix \ref{sect iron}. Si and S, also quite abundant in the ISM, can be useful dust-depletion indicators as well, but should be treated with caution, especially in the case of S \citep[e.g.,][]{Jenkins09}, as explained in Appendix \ref{sect sulphur}. Besides, the depletion of Si is typically not significant enough to make [S/Si] a solid dust indicator at low metallicity.

\subsection{The S01 method}

We derive the $\mathcal{{DT\!\!M}}${} (referred to as $k/k_J$\footnote{$d/d_J$ in \citet{Savaglio03} and \citet{Savaglio04}} in S01) from the depletion pattern, i.e., from the observed abundance of different elements, as compared to the depletion pattern observed in different Galactic environments: halo (H), disk+halo (DH), warm disk (WD), and cool disk (CD), as listed in \citet{Savage96}. Following the recommendation of \citet{Jenkins09}, we update the mean depletion values listed in Table 6 of \citet{Savage96} slightly by adding $-0.03$, $-0.04$, and $-0.01$ to the values for Fe, Si, and S respectively, here and throughout the paper. The abundances with respect to H or Zn observed in GRB-DLAs are fitted simultaneously assuming that the Galactic depletion patterns, providing a best-fit $\mathcal{{DT\!\!M}}${} and environment type. When both \hi{} and \znii{} are constrained, we treat the metallicity [Zn/H] as an input. Instead, when \hi{} is available but not Zn, we fit for the metallicity $Z/Z_\odot$ as well. In practice, we iterate among the different Galactic environments $J$ and sum over different metals $X$ to minimize the total difference between the observed abundances and the reference abundances
\begin{equation}
[X/\mbox{H}]_{\rm ref}=\log (1 + \mbox{$\mathcal{{DT\!\!M}}${}}\cdot(10^{dXj} - 1) ) + \log (Z/Z_\odot) \mbox{,}
\label{eq S01}
\end{equation}
where $dXj$ is the depletion of a metal $X$ for a given environment $J$. More details can be found in S01 and \citet{Savaglio03}. We exclude upper and lower limits on the abundances from the fit. We include measurements for at least two metals $X$ among Zn, Si, and Fe. The results of the depletion pattern fit for each absorber are shown in the Appendix (Fig. \ref{fig: dtm_sav} and \ref{fig: dtm_sav_noH}, for the case with and without \hi{} constraints respectively). Sulphur is not included in the fit because it has shown controversial depletion patterns in different Galactic environments \citep{Jenkins09}, as described in Appendix \ref{sect sulphur}. The inclusion of silicon also must be taken with caution as the intrinsic abundance of Si with respect to Fe and Zn may not depend entirely on dust, but instead it could be boosted by $\alpha$-element enhancements in star-forming galaxies. This leads to a possible degeneracy between the best-fit $\mathcal{{DT\!\!M}}${}, metallicity, and Galactic environments. We explore this possibility of an intrinsically lower Si by calculating the $\mathcal{{DT\!\!M}}${}s for slightly lower Si column densities than observed ($\log N({\rm Si}) -0.2$ dex). The effect of such change is mostly accounted for by \textit{i)} setting an upper error on the $\mathcal{{DT\!\!M}}${} of at least 0.2 for best-fit WD and DH environments, when Si is included in the fit and \textit{ii)} setting a lower error on the $\mathcal{{DT\!\!M}}${} of at least 0.2 when Zn is not constrained.

\subsection{A new method for deriving the dust-to-metal ratio for DLAs}
\label{sec method}

    \begin{figure}
   \centering
   \includegraphics[width=90mm,angle=0]{f1.eps}
   \caption{A scheme displaying two linear depletion sequences of Zn and Fe with the depletion strength factor $F_*$. Although $F_*$ is not known for a given line of sight, it can be traced by the observed [Zn/Fe] ratio.}
              \label{fig scheme}
    \end{figure}

Here we derive the absolute dust-to-metal ratio (\textit{dtm}{}) based on fundamental definitions and applying depletion corrections to the observed relative abundance of Fe with respect to Zn. The basic idea starts from the definition of the observed [Fe/Zn], where the observed gas-phase column density of an element $X$ is $N(X)_{\rm obs} = N(X)_{\rm tot}- N(X)_{\rm dust}$. If we assume that Zn is not depleted into dust and if Fe and Zn share the same nucleosynthesis (total of gas- and dust-phase [Fe/Zn]$_{\rm tot} = 0$), then a simplified version of the dust-to-metal ratio follows $\mbox{\textit{dtm}}_{\rm simplified}  =   1 - 10^{[\mbox{Fe}/\mbox{Zn}]_{\rm obs}} \mbox{.}$

To include the possible depletion of Zn\footnote{Some level of Zn depletion should be taken into account, given that GRBs are likely to reside in star-forming regions, some of them with a potentially significant dust content \citep[e.g.,][]{Perley13}.}, we assume that the depletion of an element in dust is proportional to a depletion strength factor $F_*$. This factor represents the overall strength of the dust depletion and it is unique to each line of sight, similar to what has been found for the Galaxy \citep[][e.g., their Fig. 7]{Jenkins09}. In the Galaxy, systems with little dust have $F_{*,\rm G}=0$ and almost no depletion of Zn, but the dustier systems $F_{*,\rm G}=1$ and even Zn is significantly depleted. We note that the $F_*$ scale for DLAs does not necessarily have to be the same as in the Galaxy because DLAs on average have lower metallicity and presumably lower dust contents. These linear depletion sequences reflect the tendency of each element to condensate in dust grains, i.e., they are related to the condensation temperature of each element \citep{Field74,Jenkins09}. Given that the slopes ($d$Fe, $d$Zn, $d$Si, et cetera) of these linear relations are specific to each element, the relative composition of  the dust grains changes depending on the amount of dust in the environment.

While the slopes and offsets of these linear depletion sequences have been well measured for the Galaxy \citep{Jenkins09}, in principle, we do not know how these relations change for lower-metallicity environments such as most DLAs. The observed offsets in the Galaxy are interpreted as pre-existing dust grains that cause some level of depletion even for the less dusty systems \citep{Jenkins09}. For the GRB and QSO sample of absorbers, we assume no offsets in the depletion sequences ($\delta_X=0$ at $F_*=0$), meaning that for DLAs we assume no pre-existing grains. This is expected given the relatively high redshift and the low metallicity of QSO- and GRB-DLAs, only a handful of which are above [Zn/H$]\sim-0.3$ in our DLA sample. Moreover, the evidence that most metal-poor DLAs (with assigned $F_*=0$) show [Zn/Fe] $\sim0$ \citep{Noterdaeme08,Molaro00} , i.e., no depletion, unambiguously reveals no offset in the DLA depletion sequences. \footnote{In the Galactic line-of-sight sample of \citet{Jenkins09}, the least dusty systems were not entirely dust-free, thereby leading to the observed Galactic offsets.}

In this way, the depletion of Zn and Fe can be described as
\begin{subequations}
\begin{align}
\delta_{\rm Zn} &= [\mbox{Zn/H}]_{\rm obs} - [\mbox{Zn/H}]_{\rm intrinsic} = d{\rm Zn} \cdot F_*    \label{eq linear Zn} \\
 \delta_{\rm Fe} &= [\mbox{Fe/H}]_{\rm obs} - [\mbox{Fe/H}]_{\rm intrinsic} = d{\rm Fe} \cdot F_*\mbox{,}  \label{eq linear Fe}
\end{align}
\end{subequations}
where [Zn/H]$_{\rm intrinsic}$ and [Fe/H]$_{\rm intrinsic}$ are the total abundances in the gas and dust phases, and when $F_* = 1$, $\delta_{\rm Zn} = d{\rm Zn}$. Since the observed (depleted) abundances are associated with the gas-phase metals, the fraction of an element $X$ in gas $f_X$ is
\begin{equation}
 f_X = 10^{\delta_{X}}.
\end{equation}
Figure \ref{fig scheme} visualizes these relations and the quantities we derive below. Note that we do not assume solar abundances or fixed grain compositions, rather we rely on the observed relative abundances [Fe/Zn]$_{\rm obs}$ as a function of the depletion strength. Since
\begin{equation}
F_*= (\delta_{\rm Fe} -  \delta_{\rm Zn} )/(d{\rm Fe} - d{\rm Zn}) = \mbox{[Fe/Zn]}_{\rm obs}/(d{\rm Fe} - d{\rm Zn})\mbox{,}
\label{eq F*}
\end{equation}
the dust to metals ratio \textit{dtm}{} is then defined as
\begin{equation}
dtm = \frac{  N({\rm Fe})_{\rm dust} }{N({\rm Fe})_{\rm tot}} =1 - 10^{\delta_{Fe}} =  1 - 10^{  [{\rm Fe}/{\rm Zn}]_{\rm obs}\, d{\rm Fe}  /(d{\rm Fe} - d{\rm Zn} )  }
\label{eq dtm}
\end{equation}
This definition of \textit{dtm}{} assumes only two linear dust depletion sequences for Fe and Zn respectively, and that Zn and Fe have the same nucleosynthetic history ($[{\rm Fe/Zn}]_{\rm tot}=0$), so any deviation of [Fe/Zn] from solar is due to dust depletion.

The slopes of the depletion sequences correspond to the expected level of depletion in the most dusty $(F_*=1)$ DLA systems. We assume $d{\rm Fe} = -0.95$, $d{\rm Si} = -0.26$  and $d{\rm Zn} = -0.11$, i.e., the average depletion along disk+halo lines of sight\footnote{Disk+halo lines of sight: HD 18100, HD 167756.} of Fe and Si \citep{Savage96} and Zn \citep{Roth95}. This translates to $\sim90$\% of Fe, $\sim 45$\% of Si, and $\sim 20$\% of Zn having been depleted into dust for the dustiest DLAs. The assumption of steeper slopes, such as the Galactic $d{\rm Fe} = -1.28$, $d{\rm Si} = -1.14$, and $d{\rm Zn} = -0.61$ \citep{Jenkins09}, would overestimate the dust-corrected metallicities (see Sect. \ref{discussions caveat} for a discussion on the dependence of our results on the assumed slopes). Thus, we limit our analysis to the slope values mentioned above and include an uncertainty of 0.1 on the slopes to allow for some freedom.

Finally, we normalize the \textit{dtm}{} values with respect to the Galactic value
\begin{equation}
  \mbox{$\mathcal{{DT\!\!M}}${}} = dtm / dtm\mbox{(G),}
  \end{equation}
where $dtm$(G) $=0.89$ (see the Appendix \ref{sect dtm_gal} for its derivation).

Another useful quantity that can be derived from the above formalism is the column density of iron in dust, $N({\rm Fe})_{\rm dust}$ (Col. 9 of Table \ref{tab dtm}), which provides an estimate of the dust content in the ISM, independently from $A_V$. Given that
\begin{equation}
N({\rm Fe})_{\rm tot} =  N({\rm Zn})_{\rm tot} \cdot \left( \frac{N({\rm Fe})}{N({\rm Zn})}\right)_\odot
\end{equation}
and
\begin{equation}
     N({\rm Zn})_{\rm tot} = \frac{N({\rm Zn})_{\rm obs}}{f_{\rm Zn}} =   \frac{N({\rm Zn})_{\rm obs}}{10^{{\rm[Zn/Fe]}_{\rm obs} \, d{\rm Zn} / ( d{\rm Zn} - d{\rm Fe} )}}\mbox{,}
     \label{eq Zn tot}
\end{equation}
the dust-phase column density of iron is
 \begin{align}
  N({\rm Fe})_{\rm dust} & =  N({\rm Fe})_{\rm tot} \cdot dtm  = \nonumber \\
   & = 10^{\rm[Fe/Zn]_{\rm obs}}  \cdot ( 10^{{\rm [Fe/Zn]}_{\rm obs} \, d{\rm Fe}/(d{\rm Zn} - d{\rm Fe}) } - 1 ) \nonumber \\
  &\cdot N({\rm Zn})_{\rm obs} \cdot \left( \frac{N({\rm Fe})}{N({\rm Zn})}\right)_\odot \nonumber \\
  & = N({\rm Fe})_{\rm obs}  \cdot ( 10^{{\rm [Fe/Zn]}_{\rm obs} \, d{\rm Fe}/(d{\rm Zn} - d{\rm Fe}) } - 1 ) \mbox{.}
\label{eq fe dust}
\end{align}

   \begin{figure}
   \centering
   \includegraphics[width=90mm,angle=0]{f2.eps}
   \caption{A comparison between the $\mathcal{{DT\!\!M}}${} derived with the new and the S01 methods. The symbols indicate which metal was used as a reference to calculate the [$X$/Fe] ratio, where [Zn/Fe] is the most reliable ratio because it is less sensitive to intrinsic abundance changes. The filled symbols highlight the DLAs with high-resolution spectroscopy, which typically have more robust constraints. The vicinity to the equality (dashed) line shows the agreement between the two estimates.}
              \label{fig: dtm_comp}
    \end{figure}

\section{Results}
\label{results}

\subsection{Comparison among $\mathcal{{DT\!\!M}}${} methods}

The $\mathcal{{DT\!\!M}}${} derived with the new and the S01 methods for our GRB-DLA sample are listed in Table \ref{tab dtm} and plotted against each other in Fig. \ref{fig: dtm_comp}, for comparison. The two methods show a general good agreement and thus we consider them as equivalent (as also confirmed by a Spearman rank test\footnote{This indicates only how tight a monotonic correlation between two quantities is, but they do not necessarily need to be linear.}). The results of this test are listed in Table \ref{tab spearman}. There is a possible small deviation toward higher $\mathcal{{DT\!\!M}}${}(S01) above 1, for three GRB absorbers, namely GBR\,010222, GRB\,050401, and GRB\,090323, absorbing system 2. We discuss whether such deviation could affect our results in Sect. \ref{discussions}. The overall reliability of both methods is strengthened by the agreement of the two different $\mathcal{{DT\!\!M}}${} derivations because they are independent from each other.

In addition to the $\mathcal{{DT\!\!M}}${} ratios, the S01 method also provides estimates of the metallicity in case the H column density is constrained but Zn is unconstrained, and the environment type \citep[halo, warm disk, cool disk, disk + halo, as characterized by][]{Savage96}. These are listed in the last two columns of Table \ref{tab dtm}. Note that when Si is constrained but Zn is unconstrained, the metallicity fitted from the depletion pattern is always higher than the observed [Si/H], as expected from the depletion of Si. Among the best-fit environments, a cool disk is somewhat disfavored for GRB absorbers, although a single best-fit environment could not be constrained for about half of our sample.

In the early stages of the current analysis we also derived the dust-to-metal ratio using the prescription of \citet{Vladilo98}, but we do not include those results because of the assumption of a constant grain composition (fixed fraction of each element in dust). Nevertheless, it is worth reporting that those dust-to-metal ratios are consistent with the results presented here.

\begin{landscape}
\begin{table}
\centering
\caption{dust-to-metal ratios normalized by the Galactic value ($\mathcal{{DT\!\!M}}${}) derived with the method described in this paper and Savaglio's (2001, S01).}

\begin{tabular}{ l | r r r r r r>{\columncolor[gray]{ 0.9 }} r r r>{\columncolor[gray]{ 0.9 }} r  r r}
\hline \hline
\rule[-0.2cm]{0mm}{0.8cm}
GRB       &    $z$    & $A_V$ &  $\log$ & [$X$/H]$^a$& [$X$/Fe] &   $X$    &  $\mathcal{{DT\!\!M}}${}            & [$X$/H]$_{\rm tot}^b$ & $\log$  $^c$ &  $\mathcal{{DT\!\!M}}${}                & $\log Z/Z_\odot^d$   & $J^e$ \\
             &               &      (mag) &   $N(\mbox{\hi{}})$          &                 &                &              &  (new)  &   & $N$(Fe)$_{\rm dust}${}             &  (S01) &                                &          \\
\hline
  & \\

   990123  &1.60 & $ <0.25             $ &                       &                           & $ 2.01\pm0.18   $&  Zn  &$ 1.12 \pm 0.00$& & $17.05 ^{+ 0.45}_{- 0.30}$&$ 1.11 ^{+ 0.16}_{- 0.11}$&                                &   all \\

   000926  &2.04 & $ 0.38 \pm 0.05$ & $21.30\pm0.20 $ & $-0.11\pm0.21 $ & $ 1.06\pm0.21   $&  Zn  &$ 1.06 \pm 0.04$&  $+0.03^{+0.34}_{-0.37}$ & $16.77 ^{+ 0.27}_{- 0.19}$&$ 1.00^{+0.20}_{-0.20}$&                                & D          \\

   010222  &1.48 & $ 0.24 ^{+ 0.08}_{- 0.09}$ &                       &                           & $ 1.30\pm0.17   $&  Zn  &$ 1.09 \pm 0.02$& & $16.78 ^{+ 0.33}_{- 0.23}$&$ 1.22 ^{+0.02}_{-0.02}$&                                &  H          \\

   020813  &1.25 &            &                       &                           & $ 0.90\pm0.07   $&  Zn  &$ 1.02 \pm 0.03$& & $16.45 ^{+ 0.25}_{- 0.18}$&$ 0.98 ^{+ 0.20}_{- 0.01}$&                                & D         \\

 030226$_{\rm s1}^f$  &1.99 & $ 0.05 \pm0.01$ & $20.50\pm0.30 $ & $-0.94\pm0.30 $ & $ 0.17\pm0.04   $&  Si  &$ 0.47 \pm 0.09$& $-0.87^{+0.34}_{-0.35}$ &  $14.72 ^{+ 0.19}_{- 0.15}$&$ 0.58 ^{+ 0.09}_{- 0.20}$&$-0.78 ^{+ 0.08}_{- 0.07}$ & DW       \\

 030226$_{\rm s2}^f$  &1.96 & $ 0.05 \pm0.01$ & $20.50\pm0.30 $ & $-1.04\pm0.30 $ & $ 0.45\pm0.03   $&  Si  &$ 0.86 \pm 0.06$& $-0.86^{+0.38}_{-0.39}$ & $14.99 ^{+ 0.24}_{- 0.15}$&$ 0.89 ^{+ 0.04}_{- 0.20}$&$-0.77^{+0.05}_{-0.05}$ & DW       \\

   030323  &3.37 &              & $21.90\pm0.07 $ & $-1.26\pm0.27 $ & $ 0.18\pm0.27   $&  Si  &$ 0.49 \pm0.43 $& $-1.19^{+0.25}_{-0.22}$ &$<16.46             $&$ 0.66 ^{+ 0.61}_{- 0.49}$&$-1.08 ^{+ 0.45}_{- 0.39}$ &  HDW    \\

   050401  &2.90 & $ 0.45 \pm0.03$ & $22.60\pm0.30 $ & $-0.93\pm0.42 $ & $ 1.14\pm0.36   $&  Zn  &$ 1.07 \pm0.05$& $-0.78^{+0.64}_{-0.73}$ & $17.27 ^{+ 0.53}_{- 0.45}$&$ 1.19^{+0.04}_{-0.04}$&                                &  H          \\

   050730  &3.97 & $ <0.17             $ & $22.10\pm0.10 $ & $-2.14\pm0.10 $ & $ 0.12\pm0.05   $&  Si  &$ 0.36 \pm0.12$&  $-2.09^{+0.12}_{-0.13}$ & $14.98^{+0.27}_{-0.27}$&$ 0.66 ^{+ 0.29}_{- 0.33}$&$-1.76 ^{+ 0.63}_{- 0.32}$ &  HWC    \\

     050820A  &2.62 & $ 0.27 \pm 0.04$ & $21.05\pm0.10 $ & $-0.72\pm0.10 $ & $ 0.98\pm0.12   $&  Zn  &$ 1.04 \pm0.03$&   $-0.59^{+0.21}_{-0.23}$ & $15.89 ^{+ 0.23}_{- 0.15}$&$ 1.00 ^{+ 0.18}_{- 0.13}$&                                &  HWC    \\

  050922C  &2.20 & $0.14 ^{+ 0.08}_{- 0.07}$ & $21.55\pm0.10$ & $-2.09\pm0.12$ & $ 0.35\pm0.27$&  Si &$0.76 \pm0.24$ &$-1.95^{+0.12}_{-0.16}$ & $14.89 ^{+ 0.31}_{- 0.58}$&$ 0.81 ^{+ 0.22}_{- 0.20}$&$-1.85 ^{+ 0.14}_{- 0.13}$ & DW       \\

   051111  &1.55 & $ 0.39 ^{+ 0.11}_{- 0.10}$ &                       &                           & $ 0.99\pm0.04   $&  Zn  &$ 1.04 \pm0.02$& & $16.41 ^{+ 0.25}_{- 0.17}$&$ 1.00 ^{+ 0.15}_{- 0.10}$&                                &  all \\

   060418  &1.49 & $ 0.13 ^{+ 0.01}_{- 0.02}$ &                       &                           & $ 0.71\pm0.03   $&  Zn  &$ 0.95 \pm0.04$& & $15.95 ^{+ 0.17}_{- 0.11}$&$ 0.88 ^{+ 0.20}_{- 0.02}$&                                & D          \\

   070802  &2.45 & $ 1.23 ^{+ 0.18}_{- 0.16}$ & $21.50\pm0.20 $ & $-0.16\pm0.24 $ & $ 0.37\pm0.18   $&  Zn  &$ 0.70 \pm0.19$&  $-0.11^{+0.34}_{-0.38}$ & $16.65 ^{+ 0.25}_{- 0.22}$&$ 0.61^{+0.09} _{-0.09}$&                                & C          \\

   071031  &2.69 & $ <0.11             $ & $22.15\pm0.05 $ & $-1.76\pm0.05 $ & $ 0.03\pm0.03   $&  Zn  &$ 0.08 \pm0.07$& $-1.76^{+0.07}_{-0.07}$ & $14.74 ^{+ 0.09}_{- 1.26}$&$ 0.07 ^{+ 0.07}_{- 0.05}$&                                &  all \\

   080330  &1.51 & $ <0.19             $ &                       &                           & $ 0.93\pm0.11   $&  Zn  &$ 1.03 \pm0.04$& & $15.71 ^{+ 0.26}_{- 0.19}$&$ 0.99 ^{+ 0.17}_{- 0.12}$&                                &  all \\

  080413A  &2.43 & $ <0.88             $ & $21.85\pm0.15 $ & $-1.63\pm0.16 $ & $ 0.12\pm0.07   $&  Zn  &$ 0.30 \pm0.14$& $-1.61^{+0.21}_{-0.22}$ &  $15.13 ^{+ 0.14}_{- 0.36}$&$ 0.27 ^{+ 0.13}_{- 0.10}$&                                &  HWC    \\

 090323$_{\rm s1}^f$  &3.58 & $ 0.10 \pm 0.04$ & $19.62\pm0.33 $ & $ +0.33\pm0.35 $ & $ 0.51\pm0.14   $&  Si  &$ 0.91 \pm0.10$& $+0.53^{+0.46}_{-0.50}$ & $15.52 ^{+ 0.35}_{- 0.26}$&$ 0.94 ^{+0.20}_{-0.20}$&$ 0.60^{+0.16}_{-0.16}$ & D          \\

 090323$_{\rm s2}^f$  &3.57 & $ 0.10 \pm 0.04$ & $20.72\pm0.09 $ & $ +0.22\pm0.10 $ & $ 1.41\pm0.06   $&  Zn  &$ 1.10\pm0.01$& $+0.40^{+0.28}_{-0.30}$ & $16.58 ^{+ 0.32}_{- 0.22}$&$ 1.23^{+0.01} _{-0.01}$&                                &  H          \\

  090926A  &2.11 & $ <0.15             $ & $21.73\pm0.07 $ & $-2.27\pm0.27 $ & $ 0.57\pm0.30   $&  Si  &$ 0.94 \pm0.16$&  $-2.05^{+0.25}_{-0.34}$ & $15.07 ^{+ 0.50}_{- 0.40}$&$ 1.01 ^{+ 0.24}_{- 0.20}$&$-1.94 ^{+ 0.38}_{- 0.35}$ &  HDW    \\
  & \\
  \hline \hline
 \end{tabular}
 \tablefoot{Uncertainties refer to a $1~\sigma$ confidence level, while $3~\sigma$ limits are reported for unconstrained measurements. $^a$ Observed abundance of the element $X$ relative to solar. $^b$ Abundances corrected for dust depletion. When available, [Zn/H]$_{\rm tot}$ is considered to be the metallicity of the gas. $^c$ Column density of iron in dust-phase (see text). $^d$ Metallicity as fitted with the S01 method (Eq. \ref{eq S01}), when H is unconstrained and Zn constrained. $^e$ Galactic environments fitted with the S01 method: halo (H), disk+halo (D), warm disk (W) and cool disk (C), as characterized by \citet{Savage96}. When more than one environment is possible, $\mathcal{{DT\!\!M}}${}(S01) and $\log Z/Z_\odot$ are averaged among the allowed values. $^f$ Different absorbing systems toward the same GRB are reported separately.}
\tablebib{All column densities, $z$ and $A_V$ are taken from the compilation by \citet{Schady11}.}
\label{tab dtm}
\end{table}

\end{landscape}

\subsection{Comparison with QSO-DLAs}

To compare the GRB- and QSO-DLA populations, we calculate the $\mathcal{{DT\!\!M}}${} for a sample of 72 QSO-DLAs from \citet{Noterdaeme08}, all of which have been observed with the high-resolution Very Large Telescope (VLT) Ultraviolet and Visual Echelle Spectrograph \citep[UVES,][]{Dekker00}. We choose to compute the $\mathcal{{DT\!\!M}}${} of QSO-DLAs with our new method because it is easily derived from the [$X$/Fe] reported in \citet{Noterdaeme08}. The overall sample of GRB- and QSO-DLAs spans a wide range of metallicities, from $Z\sim2\,Z_\odot$ down to $Z\sim0.002\,Z_\odot$. The average observed [Zn/Fe] in the QSO and GRB samples are 0.4 and 0.9, respectively, with a standard deviation of 0.2 and 0.5. This suggests that GRB environments are more dusty overall than QSO-DLAs. Indeed, only less than $\sim10$\% of QSO-DLAs show significant reddening due to dust \citep{Khare12}.

Figure \ref{fig: dtm_distr} shows the distribution of $\mathcal{{DT\!\!M}}${}s, derived with the new method, in GRB-DLAs (black) and QSO-DLAs (grey) as a function of metallicity (left panel) and the Zn column density (right panel) corrected for dust depletion using Eq. \ref{eq Zn tot}. The depletion corrections are typically very small, up to $\sim$0.3 dex. In Fig. \ref{fig: dtm_distr with Si}, we also include those targets that have measurements of the Si column density but lack measurements of the Zn column density. The $\mathcal{{DT\!\!M}}${} that has been estimated from Zn should be considered more reliable because the [Zn/Fe] is less affected by intrinsic changes of relative abundances than [Si/Fe].

\subsection{Comparison with the Magellanic Clouds}

We calculate the $\mathcal{{DT\!\!M}}${} values for two lines of sight through the SMC and the LMC, using the Zn and Fe column densities derived from the absorption lines observed in the literature. For the SMC, we consider the absorption in spectra of the background star Sk 108 \citep{Welty97}\footnote{We refer to the mean observed [Zn/Fe] $=0.50\pm12$ and [Zn/H] $=-0.64^{+0.13}_{-0.17}$ associated with the SMC, consistent with [Zn/Fe] $=0.66\pm20$ measured by \citet{Sofia06} for the same line of sight.}, Sk 155, and Sk 78 \citep{Welty01}. For the LMC, we use the absorption toward SN 1987A \citep{Welty99}\footnote{We refer to the mean [Zn/Fe] $=0.78^{+0.12}_{-0.16}$ and [Zn/H]$=-0.55\pm0.08$, averaged among the velocity components associated with the LMC.}. While the choice of a few specific line of sight per system may not represent the overall properties of the whole cloud, we note that typically only one line of sight can be observed toward both GRB and QSO as well. The derived $\mathcal{{DT\!\!M}}${} are $\sim$82--100\% and $\sim$98\% of the Galactic value for the SMC and the LMC, respectively, as displayed in Figs. \ref{fig: dtm_distr} and \ref{fig: dtm_distr with Si}. Given the similar [Zn/H] and $\log N$(Zn) of the SMC and LMC absorbers, it is interesting to note that the LMC has a higher [Zn/Fe], $\mathcal{{DT\!\!M}}${}, and ultimately a larger amount of dust with respect to SMC, although these differences are not $3~\sigma$ significant.

    \begin{figure*}
   \centering
   \includegraphics[width=170mm,angle=0]{f3.eps}
   \caption{\textit{Left:} The distribution of the $\mathcal{{DT\!\!M}}${} with dust-corrected [Zn/H]$_{\rm TOT}$ (the intrinsic metallicity), for the GRB-DLAs (black) in our sample and the UVES QSO-DLAs (gray) sample of \citet{Noterdaeme08}. The MW, SMC (three lines of sight) and LMC $\mathcal{{DT\!\!M}}${} values are displayed for comparison, where the latter two are two representative values derived from the observed [Zn/Fe] along two lines of sight (see text for details). Filled symbols highlight the measurements drawn from high-resolution spectroscopy. The thick green arrow shows the literature value \citep[derived from the $M_{\rm dust}/M_{\rm H}$ measured by][]{HerreraCamus12} for the nearby blue compact dwarf galaxy I Zw 18. \textit{Right:} The distribution of the $\mathcal{{DT\!\!M}}${} with the total column density of \znii{}, corrected for dust depletion.}
              \label{fig: dtm_distr}
   \includegraphics[width=170mm,angle=0]{f4.eps}
   \caption{Same as Fig. \ref{fig: dtm_distr}, but including the $\mathcal{{DT\!\!M}}${} values that have been estimated from Si and thus are less reliable. When Zn is not directly constrained, we display the equivalent \znii{} column density derived from the \siii{} column density, assuming solar relative abundances. The symbols indicate which metals are used in [$X$/Fe] to derive the $\mathcal{{DT\!\!M}}${}.}
              \label{fig: dtm_distr with Si}
    \end{figure*}

\section{Discussion}
\label{discussions}

\subsection{Strengths, caveats, and implications of our $\mathcal{{DT\!\!M}}${} method}
\label{discussions caveat}
The estimates of the dust-to-metal ratio presented in this paper rely purely on the metal absorption lines observed in the optical/UV afterglow spectra. These are selected at the GRB redshift, typically arising in the ISM of the host galaxy, hundreds of parsecs from the burst \citep[e.g.,][]{Vreeswijk07,Vreeswijk11}.

The main assumption of our $\mathcal{{DT\!\!M}}${} method is the existence of linear depletion sequences in DLAs similar to what has been observed in the Galaxy \citep{Jenkins09}. These sequences depend on the condensation temperature of each chemical element and naturally explain different dust-grain compositions in different environments. While the slopes of the Galactic depletion sequences are well studied \citep{Jenkins09}, the corresponding slopes in DLAs are unknown. Here we discuss how much our results depend on the assumption of these slopes.

At the low metallicity end, i.e., in the least dusty DLAs, the low depletions are not very sensitive to changes in slopes (see Fig. \ref{fig scheme}), while the zero offsets of the linear sequences are fully justified by the observation of [Zn/Fe] $\sim0$ in low-metallicity systems (see also Sect. \ref{sec method}). For the most dusty DLA systems, the dependence on the slopes of the depletion sequences are more significant. In comparison with the Galactic values however, we find that the possible range of slopes is limited. The slopes of the depletion sequences for DLAs must be shallower than in the Galaxy to provide reasonable dust-corrected metallicities in the DLAs. Indeed, using the Galactic values of the depletion-sequences slopes generally gives a small increase of $\mathcal{{DT\!\!M}}${} (up to $\sim0.15$), but implies excessive metallicities. In the most extreme cases, the Galactic slopes lead to dust-corrected metallicities of up to $Z\sim7\,Z_\odot$ and $Z\sim120\,Z_\odot$ for GRB\,000926, and GRB\,090926A, which are individual absorbing systems with [Zn/Fe]- and [Si/Fe]- based $\mathcal{{DT\!\!M}}${} respectively. These values are too large to be realistic. These numbers are even more extreme for dustier absorbers such as GRB\,090323, where the Galactic slopes lead to dust-corrected $Z\sim30\,Z_\odot$ and $Z\sim10^4\,Z_\odot$ for the two separate absorbing systems. These results are not justifiable, regardless of the degeneracy of the \hi{} content between the two absorbing systems. On the other hand, the slopes that we assumed for DLAs provide dust-corrected metallicities $Z\sim1.1\,Z_\odot$, $Z\sim0.01\,Z_\odot$, $Z\sim3.4\,Z_\odot$, and $Z\sim2.5\,Z_\odot$ for the systems mentioned above, respectively. Thus, the depletion levels of Si, Fe, and Zn are likely more moderate in DLAs than in the Galaxy. The $\mathcal{{DT\!\!M}}${} values given in Table \ref{tab dtm} are probably reliable within the errors, despite the uncertainties in the slopes of the depletion sequences in DLAs.

The depletion of Fe and Zn of the most dusty DLAs (with depletion factor $F_*\sim1$ and above) are similar to what has been observed in the least dusty lines of sight in the Galaxy \citep[with Galactic depletion factor $F_{*,\rm G}\sim0$,][]{Jenkins09}, such as disk+halo lines of sight studied by \citet{Savage96}. One intriguing possibility is that the depletion factor could evolve continuously from the least depleted dust-free DLAs to the most dusty Galactic lines of sight, where the depletion sequences would start at $F_*=0$ with no offset and shallow slopes and gradually evolve into the observed Galactic depletion sequences.

\subsection{The $\mathcal{{DT\!\!M}}${} distribution}

\textit{The $\mathcal{{DT\!\!M}}${} distribution of the GRB-DLAs in our sample increases with metallicity and spans $\sim$10\%--110\% of the Galactic value.  In addition, the observed trend points to low dust fractions for low-metallicity systems, which is inconsistent with a constant Galactic $\mathcal{{DT\!\!M}}${} at any metallicity, as recently suggested \citep[e.g.,][]{Zafar13}. Given these results, it is clear that $A_V/N(H)_{\rm{X}}${} should not be considered a reliable estimate of the dust-to-metal ratios in GRB-DLAs.}

The comparison between GRB- and QSO-DLAs in Fig. \ref{fig: dtm_distr} reveals a continuous distribution of the $\mathcal{{DT\!\!M}}${} between the two populations, indicating an overall similarity of their ISMs. The mean $\mathcal{{DT\!\!M}}${} for GRBs and QSOs are 0.8 and 0.6 respectively, with a standard deviation of 0.3 and 0.2. Given that GRB lines of sight preferentially cross through inner (and more dusty) regions of their star-forming galaxies, while QSO lines of sight typically intercept the haloes of intervening galaxies \citep[e.g.,][]{Prochaska07, Fynbo09}, GRBs probe the $\mathcal{{DT\!\!M}}${} distribution up to one order of magnitude larger column densities than QSO lines of sight. In the Galaxy, the average volume density of the gas is tightly correlated with the depletion factor \citep[$F_{\rm *,G}=0.772+0461\cdot\log\langle n({\rm H})\rangle$][]{Jenkins09}. For DLAs, we derive the average volume density from the observed the depletion factor $F_*$ (Eq. \ref{eq F*}), using the relation observed in the Galaxy. While the actual values of $\langle n({\rm H})\rangle$ that we find for DLAs may be unreliable because the relation might evolve with metallicity and be different for DLAs, the comparison between the densities in QSO- and GRB-DLAs are meaningful. While QSO-DLAs have $0.001<\langle n({\rm H}) \rangle<10$ cm$^{-3}$, several GRB-DLAs exceed $10$ cm$^{-3}$, confirming that GRBs are typically located in denser regions than QSO absorbers.

The $\mathcal{{DT\!\!M}}${} increases with metallicity (Fig. \ref{fig: dtm_distr} and \ref{fig: dtm_distr with Si}, left panels). Despite the large scatter, the increasing trend is clear up to [$X$/H$] \sim-1$. Above this metallicity the distribution may be consistent with a roughly constant dust-to-metal ratio for DLAs, as found by \citet{Zafar13} based on $A_V$. At lower metallicities we find low $\mathcal{{DT\!\!M}}${} values in both QSO- and GRB-DLAs, which are not constant and not consistent with the Local Group, pointing to a non universal dust-to-metal ratio.

The discrepancy between our results and the $A_V$-derived $\mathcal{{DT\!\!M}}${} \citep[][although only one single datapoint is constrained at very low metallicities]{Zafar13} might arise from an overestimate of the intrinsic dust content when estimated from the line-of-sight $A_V$ of the lower-metallicity and less dusty systems. For these low-dust systems the additional extinction due to foreground absorbers along the whole line of sight contribute significantly to the $A_V$. Indeed, the observed foreground $E(B-V)$ toward QSOs typically ranges between $\sim$0.001 and $\sim$0.1 \citep{Menard08}, i.e., $0.003 \lesssim A_V \lesssim 0.3$, so this additional source of dust extinction can be significant when compared to the intrinsically low $A_V$ of very low-metallicity systems. On the other hand, our dust-depletion analysis does not suffer from the contribution of intervening systems and therefore provides reliable estimates of the dust content of low-metallicity systems.

In Figs. \ref{fig: dtm_distr} and \ref{fig: dtm_distr with Si}, we include a literature estimate of the $\mathcal{{DT\!\!M}}${} of the blue compact dwarf galaxy I Zw 18, one of the lowest-metallicity systems known in the local universe \citep[{$\left[{\rm O/H}\right] =-1.52$}, $M_{\rm dust}/M_{\rm H}<8.1\times 10^{-5}$;][]{HerreraCamus12}, where we consider the dust-to-metal mass ratio $M_{\rm dust}/M_{\rm met}=10^{\log (M_{\rm dust}/M_{\rm H}) - {\rm [O/H]}}$ and normalize it by the Galactic value $(M_{\rm dust}/M_{\rm H})_{\rm Gal}=0.0073$ \citep{Draine07b}. The $\mathcal{{DT\!\!M}}${} $<0.37$ of I Zw 18 is consistent with the trend that we find for GRB- and QSO-DLAs, supporting the idea that low metallicity systems have lower dust fractions than typical spiral galaxies.

The $\mathcal{{DT\!\!M}}${} distribution increases with the metal column density as well (represented by the Zn or the equivalent Zn column density, right panel of Fig. \ref{fig: dtm_distr}) and flattens out above $\log N(\mbox{Zn})\sim13$. One issue that needs to be clarified is whether this flattening is physical or is artificially introduced by our analysis. As noted in Sect. \ref{results}, our method might slightly underestimate three $\mathcal{{DT\!\!M}}${} values (see Fig. \ref{fig: dtm_comp}), all of which have $\log N(\mbox{Zn})>13$. However, given the magnitude of the effect, these three points are unlikely to prove crucial. The observed flattening of the $\mathcal{{DT\!\!M}}${} at higher metal column densities might suggest that the availability of metals in the ISM can drive dust formation/growth up to some stable level where metals are largely accessible, as is the case for the Galaxy. Dust destruction due to GRBs might also play a role in limiting the amount of dust \citep[e.g.,][]{Waxman00,Draine02}.

The significance of the correlations described above is confirmed by a Spearman rank test, as listed in Table \ref{tab spearman}, indicating that $\mathcal{{DT\!\!M}}${} is most tightly correlated with [Zn/H]. There is a much weaker correlation between the $\mathcal{{DT\!\!M}}${} distribution and the \hi{} column density, as shown in Fig. \ref{fig: dtm_HI} in the Appendix. This confirms that the dust traces the metals rather than the total gas content.

While the $\mathcal{{DT\!\!M}}${} values in QSOs are uniformly distributed, we cannot exclude the presence of two populations of GRB hosts divided by their $\mathcal{{DT\!\!M}}${} properties, i.e., a standard one following the trends that have been observed for QSO-DLAs and a second group of GRB-DLAs with a lower $\mathcal{{DT\!\!M}}${}. This is most notable in the $\mathcal{{DT\!\!M}}${} distribution against the metal column density, although the gap is less evident when also including $\mathcal{{DT\!\!M}}${} estimates derived from Si. It is difficult to assess whether this separation is a real effect, given the small number statistics. If true, these low-$\mathcal{{DT\!\!M}}${} GRB-DLAs (mostly GRB\,071031 and GRB\,080413A) may correspond to systems having a smaller amount of dust for their metal content, possibly due to sputtering or sublimation of dust grains in actively star-forming regions \citep{Tielens94,Waxman00}. Further observations are clearly needed to investigate this issue.

We do not observe any trend of the $\mathcal{{DT\!\!M}}${} with the mass, star-formation rate, or specific star-formation rate of the host galaxies, although the sample for which all these estimates are available is limited to a handful of objects \citep{Vreeswijk04,Chen09,Savaglio09,Kruehler11,Savaglio12}.

\begin{table}
\centering
\caption{Spearman's rank correlation coefficients $\rho$ and significance.}
\begin{tabular}{@{}l@{\hspace{3mm}} l | l@{\hspace{3mm}} r@{\hspace{3mm}} r@{\hspace{3mm}} r@{\hspace{3mm}} r@{}}
\hline \hline
\rule[-0.2cm]{0mm}{0.8cm}

$x^a$ & $y^a$    & Fig. & DLA & $\rho^b$   & $P^c$ & $\sigma$ \\
\hline
$\mathcal{{DT\!\!M}}${}(S01) & $\mathcal{{DT\!\!M}}${} & \ref{fig: dtm_comp} & GRB &   0.94 & $<0.001$  & 6.15 \\

 \hline
 \multirow{2}{*}{[Zn/H]$_{\rm TOT}$} & \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_distr}}     & QSO &  0.660 &  $<0.001$ & 3.8\\
                                                                                &         &           & GRB &  0.667  &        0.050 & 1.96\\

   \hline
\multirow{2}{*}{$\log N(\mbox{\znii{}})_{\rm TOT}$} & \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_distr}}   & QSO &  0.464 &  0.013 & 2.48  \\
                                                                                &          &         & GRB &  0.632  &   0.020 & 2.32\\

\hline
\multirow{2}{*}{[$X$/H]$_{\rm TOT}^d$} & \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_distr with Si}}     & QSO &  0.564 &  $<0.001$ & 4.9 \\
                                                                                &         &           & GRB &  0.604  &        0.022 & 2.29\\

  \hline
\multirow{2}{*}{$\log N(\mbox{\znii{}})_{\rm TOT, Eq}^e$} & \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_distr with Si}}   & QSO &  0.265 &  0.062 & 1.86\\
                                            &         &         & GRB &  0.682  &   $<0.001$ & 3.31\\

\hline
\multirow{2}{*}{$z$} &  \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_z}}   &  QSO &  $-0.052$ &  0.671 & 0.43\\
                                                                                &      &        & GRB &  $-$0.338  &   0.144  & 1.46\\

\hline

 $N$(Fe)$_{\rm dust}${}$_{\rm, Zn, Si}$  & \multirow{5}{*}{$A_V$} & \multirow{5}{*}{\ref{fig: Av_NFedust}}  & \multirow{5}{*}{GRB} &  0.702  &  0.011 & 2.54 \\

 $N$(Fe)$_{\rm dust}${}$_{\rm, Zn}$  & & & &  0.357  &  0.385  & 0.88\\
 $N$(Fe)$_{\rm dust}${}$_{\rm, Si}$  & & & &  0.305  &  0.392  & 0.86\\
 $N$(Fe)$_{\rm dust}${}$_{\rm, Zn}^f$& & & &  0.357  &  0.431  & 0.79\\
 $N$(Fe)$_{\rm dust}${}$_{\rm, Si}^f$ & & & &  0.798  &  0.010  & 2.58\\

\hline

\multirow{2}{*}{$N$(\hi{})} & \multirow{2}{*}{$\mathcal{{DT\!\!M}}${}}  & \multirow{2}{*}{\ref{fig: dtm_HI}}   &   QSO &  $-0.123$ &  0.318 & 1.00\\
                                                                                &      &        & GRB &  $-$0.513  &  0.021 & 2.31\\

  \hline \hline
 \end{tabular}
\tablefoot{$^a$ $x$- and $y$-axis sample populations for the correlation test. $^b$ $-1 \leq \rho \leq +1$, where $\rho=+1(-1)$ for perfect monotonic increasing (decreasing) correlations. $^c$ Null-hypothesis probability, where the number of $\sigma$ indicates the level of significance of the correlation. $^d$ $X$ is either Zn or Si. $^e$ Zn or equivalent Zn column density derived from Si, see Fig. \ref{fig: dtm_distr with Si}. $^f$ Excluding the outlier GRB\,070802}
\label{tab spearman}
\end{table}

\subsection{On the origin of dust in DLAs}

We further explore the evolution of the $\mathcal{{DT\!\!M}}${} with redshift, as displayed in Fig. \ref{fig: dtm_z}. Combined with the metallicity information, this provides some further clues on the dust production in DLAs.

\subsubsection{At low redshift}
All the estimated $\mathcal{{DT\!\!M}}${} values for GRB-DLAs below $z\sim1.7$ (6 out of 20) are large and similar to the Galactic value. While the metallicity of these systems has not been measured from absorption lines because Ly-$\alpha$ is not redshifted into the observable window, the \znii{} column densities of these absorbers are all above $\log N$(\znii{}) $\gtrsim13$ \citep[with the exception of GRB\,080330 with $\log N$(\znii{}) $\sim12.8$][]{D'Elia09b}. Low-$z$ GRB absorbers follow the $\mathcal{{DT\!\!M}}${} distribution with the metal column density discussed above and it is reasonable to expect that they follow the $\mathcal{{DT\!\!M}}${} distribution with metallicity as well. If so, this would indicate that at redshift below $z\lesssim1.7$ most GRBs occur in galaxies with metallicities $Z\gtrsim0.1Z_\odot$, possibly because the mean metallicity of star-forming galaxies has increased with cosmic evolution. However, this result should be viewed with caution because the number of observations at low redshift is limited.

\subsubsection{At high redshift}
While the $\mathcal{{DT\!\!M}}${} distribution shows a large scatter above $z\gtrsim1.7$, we confirm the evidence for some high-$\mathcal{{DT\!\!M}}${} galaxies, such as GRB\,090323 at $z=3.6$ \citep{Savaglio12} or QSO-DLA Q 1441+2737 at $z=4.2$ \citep{Ledoux06}, to lie at high redshift. The presence of dusty systems at these redshifts suggests that a rapid dust-production mechanism may be required for the dust to have formed well within a Gyr. One such fast mechanism is the condensation of dust grains in cooled SN ejecta \citep[e.g.,][]{Matsuura11}, where the contribution of SNe on dust production is dominant at early times \citep[for time scales below $\sim200$ Myrs,][]{Gall11}. AGB stars start to recycle their metals into the ISM producing silicates grains after $\sim40$ Myrs \citep{DiCriscienzo13} and carbon-rich dust after a few hundreds Myrs of main-sequence evolution \citep{Galliano08}. However, at low metallicities the contribution of AGB stars to dust production is unlikely to be significant in systems with young stellar populations (see below). The observation of rapidly-produced dust (within 30--170 Myrs) in $z\gtrsim6$ QSOs suggests that SNe dominate the dust production at these redshifts, with a negligible contribution of AGB stars \citep{Gall11b}. While SNe are the dominant source of dust at early times, AGB stars are thought to start contributing at $z <$ 8--10 \citep{Valiante11}. However, extinction curves of SN-produced dust (showing a kink at 3000 \AA{}) have not been conclusively constrained in $z\sim6$ quasars \citep{Hjorth13} yet.

Grain growth in the ISM is typically considered a slow process for producing dust, but its time scale decreases with increasing metallicity \citep[the growth time scale $\tau$ is of the order of $\sim$60 Myrs for solar-metallicity systems,][]{Hirashita11}. Thus, dust production via grain growth cannot be excluded for those systems at high redshift with relatively high metallicity, such as GRB\,090323,  but also down to a few percent solar metallicity. Moreover, ISM shattering can increase the number of small grain and thereby allow grain growth to account for the amounts of dust observed in high-redshift quasars \citep{Kuo12}. Besides, grain growth is required to explain the dust content observed in high-redshift quasars \citep{Mattsson11,Valiante11}. While the current observation of the $\mathcal{{DT\!\!M}}${} at $z\sim4$ cannot put stringent limits on the origin of this dust, future observations of $\mathcal{{DT\!\!M}}${} at redshifts above 5 will be crucial to assess the extent of SN contribution at high redshift \citep{Morgan03}. The method described in this paper can in principle allow the $\mathcal{{DT\!\!M}}${} to be measured up to very high redshift.

\subsubsection{At low metallicities}
The low $\mathcal{{DT\!\!M}}${} of $Z\lesssim0.1Z_\odot$ DLAs implies that these systems have a lower fraction of dust with respect to the higher metallicity systems. This could be due to a lower efficiency of dust production and/or a higher efficiency of dust destruction. The efficiency of dust-production from AGB stars is also lower in low-metallicity systems, becoming a negligible source of dust below $Z\sim0.005Z_\odot$ \citep{DiCriscienzo13}. However, in low-metallicity environments the most massive AGB stars that are short-lived, but not massive enough to explode as SNe ($5M_\odot\lesssim M \lesssim 8M_\odot$) evolve to become N-rich and O-rich M-stars \citep{Karakas07,Gall11c} that are particularly inefficient at forming dust \citep{Ventura12}. Thus, AGB stars seem to bring a negligible contribution to dust production, when compared to SNe, in low-metallicity systems dominated by young stellar populations. Importantly, SNe dust production is not very sensitive to metallicity changes \citep{Galliano08}, and thus represents an unlikely source of the $\mathcal{{DT\!\!M}}${} trend with metallicity. On the other hand, below $Z\sim0.1 Z_\odot$ grain growth starts to be less efficient and its time scale becomes larger \citep[$\tau$ of hundreds of Myrs to Gyr, depending on the metallicity and the grain-size distribution;][]{Hirashita11}.

One possible cause of a higher efficiency in dust destruction could be a harder and more intense radiation field produced by enhanced massive-star formation in low-metallicity environments, such as for GRB host galaxies \citep[e.g.][]{Savaglio09}. However, \citet{Gall11} showed that simulated dust masses are higher for initial mass functions with more high-mass stars, meaning that SNe are overall more efficient at producing than destroying dust. An alternative cause of a higher level of dust destruction could be a grain-size distribution skewed toward smaller grains in low-metallicity systems \citep[][]{Sandstrom12}, since such dust grains are more easily destroyed \citep[e.g.,][]{Waxman00}. However, this is an unlikely scenario for QSO-DLAs, where sources of dust destruction (shocks or radiation due to SNe or GRBs) are limited. Moreover, an increasing $\mathcal{{DT\!\!M}}${} with increasing metallicity is expected only if there is a net production of dust via grain growth in the ISM over dust destruction \citep{Mattsson12}\footnote{$\mathcal{{DT\!\!M}}${} gradients that are coupled with metallicity gradients are thought to be a signature of the higher efficiency of grain growth over dust destruction \citep{Mattsson12}.}. \textit{Thus, the lower fraction of dust in the low-metallicity DLAs could be due to a lower efficiency of dust-production via grain growth, with negligible SN and AGB stars contribution.}

    \begin{figure}
   \centering
   \includegraphics[width=90mm,angle=0]{f5.eps}
   \caption{The $\mathcal{{DT\!\!M}}${} evolution with redshift. The symbols are the same as in Fig. \ref{fig: dtm_distr with Si}.}
              \label{fig: dtm_z}
    \end{figure}

\subsection{Dust extinction from the host galaxy ISM}

Given that the measurement of the dust extinction $A_V$ is integrated along the whole line of sight, it is not trivial to assess whether the intrinsic $A_V$ of the host galaxy is mostly associated with the bulk of the ISM. In principle, there could be a contribution from intervening systems \citep[although they show typically weaker absorption than GRB-DLAs themselves;][]{Vergani09} or from a dense and dusty star-forming region associated with the GRB. On the other hand, we use the metal absorption lines to infer the dust column in the host galaxy ISM, specifically the column density of Fe in dust $N$(Fe)$_{\rm dust}${} (Eq. \ref{eq fe dust}). It is insightful to compare $A_V$ and $N$(Fe)$_{\rm dust}${} because they are two entirely independent estimates of the dust content: $A_V$ is derived from the continuum shape of the optical/UV afterglow, while $N$(Fe)$_{\rm dust}${} is derived from the optical absorption lines produced by metals at the redshift of the host galaxy ISM. We compare these two quantities to investigate whether $A_V$ is produced in the ISM probed by UV absorption lines.

Figure \ref{fig: Av_NFedust} shows that $N$(Fe)$_{\rm dust}${} steeply increases with $A_V$ in GRB absorbers, at least up to $A_V\sim0.5$. The significance of the $N$(Fe)$_{\rm dust}${} correlation with $A_V$ is reported in Table \ref{tab spearman} for the measurements based on both Si and Zn, and also on the individual elements separately. While the correlation seems more solid when including both Zn and Si (2.5$\,\sigma$ significance level), we note that Zn-based measurements alone are not very helpful for the purpose of testing this correlation because of its narrow range of $A_V$. This arises from the observational difficulty of constraining Zn column densities in low-metallicity systems. The scatter of the correlation is quite large, indicating that in some cases there might be some contribution to the $A_V$ that is not related to the bulk of the host-galaxy ISM, as for the clear outlier GRB\,070802 (see below). Overall, the observed trends strongly support the general idea that $A_V$ is mostly produced in the bulk of the host galaxy ISM. A similar conclusion was also reached by \citet{Kruehler11} and \citet{Zafar11}.

GRB\,070802 stands out from the observed trend with the highest $A_V$ measurement. We note that this is one of the few GRBs where a Galactic-like 2175 \AA{} bump was observed imprinted on the optical afterglow spectrum \citep{Eliasdottir09,Zafar12}. The high extinction, well above the general trend of Fig. \ref{fig: Av_NFedust}, might strengthen the hypothesis that in this case the extinction occurs in two different regions with two different types of grains - one of them not representative of the bulk of the host galaxy - as suggested by \citet{Zafar12}. The observation of the 2175 \AA{} bump and the multi-component nature of $A_V$ makes this line of sight stand out from the rest of the GRB sample. One alternative explanation is that the distribution of $N$(Fe)$_{\rm dust}${} flattens out, as if some saturation process prevented iron from further accreting on dust grains above a certain threshold.

In general, one obvious candidate for an additional region to contribute to the $A_V$, other than the host ISM, is a dense and dusty environment close to the GRB where no low-ionization lines are produced. However, dust-destruction fronts typically move faster and reach greater distances than the ionization fronts produced by GRBs, making the dust destruction more efficient than ionization \citep{Draine02}. Thus, it seems unlikely to observe regions with dust but no low-ionization gas. Thus, foreground absorbers are more likely to be the source of additional contribution to the $A_V$. However, the positive correlation between $N$(Fe)$_{\rm dust}${} and $A_V$ confirms that for most lines of sight the main source of extinction is the GRB host galaxy.

\subsection{Molecular content}

Given the GRB association with massive star-forming regions \citep[e.g.,][]{Woosley93,Hjorth12}, we expect to observe the signature of molecular clouds in some optical afterglow spectra. In particular, dusty systems may bear the conditions for molecular formation, since dust grains can be efficient catalysts to aid the formation of molecules, such as H$_2$, on their surfaces \citep[e.g.,][]{Pirronello97}. However, molecular absorption bands are typically weak and notoriously difficult to observe in optical/near-UV spectra of extragalactic sources \citep[e.g.,][]{Noterdaeme08}. In GRB afterglows, CO was detected only once to date in the low-resolution Keck/LRIS spectrum of GRB\,080607 \citep{Prochaska09}, while H$_2$ has been recently observed in a couple of mid-resolution VLT/X-shooter afterglow spectra \citep[][Friis et~al., in preparation]{Kruehler13}. The dashed line in Fig. \ref{fig: Av_NFedust} shows the column density $\log \mbox{$N$(Fe)$_{\rm dust}${}}=14.7$ above which molecules have been observed in $\sim40$\% of QSO-DLAs \citep{Noterdaeme08}. \textit{Most GRB-DLAs lie above this column density and thus are promising sites to detect molecules.}

While the presence of molecules is expected in GRB environments, the hard radiation of the bursts are effective in destroying dust and molecules in molecular clouds \citep{Draine02}. However, the currently low detection rate of molecules observed in GRBs may be an observational effect due to the typically low spectral resolution or low S/N of the majority of GRB optical/near-UV spectra. On the other hand, current high-resolution samples might be biased against high metallicity lines of sight (potentially rich in dust and molecules) because only bright afterglows can currently be observed at high spectral resolution \citep{Ledoux09}. A large sample of mid-resolution (e.g., VLT/X-shooter) spectroscopic observations of GRB-DLAs can potentially include a significant number of those systems with the most favorable conditions for molecular formation \citep[i.e., high \hi{} and relatively high metallicity,][]{Noterdaeme08}, with sufficient S/N and spectral resolution to constrain the actual molecular content and the extent of dust destruction.

   \begin{figure}
   \centering
   \includegraphics[width=90mm,angle=0]{f6.eps}
   \caption{The optical extinction $A_V$ distribution with the column density of Fe in dust. The dashed line marks the column density above which a significant presence of molecules has been observed in QSO-DLAs \citep{Noterdaeme08}. When both are available, the measurements derived from Zn and Si are displayed in black and grey, respectively. The symbols are the same as in Fig. \ref{fig: dtm_distr with Si}.}
              \label{fig: Av_NFedust}
    \end{figure}

\section{Conclusions}
\label{conclusions}

We derive the dust-to-metal ratios ($\mathcal{{DT\!\!M}}${}) in long-duration GRB- and QSO-DLAs based on the dust-depletion pattern observed from low-ionization metal absorption lines in the optical/UV afterglow spectra. In this way, the dust-to-metal ratio is purely associated with the bulk of the neutral ISM in the GRB- or QSO-DLA, which is not influenced by the GRB, rather than integrated along the total line of sight. As a comparison, we also derive the $\mathcal{{DT\!\!M}}${} of GRB absorbers using a different method based on dust-depletion as well, described in \citet{Savaglio01}, with fully consistent results.

The dust-to-metal ratios in GRB-DLAs span $\sim$10--110\% of the Galactic value and show properties similar to the QSO-DLA distribution, with GRBs extending the study of dust-to-metal ratios out to higher column and volume densities. Above metallicities of $Z\sim0.1\,Z_\odot$, these results are partially consistent with the finding of a universally constant Galactic-like dust-to-metal ratio based on $A_V$ \citep{Zafar13}. However, at lower metallicities, down to $Z\sim0.002\,Z_\odot$, we find compelling evidence for low values of $\mathcal{{DT\!\!M}}${} for both GRB- and QSO-DLAs. We argue that our $\mathcal{{DT\!\!M}}${} estimates for low-metallicity DLAs are more reliable than those based on the dust extinction along the line of sight because low $A_V$ values are more sensitive to the contribution of foreground systems.

The $\mathcal{{DT\!\!M}}${} distribution increases with metallicity and metal column density. A similar trend was recently observed by \citet{Brinchmann13} for super-solar metallicity nearby galaxies. We observe a flattening of this trend above $\log N(\mbox{Zn})\sim13$, suggesting that the production/destruction of dust with respect to the metals stabilizes for more evolved galaxies. The low dust fraction of low-metallicity systems may be the result of inefficient dust production, e.g., for grain growth in the low-metallicity regime (where the time scale for grain growth becomes too long), with negligible contribution by SNe and AGB stars.

A possibility that needs to be further investigated is the presence of a population of low-$\mathcal{{DT\!\!M}}${} GRB-DLAs having a smaller amount of dust given their metal content, possibly due to destruction of dust grains in actively star-forming regions.

 At $z\lesssim1.7$, all the $\mathcal{{DT\!\!M}}${} estimates for the GRB-DLAs in our sample show high (Galactic-like) values. If confirmed with a larger sample, this may indicate that at lower redshift most GRBs occur in galaxies with $Z\gtrsim0.1Z_\odot$ that are richer in dust with respect to the overall host-galaxies population. This could possibly be due to the overall increase of metallicity with cosmic evolution. The presence of some of these high $\mathcal{{DT\!\!M}}${} galaxies is observed out to $z\sim4$, indicating that for these systems a fairly rapid ($\lesssim 1$ Gyr) production mechanism is required, i.e., in cooled SN ejecta as well as in AGB winds and grain growth in a $Z\sim Z_\odot$ metallicity regime. We find no trends of the $\mathcal{{DT\!\!M}}${} with the host-galaxy mass, star-formation rate, and specific star-formation rate.

The column density of Fe in dust $N$(Fe)$_{\rm dust}${} that we derive from the relative abundances observed in the host-galaxy ISM steeply increases with the dust extinction $A_V$ observed toward GRBs, up to at least $A_V\sim0.5$. This confirms that $A_V$ is mostly produced by the bulk of the ISM neutral gas. At high $A_V$, we observe one outlier of this trend, GRB\,070802, where either an additional contribution for the extinction must be included or the $N$(Fe)$_{\rm dust}${} flattens out at high $A_V$. The majority of GRB-DLAs shows high values of $N$(Fe)$_{\rm dust}${} \cite[above $\log \mbox{$N$(Fe)$_{\rm dust}${}}~14.7$, the minimum value for QSO-DLA with molecular detection][]{Noterdaeme08}, making them promising sites for the detection of molecules.

\begin{acknowledgements}
 We are most grateful to Edward B. Jenkins and Lars Mattsson for insightful comments on the manuscript. We thank Avishay Gal-Yam, Darach Watson and Tayyaba Zafar for useful discussions. ADC acknowledges support by a Grant of Excellence from the Icelandic Research Fund, the Weizmann Institute of Science Dean of Physics Fellowship, and the Koshland Center for Basic Research.
\end{acknowledgements}

\bibliographystyle{aa}

redpajama_set_name: RedPajamaArXiv


text:
Talking Point: A Step Too Far?
Sunday's Chinese Grand Prix has clearly polarised race fans, with some claiming it was a great, exciting race and others insisting that it was manipulated to within an inch of its life.
Indeed, in the first ever Pitpass post-race Podcast, the three contributors - yours truly, Glen Crompton and Mat Coch - have differing views of the race.
In the days when refuelling meant a series of short sprints people complained; now, as the sport become ever more strategic, many fans are still unhappy.
Launching its 2013 range of PZero tyres, Pirelli admitted that to produce tyres that went an entire race distance would be easy. Howeber, the powers that be had ordered them to produce tyres that would deliberately degrade and thereby spice up the action. They obliged.
From the opening race certain teams have complained about the durability of the softer compounds, which as far as the man in the street is concerned is grossly unfair on the Italian tyre manufacturer. It was given a remit and it has delivered.
Ignoring the situation in Malaysia, which saw the Red Bull and Mercedes drivers ordered to hold station, in China things got worse still. Following the first half-hour of non-action on Friday morning, for a while on Saturday afternoon it looked as if their might be no action in the final phase of qualifying, traditionally one of the most exciting parts of the weekend.
At one stage in the race Felipe Massa asked what was happening, the Brazilian clearly as baffled by the various strategies as the rest of us. Jenson Button asked if he was allowed to fight, whilst Sebastian Vettel was told not to waste time holding off Fernando Alonso.
Previously, Mark Webber, had compared the current situation to WWF (wrestling), whilst Kimi Raikkonen, one of the sport's true ten-tenths racers, when asked how he feels about this particular form of F1 replied: "It makes no difference, because this is what we have and you'd better like it or do something else."
Despite the dire warnings, in the final laps of the race, Vettel showed us what the soft tyres were really capable of, the three fastest laps of the entire race being set in the final laps by drivers on the option rubber.
In essence, Formula One 2013 is about managing one's equipment as opposed to racing, and a lot of people feel they are being short-changed.
We'll ignore, for now, the fact that the DRS zones made overtaking too easy, we'll even ignore the ongoing telemetry problems that threatened to turn the race result on its head, had (eight!) drivers been punished for using DRS in a yellow flag zone, but we cannot ignore the fact that the sport is in danger of losing fans as it becomes too strategic and too reliant on conserving the car as opposed to racing. But what do you think?
Page: 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 .... | Next
Chinese GP Podcast
Chinese GP: Driver Tyre Strategies
No further action over DRS transgression
Further misery for Webber
Bahrain grid penalty for Gutierrez
Chinese GP: Race notes - Pirelli
Webber to start from the pitlane
Webber to start from back of grid
Chinese GP: Qualifying notes - Pirelli
Chinese GP: Practice notes - Pirelli

redpajama_set_name: RedPajamaCommonCrawl


Today I met a friend for lunch and it was lovely to have a catch up with her. She is a local and I got to known her through my fiance as she is his HR contact in his job. I worked in HR when I was in the UK and she has been helping me in my job searches and we've struck up a friendship through that.
She suggested Chinese for our lunch (fine by me) I told her beforehand that I wasn't that keen on sea food so as long as there were other options I would be absolutely fine. So she took me to a Hokkien restaurant where she planned to select several dishes that were traditional Hokkien food for me to try. Hokkien is one of the Chinese dialects spoken in Singapore and so I was very excited to give it a go. She mentioned that there was fish but that it wasn't that overpowering so I figured I would be fine.
Yet again I got to practice with chop sticks and yes my quirky style is coming along nicely now. I'm sure I'm probably holding them wrong but to be honest I manage to eat the food that way so I'm not going to worry about it too much.
My friend selected a number of dishes starting with a soup. She mentioned it was slightly fishy but I said I'd be happy to try it and it was very nice. She even told me which bits were the fish. However when I asked her what type of fish it was she was a little vague saying it was fish maw, that it was a part of a fish but not to worry as it was nothing nasty. When I got home I looked fish maw up on the Internet and discovered that this is actually the part of the fish called the swim bladder, gas bladder or air bladder - nice! This part of the fish isn't actually anything to do with the bladder but is the part of the fish that helps it control its buoyancy so she was right it isn't used for anything unpleasant when the fish is alive. It was actually very nice and I gather it is quite a delicacy. However I admit if I'd know what it was even though it was nothing nasty I'm still not sure I'd have been that keen to try. Maybe this should be my philosophy from now on, don't ask just eat and decide if you like it on that basis!!
After that we had prawns (yes more sea food) mixed up with some other meat (not sure what) which were similar to spring rolls and dumplings. We had a number of dips and sides to eat with them in including possibly the hottest chili I am yet to taste. It was tiny but bought tears to my eyes and left a warm glow inside me for quite some time!
We then had a dish of spinage cooked with garlic, followed by some noodles with yet more sea food thrown in. After this we had what I can only describe as similar to a bread roll but a more doughy consistency, white in colour and sweeter tasting. These are split open and you put slices of pork in them (which has the fat left on it) and other fillings, i.e. the chilli's, if you want to and eat them rather like a sandwich. I gather that these aren't eaten that often as they are not very healthy (I can believe it).
Finally we had dessert and this was the part that I didn't finish as it really is an acquired taste in my opinion and one we just aren't that familiar with in the UK I guess. The dessert was yam (which is a type of sweet potato) served with pumpkin and some luminous yellow beans which are meant to be good for the brain. I'm not sure if that is the case as I can't remember what they were called, however I only ate one so perhaps my brain wasn't given enough. It wasn't unpleasant but had a strange consistency and although it was sort of sweet it was savoury as well. I gather that they actually fry the yam in onions and you could taste the onion which to me seemed a bit bizarre. Other than that though the meal was lovely. We washed it all down with a glass of a warm barley drink (similar to barley water but not as sweet) and some traditional Chinese tea which was very nice.
I really was delighted to try what was real food that the locals would eat. I can't wait to go again to another one of her restaurant choices so she can pick my meal again and I know she is determined to get me eating every possible type of seafood she can before she has finished!


Absolutely Angie Harmon: #FF @Angie_Harmon!
Today is Friday, which means it's time to give Angie a Follow Friday recommendation! Angie was the 72nd most recommended celebrity last week - let's see if we can beat that this week!
Note: As soon as the results are in, this post will be updated with Angie's ranking!
Edit: Angie was ranked 101st this week!Absolutely Angie: A fan site with news, photos, and commentary related to "Rizzoli & Isles" star Angie Harmon.


This is our MonkeyNotes downloadable and printable book summary / study guide / booknotes / synopsis / analysis for the book "Speak" by Laurie Halse Anderson in PDF format.
This is the only comprehensive study guide/booknotes for this title in existence. You can only get it here at the MonkeyNotes Store.


Fresco's Burleson has your catering needs covered no matter the event. We know that hosting and/or planning an event is tough enough, much less taking care of the food too! Our catering services are here to make your life easier and kick the flavors up a notch at your next event. From weddings to parties, we are here for you!
Fresco's menu offers traditional Tex Mex for those seeking the comfort foods they have grown up with, as well as delicious authentic dishes straight from Mexico.


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Home / Speakers / Mark Thompson
Sought-after executive coach advising top leaders in Fortune 500 and Global Fortune 1000 companies
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Mark C. Thompson is a world-renowned authority and top speaker on leadership, driving change and innovation, sales growth, and customer and employee engagement. Mark is an expert on executive leadership, business strategy, and innovation who has spent over 25 years leading teams and building companies from the ground up. He delivers actionable, valuable and practical advice for leaders at all levels of an organization.
Currently a highly sought after executive coach and venture investor, Forbes called Mark one of America's Top Venture Investors with the 'Midas Touch'. Mark was recently featured as one of the "World's Top Executive Coaches" by the AMA and one of the "Top 30 Communications Professionals for 2015" by Global Gurus. He works with the US State Department and the World Bank's President's Leadership Council as a key authority on growth and innovation. Mark advises top leaders in Fortune 500 and Global Fortune 1000 companies as well as the executive teams who are leading high growth startup companies in Silicon Valley today.
A New York Times bestselling author whose books include: ADMIRED: 21 Ways to Double Your Value; Now Build a Great Business; and Success Built to Last - Creating a Life that Matters, Mark is also an innovation leadership columnist for Forbes.com, Inc.com and FastCompany.com. His most recent bestseller ADMIRED is a primer on how the world's "most admired companies" achieve long-term success and growth as well as the qualities that are common to "most admired leaders". Mark has worked side by side with three of the world's most legendary disruptive innovators: Steve Jobs, Charles Schwab and Virgin Group founder Sir Richard Branson. He brings insight from decades of experience with these great leaders and research on the culture of companies and brands that achieve the highest levels of employee engagement, customer loyalty and continuous sales growth.
Mark was Charles Schwab's former chief of staff and chief customer experience officer, and the Executive Producer of Schwab.com which today has assets over $2.4 Trillion. He is a co-founder of Sir Richard Branson's Entrepreneurship Centres and an advisor to Virgin Unite Entrepreneurs. Mark is a founding advisor of the Stanford Realtime Venture Design Lab, and is a visiting scholar at his alma mater, Stanford University. He has served as faculty at the World Economic Forum and World Business Forum, is a member of the Clinton Initiative, and executive coach for TED Fellows.
A successful venture capitalist over the last two decades, Mark was as an early investor in companies like Facebook, Netflix and eSurance. He has been a Board Member for many well known technology, biotech and retail companies, including: Best Buy, Korn Ferry, and Interwoven (now owned by HP). He was the Chairman of the Board for Rioport, which popularized the MP3 player prior to the iPod. He is an investor in Cancer Genetics, a leader in DNA-based diagnostics for clinical management of cancer treatment. Mark serves as a founding Board of Directors member for Smule, the top music app company on iTunes which has over 125 million users worldwide. As a Broadway producer, Mark's plays have earned five Tony Awards and a total of ten Tony nominations, including Peter and the StarCatcher with Disney, and StickFly with Alicia Keys.
People in Right Seats
How to Transform the Customer Experience
Planning Your Customer Experience Strategy
How to Transform Your Business
Prior to your event, Mark Thompson and his Stanford team will interview your executives to create an exact fit with your theme. As a senior operating executive, chief of staff, board member, and chief customer experience officer at Schwab, Best Buy, Korn Ferry, Virgin, and Apple, Thompson brings a wealth of business acumen to every presentation.
Business Transformation: Drive Change and Create a Culture of Innovation. Disruptive innovation is happening all around us in almost every industry. "Disruptive Innovation" can mean: disrupting your competitors, customer relationships, internal processes, reward systems, management strategy, the status quo and "last century thinking". But how do you create a culture of innovation that enables a big company to think and act like a small one? Thompson shares insights on world-class companies that struggled with change - some that failed to adjust to meet changing markets and others that reinvented their business models and transformed entire industries with disruptive innovations. Thompson answers several questions that will help you understand how to:
Enable your teams to not only embrace change, but lead business transformation
Operationalize innovation while still meeting the demands of Wall Street
Remove the fear of failure for disruptive ideas
Create incentive systems that reward those that challenge "business as usual"
·Empower employees at every level to make change happen
Building A Most Admired Brand through Customer and Employee Engagement. Leaders of the world's Most Admired Companies know that the customer experience IS the brand! Customer engagement is not about transactions, it's about relationships - acting as though you'd put your own money on the line in your customer's company. If you were investing in your customer's company, you'd think differently about how you deal with them and fight for their success like it was your own. Thompson brings many examples of how the most admired brands approach customer engagement and set the standard for lasting customer relationships in their industries. These companies understand four key components that lead to lasting customer relationships:
·Every touchpoint that a customer encounters is defining your brand
Delivering a consistent experience regardless of point of contact or method of communication
A high level of employee engagement is critical to achieving customer engagement
Knowing what your MVPs (both customers and employees) value is key
Most Admired Leadership: Nobody Does It Alone! Building Great Teams. Thompson shares insights into the top leadership qualities of the world's Most Admired Leaders according to the most engaged employees. In a broad survey of over 10,000 employees in 110 countries, Thompson's research team identified the top eight leadership traits that people want from their leaders. He presents case studies from many of these leaders including his experience working directly with several of them. He outlines how the Most Admired leaders have achieved such enduring success over decades and how they consistently:
Recruit, build and retain the highest performing teams
Create a corporate culture that Inspires loyalty and engagement
Face adversity and bounce back from failures
Challenge themselves and their teams year after year to outdo themselves and achieve continuous and long-term growth
Learn what their MVP's value and what drives them in their lives and work
Fanatic Sales Growth- Success Built to Last; Growing from Good to Great to Admired. In this high-impact keynote, Thompson reveals the critical drivers behind long-term sales growth and enduring success. He lays out the key factors that differentiate companies that are good, those that become great and those that are admired.
How world-class teams generate unstoppable growth
·Avoiding common mistakes that cut sales in half
·5 Tools To Double Sales: Positioning-Pain-Promise-Proof-Planning
·The customer service strategies that drive customer retention
·Discovering what your market craves and getting ahead of the curve
Admired: 21 Ways to Double Your Value
Now, Build a Great Business!: 7 Ways to Maximize Your Profits in Any Market
Success Built to Last: Creating a Life that Matters
Sharon Wood
First North American Woman to Summit Mount Everest
Gary Bradt
Leadership and Change Expert


text:
Reflections on the inaugural season
By admin · On July 26, 2016
Daryl Stevenson: Reflections on the inaugural season
A three-sport standout athlete at Spencerport High School outside Rochester, NY, Daryl Stevenson '70 could easily have worn the red and black of Roberts Wesleyan had he followed the calling of his high school friends and a few rival competitors as high school graduation approached in 1966.
But Stevenson heeded a different call, one that brought him to Houghton to continue his family's legacy. Traditional class athletics and Houghton's heated Purple and Gold rivalry filled his need for a competitive outlet, something he took immediate advantage of as he arrived on campus during the fall of his freshman year.
As the spring semester rolled around, however, Stevenson and a few other top soccer players at Houghton were called to Coach Doug Burke's home to gauge their interest in being part of Houghton's first intercollegiate team the next fall. The students enthusiastically pledged their commitments and waited for the college to move forward.
Daryl Stevenson '70 (center) in a Fall 1969 Highlander soccer match.
By late spring, The Wesleyan Church granted each member college the option of pursuing intercollegiate competition. In June, Houghton administrators presented their proposal to the Houghton Board of Trustees—on which Stevenson's father (Herbert Stevenson '38) was serving—and the group gave their approval for Houghton student-athletes to display their talents beyond the confines of the college.
Intercollegiate athletics at Houghton was now a reality.
That summer was spent putting the teams together—men's soccer and cross country in the fall and men's basketball in the winter—and scheduling opponents to take on Houghton's fledgling programs.
Stevenson and his soccer teammates played two games in the fall of 1967, getting a win at Messiah and losing a tough contest at Roberts Wesleyan. He went on to play two more seasons and was a key contributor and leader for Houghton before graduating in 1970.
Stevenson returned to Houghton in 1982, serving on the faculty until his retirement in 2013, raising his family, following the Highlander teams and even supporting his three sons (Kyle '96, Tyler '03 and Eric '08) as they continued the Highlander tradition.
Stevenson recently offered his reflections on what it meant to be a part of one of Houghton's first teams, the impact athletics had on his life and the importance of athletics in the Houghton experience.
Why was there a push to move to intercollegiate athletics?
Everybody understood that this would be taking another step up in competition and showing how Houghton's athletes could compete against other colleges. For decades, teams of guys would go up and play against a group of guys from other schools. This had been happening since the 1930s and 1940s, so having intercollegiate teams was always on people's radars.
Was there a worry that Purple and Gold and Class competition would be lost?
We moved on. We had intramurals and intercollegiate. No one said we needed to go back to [Purple and Gold]. We appreciated the foundation and what they provided. I'm glad we celebrate what they did for us, but athletically, we elevated it to all one team who wore both Purple and Gold. It became a symbol for carrying on the foundation that Purple and Gold provided.
What was that first game and season like?
Coach Burke had contacts with Roberts Wesleyan and knew the people there, so they left open their fall homecoming game and plugged us in there for early October. Against Roberts, I think we wore our gold shirts from the Gold team, but we didn't have unified shorts. We had players wearing black and blue and brown and white shorts. It was a rag tag group.
Our first win was against Messiah. Afterward, the team came home to a welcome back event on campus. We drove the vans around campus, honking horns with people coming out and cheering. It was a big deal.
How does intercollegiate athletics play a role in the life of the college and student body today?
The word I would use is integration—the integration of faith and learning. The notion that we don't have lives of silos. We don't have a spiritual life and a professional life. All of these can be integrated.
In athletics, people learn leadership skills, the never-give-up attitude. You do things you think you could never do. Then you go out and apply those skills. There are a lot of examples of people who have come through Houghton and found ways to integrate their spiritual perspective with their profession and their athletics involvement. We are more cognizant of the pattern that unfolds in our lives. As I look back on it, I think about my athletic involvement as part of the growing process.
Student Experience: Science Honors, 2015-2016
Student Experience, East Meets West, Fall 2015
Student Experience: London Honors, Fall 2015
Dr. Eric S. Smith says: September 23, 2016 at 2:49 pm
Hi Daryl, this is Eric!
Sorry I missed your call! Try my cell next time, same area code 484-five43nine.
Yeah, I remember that first Fall of '67. I had just transferred in from GMI and thought I'd lost credit so thought I was in your class, '70. I didn't know about the soccer team initially so I went out for GOLD football for a week until I heard about soccer then switched to my first love!
The first year was a blur– all I really remember was the hard practices running up that gravel hill and back and freezing to death on that trip to Messiah. The second season, Fall '68, I remember excruciatingly well! At the homecoming game with Roberts, I started at fullback. Somewhere during the game, my knee met one of their fullback's knees and his won—bending mine backwards and sending me to the Warsaw hospital on an ambulance.
I'm not sure who won the game, but I lost…the rest of the season and almost my knee. Except, in God's economy I won, of course! After 2 months in a full leg cast, allowing God alone to heal me, he used that injury to give time to rethinking my hedonistic life and buckle down academically. By taking 19 hrs second semester and 12 hrs in summer school I graduated August, 1969, much to Coach's chagrin. He wanted me to stay another year and play soccer of course! 
I here you're retired now from good 'ol Hufftin U! I'm teaching adjunct Math at MNU and KCKCC trying to keep out of trouble! Blessings to you and your good wife Goody.
Eric. '69
Summer 2016 Alumni News and Notes
Summer 2016 In Memoriam


Skill:   •	Ensure availability of systems and infrastructure by pro-active monitoring, maintenance and management.
•	Working closely with peers and Field Office Infrastructure Director to improve support capability, suggesting and implementing new processes, technologies and tools.
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