All Figures

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig1.ps}} \end{figure}$ Figure 1: Top panel: FWHM of the cross-dispersion profile of the standard star LTT 7987 taken with VLT+FORS1 on UT 11 October 2002. The single data point with an error bar shows the mean seeing as measured by the DIMM station - namely $1.55 \pm 0.12$ $^{\prime \prime }$ (the pixel scale of FORS1 is 0.2 $^{\prime \prime }$ pix^-1) at 5000 Å. Overplotted is the FWHM-wavelength relation fixed at the DIMM data point, both for the predicted exponent (-0.20) and our best-fit value (-0.29). Lower panel: fractional residuals with respect to the $\theta \propto \lambda ^{-l}$ relation, for l=0.20 (open squares) and l=0.29 (filled squares).
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig2.ps}} \end{figure}$ Figure 2: Illustration of SSF synthesis using specpsf. The input spectrum is the same as in Fig. 1. Top panel: FWHM of LTT 7987 (open squares) and of the synthetic SSF (filled triangles). The dashed line shows a polynomial fit to the synthetic SSF. Lower panel: residual plots of the FWHM of the synthesized SSF (open squares) and polynomial fit to the synthetic SSF (filled circles) with respect to the input SSF.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig3.ps}} \end{figure}$ Figure 3: Examples of SSFs used to extract SN 2002go: (1) the supernova itself; (2) a bright PSF star that happened to be on the same slit; (3) the closest FORS1 standard star to match the supernova profile. Top panel: the dashed line is a polynomial fit to the SN profile, from which low S/N points affected by the increase in sky background have been excluded. Lower panel: fractional differences in the SSF FWHM with respect to the polynomial fit.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig4.ps}} \end{figure}$ Figure 4: Impact of the SSF on the restored point source spectrum of SN 2002go. Refer to Fig. 3 for the meaning of the line annotations (1), (2) and (3), noting that (1) corresponds to the polynomial fit to the SN 2002go profile. The two inlays zoom in on the blueshifted Ca II H&K and Si II features, both prominent in SN Ia spectra, and highlight the impact of non-optimal spectral extractions on empirical correlations involving line strengths (see text).
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig5.ps}} \end{figure}$ Figure 5: Impact of the width of the spatial resolution kernel $\sigma _{\rm kernel}$ on the background restoration. Top panel: input average (dashed line) and restored background (solid line) cross-dispersion profiles. Middle panel: residuals of the previous plot, revealing the point source channel (i.e. the supernova itself). Lower panel: spatial residuals of the input and restored 2D frames. Negative (positive) values in the residual plots mean we are over (under)-restoring the flux at that location.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig6.ps}} \end{figure}$ Figure 6: Restored point source spectra in units of the statistical noise of the input pure galaxy spectrum. The different plots correspond to different positions of the point source to extract, marked by a filled square in the galaxy spatial profiles shown in the right column. The different lines correspond to different seeing conditions. The horizontal dashed line marks the limit below which no point source was detected in the background. Note the change of scale in the lower plot, where no flux at all is restored in many bandpasses. The peak above the dashed line in the uppermost plot is due to bad cosmic ray removal.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig7.ps}} \end{figure}$ Figure 7: Absolute flux-calibrated galaxy and sky spectra used in the simulation. The spectra are shown in observed wavelength at z=0.5, and without shot noise for sake of clarity. The prominent [O II] emission and the Ca II H&K absorption in NGC 6181 are labelled accordingly. Overplotted (dashed lines) are the spectra of SN 1994D at maximum intensity (top) and ten days before maximum (bottom).
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig8.ps}} \end{figure}$ Figure 8: Smoothed galaxy spatial profile used in the simulation, resulting from the convolution of a standard spiral galaxy luminosity profile and a 1 $^{\prime \prime }$ seeing Gaussian kernel. The abscissa is in units of FWHM of the convolved galaxy profile ( $\cong 3.06$ pix). The effective radius $r_{\rm e}$ in these units is at $\sim 7.36$ . Filled squares indicate the position of the SN used in this simulation, namely 0.75, 1.00, 1.25, 1.50 and 1.75.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig9.ps}} \end{figure}$ Figure 9: SN trace position residuals as a function of the SN phase, for different locations of the SN with respect to the galaxy centroid. Each curve corresponds to a specific SN position, given in units of FWHM $_{\rm gal}$ .
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fg10.ps}} \end{figure}$ Figure 10: SN trace FWHM residuals as a function of the SN phase, for different locations of the SN with respect to the galaxy centroid. The curves and plotting symbols have the same meaning as in Fig. 9.
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In the text

$\begin{figure} \par\includegraphics[width=14cm]{2009fg11.ps} \end{figure}$ Figure 11: Top panel: flux residuals $\delta F$ as a function of the SN phase for different positions of the SN with respect to the centroid of the galaxy trace, given in units of FWHM $_{\rm gal}$ . $\delta F \leq 1$ means the SN spectrum has been restored to the statistical noise limit. The solid and dashed lines correspond to runs A and B, respectively (see Sect. 5.2.3). Lower panel: [O II] flux residuals as a function of phase for different SN positions.
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In the text

$\begin{figure} \par\includegraphics[width=14cm]{2009fg12.ps} \end{figure}$ Figure 12: Top panel: normalised average spatial profiles of the input (dashed line) and restored (solid line) 2D background spectra. Two runs of specinholucy were executed, one including the point source in the restored 2D background spectrum and the other excluding it, so as to appreciate how well the background underneath the SN was fit. Lower panel: wavelength-averaged spatial residuals in units of the statistical noise of the input 2D spectrum. For all cases we have $\delta F_{\rm tot} \leq 1$ , meaning the combined SN+background spatial profile is restored to the statistical noise limit over the whole spatial range.
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In the text

$\begin{figure} \par\includegraphics[width=15cm]{2009fg13.ps}\end{figure}$ Figure 13: Top panel: normalised restored point source spectra (solid line) and underlying background, both including (dashed line) and excluding (dotted line) the point source. The spectra have been normalised to the integral of the underlying background flux. The symbol $\oplus$ denotes the atmospheric A-band ( $\sim$ 7600-7630 Å), whilst arrows indicate strong sky emission lines. Lower panel: spectral residuals in units of the statistical noise of the input 2D spectrum.
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In the text

$\begin{figure} \par\includegraphics[width=15cm]{2009fg14.ps} \end{figure}$ Figure 14: Top panel: restored supernova spectra using specinholucy (solid line) and other methods presented in Sect. 7. The spectra are normalised to the maximum flux value of the specinholucy output. Due to the specificities of $\mathcal{SN}$ -fit - namely the restriction of the local SN template spectra to epochs $-20~{\rm d}<t<+20~{\rm d}$ , we restrict its application to SNe 2002gr and 2002go (we plot the solution corresponding to the smallest $\chi ^2$ - see text.), for which we have not plotted the gaussextract output for the sake of clarity. The symbol $\oplus$ and arrows have the same meaning as in Fig. 13. Lower panel: ratios of the various spectra to the specinholucy output. We have deliberately restricted the y-axis range to [0, 2] to be able to visualise small $\sim$ 20% differences in the SN flux.
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In the text

$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fig9.ps}} \end{figure}$	Figure 9: SN trace position residuals as a function of the SN phase, for different locations of the SN with respect to the galaxy centroid. Each curve corresponds to a specific SN position, given in units of FWHM $_{\rm gal}$ .
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$\begin{figure} \par\resizebox{8.5cm}{!}{\includegraphics[width=10cm]{2009fg10.ps}} \end{figure}$	Figure 10: SN trace FWHM residuals as a function of the SN phase, for different locations of the SN with respect to the galaxy centroid. The curves and plotting symbols have the same meaning as in Fig. 9.
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