Astronomy & Astrophysics

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$\begin{figure} \par\includegraphics[width=8.5cm,clip=true]{0863fig1.eps}\end{figure}$ Figure 1: The constraint $t_{\rm s}$ has to fulfill so that the Ly- ${\alpha }$ flux is detectable at z₀. The big black point marks the minimum flux detectable at z₀=z(t₀) with the detection limit $S_{\rm lim}$ . In order to be detectable in Ly- ${\alpha }$ , the ignition epoch $t_{\rm s}$ for the Ly- ${\alpha }$ emission has to be in the interval $[t_0-\Delta t_2, t_0 - \Delta t_1]$ . This interval is marked by the thick vertical line. The short dashed, solid and long dashed curves show the possible Ly- ${\alpha }$ luminosity of PGs as a function of time with different ignition times $t_{\rm s}$ . The short dashed curve shows the time evolution of the Ly- ${\alpha }$ luminosity of a PG with an $t_{\rm s}$ at the lower bound of the relevant time interval. At t₀ the Ly- ${\alpha }$ luminosity of such a PG is already very week e.g. because of ongoing dust formation. The solid curve corresponds to a PG with an ignition time $t_{\rm s}$ centered in the relevant time interval. It reaches its maximal Ly- ${\alpha }$ luminosity at the epoch t₀ corresponding to the observed redshift z₀. Therefore, such a PG should be detectable. On the other hand, the long dashed curve corresponds to a PG with a $t_{\rm s}$ at the right end of the relevant time interval. The Ly- ${\alpha }$ luminosity of such a PG has just reached detectable values and will rise further.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.3cm,clip]{0863fig2.ps}\end{figure}$ Figure 2: Most optimistic (solid line) and pessimistic (dashed line) number density predictions for Ly- ${\alpha }$ emitting PGs for z₀=4.8 and $\Delta z = 0.1$ according to the parameters of Baron & White (1987) together with the early upper limits of the Palomar Fabry-Perot survey of Thompson et al. (1995a) (triangles) and more recent searches by Maier et al. (2003) (small arrows) and Rhoads et al. (2003) (open star with arrow).
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In the text

$\begin{figure} \includegraphics[angle=270,width=8.2cm,clip]{0863fig3.eps}\end{figure}$ Figure 3: The distribution function $p(\nu )$ for $\gamma = 0.58$ corresponding to an effective power-law index of the power spectrum of n=-2. The solid curve shows the result of the exact calculation and the dashed one is calculated with the fitting formula given by BBKS.
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In the text

$\begin{figure} \includegraphics[angle=270,width=8.2cm,clip]{0863fig4.eps}\end{figure}$ Figure 4: Distribution of collapse times for the three different masses $0.1\times M_*$ (dotted-dashed line), M_* (solid line) and $5\times M_*$ (dashed line).
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In the text

$\begin{figure} \includegraphics[angle=270,width=8.3cm,clip=true]{0863fig5.eps}\end{figure}$ Figure 5: The same curves as in Fig. 4, but with the time axis transformed into redshift.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=17cm,clip]{0863fig6.ps}\end{figure}$ Figure 6: Expected number density per deg² and $\Delta z = 0.1$ of Ly- ${\alpha }$ emitting PGs with a minimum detectable Ly- ${\alpha }$ flux of $S_{\rm lim} = 3 \times 10^{-20}$ W m^-2. $\Delta t _{\rm Ly\alpha }$ was fixed to 0.35 Gyr according to our "basic model''. The different panels show the results for different observing redshifts z₀. The three different curves in each panel correspond to different cosmologies: the solid line corresponds to $\Omega _{\rm M} =0.3$ , $\Omega _\Lambda =0.0$ , the dashed line corresponds to $\Omega _{\rm M} =1.0$ , $\Omega _\Lambda =0.0$ and the dashed dotted line corresponds to $\Omega _{\rm M} =0.3$ , $\Omega _\Lambda =0.7$ .
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{0863fig7.eps}\end{figure}$ Figure 7: P_M(t) for elliptical galaxies with M=M_* and different $z_{\rm max}=3,6,9$ and 12.The two vertical lines mark the interval (5) for z₀=3.5. The dashed vertical line very close to the left border of the interval (5) marks the observing redshfit z₀=3.5.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=11.1cm,clip]{0863fig8.ps} \hfill \end{figure}$ Figure 8: Expected number density per deg² and $\Delta z = 0.1$ of Ly- ${\alpha }$ emitting PGs as a function of $\sigma _{\rm Ly\alpha }$ (see 23) for fixed $S_{\rm lim} = 3\times 10^{-20}\; \;{\rm W~m^{-2}}$ . The cosmology is fixed to $\Omega _{\rm M} =0.3$ , $\Omega _\Lambda =0.7$ . The solid curves correspond to $z_{\rm max}=3.4$ , the dashed curves to $z_{\rm max}=6$ and the dotted dashed curves to $z_{\rm max}=10$ . The arrow marks the value $\sigma _{\rm Ly-\alpha }=0.15$ of our "basic model''.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=16cm,clip]{0863fig9.ps} \hfill \end{figure}$ Figure 9: Expected number density per deg² and $\Delta z = 0.1$ of Ly- ${\alpha }$ emitting PGs as a function of the minimum detectable Ly $_{\alpha }$ flux of $S_{\rm lim}$ according to our "basic model'' parameters $\Delta t _{\rm Ly-\alpha }=0.35$ Gyr and $\Omega _{\rm M} =0.3$ , $\Omega _\Lambda =0.7$ . The solid curves correspond to $z_{\rm max}=3.4$ , the dashed curves to $z_{\rm max}=6$ and the dashed dotted curves to $z_{\rm max}=10$ .
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.3cm,clip]{0863fig10.ps} \end{figure}$ Figure 10: Comparison of our "basic model'' with observational data. Big open star: LALA survey of Rhoads et al. (2003); filled square: Hu et al. (1999); small stars and arrows: CADIS Maier et al. (2003); open boxes: Hu et al. (1998);open circles: Kudritzki et al. (2000); filled star with arrow: LALA survey of Rhoads et al. (2003) for z₀=4.8; solid line: z₀=3.5; dashed line: z₀=5.7; dotted dashed line: z₀=4.8.
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0863fig11.ps}\end{figure}$ Figure 11: Expected number density per deg² and $\Delta z = 0.1$ of ${\rm Ly-\alpha }$ emitting PGs as a function of the observation redshift z₀ for $\Delta t _{\rm Ly\alpha} = 2\sigma _{\rm Ly-\alpha } \sqrt{2 \ln 2}= 0.35$ Gyr (according to our "basic model'') at a detection limit of log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.5$ . The three curves correspond to $z_{\rm max}=3.4$ (solid curve), 4.5 (dashed curve), 5.5 (dashed dotted curve). The cosmology is fixed to $\Omega _{\rm M} =0.3$ , $\Omega _V=0.7$ (according to our "basic model''). The symbols mark observational data: open box: Hu et al. (1998) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.5$ ; open circle: Kudritzki et al. (2000) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.5$ ; small star: CADIS Maier et al. (2003) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.54$ .
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In the text

$\begin{figure} \par\includegraphics[angle=-90,width=8.8cm,clip]{0863fig12.ps} \end{figure}$ Figure 12: Expected number density per deg² and $\Delta z = 0.1$ of Ly- ${\rm\alpha }$ emitting PGs as a function of the observation redshift z₀ for $\Delta t _{\rm Ly\alpha} = 2\sigma _{\rm Ly-\alpha } \sqrt{2 \ln 2}= 0.35$ Gyr and the detection limits of log $(S_{\rm lim}[{\rm W~m^{-2}}]) = -21.0$ (solid line), -20.0 (dashed line), -19.0 (dashed dotted line). $z_{\rm max}$ is fixed to 3.4 and the cosmology is fixed to $\Omega _{\rm M} =0.3$ , $\Omega _\Lambda =0.7$ (according to our "basic model''). The symbols mark observational data: open box: Hu et al. (1998) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.1, -19,9$ ; open circle: Kudritzki et al. (2000) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.0, -19.8$ ; small stars: CADIS Maier et al. (2003) for log $(S_{\rm lim} [{\rm W~m^{-2}}]) = -19.54,-19.32,-19.19$ .
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In the text

$\begin{figure} \includegraphics[angle=270,width=8.2cm,clip]{0863fig3.eps}\end{figure}$	Figure 3: The distribution function $p(\nu )$ for $\gamma = 0.58$ corresponding to an effective power-law index of the power spectrum of n=-2. The solid curve shows the result of the exact calculation and the dashed one is calculated with the fitting formula given by BBKS.
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$\begin{figure} \includegraphics[angle=270,width=8.2cm,clip]{0863fig4.eps}\end{figure}$	Figure 4: Distribution of collapse times for the three different masses $0.1\times M_$ (dotted-dashed line), M_ (solid line) and $5\times M_*$ (dashed line).
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$\begin{figure} \includegraphics[angle=270,width=8.3cm,clip=true]{0863fig5.eps}\end{figure}$	Figure 5: The same curves as in Fig. 4, but with the time axis transformed into redshift.
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$\begin{figure} \par\includegraphics[angle=-90,width=8cm,clip]{0863fig7.eps}\end{figure}$	Figure 7: P_M(t) for elliptical galaxies with M=M_* and different $z_{\rm max}=3,6,9$ and 12.The two vertical lines mark the interval (5) for z₀=3.5. The dashed vertical line very close to the left border of the interval (5) marks the observing redshfit z₀=3.5.
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