High redshift galaxies in the HUDF

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The discussion focuses on estimating the number of high redshift galaxies with redshift z=7 in the Hubble Ultra Deep Field, utilizing the provided formulas for source density, star formation rate, and luminosity. Participants are exploring how to design a survey aimed at identifying 100 galaxies at this redshift while minimizing exposure time through single band imaging of the rest frame UV. Key calculations involve understanding the relationships between star formation rate, luminosity, and flux density to optimize survey parameters. The conversation emphasizes the importance of precise measurements and efficient survey strategies to achieve the research goals. Overall, the thread seeks practical solutions for targeting high redshift galaxies effectively.
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In the Hubble Ultra Deep Field ( http://en.wikipedia.org/wiki/Hubble_Ultra-Deep_Field ) there are almost 10.000 galaxies and some of them with redshift Z>6 . Making some approximations i need to compute the number of galaxies with redshift z = 7.

If the source density ( number / arcmin^2 ) at z=7 is given by,

\Sigma( > SFR ) = 10 ( SFR )^{-2.1}

and the relation between star formation rate and the rest frame UV luminosity is given by,

SFR = 1.4 10^{-28} L_{UV}

The relation between luminosity and flux density is,

f_v =\frac{L_v (1+z)}{4 \pi d_l^2}

and finally the minimum luminosity observed for an exposure time for a given filter is given

f = f_1 t_{exp}^{-1/2}

Given that information how can i design a survey that is targeting 100 galaxies with redshift z=7 and how could i minimize the exposure time , by taking single band imaging of the rest frame UV. Any ideas ?
 
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