We present predictions for the surface density of ultracool dwarfs ( with spectral types M8–T8 ) for a host of deep fields that are likely to be observed with the James Webb Space Telescope .
Based on simple thin and thick/thin disk ( exponential ) models , we show the typical distance modulus is \mu \approx 9.8 mag , which at high Galactic latitude is 5 \log { ( 2 z _ { scl } ) } -5 .
Since this is a property of the density distribution of an exponential disk , it is independent of spectral type or stellar sample .
Using the published estimates of the ultracool dwarf luminosity function , we show that their number counts typically peak around J \sim 24 mag with a total surface density of \Sigma \sim 0.3 arcmin ^ { -2 } , but with a strong dependence on galactic coordinate and spectral type .
Owing to the exponential shape of the disk , the ultracool dwarfs are very rare at faint magnitudes ( J \geq 27 mag ) , with typical densities of \Sigma \sim 0.005 arcmin ^ { -2 } ( or \sim 20 % of the total contribution within the field ) .
Therefore in the very narrow and deep fields , we predict there are only a few ultracool dwarfs , and hence these stars are likely not a severe contaminant in searches for high-redshift galaxies .
Furthermore the ultracool dwarfs are expected to be considerably brighter than the high-redshift galaxies , so samples near the faint-end of the high-redshift galaxy population will be the purest .
We present the star-count formalism in a simplified way so that observers may easily predict the number of stars for their conditions ( field , depth , wavelength , etc .
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