Searching for Low Surface Brightness Galaxies in the Hubble Ultra Deep Field: Implications for the Star Formation Efficiency in Neutral Gas at \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss…

(Abridged) The Kennicutt--Schmidt law relates the face-on star formation rate(SFR) per unit area with the face-on gaseous column density in nearby galaxies.Applying this relation to damped Lya absorption systems (DLAs) of neutralhydrogen column density N > 1.6x10^21 cm^-2 leads to an estimate that threepercent of the sky should be covered with extended sources brighter thanmu_V~28.4 mag arcsec^-2, if DLAs at redshift z=[2.5,3.5] undergo in situ starformation. We test this hypothesis by searching the Hubble Ultra Deep Field(UDF) F606W image for low surface-brightness features of angular sizes, rangingbetween theta_dla=0.25" and 4.0". Our search yields upper limits on thecomoving SFR densities that are between factors of 30 and 100 lower thanpredictions, suggesting a reduction by more than a factor of 10 in starformation efficiency at z~3. We consider several mechanisms that could reducestar formation efficiency at high redshift. We find that the cosmologicalincrease with redshift of the critical surface density for the Toomreinstability may be sufficient to suppress star formation to the levels impliedby the UDF observations. However, the uncertainties are such that Toomreinstabilities may still exist. In that case star formation at column densitiesless than 10^22 cm^-2 may be suppressed by the low molecular content of the DLAgas. The upper limits on in situ star formation reduce the predictedmetallicities at z~3 to be significantly lower than observed, and reduce theheat input in the gas to be substantially lower than the inferred coolingrates. In contrast, the radiative output from compact Lyman Break Galaxies(LBGs) with R<27 is sufficient to balance the comoving cooling rate.