We analyze the redshift- and luminosity-dependent sizes of dropout galaxy candidates in the redshift range z \sim 7 - 12 using deep images from the 2012 Hubble Ultra Deep Field ( UDF12 ) campaign , data which offers two distinct advantages over that used in earlier work .
Firstly , we utilize the increased signal-to-noise ratio offered by the UDF12 imaging to provide improved size measurements for known galaxies at z \simeq 6.5 - 8 in the HUDF .
Specifically , we stack the new deep F140W image with the existing F125W data in order to provide improved measurements of the half-light radii of z ^ { \prime } -band dropouts ( at z \simeq 7 ) .
Similarly we stack this image with the new deep UDF12 F160W image to obtain new size measurements for a sample of Y -band dropouts ( at z \simeq 8 ) .
Secondly , because the UDF12 data have allowed the construction of the first robust galaxy sample in the HUDF at z > 8 , we have been able to extend the measurement of average galaxy size out to significantly higher redshifts .
Restricting our size measurements to sources which are now detected at > 15 \sigma , we confirm earlier indications that the average half-light radii of z \sim 7 - 12 galaxies are extremely small , 0.3 - 0.4 kpc , comparable to the sizes of giant molecular associations in local star-forming galaxies .
We also confirm that there is a clear trend of decreasing half-light radius with increasing redshift , and provide the first evidence that this trend continues beyond z \simeq 8 .
Modeling the evolution of the average half-light radius as a power-law , \propto ( 1 + z ) ^ { s } , we obtain a best-fit index of s = -1.28 \pm 0.13 over the redshift range z \sim 4 - 12 , mid-way between the physically expected evolution for baryons embedded in dark halos of constant mass ( s = -1 ) and constant velocity ( s = -1.5 ) .
A clear size-luminosity relation , such as that found at lower redshift , is also evident in both our z - and Y -dropout sample .
This relation can be interpreted in terms of a constant surface density of star formation over a range in luminosity of 0.05 - 1.0 L ^ { \ast } _ { z = 3 } .
Our results also strengthen previous claims that the star-formation surface density in dropout galaxies is broadly unchanged from z \simeq 4 to z \simeq 8 at \Sigma _ { SFR } \simeq 2 { M } _ { \odot } { yr } ^ { -1 } { kpc } ^ { -2 } .
This value is 2 - 3 orders of magnitude lower than that found in extreme starburst galaxies , but is very comparable to that seen today in the centers of normal disk galaxies .
This provides further support for a steady smooth build-up of the stellar populations in galaxies in the young universe .