We investigate the build-up of galaxies at z~1 using maps of Halpha and stellar continuum emission for a sample of 57 galaxies with rest-frame Halpha equivalent widths >100 Angstroms in the 3D-HST grism survey. We find that the Halpha emission broadly follows the rest-frame R-band light but that it is typically somewhat more extended and clumpy. We quantify the spatial distribution with the half-light radius. The median Halpha effective radius r_e(Halpha) is 4.2+-0.1 kpc but the sizes span a large range, from compact objects with r_e(Halpha) ~ 1.0 kpc to extended disks with r_e(Halpha) ~ 15 kpc. Comparing Halpha sizes to continuum sizes, we find <r_e(Halpha)/r_e(R)>=1.3+-0.1 for the full sample. That is, star formation, as traced by Halpha, typically occurs out to larger radii than the rest-frame R-band stellar continuum; galaxies are growing their radii and building up from the inside out. This effect appears to be somewhat more pronounced for the largest galaxies. Using the measured Halpha sizes, we derive star formation rate surface densities. We find that they range from ~0.05 Msun yr^{-1} kpc^{-2} for the largest galaxies to ~5 Msun yr^{-1} kpc^{-2} for the smallest galaxies, implying a large range in physical conditions in rapidly star-forming z~1 galaxies. Finally, we infer that all galaxies in the sample have very high gas mass fractions and stellar mass doubling times < 500 Myr. Although other explanations are also possible, a straightforward interpretation is that we are simultaneously witnessing the rapid formation of compact bulges and large disks at z~1.
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