  A randomly chosen star in today's Universe is most likely to live in a galaxy
with a stellar mass between that of the Milky Way and Andromeda. Yet it remains
uncertain how the structural evolution of these bulge-disk systems proceeded.
Most of the unobscured star formation we observe building Andromdeda
progenitors at 0.7<z<1.5 occurs in disks, but >90% of their star formation is
reprocessed by dust and remains unaccounted for. Here we map 500micron dust
continuum emission in an Andromeda progenitor at z=1.25 to probe where it is
growing through dust-obscured star formation. Combining resolved dust
measurements from the NOEMA interferometer with Hubble Space Telescope Halpha
maps and multicolor imaging (including new UV data from the HDUV survey), we
find a bulge growing by dust-obscured star formation: while the unobscured star
formation is centrally suppressed, the dust continuum is centrally
concentrated, filling in the ring-like structures evident in the Halpha and UV
emission. Reflecting this, the dust emission is more compact than the
optical/UV tracers of star formation with r_e(dust)=3.4kpc,
r_e(Halpha)/r_e(dust)=1.4, and r_e(UV)/r_e(dust)=1.8. Crucially, however, the
bulge and disk of this galaxy are building simultaneously; although the dust
emission is more compact than the rest-optical emission
(r_e(optical)/r_e(dust)=1.4), it is somewhat less compact than the stellar mass
(r_e(M_*)/r_e(dust)=0.9). Taking the 500micron emission as a tracer of star
formation, the expected structural evolution of this galaxy can be accounted
for by star formation: it will grow in size by Delta(r_e)/Delta(M_*)~0.3 and
central surface density by Delta(Sigma_cen)/Delta(M_*)~0.9. Finally, our
observations are consistent with a picture in which merging and disk
instabilities drive gas to the center of galaxies, boosting global star
formation rates above the main sequence and building bulges.
