  Ortho-to-para (o/p) ratios of species like water, ammonia and formaldehyde
(H2CO) are believed to encode information about the formation history of the
molecule. Measurements of o/p ratios in protoplanetary disks could thus be used
to constrain their physical and chemical histories. We present the first
measurement of the H2CO o/p ratio in a protoplanetary disk, using three ortho
and two para lines observed with the Sub-millimeter Array (SMA) combined with
one highly resolved measurement of a single H2CO line with ALMA toward the disk
around Herbig Ae star HD 163296. We find a disk-averaged H2CO o/p ratio of
1.8-2.8 (depending on the assumed disk structure), corresponding to a spin
temperature of 11-22 K. We also derive a rotational temperature of 24 K from
the flux ratio of the three ortho lines. The observed spatial distribution, as
seen by ALMA, as well as the rotational temperature and the o/p ratio, at the
large scales the SMA is most sensitive to, are consistent with a
low-temperature formation pathway, most likely grain surface chemistry, of H2CO
in this disk.
