  DH Tau is a young ($\sim$1 Myr) classical T Tauri star. It is one of the few
young PMS stars known to be associated with a planetary mass companion, DH Tau
b, orbiting at large separation and detected by direct imaging. DH Tau b is
thought to be accreting based on copious H${\alpha}$ emission and exhibits
variable Paschen Beta emission. NOEMA observations at 230 GHz allow us to place
constraints on the disk dust mass for both DH Tau b and the primary in a regime
where the disks will appear optically thin. We estimate a disk dust mass for
the primary, DH Tau A of $17.2\pm1.7\,M_{\oplus}$, which gives a disk-to-star
mass ratio of 0.014 (assuming the usual Gas-to-Dust mass ratio of 100 in the
disk). We find a conservative disk dust mass upper limit of 0.42$M_{\oplus}$
for DH Tau b, assuming that the disk temperature is dominated by irradiation
from DH Tau b itself. Given the environment of the circumplanetary disk,
variable illumination from the primary or the equilibrium temperature of the
surrounding cloud would lead to even lower disk mass estimates. A MCFOST
radiative transfer model including heating of the circumplanetary disk by DH
Tau b and DH Tau A suggests that a mass averaged disk temperature of 22 K is
more realistic, resulting in a dust disk mass upper limit of 0.09$M_{\oplus}$
for DH Tau b. We place DH Tau b in context with similar objects and discuss the
consequences for planet formation models.
