We place direct observational constraints on the black-hole masses ( M _ { BH } ) of the cosmologically important z \approx 2 submillimeter-emitting galaxy ( SMG ; f _ { 850 { \mu } m } \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 4 mJy ) population , and use measured host-galaxy masses to explore their evolutionary status .
We employ the well-established virial black-hole mass estimator to “ weigh ” the black holes of a sample of z \approx 2 SMGs which exhibit broad H \alpha or H \beta emission .
We find that the average black-hole mass and Eddington ratio ( \eta = L _ { bol } / L _ { Edd } ) of the lower-luminosity broad-line SMGs ( L _ { X } \approx 10 ^ { 44 } erg s ^ { -1 } ) are log ( M _ { BH } / M _ { \odot } ) \approx 8.0 and \eta \approx 0.2 , respectively ; by comparison , X-ray luminous broad-line SMGs ( L _ { X } \approx 10 ^ { 45 } erg s ^ { -1 } ) have log ( M _ { BH } / M _ { \odot } ) \approx 8.4 and \eta \approx 0.6 .
The lower-luminosity broad-line SMGs lie in the same location of the L _ { X } – L _ { FIR } plane as more typical SMGs hosting X-ray obscured active galactic nuclei and may be intrinsically similar systems , but orientated so that the rest-frame optical nucleus is visible .
Under this hypothesis , we conclude that SMGs host black holes with log ( M _ { BH } / M _ { \odot } ) \approx 7.8 ; we find supporting evidence from observations of local ultra-luminous infrared galaxies .
Combining these black-hole mass constraints with measured host-galaxy masses , we find that the black holes in SMGs are \buildrel > \over { \sim } 3 times smaller than those found in comparably massive normal galaxies in the local Universe , albeit with considerable uncertainty , and \buildrel > \over { \sim } 10 times smaller than those predicted for z \approx 2 luminous quasars and radio galaxies .
These results imply that the growth of the black hole lags that of the host galaxy in SMGs , in stark contrast with that previously suggested for radio galaxies and luminous quasars at z \approx 2 .
On the basis of current host-galaxy mass constraints , we show that SMGs and their descendants can not lie significantly above the locally defined M _ { BH } – M _ { GAL } relationship .
We argue that the black holes in the z \approx 0 descendents of SMGs will have log ( M _ { BH } / M _ { \odot } ) \approx 8.6 , indicating that they only need to grow by a factor of \approx 6 by the present day .
We show that this amount of black-hole growth can be achieved within current estimates for the submm-bright lifetime of SMGs , provided that the black holes can grow at rates close to the Eddington limit .