3.1. Reverberation Mapping Assumptions
There are a number of simplifying assumptions that we can
- The continuum originates in a single central source.
The size of an accretion disk around a supermassive
hole is of the order of
1013-14 cm. A typical size for the BLR in the
same system would be of order a few light days,
i.e., ~ 1016 cm. Note that it is specifically
not required that the continuum source emits radiation
isotropically, though this is a useful starting point.
The "point-source" assumption greatly simplifies
the reverberation process. However, we should mention
that the point-source assumption is probably not applicable to
X-ray reverberation, as the Fe
K emission and
the hard X-rays that drive this line probably arise in
regions that are of similar size, and perhaps co-spatial
- Light-travel time is the most important time scale.
We assume specifically that emission-line clouds respond
instantaneously to changes in the continuum flux. The time scale
to re-establish photoionization equilibrium is the
The time it takes a Lyman
photon to diffuse outward from
the Strömgren depth is about 20 times the direct light-travel time
We also need to carry out our reverberation-mapping experiment
on a time scale short enough that the structure of the BLR
can be assumed to be stable. The dynamical, or cloud-crossing, time
scale for the BLR is typically
where VFWHM is the Doppler width of the broad line for
which the response time =
r/c has been measured.
Any reverberation-mapping experiment has to be short relative
to the crossing time or the structural information might be
washed out by cloud motions.
- There is a simple, though not necessarily linear, relationship
between the observed continuum and the ionizing continuum.