(Abridged) XTE J1810-197 and 1E 1547.0-5408 are two transient AXPs exhibiting
radio emission with unusual properties. In addition, their spin down rates
during outburst show opposite trends, which so far has no explanation. Here, we
extend our quark-nova model for AXPs to include transient AXPs, in which the
outbursts are caused by transient accretion events from a Keplerian (iron-rich)
degenerate ring. For a ring with inner and outer radii of 23.5 km and 26.5 km,
respectively, our model gives a good fit to the observed X-ray outburst from
XTE J1810-197 and the behavior of temperature, luminosity, and area of the two
X-ray blackbodies with time. The two blackbodies in our model are related to a
heat front (i.e. Bohm diffusion front) propagating along the ring's surface and
an accretion hot spot on the quark star surface. Radio pulsations in our model
are caused by dissipation at the light cylinder of magnetic bubbles, produced
near the ring during the X-ray outburst. The delay between X-ray peak emission
and radio emission in our model is related to the propagation time of these
bubbles to the light cylinder. We predict a ~1 year and ~1 month delay for XTE
J1810-197 and 1E 1547.0-5408, respectively. The observed flat spectrum, erratic
pulse profile, and the pulse duration are all explained in our model as a
result of X-point reconnection events induced by the dissipation of the bubbles
at the light cylinder. The spin down rate of the central quark star can either
increase or decrease depending on how the radial drift velocity of the magnetic
islands changes with distance from the central star. We suggest an evolutionary
connection between transient AXPs and typical AXPs in our model.Comment: 16 journal pages, 4 figures and 1 table [Version accepted for
publication in A&A