  The disparity between the density profiles of galactic dark matter haloes
predicted by dark matter only cosmological simulations and those inferred from
rotation curve decomposition, the so-called cusp-core problem, suggests that
baryonic physics has an impact on dark matter density in the central regions of
galaxies. Feedback from black holes, supernovae and massive stars may each play
a role by removing matter from the centre of the galaxy on shorter timescales
than the dynamical time of the dark matter halo. Our goal in this paper is to
determine constraints on such feedback scenarios based on the observed
properties of a set of nearby galaxies.
  Using a Markov Chain Monte Carlo (MCMC) analysis of galactic rotation curves,
via a method developed in a previous paper, we constrain density profiles and
an estimated minimum radius for baryon influence, $r_1$, which we couple with a
feedback model to give an estimate of the fraction of matter within that radius
that must be expelled to produce the presently observed halo profile. We show
that in the case of the gas rich dwarf irregular galaxy DDO 154, an outflow
from a central source (e.g. a black hole or star forming region) could produce
sufficient feedback on the halo without removing the disk gas.
  We examine the rotation curves of 8 galaxies taken from the THINGS data set
and determine constraints on the radial density profiles of their dark matter
haloes. For some of the galaxies, both cored haloes and cosmological $\rho
\propto r^{-1}$ cusps are excluded. These intermediate central slopes require
baryonic feedback to be finely tuned. We also find for galaxies which exhibit
extended cores in their haloes (e.g. NGC 925), the use of a split power-law
halo profile yields models without the unphysical, sharp features seen in
models based on the Einasto profile.
