  We have measured electron-ion recombination for Fe$^{9+}$ forming Fe$^{8+}$
and for Fe$^{10+}$ forming Fe$^{9+}$ using merged beams at the TSR heavy-ion
storage-ring in Heidelberg. The measured merged beams recombination rate
coefficients (MBRRC) for relative energies from 0 to 75 eV are presented,
covering all dielectronic recombination (DR) resonances associated with 3s->3p
and 3p->3d core transitions in the spectroscopic species Fe X and Fe XI,
respectively. We compare our experimental results to multi-configuration
Breit-Pauli (MCBP) calculations and find significant differences. From the
measured MBRRC we have extracted the DR contributions and transform them into
plasma recombination rate coefficients (PRRC) for astrophysical plasmas with
temperatures from 10^2 to 10^7 K. This spans across the regimes where each ion
forms in photoionized or in collisionally ionized plasmas. For both temperature
regimes the experimental uncertainties are 25% at a 90% confidence level. The
formerly recommended DR data severely underestimated the rate coefficient at
temperatures relevant for photoionized gas. At the temperatures relevant for
photoionized gas, we find agreement between our experimental results and MCBP
theory. At the higher temperatures relevant for collisionally ionized gas, the
MCBP calculations yield a Fe XI DR rate coefficent which is significantly
larger than the experimentally derived one. We present parameterized fits to
our experimentally derived DR PRRC.
