  A search for new particles that decay into top quark pairs is reported. The
search is performed with the ATLAS experiment at the LHC using an integrated
luminosity of 20.3 fb$^{-1}$ of proton-proton collision data collected at a
centre-of-mass energy of $\sqrt{s}=8$ TeV. The lepton-plus-jets final state is
used, where the top pair decays to $W^+bW^-\bar{b}$, with one $W$ boson
decaying leptonically and the other hadronically. The invariant mass spectrum
of top quark pairs is examined for local excesses or deficits that are
inconsistent with the Standard Model predictions. No evidence for a top quark
pair resonance is found, and 95% confidence-level limits on the production rate
are determined for massive states in benchmark models. The upper limits on the
cross-section times branching ratio of a narrow $Z'$ boson decaying to top
pairs range from 4.2 pb to 0.03 pb for resonance masses from 0.4 TeV to 3.0
TeV. A narrow leptophobic topcolour $Z'$ boson with mass below 1.8 TeV is
excluded. Upper limits are set on the cross-section times branching ratio for a
broad colour-octet resonance with $\Gamma/m =$ 15% decaying to $t\bar{t}$.
These range from 2.5 pb to 0.03 pb for masses from 0.4 TeV to 3.0 TeV. A
Kaluza-Klein excitation of the gluon in a Randall-Sundrum model is excluded for
masses below 2.2 TeV.
