Common-red-signal analysis with 24-yr high-precision timing of the
  European Pulsar Timing Array: Inferences in the stochastic gravitational-wave
  background search
  We present results from the search for a stochastic gravitational-wave
background (GWB) as predicted by the theory of General Relativity using six
radio millisecond pulsars from the Data Release 2 (DR2) of the European Pulsar
Timing Array (EPTA) covering a timespan up to 24 years. A GWB manifests itself
as a long-term low-frequency stochastic signal common to all pulsars, a common
red signal (CRS), with the characteristic Hellings-Downs (HD) spatial
correlation. Our analysis is performed with two independent pipelines,
\eprise{} and \tn{}+\ftwo{}, which produce consistent results. A search for a
CRS with simultaneous estimation of its spatial correlations yields spectral
properties compatible with theoretical GWB predictions, but does not result in
the required measurement of the HD correlation, as required for GWB detection.
Further Bayesian model comparison between different types of CRSs, including a
GWB, finds the most favoured model to be the common uncorrelated red noise
described by a power-law with $A = 5.13_{-2.73}^{+4.20} \times 10^{-15}$ and
$\gamma = 3.78_{-0.59}^{+0.69}$ (95\% credible regions). Fixing the spectral
index to $\gamma=13/3$ as expected from the GWB by circular, inspiralling
supermassive black-hole binaries results in an amplitude of $A
=2.95_{-0.72}^{+0.89} \times 10^{-15}$. We implement three different models,
BAYESEPHEM, LINIMOSS and EPHEMGP, to address possible Solar-system ephemeris
(SSE) systematics and conclude that our results may only marginally depend on
these effects. This work builds on the methods and models from the studies on
the EPTA DR1. We show that under the same analysis framework the results remain
consistent after the data set extension.
