  An important property of star-forming galaxies at z~1-2 is the high local
star-formation intensities they maintain over tens of kiloparsecs at levels
that are only observed in the nearby Universe in the most powerful nuclear
starbursts. To investigate how these high star-formation intensities affect the
warm ionized medium, we present an analysis of the average spectra of about 50
such galaxies at z~1.2-2.6 and of subsamples selected according to their local
and global star-formation intensity. Stacking allows us to probe relatively
weak lines like [SII]\lambda \lambda 6716,6731 and [OI]\lambda 6300, which are
tracers of the conditions of the ISM and are undetectable in most individual
targets. We find higher gas densities (hence pressures) in intensely
star-forming regions compared to fainter diffuse gas and, overall, values that
are comparable to starburst regions and the diffuse ISM in nearby galaxies. By
modeling the H\alpha\ surface brightnesses and [SII]/H\alpha\ line ratios with
the Cloudy photoionization code, we find that our galaxies continue trends
observed in local galaxies, where gas pressures scale with star-formation
intensity. We discuss these results in the context of models of self-regulated
star formation, where star formation determines the average thermal and
turbulent pressure in the ISM, which in turn determines the rate at which stars
can form, finding good agreement with our data. We also confirm the detection
of broad, faint lines underlying H\alpha\ and [NII], which have previously been
considered evidence of either outflows or active galactic nuclei. Finding that
the broad component is only significantly detected in stacks with the highest
average local and global star-formation intensities strongly supports the
outflow interpretation, and further emphasizes the importance of star-formation
feedback and self-regulation in the early Universe.
