Does Lyman continuum escape fraction correlate with spectral hardness?
  The properties that govern the production and escape of hydrogen ionizing
photons (Lyman continuum; LyC with energies >13.6 eV) in star-forming galaxies
are still poorly understood, but they are key to identifying and characterizing
the sources that reionized the Universe. Here we empirically explore the
relationship between the hardness of ionizing radiation and the LyC leakage in
a large sample of low-$z$ star-forming galaxies from the recent HST Low-$z$
Lyman Continuum Survey. Using SDSS stacks and deep XShooter observations, we
investigate the hardness of the ionizing spectra ($Q_{\rm He^+}/Q_{\rm H}$)
between 54.4 eV (He$^{+}$) and 13.6 eV (H) from the optical recombination lines
HeII 4686A and H$\beta$ 4861A for galaxies with LyC escape fractions spanning a
wide range, $f_{\rm esc} \rm (LyC) \simeq 0 - 90\%$. We find that the observed
intensity of HeII/H$\beta$ is primarily driven by variations in the
metallicity, but is not correlated with LyC leakage. Both very strong ($<f_{\rm
esc} \rm (LyC)> \simeq 0.5$) and non-leakers ($ < f_{\rm esc} \rm (LyC) >
\simeq 0$) present similar observed intensities of HeII/H$\beta$ at comparable
metallicity, between $\simeq 0.01$ and $\simeq 0.02$ for $12 + \log({\rm O/H})
> 8.0$ and $<8.0$, respectively. Our results demonstrate that $Q_{\rm
He^+}/Q_{\rm H}$ does not correlate with $f_{\rm esc} \rm (LyC)$, which implies
that strong LyC emitters do not show harder ionizing spectra than non-leakers
at similar metallicity.
