What controls the UV-to-X-ray continuum shape in quasars?

We present an investigation of the interdependence of the optical-to-X-ray spectral slope (α_ox), the He II equivalent-width (EW), and the monochromatic luminosity at 2500 Å (L₂₅₀₀). The values of α_ox and He II EW are indicators of the strength/shape of the quasar ionizing continuum, from the ultraviolet (UV; 1500-2500 Å), through the extreme ultraviolet (EUV; 300-50 Å), to the X-ray (2 keV) regime. For this investigation, we measure the He II EW of 206 radioquiet quasars devoid of broad absorption lines that have high-quality spectral observations of the UV and 2 keV X-rays. The sample spans wide redshift (≈0.13-3.5) and luminosity (log(L₂₅₀₀) ≈ 29.2-32.5 erg s^-1 Hz^-1) ranges. We recover the well-known α_ox-L₂₅₀₀ and He II EW-L₂₅₀₀ anticorrelations, and we find a similarly strong correlation between α_ox and He II EW, and thus the overall spectral shape from the UV, through the EUV, to the X-ray regime is largely set by luminosity. A significant α_ox- He II EW correlation remains after removing the contribution of L₂₅₀₀ from each quantity, and thus the emission in the EUV and the X-rays are also directly tied. This set of relations is surprising, since the UV, EUV, and X-ray emission are expected to be formed in three physically distinct regions. Our results indicate the presence of a redshift-independent physical mechanism that couples the continuum emission from these three different regions, and thus controls the overall continuum shape from the UV to the X-ray regime.