Multiwavelength observations of short time-scale variability in NGC   4151. IV. Analysis of multiwavelength continuum variability
  This paper combines data from the three preceding papers in order to analyze the multi-waveband variability and spectral energy distribution of the Seyfert~1 galaxy NGC~4151 during the December 1993 monitoring campaign. The source, which was near its peak historical brightness, showed strong, correlated variability at X-ray, ultraviolet, and optical wavelengths. The strongest variations were seen in medium energy ($\sim$1.5~keV) X-rays, with a normalized variability amplitude (NVA) of 24\%. Weaker (NVA = 6\%) variations (uncorrelated with those at lower energies) were seen at soft $\gamma$-ray energies of $\sim$100~keV. No significant variability was seen in softer (0.1--1~keV) X-ray bands. In the ultraviolet/optical regime, the NVA decreased from 9\% to 1\% as the wavelength increased from 1275~\AA\ to 6900~\AA. These data do not probe extreme ultraviolet (1200~\AA\ to 0.1~keV) or hard X-ray (2--50~keV) variability. The phase differences between variations in different bands were consistent with zero lag, with upper limits of $\ls$0.15~day between 1275~\AA\ and the other ultraviolet bands, $\ls$0.3~day between 1275~\AA\ and 1.5~keV, and $\ls$1~day between 1275~\AA\ and 5125~\AA. These tight limits represent more than an order of magnitude improvement over those determined in previous multi-waveband AGN monitoring campaigns. The ultraviolet fluctuation power spectra showed no evidence for periodicity, but were instead well-fitted with a very steep, red power-law ($ a = -2.5 $).   If photons emitted at a ``primary" waveband are absorbed by nearby material and ``reprocessed" to produce emission at a secondary waveband, causality arguments require that variations in the secondary band follow those in the primary band. The tight interband correlation and limits on the ultraviolet and 
R. A. Edelson et al