Ultraviolet Flux Decrease Under a Grand Minimum from IUE Short Wavelength Observation of Solar Analogs

We have identified a sample of 33 Sun-like stars observed by the {\it International Ultraviolet Explorer (IUE)} with the short wavelength (SW) spectrographs that have ground-based detections of chromospheric Ca\,II H+K activity. Our objective is to determine if these observations can provide an estimate of the decrease in ultraviolet (UV) surface flux associated with a transition from a normal stellar cycle to a grand minimum state. The activity detections, corrected to solar metallicity, span the range $-$5.16 $<$ log $R'$$_{HK}$ $<$ $-$4.26, and eight stars have log $R'$$_{HK}$ $<$ $-$5.00. The {\it IUE}-observed flux spectra are integrated over the wavelength range 1250$-$1910 \AA , transformed to surface fluxes, and then normalized to solar B $-$ V. These normalized surface fluxes show a strong linear relationship with activity $R'$$_{HK}$ ($R^2$ $=$ 0.857 after three outliers are omitted). From this linear regression we estimate a range in UV flux of 9.3\% over solar cycle 22, and a reduction of 6.9\% below solar cycle minimum under a grand minimum. The 95\% confidence interval in this grand minimum estimate is 5.5\%$-$8.4\%. An alternative estimate is provided by the {\it IUE} observations of $\tau$\,Cet (HD\,10700), a star having strong evidence of being in a grand-minimum state, and this star's normalized surface flux is 23.0$\pm$5.7\% lower than solar cycle minimum.