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Recent HST and IUE observations show ultraviolet (1400\AA) and visible (4000\AA) light from the X-ray burster 4U1820--30 in the core of the globular cluster NGC 6624. The spectrum in the optical and the UV is Rayleigh--Jeans, with $f_\nu $(1400\AA)$\> \approx 2$ mJy. We show that this flux is due to the reprocessing of X-rays incident on an accretion disk around the neutron star, as well as on the low mass, degenerate dwarf companion. Approximately 90\% of the light at 1400\AA\ comes from reprocessing of X-rays in the disk. The disk is small in this ultracompact binary ($P_{\rm orbit} \approx 11$ minutes), with disk radius $\varpi_D = (0.5$--$1) \times 10^{10}$ cm. The small disk size causes the spectrum to be almost Rayleigh--Jeans at wavelengths longer than 1200\AA. The ``standard'' thin disk spectrum $f_\nu \propto \nu^{1/3}$ would not appear until wavelengths shorter than 130\AA.
The lack of X-ray eclipses implies $i < 80^\circ$. The reprocessed light from the star varies at the orbital period, with the orbitally modulated fraction $\approx 7\sin i$ \% of the flux at 1400\AA. Measurement of this modulation would constrain the orbital geometry. The X-ray flux also shows small amplitude quasi-periodic oscillations (QPO) peaking at $f \approx 50$ Hz as well as red noise extending down to a few Hz. If the disk is axisymmetric and reprocesses instantaneously, the Rayleigh--Jeans part of the disk spectrum has a fluctuation power spectrum $P_r (f) = T(ft_D) P_X(f)$, where $P_X (f)$ is the X-ray power spectrum and $t_D = \varpi_D /c$. $T \rightarrow 1/16$ for $f \ll 1/2\pi t_D \sim 2$ Hz, while for $f \gg 1/2\pi t_D$, $T \propto (ft_D)^{-3}$. The red noise in the X-rays might appear in the reprocessed light at the $\sim 0.1$ \% level, while QPO in the reprocessed light should be much weaker. Such reprocessing fluctuations can yield valuable insight into the physics of the disk, especially if the finite reprocessing time in the disk and departures from axisymmetry introduce further features into the transfer function $T(f)$.
