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In X-ray observations, estimation of the particle-induced background isimportant especially for faint and/or diffuse sources. Although software existsto generate total (sky and detector) background data suitable for a givenChandra ACIS observation, no public software exists to model theparticle-induced background separately. We aim to understand the spatial andtemporal variations of the particle-induced background of Chandra ACIS obtainedin the two data modes, VFAINT and FAINT. Observations performed with ACIS inthe stowed position shielded from the sky and the Chandra Deep Field South datasets are used. The spectra are modeled with a combination of the instrumentallines of Al, Si, Ni, and Au and continuum components. Similar spatialvariations of the spectral shape are found in VFAINT and FAINT data, which aremainly due to inappropriate correction of charge transfer inefficiency forevents that convert in the frame-store regions as explained by Bartalucci etal. 2014. Temporal variation of the spectral hardness ratio is found to be$\sim 10\%$ at maximum, which seems to be largely due to solar activity. Wemodel this variation by modifying the spectral hardnesses according to thetotal count rate. Incorporating these properties, we have developed a tool``mkacispback'' to generate the particle-induced background spectral modelcorresponding to an arbitrary celestial observation. As an example application,we use the background spectrum produced by the mkacispback tool in an analysisof the Cosmic X-ray Background in the CDF-S observations. We find an intensityof 3.10 (2.98--$3.21)\times 10^{-12}$ erg s$^{-1}$ cm$^{-2}$ deg$^{-2}$ in the2--8 keV band, consistent with or lower than previous estimates. The toolmkacispback is available at https://github.com/hiromasasuzuki/mkacispback.

Spatial and Temporal Variations of the Chandra ACIS Particle-Induced Background and Development of a Spectral-Model Generation Tool