R(V) parameter of the dust extinction curve: Mapping based on hot stars and connections to diffuse interstellar bands

Favored carriers of the diffuse interstellar bands (DIBs) are carbon-based molecules whose constituents have presumably been expelled by dying stars along with those of interstellar dust grains. Some resemblance has been found between sky maps of the R_ parameter of the extinction curve, governed by grain properties, and those of the 8620 Å (Gaia) DIB abundance relative to extinction density, or DIB strength, but the parallel evolution of DIB carriers and grains and their potential interplay are unknown. Our goal is to compare DIB strengths and R_ values either in 3D space using maps or along lines of sight (LOS) toward the hot stars that serve as the sources of individual R_ measurements and for which DIBs can easily be measured. Independently of the DIBs, these hot stars provide a new partial map of R_ We assembled R_ measurements from the literature for the LOS toward 505 hot stars. We computed a new 3D map of the extinction density, obtained by inverting the recently published catalog of extinction data based on Gaia XP spectra and near-IR photometry. We used this map to locate the opaque areas that cause R_ for each hot-star LOS, and we searched for large spatial scale variations in R_ in this new distribution. We compared recent 3D maps of local and LOS-integrated R_ values with the corresponding local or LOS Gaia DIB strengths, calculated from our 3D maps of the DIB and of extinction density. Using archived spectra, we fitted and measured the 5780, 5797, and 8620 Å DIBs for most of the hot stars with R_ data, combined them with published data for about 90 stars, and then compared the DIB strengths and the R_ values. R_ from early-type stars reveal variations on large spatial scales. This confirms with entirely independent data the already published 3D pattern. Gaia DIB strength maps show variations at large spatial scale similar to those of R_ maps, with the higher abundance of DIB carriers corresponding to higher R_ The LOS-integrated Gaia DIB strengths and R_ based on 3D maps also correlate positively in the R_ range 2.3-3.4, but there is no connection between the Gaia DIB and R_ for higher R_ values. We interpret this absence as due to the disappearance of Gaia DIB carriers in dense clouds containing large grains and with high R_ since for the LOS crossing of such clouds, this anticorrelation produces a counteracting effect. Despite strong averaging effects along the LOS to hot stars, the DIB and R_ comparisons reveal significant differences in R_ relations among the three DIBs, with an evolution from a negative to a positive correlation with R_ from the ζ-type 5797 Å to the σ-type 5780 Å and then 8620 Å DIBs. Various combinations of DIB strengths or DIB ratios allow us to constrain the R_ range. The relation between DIB and R_ seems to depend on the definition of R_ 3D maps show that variations in the environmental conditions on large spatial scale affect the grains and the 8620 Å DIB. The LOS data show that each DIB has its own specific link between its strength and R_ The different signs of correlations can be understood in the frame of the recently found bimodal evolution of R_ with the extinction, with the 8620 (5797) Å DIB carrier disappearance in the decreasing (increasing) phase of R_ The DIB dependence on the R_ definition suggests that the carrier abundance of each DIB depends on a specific wavelength range of the extinction curve.