The physical and chemical structure of Sagittarius B2 II. Continuum millimeter emission of Sgr B2(M) and Sgr B2(N) with ALMA

Context. The two hot molecular cores Sgr B2(M) and Sgr B2(N), which are located at the center of the giant molecular cloud complex Sagittarius B2, have been the targets of numerous spectral line surveys, revealing a rich and complex chemistry. Aims. We seek to characterize the physical and chemical structure of the two high-mass star-forming sites Sgr B2(M) and Sgr B2(N) using high-angular resolution observations at millimeter wavelengths, reaching spatial scales of about 4000 au. Methods. We used the Atacama Large Millimeter/submillimeter Array (ALMA) to perform an unbiased spectral line survey of both regions in the ALMA band 6 with a frequency coverage from 211 GHz to 275 GHz. The achieved angular resolution is 0".4, which probes spatial scales of about 4000 au, i.e., able to resolve different cores and fragments. In order to determine the continuum emission in these line-rich sources, we used a new statistical method, STATCONT, which has been applied successfully to this and other ALMA datasets and to synthetic observations. Results. We detect 27 continuum sources in Sgr B2(M) and 20 sources in Sgr B2(N). We study the continuum emission variation across the ALMA band 6 (i.e., spectral index) and compare the ALMA 1.3 mm continuum emission with previous SMA 345 GHz and VLA 40 GHz observations to study the nature of the sources detected. The brightest sources are dominated by (partially optically thick) dust emission, while there is an important degree of contamination from ionized gas free-free emission in weaker sources. While the total mass in Sgr B2(M) is distributed in many fragments, most of the mass in Sgr B2(N) arises from a single object, with filamentary-like structures converging toward the center. There seems to be a lack of low-mass dense cores in both regions. We determine H-2 volume densities for the cores of about 10(7)-10(9) cm(-3) (or 10(5)-10(7) M-circle dot pc(-3)), i.e., one to two orders of magnitude higher than the stellar densities of super star clusters. We perform a statistical study of the chemical content of the identified sources. In general, Sgr B2(N) is chemically richer than Sgr B2(M). The chemically richest sources have about 100 lines per GHz and the fraction of luminosity contained in spectral lines at millimeter wavelengths with respect to the total luminosity is about 20%-40%. There seems to be a correlation between the chemical richness and the mass of the fragments, where more massive clumps are more chemically rich. Both Sgr B2(N) and Sgr B2(M) harbor a cluster of hot molecular cores. We compare the continuum images with predictions from a detailed 3D radiative transfer model that reproduces the structure of Sgr B2 from 45 pc down to 100 au. Conclusions. This ALMA dataset, together with other ongoing observational projects in the range 5 GHz to 200 GHz, better constrain the 3D structure of Sgr B2 and allow us to understand its physical and chemical structure.