Nature of the Galactic centre NIR-excess sources - I. What can we learn from the continuum observations of the DSO/G2 source?

Context. The Dusty S-cluster Object (DSO/G2) orbiting the supermassive black hole (Sgr A*) in the Galactic centre has been monitored in both near-infrared continuum and line emission. There has been a dispute about the character and the compactness of the object: it being interpreted as either a gas cloud or a dust-enshrouded star. A recent analysis of polarimetry data in K-s-band (2.2 mu m) allows us to put further constraints on the geometry of the DSO. Aims. The purpose of this paper is to constrain the nature and the geometry of the DSO. Methods. We compared 3D radiative transfer models of the DSO with the near-infrared (NIR) continuum data including polarimetry. In the analysis, we used basic dust continuum radiative transfer theory implemented in the 3D Monte Carlo code Hyperion. Moreover, we implemented analytical results of the two-body problem mechanics and the theory of non-thermal processes. Results. We present a composite model of the DSO - a dust-enshrouded star that consists of a stellar source, dusty, optically thick envelope, bipolar cavities, and a bow shock. This scheme can match the NIR total as well as polarized properties of the observed spectral energy distribution (SED). The SED may be also explained in theory by a young pulsar wind nebula that typically exhibits a large linear polarization degree due to magnetospheric synchrotron emission. Conclusions. The analysis of NIR polarimetry data combined with the radiative transfer modelling shows that the DSO is a peculiar source of compact nature in the S cluster (r less than or similar to 0.04 pc). It is most probably a young stellar object embedded in a non-spherical dusty envelope, whose components include optically thick dusty envelope, bipolar cavities, and a bow shock. Alternatively, the continuum emission could be of a non-thermal origin due to the presence of a young neutron star and its wind nebula. Although there has been so far no detection of X-ray and radio counterparts of the DSO, the analysis of the neutron star model shows that young, energetic neutron stars similar to the Crab pulsar could in principle be detected in the S cluster with current NIR facilities and they appear as apparent reddened, near-infrared-excess sources. The searches for pulsars in the NIR bands can thus complement standard radio searches, which can put further constraints on the unexplored pulsar population in the Galactic centre. Both thermal and non-thermal models are in accordance with the observed compactness, total as well polarized continuum emission of the DSO.