Context. Small-scale bright features in the photosphere of the Sun, such as faculae or G-band bright points, appear in connection with small-scale magnetic flux concentrations. Aims. Here we report on a new class of photospheric bright points that are free of magnetic fields. So far, these are visible in numerical simulations only. We explore conditions required for their observational detection. Methods. Numerical radiation (magneto-)hydrodynamic simulations of the near-surface layers of the Sun were carried out. The magnetic field-free simulations show tiny bright points, reminiscent of magnetic bright points, only smaller. A simple toy model for these non-magnetic bright points (nMBPs) was established that serves as a base for the development of an algorithm for their automatic detection. Basic physical properties of 357 detected nMBPs were extracted and statistically evaluated. We produced synthetic intensity maps that mimic observations with various solar telescopes to obtain hints on their detectability. Results. The nMBPs of the simulations show a mean bolometric intensity contrast with respect to their intergranular surroundings of approximately 20%, a size of 60-80 km, and the isosurface of optical depth unity is at their location depressed by 80-100 km. They are caused by swirling downdrafts that provide, by means of the centripetal force, the necessary pressure gradient for the formation of a funnel of reduced mass density that reaches from the subsurface layers into the photosphere. Similar, frequently occurring funnels that do not reach into the photosphere, do not produce bright points. Conclusions. Non-magnetic bright points are the observable manifestation of vertically extending vortices (vortex tubes) in the photosphere. The resolving power of 4-m-class telescopes, such as the DKIST, is needed for an unambiguous detection of them.
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