Illustration of radiation and hydrodynamical properties computed by HERACLES for model mdot0p01/rcsm8e14. Top row: Variation in the velocity at multiple epochs versus radius (top left) and versus the distance above the shock (top right). Bottom left: Evolution of the velocity of “mass parcels” initially at radii 0.1, 0.2, 0.35, 0.5, 0.7, 1.0, 1.5, and 3.95 × 10¹⁵ cm (the last radius is near the outer grid boundary) and over the full duration of 15 d of the HERACLES simulation. The solid line shows the value of this velocity as read in directly from the simulation. The dashed line shows the same quantity but estimated through a time integral of the radiative acceleration (see the discussion in Sect. 3.1). In all cases, the two curves agree closely until the mass parcel is shocked, which corresponds to the near-vertical jump of the solid lines. The black circles and the stars indicate the velocity at the location where the electron-scattering optical depth is 2/3 (i.e., the photosphere) and at 0.01. Bottom right: Counterpart of the top-left panel but for the luminosity (i.e., quantity L_r = 4πr²F_r). Only the inner half of the grid is shown.