tokens: one typically utilizes higher resolution grid elements in regions of higher stellar volume emissivity and dust density. Although reasonable to expect a more rapid variation of the radiation field in those regions, there is no guarantee that the spatial resolution is adequate everywhere on the grid. In the absence of iterative procedures to increase the spatial resolution during the RT calculation, the effect of the grid discretization on the numerical accuracy can only be checked by repeating the calculations at progressively higher spatial resolutions. Similarly, the finite number of angular directions of the rays that are cast from each radiation source, as well as the discretization of the scattering source function, also affect the calculation accuracy. Apart from these factors, common to all 3D dust RT codes although in different forms 6 , in DART-Ray the numerical accuracy is also affected by the estimate of the extent of the source influence volumes. This is because DART-Ray calculates the RFED contributions from each source only within this volume surrounding the source itself, thus neglecting the contributions outside it. Since this is a core characteristic of DART-Ray, we are interested in quantifying the accuracy error due to the cut off of the rays when they reach the boundary of the estimated source influence volume. We note that this accuracy error is systematic, since it will always produce RFEDs which are underestimated compared to the correct value. The ray cut off occurs when the RFED contribution carried by a ray satisfy the criterion 1 . So, once a lower limit to the RFED distribution has been estimated, the input-defined parameter is the key factor affecting the numerical accuracy of the calculation. In N14, we stated that should be low enough to preserve energy balance, in the sense that, at the end of the calculation, the total radiation luminosity that has been neglected because of the ray cut-off should be only a small fraction of the total luminosity of the model. In this case, the effect of cutting the rays is minimal because almost all the radiation luminosity has been followed in its propagation throughout the model. However, since this energy balance can only be checked at the end of the RT run, potentially several attempts had to be made to find the appropriate value for . Instead, in the following, we show how the value of the parameter can be set before an RT run such to guarantee the desired level of accuracy. We have been able to find a relation between and the accuracy of the derived RFED distribution by making a minor change in the definition of in formula 1 , compared to NA14. This is now defined as: where is the average specific intensity of the ray within the ray-cell intersection path, is the area of the emitting cell originating the ray, is the solid angle subtended by the intersected cell, is the linear size of the intersected cell, its volume and the light speed. This formula differs only slightly
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