Table 1.
Accuracy of approximations to 3D density and mass profiles.
| rms | rms | |
|---|---|---|
| Author |  |
 |
| Prugniel & Simien (1997) | 0.1052 | 0.1187 |
| Lima Neto et al. (1999) | 0.0905 | 0.1021 |
| Simonneau & Prada (2004) (n > 1) | 0.0238 | 0.0098 |
| Trujillo et al. (2002) | 0.1496 | – |
| Emsellem & van de Ven (2008) | 0.0382 | – |
| New | 0.0005 | 0.0007 |
| Hybrid-1 (optimized for ncut) | 0.0004 | 0.0005 |
| Hybrid-2 (optimized for rcut) | 0.0004 | 0.0005 |
Notes. The rms accuracies are computed over the full range of radii −3 ≤ log(r/Re) ≤ 3 (100 steps) and 0.5 ≤ n ≤ 10 (50 steps), except for the SP formula, which does not allow n ≤ 1, and also avoiding the domain where ρ(r) < 10−30 ρ(Re). Trujillo et al. (2002) and EV do not provide analytical mass profiles. The lower two rows display hybrid models, both with our new approximation 
for n < 3.4 and 
for n ≥ 3.4. The first hybrid model has a mass profile 
for n < 3 and 
for n ≥ 3, while in hybrid model 2, the mass profile is 
for r < Re and 
for r ≥ Re. The values in bold highlight the accuracies with our approximations.
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