An accurate and simple asymptotically matched deprojection of the Sérsic law

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Volume 694 (February 2025)

A&A, 694 (2025) A118

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Table 1.

Maximum relative errors.

n	ℰ^max	log s^max	Δμ^max	log η^max
(1)	(2)	(3)	(4)	(5)
1.5	0.089	−2.616	−0.047	−3.778
2.0	0.033	−2.591	−0.024	−3.499
2.5	0.018	−2.789	−0.015	−3.624
3.0	0.012	−3.071	−0.011	−3.911
3.5	0.009	−3.445	−0.009	−4.000
4.0	0.008	−3.854	−0.007	−4.000
4.5	0.007	−4.000	−0.006	−4.000
5.0	0.006	−4.000	−0.005	−4.000
5.5	0.005	−4.000	−0.005	−4.000
6.0	0.004	−4.000	−0.004	−4.000
6.5	0.004	−4.000	−0.003	−4.000
7.0	0.003	−4.000	−0.003	−4.000
7.5	0.003	−4.000	−0.003	−4.000
8.0	0.003	−4.000	−0.003	−4.000
8.5	0.002	−4.000	−0.002	−4.000
9.0	0.002	−4.000	−0.002	−4.000
9.5	0.002	−4.000	−0.002	−4.000
10	0.002	−4.000	−0.002	−4.000

Notes. Column (2): largest relative deviation of ν_a(r) in Eq. (13) compared to the true, numerically deprojected ν(r) in Eq. (18), computed from ℰ(r) in Eq. (17). Column (3): position s^max of the largest deviation ℰ^max. When s^max < 10⁻⁴, the deviation at $s = r / R_{e} = 10^{- 4}$ $s=r/{R_{\rm{e}}}=10^{-4}$ is reported. Column (4): largest surface brightness difference (in magnitudes) between the true Sérsic profile and the projection of ν_a(r), computed from Δμ(R) in Eq. (19). Column (5): position η^max of the largest magnitude difference Δμ^max. When η^max < 10⁻⁴, the magnitude deviation at $η = R / R_{e} = 10^{- 4}$ $\eta=R/{R_{\rm{e}}}= 10^{-4}$ is given.

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