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Table A.1.

Numerical values for a number of important properties of the Sérsic models, as a function of the Sérsic index m.

m b bm I0 ν0 Ψ0 σ0 σp, 0
0.0 0.0 0.7071067812 0.1591549431 0.03582244802 0.9003163162 0.6709382670 0.4882770668
0.1 0.02074633919 0.6787254708 0.1597040458 0.03687117924 0.8954110224 0.6467405417 0.4745932365
0.2 0.1450781416 0.6797048938 0.1657441274 0.04174912260 0.8955714657 0.6052798406 0.4549379359
0.3 0.3157020170 0.7075924771 0.1783670066 0.05214840909 0.9049229140 0.5576761459 0.4365182562
0.4 0.5013512264 0.7586768505 0.1967139352 0.07074452800 0.9202187043 0.5054510861 0.4198025544
0.5 0.6931471806 0.8325546112 0.2206356002 0.1036366539 0.9394372787 0.4490044158 0.4046143026
0.6 0.8879362135 0.9311701833 0.2504981367 0.1646935035 0.9614737847 0.3883701725 0.3907268693
0.7 1.084371511 1.058338681 0.2870242952 0.2892627286 0.9857010672 0.3231072572 0.3779411016
0.8 1.281796137 1.219706019 0.3312367088 0.5903862892 1.011747061 0.2516350723 0.3660931503
0.9 1.479856427 1.422976161 0.3844538418 1.656657118 1.039383734 0.1684024227 0.3550500768
1.0 1.678346990 1.678346990 0.4483153816 ∞ 1.068468879 0.0 0.3447039338
1.5 2.674060314 4.372771642 1.014407550 ∞ 1.233536106 0.0 0.3008238298
2.0 3.672060749 13.48403014 2.411450297 ∞ 1.430700033 0.0 0.2658868180
2.5 4.670908883 47.15236589 5.897607399 ∞ 1.662679605 0.0 0.2367684306
3.0 5.670161189 182.2998096 14.69230924 ∞ 1.934261054 0.0 0.2118423541
3.5 6.669637075 766.2274547 37.07959732 ∞ 2.251549732 0.0 0.1901483907
4.0 7.669249443 3459.485015 94.48274697 ∞ 2.621876860 0.0 0.1710622608
4.5 8.668951184 16628.36345 242.5415290 ∞ 3.053889794 0.0 0.1541466369
5.0 9.668714615 84497.47049 626.2886060 ∞ 3.557722251 0.0 0.1390769232

Notes. The different columns correspond to the scaling parameter b, the ratio bm = Re/h, the central surface brightness I0, the central luminosity density ν0, the central value of the gravitational potential Ψ0, the central velocity dispersion σ0, and the central projected velocity dispersion σp, 0. All quantities are given in dimensionless units, or equivalently, for a model with Re = L = M = 1.

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