Table 3
Model quantities and results of mantle concentrations and heat output of radionuclides in a putative α-Cen-Earth.
Constraint | Value | Reference | |
---|---|---|---|
[Eu/Mg] (a) | − 0.152 ± 0.047 | This work & M18 | |
[Th/Eu] (b) | 0.014 ± 0.045 | Botelho et al. (2019) | |
238U/Th | ![]() |
Dauphas (2005) | |
235U/238U(c) | 24.286/75.712 | Lodders et al. (2009) & Frank et al. (2014) | |
MMantle (1024 kg) | 4.0312 ± 0.0179 | Wang et al. (2018) | |
Mantle concentration (ppb) | |||
Nuclide (X) | X/Mg(d) | Upon formation(e) | Present-day(f) |
232Th | ![]() |
![]() |
![]() |
235U | ![]() |
![]() |
0.02 ± 0.01 |
238U | ![]() |
![]() |
![]() |
40K | ... | 353.6 ± 37.3 (g) | 12.7 ± 1.3 (g) |
Heat (TW) | |||
Nuclide (X) | h (W kg−1)(h) | Upon formation(i) | Present-day(i) |
232Th | 2.628 × 10−5 | ![]() |
![]() |
235U | 5.6847 × 10−4 | ![]() |
![]() |
238U | 9.513 × 10−5 | ![]() |
![]() |
40K | 2.847 × 10−5 | 12.7 ± 1.3 | 1.5 ± 0.2 |
Total | ... | ![]() |
![]() |
Notes. (a) [Eu/Mg] (dex) is calculated from [Eu/Fe] – [Mg/Fe], where [Mg/Fe] comes from the weighted average of the results in M18 obtained using the Me14 and Re03 line lists. (b)100% of Th is 232Th. (c) As explained in the text, 235U/238U refers to the Solar System value at the time of its formation (Lodders et al. 2009) based on the limited variance of the ratio within 6–9 Ga into the Galactic history (Frank et al. 2014). (d) X/Mg is a mass ratio. While converting differential values (e.g. [232Th/Mg] = [232Th/Eu] – [Eu/Mg], in dex) into the mass ratios (e.g. 232Th/Mg) in a linear scale, the reference solar abundances come from Asplund et al. (2009) and the atomic and isotopic masses are takent from Wieser et al. (2013) and Audi & Wapstra (1993), respectively. (e) See text.
, where C0 represents the mantle concentration of an individual radionuclide upon the planet formation; X/Mg (α-Cen-Earth) refers to Col. 2 in panel 2 of this table (40K is excluded from this calculation); X/Mg (Earth) refers to Table A.1 (for normalisation purposes, the Mg concentration was kept unchanged over geological time). (f) See text. Ct = C0 × e−t ln 2∕T1∕2, where t represents the system age (the current age of α Cen AB is 6 ± 1 Ga as of M18); T1∕2 are the half-lives of these radionuclides (232Th – 14.0 Ga; 235U – 0.704 Ga; 238U – 4.47 Ga; 40K – 1.25 Ga; Turcotte & Schubert 2002). (g)See text. Concentration of 40K upon planet formation,
, is supplemented by the starting mantle concentration of 40K in the Earth upon its formation, according to the GCE model for cosmochemically Earth-like planets (Frank et al. 2014); the present-day concentration of 40K is calculated based on the radioactive decay process following the equation in footnote (f). (h) h (the rate ofheating per unit mass of a radionuclide) is taken from Dye (2012). (i) Calculated by multiplying the corresponding concentrations (upon planet formation and at the present day) with the heat generation rates, h, of individual radionuclides.
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