J/A+A/654/A156 Chaotic diffusion of fundamental frequencies (Hoang+, 2021)
Chaotic diffusion of the fundamental frequencies in the Solar System.
Hoang N.H., Mogavero F., Laskar J.
<Astron. Astrophys. 654, A156 (2021)>
=2021A&A...654A.156H 2021A&A...654A.156H (SIMBAD/NED BibCode)
ADC_Keywords: Solar system ; Models
Keywords: chaos - diffusion - celestial mechanics - methods: statistical
Abstract:
The long-term variations of the orbit of the Earth govern the
insolation on its surface and hence its climate. The use of the
astronomical signal, whose imprint has been recovered in the geological
records, has revolutionized the determination of the geological time
scales (e.g. Gradstein & Ogg, 2020, in Geologic Time Scale (Amsterdam:
Elsevier), 21). However, the orbital variations beyond 60Myr cannot be
reliably predicted because of the A,chaotic dynamics of the planetary
orbits in the Solar System (Laskar, 1989Natur.338..237L 1989Natur.338..237L). Taking into
account this dynamical uncertainty is necessary for a complete
astronomical calibration of geological records. Our work addresses
this problem with a statistical analysis on 120000 orbital solutions
of the secular model of the Solar System ranging from 500Myr to 5Gyr.
We obtain the marginal probability density functions of the
fundamental secular frequencies using kernel density estimation. The
uncertainty of the density estimation is also obtained here in the
form of confidence intervals determined by the moving block bootstrap
method. The results of the secular model are shown to be in good
agreement with those of the direct integrations of a comprehensive
model of the Solar System. Applicationof our work is illustrated on
two geological data: the Newark-Hartford
Description:
Density estimations of the fundamental frequencies of the Solar System
of some of their combinations from 100Myr to 5Gyr.
File Summary:
--------------------------------------------------------------------------------
FileName Lrecl Records Explanations
--------------------------------------------------------------------------------
ReadMe 80 . This file
list.dat 82 66 List of files
data/* . 66 Individual files
--------------------------------------------------------------------------------
Byte-by-byte Description of file: list.dat
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 11 A11 --- FileName Name of the file in subdirectory data (1)
14- 83 A70 --- Title Title of the file
--------------------------------------------------------------------------------
Note (1): The first row (column heading) contains the times of the PDF
estimation, unit is yr (-99 for Freq).
The first column (row heading) contains the frequency values of the PDF
estimation, unit is arcsec/yr.
The rest (from the 2nd column to the 99th column) contains the PDF
estimations at the time corresponding to its column heading.
--------------------------------------------------------------------------------
See also:
VI/63 : Earth Orbit, Precession and Insolation -20Myr to +10Myr
(Laskar+ 1993)
VI/66 : Precession Formulae and Mean Elements for Moon and Planets
(Simon+ 1994)
J/A+A/532/A89 : La2010: orbital solution for long term Earth motion
(Laskar+ 2011)
J/A+A/605/A72 : Planetary systems AMD-stability (Laskar+, 2017)
J/A+A/628/A84 : Slowly diffusing planetary solutions freq. analysis (Fu+, 2019)
Byte-by-byte Description of file (#): data/*
--------------------------------------------------------------------------------
Bytes Format Units Label Explanations
--------------------------------------------------------------------------------
1- 23 E23.18 arcsec/yr Freq Frequency value of the probability density
function (PDF) estimation
25- 47 E23.18 --- PDF1 PDF estimation at the time -1.00e+08yr
49- 71 E23.18 --- PDF2 PDF estimation at the time -1.50e+08yr
73- 95 E23.18 --- PDF3 PDF estimation at the time -2.00e+08yr
97- 119 E23.18 --- PDF4 PDF estimation at the time -2.50e+08yr
121- 143 E23.18 --- PDF5 PDF estimation at the time -3.00e+08yr
145- 167 E23.18 --- PDF6 PDF estimation at the time -3.50e+08yr
169- 191 E23.18 --- PDF7 PDF estimation at the time -4.00e+08yr
193- 215 E23.18 --- PDF8 PDF estimation at the time -4.50e+08yr
217- 239 E23.18 --- PDF9 PDF estimation at the time -5.00e+08yr
241- 263 E23.18 --- PDF10 PDF estimation at the time -5.50e+08yr
265- 287 E23.18 --- PDF11 PDF estimation at the time -6.00e+08yr
289- 311 E23.18 --- PDF12 PDF estimation at the time -6.50e+08yr
313- 335 E23.18 --- PDF13 PDF estimation at the time -7.00e+08yr
337- 359 E23.18 --- PDF14 PDF estimation at the time -7.50e+08yr
361- 383 E23.18 --- PDF15 PDF estimation at the time -8.00e+08yr
385- 407 E23.18 --- PDF16 PDF estimation at the time -8.50e+08yr
409- 431 E23.18 --- PDF17 PDF estimation at the time -9.00e+08yr
433- 455 E23.18 --- PDF18 PDF estimation at the time -9.50e+08yr
457- 479 E23.18 --- PDF19 PDF estimation at the time -1.00e+09yr
481- 503 E23.18 --- PDF20 PDF estimation at the time -1.05e+09yr
505- 527 E23.18 --- PDF21 PDF estimation at the time -1.10e+09yr
529- 551 E23.18 --- PDF22 PDF estimation at the time -1.15e+09yr
553- 575 E23.18 --- PDF23 PDF estimation at the time -1.20e+09yr
577- 599 E23.18 --- PDF24 PDF estimation at the time -1.25e+09yr
601- 623 E23.18 --- PDF25 PDF estimation at the time -1.30e+09yr
625- 647 E23.18 --- PDF26 PDF estimation at the time -1.35e+09yr
649- 671 E23.18 --- PDF27 PDF estimation at the time -1.40e+09yr
673- 695 E23.18 --- PDF28 PDF estimation at the time -1.45e+09yr
697- 719 E23.18 --- PDF29 PDF estimation at the time -1.50e+09yr
721- 743 E23.18 --- PDF30 PDF estimation at the time -1.55e+09yr
745- 767 E23.18 --- PDF31 PDF estimation at the time -1.60e+09yr
769- 791 E23.18 --- PDF32 PDF estimation at the time -1.65e+09yr
793- 815 E23.18 --- PDF33 PDF estimation at the time -1.70e+09yr
817- 839 E23.18 --- PDF34 PDF estimation at the time -1.75e+09yr
841- 863 E23.18 --- PDF35 PDF estimation at the time -1.80e+09yr
865- 887 E23.18 --- PDF36 PDF estimation at the time -1.85e+09yr
889- 911 E23.18 --- PDF37 PDF estimation at the time -1.90e+09yr
913- 935 E23.18 --- PDF38 PDF estimation at the time -1.95e+09yr
937- 959 E23.18 --- PDF39 PDF estimation at the time -2.00e+09yr
961- 983 E23.18 --- PDF40 PDF estimation at the time -2.05e+09yr
985-1007 E23.18 --- PDF41 PDF estimation at the time -2.10e+09yr
1009-1031 E23.18 --- PDF42 PDF estimation at the time -2.15e+09yr
1033-1055 E23.18 --- PDF43 PDF estimation at the time -2.20e+09yr
1057-1079 E23.18 --- PDF44 PDF estimation at the time -2.25e+09yr
1081-1103 E23.18 --- PDF45 PDF estimation at the time -2.30e+09yr
1105-1127 E23.18 --- PDF46 PDF estimation at the time -2.35e+09yr
1129-1151 E23.18 --- PDF47 PDF estimation at the time -2.40e+09yr
1153-1175 E23.18 --- PDF48 PDF estimation at the time -2.45e+09yr
1177-1199 E23.18 --- PDF49 PDF estimation at the time -2.50e+09yr
1201-1223 E23.18 --- PDF50 PDF estimation at the time -2.55e+09yr
1225-1247 E23.18 --- PDF51 PDF estimation at the time -2.60e+09yr
1249-1271 E23.18 --- PDF52 PDF estimation at the time -2.65e+09yr
1273-1295 E23.18 --- PDF53 PDF estimation at the time -2.70e+09yr
1297-1319 E23.18 --- PDF54 PDF estimation at the time -2.75e+09yr
1321-1343 E23.18 --- PDF55 PDF estimation at the time -2.80e+09yr
1345-1367 E23.18 --- PDF56 PDF estimation at the time -2.85e+09yr
1369-1391 E23.18 --- PDF57 PDF estimation at the time -2.90e+09yr
1393-1415 E23.18 --- PDF58 PDF estimation at the time -2.95e+09yr
1417-1439 E23.18 --- PDF59 PDF estimation at the time -3.00e+09yr
1441-1463 E23.18 --- PDF60 PDF estimation at the time -3.05e+09yr
1465-1487 E23.18 --- PDF61 PDF estimation at the time -3.10e+09yr
1489-1511 E23.18 --- PDF62 PDF estimation at the time -3.15e+09yr
1513-1535 E23.18 --- PDF63 PDF estimation at the time -3.20e+09yr
1537-1559 E23.18 --- PDF64 PDF estimation at the time -3.25e+09yr
1561-1583 E23.18 --- PDF65 PDF estimation at the time -3.30e+09yr
1585-1607 E23.18 --- PDF66 PDF estimation at the time -3.35e+09yr
1609-1631 E23.18 --- PDF67 PDF estimation at the time -3.40e+09yr
1633-1655 E23.18 --- PDF68 PDF estimation at the time -3.45e+09yr
1657-1679 E23.18 --- PDF69 PDF estimation at the time -3.50e+09yr
1681-1703 E23.18 --- PDF70 PDF estimation at the time -3.55e+09yr
1705-1727 E23.18 --- PDF71 PDF estimation at the time -3.60e+09yr
1729-1751 E23.18 --- PDF72 PDF estimation at the time -3.65e+09yr
1753-1775 E23.18 --- PDF73 PDF estimation at the time -3.70e+09yr
1777-1799 E23.18 --- PDF74 PDF estimation at the time -3.75e+09yr
1801-1823 E23.18 --- PDF75 PDF estimation at the time -3.80e+09yr
1825-1847 E23.18 --- PDF76 PDF estimation at the time -3.85e+09yr
1849-1871 E23.18 --- PDF77 PDF estimation at the time -3.90e+09yr
1873-1895 E23.18 --- PDF78 PDF estimation at the time -3.95e+09yr
1897-1919 E23.18 --- PDF79 PDF estimation at the time -4.00e+09yr
1921-1943 E23.18 --- PDF80 PDF estimation at the time -4.05e+09yr
1945-1967 E23.18 --- PDF81 PDF estimation at the time -4.10e+09yr
1969-1991 E23.18 --- PDF82 PDF estimation at the time -4.15e+09yr
1993-2015 E23.18 --- PDF83 PDF estimation at the time -4.20e+09yr
2017-2039 E23.18 --- PDF84 PDF estimation at the time -4.25e+09yr
2041-2063 E23.18 --- PDF85 PDF estimation at the time -4.30e+09yr
2065-2087 E23.18 --- PDF86 PDF estimation at the time -4.35e+09yr
2089-2111 E23.18 --- PDF87 PDF estimation at the time -4.40e+09yr
2113-2135 E23.18 --- PDF88 PDF estimation at the time -4.45e+09yr
2137-2159 E23.18 --- PDF89 PDF estimation at the time -4.50e+09yr
2161-2183 E23.18 --- PDF90 PDF estimation at the time -4.55e+09yr
2185-2207 E23.18 --- PDF91 PDF estimation at the time -4.60e+09yr
2209-2231 E23.18 --- PDF92 PDF estimation at the time -4.65e+09yr
2233-2255 E23.18 --- PDF93 PDF estimation at the time -4.70e+09yr
2257-2279 E23.18 --- PDF94 PDF estimation at the time -4.75e+09yr
2281-2303 E23.18 --- PDF95 PDF estimation at the time -4.80e+09yr
2305-2327 E23.18 --- PDF96 PDF estimation at the time -4.85e+09yr
2329-2351 E23.18 --- PDF97 PDF estimation at the time -4.90e+09yr
2353-2375 E23.18 --- PDF98 PDF estimation at the time -4.95e+09yr
--------------------------------------------------------------------------------
Acknowledgements:
Nam H. Hoang, hhnam96(at)gmail.com
(End) Patricia Vannier [CDS] 16-May-2021