astrochron (version 1.8)

hoangPriors: Priors for the fundamental frequencies of the Solar System, using the formulas in Table 2 of Hoang et al. (2021)

Description

Priors for the fundamental frequencies of the Solar System, using the formulas in Table 2 of Hoang et al. (2021). This function will return the value of the prior pdf of the i-th fundamental frequency (g_i or s_i) at a given age, from the formulas in Table 2 of Hoang et al. 2021.

Usage

hoangPriors(ssftype=NULL,i=NULL,age=NULL,ssfi=NULL)

Arguments

ssftype

The type of fundamental frequency to calculate ('g' or 's').

i

Index indicating the fundamental frequency of interest. For 'g', integer values from 1-5 are permitted. For 's', integer values from 1-4 and 6 are permitted.

age

Age in billions of years before present, Ga.

ssfi

Optional values of the fundamental frequencies for which you'd like to determine the prior. If not specified, the time-dependent parameters of the skew normal pdf are reported.

References

Hoang, N.H., Mogavero, F., Laskar, J., 2021, Chaotic diffusion of the fundamental frequencies in the Solar System: Astronomy & Astrophysics, 654, A156.

Examples

# View the priors for the g and s frequencies at 1 Ga, for comparison 
#  with Figure 9 of Hoang et al., 2021

# set up figure
dev.new(height = 4.5, width = 9.5, title = "Fundamental Frequencies")
par(mfrow = c(2, 5))

# age in billions of years before present
  age=1
  
# g1 through g5
  gmin=c(5, 7.40, 16.9, 17.5, 4.2573)
  gmax=c(6, 7.54, 17.7, 18.5, 4.2576)
# loop over g frequencies
  for (i in 1:5)
   {
# compute range of g_i
        x=seq(gmin[i],gmax[i],(gmax[i]-gmin[i])/500)     
# compute pdf and its integral
        pdfRes=hoangPriors(ssftype="g",i,age,x)
# plot prior pdf of g_i
        plot(x,pdfRes$ssfipdf,type="l",lwd=2,col="red",xlab="arcsec",ylab="",main=paste("g",i))
    }
   
# s1, s2, s3, s4, s6 (s5 set as NaN)
  xmin=c(-6.5, -8.5, -19.5, -18.3, NaN ,-26.3489) 
  xmax=c(-4.8, -6, -18, -17.4, NaN, -26.3469)
# loop over s frequencies
  for (i in 1:6)
   {
      if(i != 5) {
# compute range of s_i
        x=seq(xmin[i],xmax[i],(xmax[i]-xmin[i])/500)     
# compute pdf and its integral
        pdfRes=hoangPriors(ssftype="s",i,age,x)
# plot prior pdf of s_i
        plot(x,pdfRes$ssfipdf,type="l",lwd=2,col="red",xlab="arcsec",ylab="",main=paste("s",i))
      }
   }