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ExoMult.R
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#!/usr/bin/Rscript
### E x o M u l t - Created by Jon Zink ###
### Devolped on R 3.4.3 ###
### If you make use of this code, please cite: ###
### J. K. Zink, J. L. Christiansen, and B. M. S. Hansen 2019, MNRAS 483, 4479 ###
####Broken Powerlaw Distribution Draw####
brokenPow <- function(n,aCon,bCon,xmix,xmin,xmax){
constant1=((xmix^(aCon+1)-xmin^(aCon+1))/(aCon+1)+(xmix^aCon/xmix^bCon)*(xmax^(bCon+1)-xmix^(bCon+1))/(bCon+1))^-1
constant2=constant1*(xmix^aCon/xmix^bCon)
turn=constant1*(xmix^(aCon+1)-xmin^(aCon+1))/(aCon+1)
rValue=runif(n)
results=ifelse(rValue<=turn,(rValue*(aCon+1)/constant1+xmin^(aCon+1))^(1/(aCon+1)),((rValue-turn)*(bCon+1)/constant2+xmix^(bCon+1))^(1/(bCon+1)))
return(results)
}
####Rayleigh Distribution####
rrayleigh <- function(n,sigma){
yValue=runif(n)
invCDF=sqrt(-2*sigma^2*log(1-yValue))
return(invCDF)
}
###Function for MES calculation
MES_calc<-function(star, period, radius,cdpp){
######Determine Stellar Limb Darkening parameters
limb_u1=-.000193*star$T_eff+1.5169
limb_u2=.000125*star$T_eff-0.4601
######Calculate Transit Depth####
krp=radius/star$Rad*0.00916399
c0 = 1.0 - (limb_u1+limb_u2)
omega = c0/4+0/5+(limb_u1+2*limb_u2)/6+0/7-limb_u2/8
ksq = 1.0 - krp^2
tmp0 = c0/4 * ksq
tmp2 = (limb_u1+2*limb_u2)/6* ksq^(3.0/2.0)
tmp4 = -limb_u2/8 * ksq^2
depth=(1.0 - (tmp0 + tmp2 + tmp4)/omega) * 1.0e6
######Calculate MES####
number_transits=star$d_span/period
MES=depth/(cdpp)*1.003*number_transits^.5
return(MES)
}
######Function for detection probability#################
probability_detection<-function(star, period, radius,cdpp,plNum){
######Calculate MES####
MES=MES_calc(star, period, radius,cdpp)
######Window Function#########
number_transits=star$d_span/period
probabilty_window=1-(1-star$duty)^number_transits-number_transits*star$duty*(1-star$duty)^(number_transits-1)-number_transits*(number_transits-1)/2*star$duty^2*(1-star$duty)^(number_transits-2)
probabilty_window=ifelse(number_transits<1,0,probabilty_window)
probabilty_window=ifelse(probabilty_window<0,0,probabilty_window)
probabilty_window=ifelse(probabilty_window>1,1,probabilty_window)
###Calulate the fraction detected at this MES
if(plNum==1){
fdet=ifelse(period>200,pgamma(MES-1.0984,shape=18.4119, scale=0.3959)*0.9051,pgamma(MES-0.0102,shape=29.3363, scale=0.2856)*0.9825)
} else{
fdet=ifelse(period>200,pgamma(MES-2.9774,shape=5.5213, scale=1.2307)*0.7456,pgamma(MES-0.0093,shape=21.3265, scale=0.4203)*0.9276)
}
return(fdet*probabilty_window)
}
#####Function to determine impact parameter
impactDraw <- function(n,star,inclination,average_mutInc,per,node,ecc,arg_peri,plNum){
if(plNum==1){
mutual_inclination=0
} else{
mutual_inclination=rrayleigh(n,average_mutInc)*(2*pi)/360
}
###Draw argument of periapsis
w=asin(runif(n,0,1))
####Calculate Planet Inclination
if(plNum==1){
inclination_m=acos(cos(inclination)*cos(mutual_inclination)+sin(inclination)*sin(mutual_inclination)*cos(node))
} else{
inclination_m=acos(cos(inclination)*cos(mutual_inclination)+sin(inclination)*sin(mutual_inclination)*cos(w))
}
###Planet Semi-major axis
gravConstant=6.674e-11*1.98855e30*(86400)^2/(6.957e8)^3
semiMajor=(per^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
return(abs(semiMajor/star$Rad*(1-ecc^2)/(1+ecc*sin(arg_peri))*(sin(inclination_m)*sin(node)-cos(inclination_m)*cos(node))))
}
ExoMult <- function(rMin=0.5,rMax=16,alpha_1=-1.65,rad_break=2.66,alpha_2=-4.35,pMin=.5,pMax=500,beta_1=0.76,per_break=7.09,beta_2=-0.64,
mut_Ray=1,ecc_alpha=0,ecc_beta=1,frac_m1=.72,frac_m2=.68,frac_m3=.66,frac_m4=.63,frac_m5=.60,frac_m6=.55,frac_m7=.40,export_csv=TRUE){
###Input Errors
if(frac_m1<=frac_m2 | frac_m2<=frac_m3 | frac_m3<=frac_m4 | frac_m4<=frac_m5 | frac_m5<=frac_m6 | frac_m6<=frac_m7){
print("frac values must be in descending order")
return()
}
if(rMin>rMax | pMin>pMax){
print("Population limits are defined incorrectly")
return()
}
if(rad_break<rMin | rad_break>pMax){
print("rad_break must be within the population limits")
return()
}
if(per_break<rMin | per_break>pMax){
print("per_break must be within the population limits")
return()
}
print("Importing stellar population parameters")
###Import the stellar population
tryCatch({star=read.table("kepler_solar-like_stellar_parameters.csv", header=FALSE, sep=",",skip = 2,
col.names=c("KIC","T_eff","Teff_errp","Teff_errm","logg","logg_errp","logg_errm","Rad","Rad_errp","Rad_errm","Mass","Mass_errp","Mass_errm",
"duty","d_span","CDPP1.5","CDPP2","CDPP2.5","CDPP3","CDPP3.5","CDPP4.5","CDPP5","CDPP6","CDPP7.5","CDPP9","CDPP10.5","CDPP12","CDPP12.5","CDPP15"))},
error=function(e) {
print("Error loading stellar data")
return()})
number_stars=nrow(star)
####Read CDPP Data into a matrix
CDPPx=c(1.5,2,2.5,3,3.5,4.5,5,6,7.5,9,10.5,12,12.5,15)
CDPPy=matrix(data=0, nrow=14,ncol=number_stars)
CDPPy[1,]=star$CDPP1.5
CDPPy[2,]=star$CDPP2
CDPPy[3,]=star$CDPP2.5
CDPPy[4,]=star$CDPP3
CDPPy[5,]=star$CDPP3.5
CDPPy[6,]=star$CDPP4.5
CDPPy[7,]=star$CDPP5
CDPPy[8,]=star$CDPP6
CDPPy[9,]=star$CDPP7.5
CDPPy[10,]=star$CDPP9
CDPPy[11,]=star$CDPP10.5
CDPPy[12,]=star$CDPP12
CDPPy[13,]=star$CDPP12.5
CDPPy[14,]=star$CDPP15
########Create Blank Arrays
cdpp_m1=numeric(number_stars)
cdpp_m2=numeric(number_stars)
cdpp_m3=numeric(number_stars)
cdpp_m4=numeric(number_stars)
cdpp_m5=numeric(number_stars)
cdpp_m6=numeric(number_stars)
cdpp_m7=numeric(number_stars)
rad_sorted_m1=numeric(number_stars)
rad_sorted_m2=numeric(number_stars)
rad_sorted_m3=numeric(number_stars)
rad_sorted_m4=numeric(number_stars)
rad_sorted_m5=numeric(number_stars)
rad_sorted_m6=numeric(number_stars)
rad_sorted_m7=numeric(number_stars)
per_sorted_m1=numeric(number_stars)
per_sorted_m2=numeric(number_stars)
per_sorted_m3=numeric(number_stars)
per_sorted_m4=numeric(number_stars)
per_sorted_m5=numeric(number_stars)
per_sorted_m6=numeric(number_stars)
per_sorted_m7=numeric(number_stars)
eccentricity_sorted_m1=numeric(number_stars)
eccentricity_sorted_m2=numeric(number_stars)
eccentricity_sorted_m3=numeric(number_stars)
eccentricity_sorted_m4=numeric(number_stars)
eccentricity_sorted_m5=numeric(number_stars)
eccentricity_sorted_m6=numeric(number_stars)
eccentricity_sorted_m7=numeric(number_stars)
CDPP_sorted_m1=numeric(number_stars)
CDPP_sorted_m2=numeric(number_stars)
CDPP_sorted_m3=numeric(number_stars)
CDPP_sorted_m4=numeric(number_stars)
CDPP_sorted_m5=numeric(number_stars)
CDPP_sorted_m6=numeric(number_stars)
CDPP_sorted_m7=numeric(number_stars)
print("Drawing exoplanet population from broken power-law distribution")
#######Draw Planet Population
rad_m1=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m2=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m3=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m4=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m5=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m6=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
rad_m7=brokenPow(number_stars,alpha_1,alpha_2,rad_break,rMin,rMax)
per_m1=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m2=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m3=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m4=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m5=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m6=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
per_m7=brokenPow(number_stars,beta_1,beta_2,per_break,pMin,pMax)
#Remove planets to correct for population fractions
##In oder to maintain arrays of similar size we set these discared planets to parameter at undetectable limits
truePl=runif(number_stars,0,1)
per_m1=ifelse(truePl<frac_m1,per_m1,Inf)
per_m2=ifelse(truePl<frac_m2,per_m2,Inf)
per_m3=ifelse(truePl<frac_m3,per_m3,Inf)
per_m4=ifelse(truePl<frac_m4,per_m4,Inf)
per_m5=ifelse(truePl<frac_m5,per_m5,Inf)
per_m6=ifelse(truePl<frac_m6,per_m6,Inf)
per_m7=ifelse(truePl<frac_m7,per_m7,Inf)
rad_m1=ifelse(truePl<frac_m1,rad_m1,0)
rad_m2=ifelse(truePl<frac_m2,rad_m2,0)
rad_m3=ifelse(truePl<frac_m3,rad_m3,0)
rad_m4=ifelse(truePl<frac_m4,rad_m4,0)
rad_m5=ifelse(truePl<frac_m5,rad_m5,0)
rad_m6=ifelse(truePl<frac_m6,rad_m6,0)
rad_m7=ifelse(truePl<frac_m7,rad_m7,0)
###Draw Inclination Parameters
system_inclination=asin(runif(number_stars,0,1))
system_average_mutInc=rrayleigh(number_stars,mut_Ray)
intial_w=asin(runif(number_stars,0,1))
###Draw Eccentricity Parameters
eccentricity_m1=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m2=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m3=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m4=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m5=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m6=rbeta(number_stars,ecc_alpha,ecc_beta)
eccentricity_m7=rbeta(number_stars,ecc_alpha,ecc_beta)
argPericenter_m1=asin(runif(number_stars,-1,1))
argPericenter_m2=asin(runif(number_stars,-1,1))
argPericenter_m3=asin(runif(number_stars,-1,1))
argPericenter_m4=asin(runif(number_stars,-1,1))
argPericenter_m5=asin(runif(number_stars,-1,1))
argPericenter_m6=asin(runif(number_stars,-1,1))
argPericenter_m7=asin(runif(number_stars,-1,1))
###Calculate Impact parameters
impact_m1=impactDraw(number_stars,star,system_inclination,0,per_m1,intial_w,eccentricity_m1,argPericenter_m1,1)
impact_m2=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m2,intial_w,eccentricity_m2,argPericenter_m2,2)
impact_m3=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m3,intial_w,eccentricity_m3,argPericenter_m3,3)
impact_m4=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m4,intial_w,eccentricity_m4,argPericenter_m4,4)
impact_m5=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m5,intial_w,eccentricity_m5,argPericenter_m5,5)
impact_m6=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m6,intial_w,eccentricity_m6,argPericenter_m6,6)
impact_m7=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m7,intial_w,eccentricity_m7,argPericenter_m7,7)
####Discard planets with impact parameters greater than 1
rad_m1=ifelse(impact_m1>1,0,rad_m1)
rad_m2=ifelse(impact_m2>1,0,rad_m2)
rad_m3=ifelse(impact_m3>1,0,rad_m3)
rad_m4=ifelse(impact_m4>1,0,rad_m4)
rad_m5=ifelse(impact_m5>1,0,rad_m5)
rad_m6=ifelse(impact_m6>1,0,rad_m6)
rad_m7=ifelse(impact_m7>1,0,rad_m7)
### Set an upper limit of 1 for impact parameters to avoid imaginary transit chord values
impact_m1=ifelse(impact_m1<=1,impact_m1,1)
impact_m2=ifelse(impact_m2<=1,impact_m2,1)
impact_m3=ifelse(impact_m3<=1,impact_m3,1)
impact_m4=ifelse(impact_m4<=1,impact_m4,1)
impact_m5=ifelse(impact_m5<=1,impact_m5,1)
impact_m6=ifelse(impact_m6<=1,impact_m6,1)
impact_m7=ifelse(impact_m7<=1,impact_m7,1)
###Calculate Transit Chords
tran_chord_m1=(1-impact_m1^2)^.5
tran_chord_m2=(1-impact_m2^2)^.5
tran_chord_m3=(1-impact_m3^2)^.5
tran_chord_m4=(1-impact_m4^2)^.5
tran_chord_m5=(1-impact_m5^2)^.5
tran_chord_m6=(1-impact_m6^2)^.5
tran_chord_m7=(1-impact_m7^2)^.5
##Calculate Semi-Major Axis
gravConstant=6.674e-11*1.98855e30*(86400)^2/(6.957e8)^3
semiMajor_m1=(per_m1^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m2=(per_m2^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m3=(per_m3^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m4=(per_m4^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m5=(per_m5^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m6=(per_m6^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m7=(per_m7^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
#Calculate Transit Duration
tran_duration_m1=star$Rad*per_m1/(semiMajor_m1*pi)*tran_chord_m1*(1-eccentricity_m1^2)^.5/(1+eccentricity_m1*sin(argPericenter_m1))*24
tran_duration_m2=star$Rad*per_m2/(semiMajor_m2*pi)*tran_chord_m2*(1-eccentricity_m2^2)^.5/(1+eccentricity_m2*sin(argPericenter_m2))*24
tran_duration_m3=star$Rad*per_m3/(semiMajor_m3*pi)*tran_chord_m3*(1-eccentricity_m3^2)^.5/(1+eccentricity_m3*sin(argPericenter_m3))*24
tran_duration_m4=star$Rad*per_m4/(semiMajor_m4*pi)*tran_chord_m4*(1-eccentricity_m4^2)^.5/(1+eccentricity_m4*sin(argPericenter_m4))*24
tran_duration_m5=star$Rad*per_m5/(semiMajor_m5*pi)*tran_chord_m5*(1-eccentricity_m5^2)^.5/(1+eccentricity_m5*sin(argPericenter_m5))*24
tran_duration_m6=star$Rad*per_m6/(semiMajor_m6*pi)*tran_chord_m6*(1-eccentricity_m6^2)^.5/(1+eccentricity_m6*sin(argPericenter_m6))*24
tran_duration_m7=star$Rad*per_m7/(semiMajor_m7*pi)*tran_chord_m7*(1-eccentricity_m7^2)^.5/(1+eccentricity_m7*sin(argPericenter_m7))*24
#Remove NaN from transit durations
tran_duration_m1=ifelse(is.nan(tran_duration_m1),Inf,tran_duration_m1)
tran_duration_m2=ifelse(is.nan(tran_duration_m2),Inf,tran_duration_m2)
tran_duration_m3=ifelse(is.nan(tran_duration_m3),Inf,tran_duration_m3)
tran_duration_m4=ifelse(is.nan(tran_duration_m4),Inf,tran_duration_m4)
tran_duration_m5=ifelse(is.nan(tran_duration_m5),Inf,tran_duration_m5)
tran_duration_m6=ifelse(is.nan(tran_duration_m6),Inf,tran_duration_m6)
tran_duration_m7=ifelse(is.nan(tran_duration_m7),Inf,tran_duration_m7)
print("Interpolating stellar fluctuation values for each transit duration")
###Interpolate the CDPP values for each star
for (w in 1:number_stars) {
cdpp_m1[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m1[w], rule=2)$y)
cdpp_m2[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m2[w], rule=2)$y)
cdpp_m3[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m3[w], rule=2)$y)
cdpp_m4[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m4[w], rule=2)$y)
cdpp_m5[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m5[w], rule=2)$y)
cdpp_m6[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m6[w], rule=2)$y)
cdpp_m7[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m7[w], rule=2)$y)
}
####Calculate signal scale
MES_m1=MES_calc(star, per_m1, rad_m1, cdpp_m1)
MES_m2=MES_calc(star, per_m2, rad_m2, cdpp_m2)
MES_m3=MES_calc(star, per_m3, rad_m3, cdpp_m3)
MES_m4=MES_calc(star, per_m4, rad_m4, cdpp_m4)
MES_m5=MES_calc(star, per_m5, rad_m5, cdpp_m5)
MES_m6=MES_calc(star, per_m6, rad_m6, cdpp_m6)
MES_m7=MES_calc(star, per_m7, rad_m7, cdpp_m7)
print("Sorting planets by MES values")
#####Sort MES Values
for (i in 1:number_stars){
#####Sorting MES Values
sortOrder=sort(c(MES_m1[i],MES_m2[i],MES_m3[i],MES_m4[i],MES_m5[i],MES_m6[i],MES_m7[i]))
####Sorting Period Values
per_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],per_m1[i],ifelse(MES_m2[i]==sortOrder[7],per_m2[i],ifelse(MES_m3[i]==sortOrder[7],per_m3[i],ifelse(MES_m4[i]==sortOrder[7],per_m4[i],ifelse(MES_m5[i]==sortOrder[7],per_m5[i],ifelse(MES_m6[i]==sortOrder[7],per_m6[i],per_m7[i]))))))
per_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],per_m1[i],ifelse(MES_m2[i]==sortOrder[6],per_m2[i],ifelse(MES_m3[i]==sortOrder[6],per_m3[i],ifelse(MES_m4[i]==sortOrder[6],per_m4[i],ifelse(MES_m5[i]==sortOrder[6],per_m5[i],ifelse(MES_m6[i]==sortOrder[6],per_m6[i],per_m7[i]))))))
per_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],per_m1[i],ifelse(MES_m2[i]==sortOrder[5],per_m2[i],ifelse(MES_m3[i]==sortOrder[5],per_m3[i],ifelse(MES_m4[i]==sortOrder[5],per_m4[i],ifelse(MES_m5[i]==sortOrder[5],per_m5[i],ifelse(MES_m6[i]==sortOrder[5],per_m6[i],per_m7[i]))))))
per_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],per_m1[i],ifelse(MES_m2[i]==sortOrder[4],per_m2[i],ifelse(MES_m3[i]==sortOrder[4],per_m3[i],ifelse(MES_m4[i]==sortOrder[4],per_m4[i],ifelse(MES_m5[i]==sortOrder[4],per_m5[i],ifelse(MES_m6[i]==sortOrder[4],per_m6[i],per_m7[i]))))))
per_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],per_m1[i],ifelse(MES_m2[i]==sortOrder[3],per_m2[i],ifelse(MES_m3[i]==sortOrder[3],per_m3[i],ifelse(MES_m4[i]==sortOrder[3],per_m4[i],ifelse(MES_m5[i]==sortOrder[3],per_m5[i],ifelse(MES_m6[i]==sortOrder[3],per_m6[i],per_m7[i]))))))
per_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],per_m1[i],ifelse(MES_m2[i]==sortOrder[2],per_m2[i],ifelse(MES_m3[i]==sortOrder[2],per_m3[i],ifelse(MES_m4[i]==sortOrder[2],per_m4[i],ifelse(MES_m5[i]==sortOrder[2],per_m5[i],ifelse(MES_m6[i]==sortOrder[2],per_m6[i],per_m7[i]))))))
per_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],per_m1[i],ifelse(MES_m2[i]==sortOrder[1],per_m2[i],ifelse(MES_m3[i]==sortOrder[1],per_m3[i],ifelse(MES_m4[i]==sortOrder[1],per_m4[i],ifelse(MES_m5[i]==sortOrder[1],per_m5[i],ifelse(MES_m6[i]==sortOrder[1],per_m6[i],per_m7[i]))))))
####Sorting Radius Values
rad_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],rad_m1[i],ifelse(MES_m2[i]==sortOrder[7],rad_m2[i],ifelse(MES_m3[i]==sortOrder[7],rad_m3[i],ifelse(MES_m4[i]==sortOrder[7],rad_m4[i],ifelse(MES_m5[i]==sortOrder[7],rad_m5[i],ifelse(MES_m6[i]==sortOrder[7],rad_m6[i],rad_m7[i]))))))
rad_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],rad_m1[i],ifelse(MES_m2[i]==sortOrder[6],rad_m2[i],ifelse(MES_m3[i]==sortOrder[6],rad_m3[i],ifelse(MES_m4[i]==sortOrder[6],rad_m4[i],ifelse(MES_m5[i]==sortOrder[6],rad_m5[i],ifelse(MES_m6[i]==sortOrder[6],rad_m6[i],rad_m7[i]))))))
rad_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],rad_m1[i],ifelse(MES_m2[i]==sortOrder[5],rad_m2[i],ifelse(MES_m3[i]==sortOrder[5],rad_m3[i],ifelse(MES_m4[i]==sortOrder[5],rad_m4[i],ifelse(MES_m5[i]==sortOrder[5],rad_m5[i],ifelse(MES_m6[i]==sortOrder[5],rad_m6[i],rad_m7[i]))))))
rad_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],rad_m1[i],ifelse(MES_m2[i]==sortOrder[4],rad_m2[i],ifelse(MES_m3[i]==sortOrder[4],rad_m3[i],ifelse(MES_m4[i]==sortOrder[4],rad_m4[i],ifelse(MES_m5[i]==sortOrder[4],rad_m5[i],ifelse(MES_m6[i]==sortOrder[4],rad_m6[i],rad_m7[i]))))))
rad_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],rad_m1[i],ifelse(MES_m2[i]==sortOrder[3],rad_m2[i],ifelse(MES_m3[i]==sortOrder[3],rad_m3[i],ifelse(MES_m4[i]==sortOrder[3],rad_m4[i],ifelse(MES_m5[i]==sortOrder[3],rad_m5[i],ifelse(MES_m6[i]==sortOrder[3],rad_m6[i],rad_m7[i]))))))
rad_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],rad_m1[i],ifelse(MES_m2[i]==sortOrder[2],rad_m2[i],ifelse(MES_m3[i]==sortOrder[2],rad_m3[i],ifelse(MES_m4[i]==sortOrder[2],rad_m4[i],ifelse(MES_m5[i]==sortOrder[2],rad_m5[i],ifelse(MES_m6[i]==sortOrder[2],rad_m6[i],rad_m7[i]))))))
rad_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],rad_m1[i],ifelse(MES_m2[i]==sortOrder[1],rad_m2[i],ifelse(MES_m3[i]==sortOrder[1],rad_m3[i],ifelse(MES_m4[i]==sortOrder[1],rad_m4[i],ifelse(MES_m5[i]==sortOrder[1],rad_m5[i],ifelse(MES_m6[i]==sortOrder[1],rad_m6[i],rad_m7[i]))))))
###Sorting Eccentricity
eccentricity_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[7],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[7],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[7],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[7],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[7],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[6],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[6],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[6],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[6],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[6],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[5],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[5],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[5],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[5],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[5],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[4],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[4],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[4],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[4],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[4],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[3],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[3],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[3],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[3],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[3],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[2],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[2],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[2],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[2],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[2],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[1],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[1],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[1],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[1],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[1],eccentricity_m6[i],eccentricity_m7[i]))))))
##Sorting CDPP values
CDPP_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[7],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[7],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[7],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[7],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[7],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[6],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[6],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[6],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[6],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[6],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[5],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[5],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[5],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[5],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[5],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[4],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[4],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[4],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[4],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[4],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[3],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[3],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[3],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[3],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[3],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[2],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[2],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[2],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[2],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[2],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[1],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[1],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[1],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[1],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[1],cdpp_m6[i],cdpp_m7[i]))))))
}
#Calculate the probabilty of detection for each planet
prob_detection_m1=probability_detection(star, per_sorted_m1, rad_sorted_m1, CDPP_sorted_m1,1)
prob_detection_m2=probability_detection(star, per_sorted_m2, rad_sorted_m2, CDPP_sorted_m2,2)
prob_detection_m3=probability_detection(star, per_sorted_m3, rad_sorted_m3, CDPP_sorted_m3,3)
prob_detection_m4=probability_detection(star, per_sorted_m4, rad_sorted_m4, CDPP_sorted_m4,4)
prob_detection_m5=probability_detection(star, per_sorted_m5, rad_sorted_m5, CDPP_sorted_m5,5)
prob_detection_m6=probability_detection(star, per_sorted_m6, rad_sorted_m6, CDPP_sorted_m6,6)
prob_detection_m7=probability_detection(star, per_sorted_m7, rad_sorted_m7, CDPP_sorted_m7,7)
#Force detection probabilty to follow the sort order
prob_detection_m2=ifelse(prob_detection_m1<prob_detection_m2,prob_detection_m1,prob_detection_m2)
prob_detection_m3=ifelse(prob_detection_m2<prob_detection_m3,prob_detection_m2,prob_detection_m3)
prob_detection_m4=ifelse(prob_detection_m3<prob_detection_m4,prob_detection_m3,prob_detection_m4)
prob_detection_m5=ifelse(prob_detection_m4<prob_detection_m5,prob_detection_m4,prob_detection_m5)
prob_detection_m6=ifelse(prob_detection_m5<prob_detection_m6,prob_detection_m5,prob_detection_m6)
prob_detection_m7=ifelse(prob_detection_m6<prob_detection_m7,prob_detection_m6,prob_detection_m7)
#Remove planets based on their detection probabilty
random_detection_threshold=runif(number_stars,0,1)
rad_sorted_m1=ifelse(prob_detection_m1>random_detection_threshold,rad_sorted_m1,NA)
rad_sorted_m2=ifelse(prob_detection_m2>random_detection_threshold,rad_sorted_m2,NA)
rad_sorted_m3=ifelse(prob_detection_m3>random_detection_threshold,rad_sorted_m3,NA)
rad_sorted_m4=ifelse(prob_detection_m4>random_detection_threshold,rad_sorted_m4,NA)
rad_sorted_m5=ifelse(prob_detection_m5>random_detection_threshold,rad_sorted_m5,NA)
rad_sorted_m6=ifelse(prob_detection_m6>random_detection_threshold,rad_sorted_m6,NA)
rad_sorted_m7=ifelse(prob_detection_m7>random_detection_threshold,rad_sorted_m7,NA)
per_sorted_m1=ifelse(prob_detection_m1>random_detection_threshold,per_sorted_m1,NA)
per_sorted_m2=ifelse(prob_detection_m2>random_detection_threshold,per_sorted_m2,NA)
per_sorted_m3=ifelse(prob_detection_m3>random_detection_threshold,per_sorted_m3,NA)
per_sorted_m4=ifelse(prob_detection_m4>random_detection_threshold,per_sorted_m4,NA)
per_sorted_m5=ifelse(prob_detection_m5>random_detection_threshold,per_sorted_m5,NA)
per_sorted_m6=ifelse(prob_detection_m6>random_detection_threshold,per_sorted_m6,NA)
per_sorted_m7=ifelse(prob_detection_m7>random_detection_threshold,per_sorted_m7,NA)
eccentricity_sorted_m1=ifelse(prob_detection_m1>random_detection_threshold,eccentricity_sorted_m1,NA)
eccentricity_sorted_m2=ifelse(prob_detection_m2>random_detection_threshold,eccentricity_sorted_m2,NA)
eccentricity_sorted_m3=ifelse(prob_detection_m3>random_detection_threshold,eccentricity_sorted_m3,NA)
eccentricity_sorted_m4=ifelse(prob_detection_m4>random_detection_threshold,eccentricity_sorted_m4,NA)
eccentricity_sorted_m5=ifelse(prob_detection_m5>random_detection_threshold,eccentricity_sorted_m5,NA)
eccentricity_sorted_m6=ifelse(prob_detection_m6>random_detection_threshold,eccentricity_sorted_m6,NA)
eccentricity_sorted_m7=ifelse(prob_detection_m7>random_detection_threshold,eccentricity_sorted_m7,NA)
print("Removing undetected systems")
###Move data to date frame and remove non-detected systems
return_df=data.frame(star$KIC,rad_sorted_m1,per_sorted_m1,eccentricity_sorted_m1,rad_sorted_m2,per_sorted_m2,eccentricity_sorted_m2,
rad_sorted_m3,per_sorted_m3,eccentricity_sorted_m3,rad_sorted_m4,per_sorted_m4,eccentricity_sorted_m4,
rad_sorted_m5,per_sorted_m5,eccentricity_sorted_m5,rad_sorted_m6,per_sorted_m6,eccentricity_sorted_m6,
rad_sorted_m7,per_sorted_m7,eccentricity_sorted_m7)
return_df=return_df[!is.na(return_df["rad_sorted_m1"]),]
if(export_csv){
#Print to csv
print("Printing detected population to CSV file...simulated_detect_pop.csv")
write.csv(return_df, file = "simulated_detect_pop.csv",row.names=FALSE, na="",quote = FALSE)
}
return(return_df)
}
ExoMult.Prob <- function(radius,period,eccentricity,mut_Ray=0){
###Input Errors
if(length(radius)!=length(period)){
print("ERROR: radius and period vectors are of differing length")
return()
}
if(length(radius)!=length(eccentricity)){
print("ERROR: radius and eccentricity vectors are of differing length")
return()
}
if(length(period)!=length(eccentricity)){
print("ERROR: period and eccentricity vectors are of differing length")
return()
}
if(length(period)!=length(unique(period))){
print("ERROR: period values must all be unique")
return()
}
if(length(period)>7){
print("ERROR: More than seven planets in the system. ExoMult can only provide probabilities for up to seven planet systems")
return()
}
if(length(radius)<7){
clip=length(radius)
radius=c(radius,0*1:(7-clip))
period=c(period,Inf*1:(7-clip))
eccentricity=c(eccentricity,0*1:(7-clip))
} else{
clip=0
}
print("Importing stellar population parameters")
###Import the stellar population
tryCatch({star=read.table("kepler_solar-like_stellar_parameters.csv", header=FALSE, sep=",",skip = 2,
col.names=c("KIC","T_eff","Teff_errp","Teff_errm","logg","logg_errp","logg_errm","Rad","Rad_errp","Rad_errm","Mass","Mass_errp","Mass_errm",
"duty","d_span","CDPP1.5","CDPP2","CDPP2.5","CDPP3","CDPP3.5","CDPP4.5","CDPP5","CDPP6","CDPP7.5","CDPP9","CDPP10.5","CDPP12","CDPP12.5","CDPP15"))},
error=function(e) {
print("Error loading stellar data")
return()})
number_stars=nrow(star)
####Read CDPP Data into a matrix
CDPPx=c(1.5,2,2.5,3,3.5,4.5,5,6,7.5,9,10.5,12,12.5,15)
CDPPy=matrix(data=0, nrow=14,ncol=number_stars)
CDPPy[1,]=star$CDPP1.5
CDPPy[2,]=star$CDPP2
CDPPy[3,]=star$CDPP2.5
CDPPy[4,]=star$CDPP3
CDPPy[5,]=star$CDPP3.5
CDPPy[6,]=star$CDPP4.5
CDPPy[7,]=star$CDPP5
CDPPy[8,]=star$CDPP6
CDPPy[9,]=star$CDPP7.5
CDPPy[10,]=star$CDPP9
CDPPy[11,]=star$CDPP10.5
CDPPy[12,]=star$CDPP12
CDPPy[13,]=star$CDPP12.5
CDPPy[14,]=star$CDPP15
########Create Blank Arrays
cdpp_m1=numeric(number_stars)
cdpp_m2=numeric(number_stars)
cdpp_m3=numeric(number_stars)
cdpp_m4=numeric(number_stars)
cdpp_m5=numeric(number_stars)
cdpp_m6=numeric(number_stars)
cdpp_m7=numeric(number_stars)
rad_sorted_m1=numeric(number_stars)
rad_sorted_m2=numeric(number_stars)
rad_sorted_m3=numeric(number_stars)
rad_sorted_m4=numeric(number_stars)
rad_sorted_m5=numeric(number_stars)
rad_sorted_m6=numeric(number_stars)
rad_sorted_m7=numeric(number_stars)
per_sorted_m1=numeric(number_stars)
per_sorted_m2=numeric(number_stars)
per_sorted_m3=numeric(number_stars)
per_sorted_m4=numeric(number_stars)
per_sorted_m5=numeric(number_stars)
per_sorted_m6=numeric(number_stars)
per_sorted_m7=numeric(number_stars)
eccentricity_sorted_m1=numeric(number_stars)
eccentricity_sorted_m2=numeric(number_stars)
eccentricity_sorted_m3=numeric(number_stars)
eccentricity_sorted_m4=numeric(number_stars)
eccentricity_sorted_m5=numeric(number_stars)
eccentricity_sorted_m6=numeric(number_stars)
eccentricity_sorted_m7=numeric(number_stars)
CDPP_sorted_m1=numeric(number_stars)
CDPP_sorted_m2=numeric(number_stars)
CDPP_sorted_m3=numeric(number_stars)
CDPP_sorted_m4=numeric(number_stars)
CDPP_sorted_m5=numeric(number_stars)
CDPP_sorted_m6=numeric(number_stars)
CDPP_sorted_m7=numeric(number_stars)
#######Draw Planet Population
rad_m1=rep(radius[1],number_stars)
rad_m2=rep(radius[2],number_stars)
rad_m3=rep(radius[3],number_stars)
rad_m4=rep(radius[4],number_stars)
rad_m5=rep(radius[5],number_stars)
rad_m6=rep(radius[6],number_stars)
rad_m7=rep(radius[7],number_stars)
per_m1=rep(period[1],number_stars)
per_m2=rep(period[2],number_stars)
per_m3=rep(period[3],number_stars)
per_m4=rep(period[4],number_stars)
per_m5=rep(period[5],number_stars)
per_m6=rep(period[6],number_stars)
per_m7=rep(period[7],number_stars)
###Draw Inclination Parameters
print("Drawing inclination parameters")
system_inclination=asin(runif(number_stars,0,1))
system_average_mutInc=rrayleigh(number_stars,mut_Ray)
intial_w=asin(runif(number_stars,0,1))
###Draw Eccentricity Parameters
eccentricity_m1=rep(eccentricity[1],number_stars)
eccentricity_m2=rep(eccentricity[2],number_stars)
eccentricity_m3=rep(eccentricity[3],number_stars)
eccentricity_m4=rep(eccentricity[4],number_stars)
eccentricity_m5=rep(eccentricity[5],number_stars)
eccentricity_m6=rep(eccentricity[6],number_stars)
eccentricity_m7=rep(eccentricity[7],number_stars)
argPericenter_m1=asin(runif(number_stars,-1,1))
argPericenter_m2=asin(runif(number_stars,-1,1))
argPericenter_m3=asin(runif(number_stars,-1,1))
argPericenter_m4=asin(runif(number_stars,-1,1))
argPericenter_m5=asin(runif(number_stars,-1,1))
argPericenter_m6=asin(runif(number_stars,-1,1))
argPericenter_m7=asin(runif(number_stars,-1,1))
###Calculate Impact parameters
impact_m1=impactDraw(number_stars,star,system_inclination,0,per_m1,intial_w,eccentricity_m1,argPericenter_m1,1)
impact_m2=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m2,intial_w,eccentricity_m2,argPericenter_m2,2)
impact_m3=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m3,intial_w,eccentricity_m3,argPericenter_m3,3)
impact_m4=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m4,intial_w,eccentricity_m4,argPericenter_m4,4)
impact_m5=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m5,intial_w,eccentricity_m5,argPericenter_m5,5)
impact_m6=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m6,intial_w,eccentricity_m6,argPericenter_m6,6)
impact_m7=impactDraw(number_stars,star,system_inclination,system_average_mutInc,per_m7,intial_w,eccentricity_m7,argPericenter_m7,7)
####Discard planets with impact parameters greater than 1
rad_m1=ifelse(impact_m1>1,0,rad_m1)
rad_m2=ifelse(impact_m2>1,0,rad_m2)
rad_m3=ifelse(impact_m3>1,0,rad_m3)
rad_m4=ifelse(impact_m4>1,0,rad_m4)
rad_m5=ifelse(impact_m5>1,0,rad_m5)
rad_m6=ifelse(impact_m6>1,0,rad_m6)
rad_m7=ifelse(impact_m7>1,0,rad_m7)
### Set an upper limit of 1 for impact parameters to avoid imaginary transit chord values
impact_m1=ifelse(impact_m1<=1,impact_m1,1)
impact_m2=ifelse(impact_m2<=1,impact_m2,1)
impact_m3=ifelse(impact_m3<=1,impact_m3,1)
impact_m4=ifelse(impact_m4<=1,impact_m4,1)
impact_m5=ifelse(impact_m5<=1,impact_m5,1)
impact_m6=ifelse(impact_m6<=1,impact_m6,1)
impact_m7=ifelse(impact_m7<=1,impact_m7,1)
###Calculate Transit Chords
tran_chord_m1=(1-impact_m1^2)^.5
tran_chord_m2=(1-impact_m2^2)^.5
tran_chord_m3=(1-impact_m3^2)^.5
tran_chord_m4=(1-impact_m4^2)^.5
tran_chord_m5=(1-impact_m5^2)^.5
tran_chord_m6=(1-impact_m6^2)^.5
tran_chord_m7=(1-impact_m7^2)^.5
##Calculate Semi-Major Axis
gravConstant=6.674e-11*1.98855e30*(86400)^2/(6.957e8)^3
semiMajor_m1=(per_m1^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m2=(per_m2^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m3=(per_m3^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m4=(per_m4^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m5=(per_m5^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m6=(per_m6^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
semiMajor_m7=(per_m7^2*star$Mass*gravConstant/(4*pi^2))^(1/3)
#Calculate Transit Duration
tran_duration_m1=star$Rad*per_m1/(semiMajor_m1*pi)*tran_chord_m1*(1-eccentricity_m1^2)^.5/(1+eccentricity_m1*sin(argPericenter_m1))*24
tran_duration_m2=star$Rad*per_m2/(semiMajor_m2*pi)*tran_chord_m2*(1-eccentricity_m2^2)^.5/(1+eccentricity_m2*sin(argPericenter_m2))*24
tran_duration_m3=star$Rad*per_m3/(semiMajor_m3*pi)*tran_chord_m3*(1-eccentricity_m3^2)^.5/(1+eccentricity_m3*sin(argPericenter_m3))*24
tran_duration_m4=star$Rad*per_m4/(semiMajor_m4*pi)*tran_chord_m4*(1-eccentricity_m4^2)^.5/(1+eccentricity_m4*sin(argPericenter_m4))*24
tran_duration_m5=star$Rad*per_m5/(semiMajor_m5*pi)*tran_chord_m5*(1-eccentricity_m5^2)^.5/(1+eccentricity_m5*sin(argPericenter_m5))*24
tran_duration_m6=star$Rad*per_m6/(semiMajor_m6*pi)*tran_chord_m6*(1-eccentricity_m6^2)^.5/(1+eccentricity_m6*sin(argPericenter_m6))*24
tran_duration_m7=star$Rad*per_m7/(semiMajor_m7*pi)*tran_chord_m7*(1-eccentricity_m7^2)^.5/(1+eccentricity_m7*sin(argPericenter_m7))*24
#Remove NaN from transit durations
tran_duration_m1=ifelse(is.nan(tran_duration_m1),0,tran_duration_m1)
tran_duration_m2=ifelse(is.nan(tran_duration_m2),0,tran_duration_m2)
tran_duration_m3=ifelse(is.nan(tran_duration_m3),0,tran_duration_m3)
tran_duration_m4=ifelse(is.nan(tran_duration_m4),0,tran_duration_m4)
tran_duration_m5=ifelse(is.nan(tran_duration_m5),0,tran_duration_m5)
tran_duration_m6=ifelse(is.nan(tran_duration_m6),0,tran_duration_m6)
tran_duration_m7=ifelse(is.nan(tran_duration_m7),0,tran_duration_m7)
print("Interpolating stellar fluctuation values for each transit duration")
###Interpolate the CDPP values for each star
for (w in 1:number_stars) {
cdpp_m1[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m1[w], rule=2)$y)
cdpp_m2[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m2[w], rule=2)$y)
cdpp_m3[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m3[w], rule=2)$y)
cdpp_m4[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m4[w], rule=2)$y)
cdpp_m5[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m5[w], rule=2)$y)
cdpp_m6[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m6[w], rule=2)$y)
cdpp_m7[w]=as.vector(approx(x=CDPPx,y=CDPPy[,w], xout=tran_duration_m7[w], rule=2)$y)
}
####Calculate signal scale
MES_m1=MES_calc(star, per_m1, rad_m1, cdpp_m1)
MES_m2=MES_calc(star, per_m2, rad_m2, cdpp_m2)
MES_m3=MES_calc(star, per_m3, rad_m3, cdpp_m3)
MES_m4=MES_calc(star, per_m4, rad_m4, cdpp_m4)
MES_m5=MES_calc(star, per_m5, rad_m5, cdpp_m5)
MES_m6=MES_calc(star, per_m6, rad_m6, cdpp_m6)
MES_m7=MES_calc(star, per_m7, rad_m7, cdpp_m7)
print("Sorting planets by MES values")
#####Sort MES Values
for (i in 1:number_stars){
#####Sorting MES Values
sortOrder=sort(c(MES_m1[i],MES_m2[i],MES_m3[i],MES_m4[i],MES_m5[i],MES_m6[i],MES_m7[i]))
####Sorting Period Values
per_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],per_m1[i],ifelse(MES_m2[i]==sortOrder[7],per_m2[i],ifelse(MES_m3[i]==sortOrder[7],per_m3[i],ifelse(MES_m4[i]==sortOrder[7],per_m4[i],ifelse(MES_m5[i]==sortOrder[7],per_m5[i],ifelse(MES_m6[i]==sortOrder[7],per_m6[i],per_m7[i]))))))
per_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],per_m1[i],ifelse(MES_m2[i]==sortOrder[6],per_m2[i],ifelse(MES_m3[i]==sortOrder[6],per_m3[i],ifelse(MES_m4[i]==sortOrder[6],per_m4[i],ifelse(MES_m5[i]==sortOrder[6],per_m5[i],ifelse(MES_m6[i]==sortOrder[6],per_m6[i],per_m7[i]))))))
per_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],per_m1[i],ifelse(MES_m2[i]==sortOrder[5],per_m2[i],ifelse(MES_m3[i]==sortOrder[5],per_m3[i],ifelse(MES_m4[i]==sortOrder[5],per_m4[i],ifelse(MES_m5[i]==sortOrder[5],per_m5[i],ifelse(MES_m6[i]==sortOrder[5],per_m6[i],per_m7[i]))))))
per_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],per_m1[i],ifelse(MES_m2[i]==sortOrder[4],per_m2[i],ifelse(MES_m3[i]==sortOrder[4],per_m3[i],ifelse(MES_m4[i]==sortOrder[4],per_m4[i],ifelse(MES_m5[i]==sortOrder[4],per_m5[i],ifelse(MES_m6[i]==sortOrder[4],per_m6[i],per_m7[i]))))))
per_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],per_m1[i],ifelse(MES_m2[i]==sortOrder[3],per_m2[i],ifelse(MES_m3[i]==sortOrder[3],per_m3[i],ifelse(MES_m4[i]==sortOrder[3],per_m4[i],ifelse(MES_m5[i]==sortOrder[3],per_m5[i],ifelse(MES_m6[i]==sortOrder[3],per_m6[i],per_m7[i]))))))
per_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],per_m1[i],ifelse(MES_m2[i]==sortOrder[2],per_m2[i],ifelse(MES_m3[i]==sortOrder[2],per_m3[i],ifelse(MES_m4[i]==sortOrder[2],per_m4[i],ifelse(MES_m5[i]==sortOrder[2],per_m5[i],ifelse(MES_m6[i]==sortOrder[2],per_m6[i],per_m7[i]))))))
per_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],per_m1[i],ifelse(MES_m2[i]==sortOrder[1],per_m2[i],ifelse(MES_m3[i]==sortOrder[1],per_m3[i],ifelse(MES_m4[i]==sortOrder[1],per_m4[i],ifelse(MES_m5[i]==sortOrder[1],per_m5[i],ifelse(MES_m6[i]==sortOrder[1],per_m6[i],per_m7[i]))))))
####Sorting Radius Values
rad_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],rad_m1[i],ifelse(MES_m2[i]==sortOrder[7],rad_m2[i],ifelse(MES_m3[i]==sortOrder[7],rad_m3[i],ifelse(MES_m4[i]==sortOrder[7],rad_m4[i],ifelse(MES_m5[i]==sortOrder[7],rad_m5[i],ifelse(MES_m6[i]==sortOrder[7],rad_m6[i],rad_m7[i]))))))
rad_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],rad_m1[i],ifelse(MES_m2[i]==sortOrder[6],rad_m2[i],ifelse(MES_m3[i]==sortOrder[6],rad_m3[i],ifelse(MES_m4[i]==sortOrder[6],rad_m4[i],ifelse(MES_m5[i]==sortOrder[6],rad_m5[i],ifelse(MES_m6[i]==sortOrder[6],rad_m6[i],rad_m7[i]))))))
rad_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],rad_m1[i],ifelse(MES_m2[i]==sortOrder[5],rad_m2[i],ifelse(MES_m3[i]==sortOrder[5],rad_m3[i],ifelse(MES_m4[i]==sortOrder[5],rad_m4[i],ifelse(MES_m5[i]==sortOrder[5],rad_m5[i],ifelse(MES_m6[i]==sortOrder[5],rad_m6[i],rad_m7[i]))))))
rad_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],rad_m1[i],ifelse(MES_m2[i]==sortOrder[4],rad_m2[i],ifelse(MES_m3[i]==sortOrder[4],rad_m3[i],ifelse(MES_m4[i]==sortOrder[4],rad_m4[i],ifelse(MES_m5[i]==sortOrder[4],rad_m5[i],ifelse(MES_m6[i]==sortOrder[4],rad_m6[i],rad_m7[i]))))))
rad_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],rad_m1[i],ifelse(MES_m2[i]==sortOrder[3],rad_m2[i],ifelse(MES_m3[i]==sortOrder[3],rad_m3[i],ifelse(MES_m4[i]==sortOrder[3],rad_m4[i],ifelse(MES_m5[i]==sortOrder[3],rad_m5[i],ifelse(MES_m6[i]==sortOrder[3],rad_m6[i],rad_m7[i]))))))
rad_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],rad_m1[i],ifelse(MES_m2[i]==sortOrder[2],rad_m2[i],ifelse(MES_m3[i]==sortOrder[2],rad_m3[i],ifelse(MES_m4[i]==sortOrder[2],rad_m4[i],ifelse(MES_m5[i]==sortOrder[2],rad_m5[i],ifelse(MES_m6[i]==sortOrder[2],rad_m6[i],rad_m7[i]))))))
rad_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],rad_m1[i],ifelse(MES_m2[i]==sortOrder[1],rad_m2[i],ifelse(MES_m3[i]==sortOrder[1],rad_m3[i],ifelse(MES_m4[i]==sortOrder[1],rad_m4[i],ifelse(MES_m5[i]==sortOrder[1],rad_m5[i],ifelse(MES_m6[i]==sortOrder[1],rad_m6[i],rad_m7[i]))))))
###Sorting Eccentricity
eccentricity_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[7],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[7],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[7],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[7],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[7],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[6],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[6],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[6],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[6],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[6],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[5],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[5],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[5],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[5],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[5],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[4],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[4],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[4],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[4],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[4],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[3],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[3],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[3],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[3],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[3],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[2],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[2],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[2],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[2],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[2],eccentricity_m6[i],eccentricity_m7[i]))))))
eccentricity_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],eccentricity_m1[i],ifelse(MES_m2[i]==sortOrder[1],eccentricity_m2[i],ifelse(MES_m3[i]==sortOrder[1],eccentricity_m3[i],ifelse(MES_m4[i]==sortOrder[1],eccentricity_m4[i],ifelse(MES_m5[i]==sortOrder[1],eccentricity_m5[i],ifelse(MES_m6[i]==sortOrder[1],eccentricity_m6[i],eccentricity_m7[i]))))))
##Sorting CDPP values
CDPP_sorted_m1[i]=ifelse(MES_m1[i]==sortOrder[7],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[7],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[7],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[7],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[7],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[7],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m2[i]=ifelse(MES_m1[i]==sortOrder[6],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[6],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[6],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[6],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[6],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[6],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m3[i]=ifelse(MES_m1[i]==sortOrder[5],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[5],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[5],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[5],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[5],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[5],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m4[i]=ifelse(MES_m1[i]==sortOrder[4],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[4],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[4],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[4],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[4],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[4],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m5[i]=ifelse(MES_m1[i]==sortOrder[3],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[3],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[3],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[3],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[3],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[3],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m6[i]=ifelse(MES_m1[i]==sortOrder[2],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[2],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[2],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[2],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[2],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[2],cdpp_m6[i],cdpp_m7[i]))))))
CDPP_sorted_m7[i]=ifelse(MES_m1[i]==sortOrder[1],cdpp_m1[i],ifelse(MES_m2[i]==sortOrder[1],cdpp_m2[i],ifelse(MES_m3[i]==sortOrder[1],cdpp_m3[i],ifelse(MES_m4[i]==sortOrder[1],cdpp_m4[i],ifelse(MES_m5[i]==sortOrder[1],cdpp_m5[i],ifelse(MES_m6[i]==sortOrder[1],cdpp_m6[i],cdpp_m7[i]))))))
}
#Calculate the probabilty of detection for each planet
print("Calculating detection probabilities")
prob_detection_m1=probability_detection(star, per_sorted_m1, rad_sorted_m1, CDPP_sorted_m1,1)
prob_detection_m2=probability_detection(star, per_sorted_m2, rad_sorted_m2, CDPP_sorted_m2,2)
prob_detection_m3=probability_detection(star, per_sorted_m3, rad_sorted_m3, CDPP_sorted_m3,3)
prob_detection_m4=probability_detection(star, per_sorted_m4, rad_sorted_m4, CDPP_sorted_m4,4)
prob_detection_m5=probability_detection(star, per_sorted_m5, rad_sorted_m5, CDPP_sorted_m5,5)
prob_detection_m6=probability_detection(star, per_sorted_m6, rad_sorted_m6, CDPP_sorted_m6,6)
prob_detection_m7=probability_detection(star, per_sorted_m7, rad_sorted_m7, CDPP_sorted_m7,7)
#Force detection probabilty to follow the sort order
prob_detection_m2=ifelse(prob_detection_m1<prob_detection_m2,prob_detection_m1,prob_detection_m2)
prob_detection_m3=ifelse(prob_detection_m2<prob_detection_m3,prob_detection_m2,prob_detection_m3)
prob_detection_m4=ifelse(prob_detection_m3<prob_detection_m4,prob_detection_m3,prob_detection_m4)
prob_detection_m5=ifelse(prob_detection_m4<prob_detection_m5,prob_detection_m4,prob_detection_m5)
prob_detection_m6=ifelse(prob_detection_m5<prob_detection_m6,prob_detection_m5,prob_detection_m6)
prob_detection_m7=ifelse(prob_detection_m6<prob_detection_m7,prob_detection_m6,prob_detection_m7)
prob_detection_m1_unsorted=c(prob_detection_m1[per_sorted_m1==period[1] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[1] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[1] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[1] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[1] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[1] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[1] & prob_detection_m7>0])
prob_detection_m2_unsorted=c(prob_detection_m1[per_sorted_m1==period[2] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[2] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[2] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[2] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[2] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[2] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[2] & prob_detection_m7>0])
prob_detection_m3_unsorted=c(prob_detection_m1[per_sorted_m1==period[3] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[3] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[3] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[3] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[3] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[3] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[3] & prob_detection_m7>0])
prob_detection_m4_unsorted=c(prob_detection_m1[per_sorted_m1==period[4] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[4] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[4] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[4] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[4] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[4] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[4] & prob_detection_m7>0])
prob_detection_m5_unsorted=c(prob_detection_m1[per_sorted_m1==period[5] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[5] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[5] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[5] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[5] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[5] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[5] & prob_detection_m7>0])
prob_detection_m6_unsorted=c(prob_detection_m1[per_sorted_m1==period[6] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[6] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[6] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[6] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[6] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[6] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[6] & prob_detection_m7>0])
prob_detection_m7_unsorted=c(prob_detection_m1[per_sorted_m1==period[7] & prob_detection_m1>0],
prob_detection_m2[per_sorted_m2==period[7] & prob_detection_m2>0],
prob_detection_m3[per_sorted_m3==period[7] & prob_detection_m3>0],
prob_detection_m4[per_sorted_m4==period[7] & prob_detection_m4>0],
prob_detection_m5[per_sorted_m5==period[7] & prob_detection_m5>0],
prob_detection_m6[per_sorted_m6==period[7] & prob_detection_m6>0],
prob_detection_m7[per_sorted_m7==period[7] & prob_detection_m7>0])
meanProb=c(sum(prob_detection_m1_unsorted)/number_stars,
sum(prob_detection_m2_unsorted)/number_stars,
sum(prob_detection_m3_unsorted)/number_stars,
sum(prob_detection_m4_unsorted)/number_stars,
sum(prob_detection_m5_unsorted)/number_stars,
sum(prob_detection_m6_unsorted)/number_stars,
sum(prob_detection_m7_unsorted)/number_stars)
meanSeven=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m3[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m4[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m5[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m6[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0],
prob_detection_m7[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0 & prob_detection_m7>0]))/number_stars
meanSix=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0],
prob_detection_m3[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0],
prob_detection_m4[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0],
prob_detection_m5[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0],
prob_detection_m6[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0 & prob_detection_m6>0]))/number_stars
meanFive=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0],
prob_detection_m3[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0],
prob_detection_m4[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0],
prob_detection_m5[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0 & prob_detection_m5>0]))/number_stars
meanFour=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0],
prob_detection_m3[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0],
prob_detection_m4[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0 & prob_detection_m4>0]))/number_stars
meanThree=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0],
prob_detection_m3[prob_detection_m1>0 & prob_detection_m2>0 & prob_detection_m3>0]))/number_stars
meanTwo=sum(pmin(prob_detection_m1[prob_detection_m1>0 & prob_detection_m2>0],
prob_detection_m2[prob_detection_m1>0 & prob_detection_m2>0]))/number_stars
meanOne=sum(prob_detection_m1[prob_detection_m1>0])/number_stars
if(is.nan(meanSeven)){
meanSeven=0
}
if(is.nan(meanSix)){
meanSix=0
}
if(is.nan(meanFive)){
meanFive=0
}
if(is.nan(meanFour)){
meanFour=0
}
if(is.nan(meanThree)){
meanThree=0
}
if(is.nan(meanTwo)){
meanTwo=0
}
if(is.nan(meanOne)){
meanOne=0
}
freq_m1=length(prob_detection_m1_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m2=length(prob_detection_m2_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m3=length(prob_detection_m3_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m4=length(prob_detection_m4_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m5=length(prob_detection_m5_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m6=length(prob_detection_m6_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_m7=length(prob_detection_m7_unsorted)/length(prob_detection_m1[prob_detection_m1>0])
freq_detect=c(freq_m1,freq_m2,freq_m3,freq_m4,freq_m5,freq_m6,freq_m7)
prob_Multiplicty=c(meanOne,meanTwo,meanThree,meanFour,meanFive,meanSix,meanSeven)
order_Multiplicity=order(meanProb, decreasing=TRUE)
if (clip==0){
return_df=data.frame(radius[order_Multiplicity],period[order_Multiplicity],eccentricity[order_Multiplicity],
meanProb[order_Multiplicity],freq_detect[order_Multiplicity],prob_Multiplicty)
} else{
return_df=data.frame(radius[order_Multiplicity][1:clip],period[order_Multiplicity][1:clip],eccentricity[order_Multiplicity][1:clip],
meanProb[order_Multiplicity][1:clip],freq_detect[order_Multiplicity][1:clip],prob_Multiplicty[1:clip])
}
names(return_df)=c("Radius","Period","Eccentricity","Probability_Detection","Frequency_Detection","Probability_Detecting_m_Planets")
return(return_df)
}