ProFit/ProFound: Using Isophotal Ellipses

Aaron Robotham

2017-12-08

First load the libraries we need:

library(ProFit)
## Loading required package: Rcpp
## Warning: package 'Rcpp' was built under R version 3.4.2
## Loading required package: FITSio
library(ProFound)
## Loading required package: data.table

Load data:

image = readFITS(system.file("extdata", 'KiDS/G278109fitim.fits', package="ProFit"))$imDat
segim = readFITS(system.file("extdata", 'KiDS/G278109segim.fits', package="ProFit"))$imDat
sigma = readFITS(system.file("extdata", 'KiDS/G278109sigma.fits', package="ProFit"))$imDat
segim = readFITS(system.file("extdata", 'KiDS/G278109segim.fits', package="ProFit"))$imDat
psf = readFITS(system.file("extdata", 'KiDS/G278109psfim.fits', package="ProFit"))$imDat

Extract isophotal ellispes, notice we allow for boxy isophotes:

ellipses_box = profoundGetEllipses(image=image, segim=segim, levels=20, dobox=TRUE, pixscale=1)

Show the extracted isophotal surface brightness profile:

magplot(ellipses_box$ellipses[,c("radhi","SB")], xlim=c(0,100), ylim=c(30,20), grid=TRUE, xlab=' Radius / pixels', ylab='mag / pix^2')

Setup the 1D function we want to minimise for our rough fit:

sumsq1D=function(par=c(17.6, log10(1.7), log10(3), 17.4, log10(13), log10(0.7)), rad, SB, pixscale=1){
  bulge=profitRadialSersic(rad, mag=par[1], re=10^par[2], nser=10^par[3])
  disk=profitRadialSersic(rad, mag=par[4], re=10^par[5], nser=10^par[6])
  total=profitFlux2SB(bulge+disk, pixscale=pixscale)
  return=sum((total-SB)^2)
}

Do the 1D optimisation:

lower=c(10,0,0,10,0,-0.5)
upper=c(30,2,1,30,2,0.5)

fit1D=optim(sumsq1D, par=c(15, log10(5), log10(4), 15, log10(50), log10(1)),
rad=ellipses_box$ellipses$radhi, SB=ellipses_box$ellipses$SB, pixscale=1,
method='L-BFGS-B', lower=lower, upper=upper)$par

Plot the data and the fitted bulge/disk/total model:

magplot(ellipses_box$ellipses$radhi, ellipses_box$ellipses$SB, xlim=c(0,100), ylim=c(30,20), grid=TRUE, type='l', xlab=' Radius / pixels', ylab='mag / pix^2')
#A simple bulge+disk surface brightness profile:
rlocs=seq(0,100,by=0.1)
bulge=profitRadialSersic(rlocs, mag=fit1D[1], re=10^fit1D[2], nser=10^fit1D[3])
disk=profitRadialSersic(rlocs, mag=fit1D[4], re=10^fit1D[5], nser=10^fit1D[6])
lines(rlocs, profitFlux2SB(bulge, pixscale=1), col='red')
lines(rlocs, profitFlux2SB(disk, pixscale=1), col='blue')
lines(rlocs, profitFlux2SB(bulge+disk, pixscale=1), col='green')

Setup the initla model list based on our approximate 1D fit solution:

bulgedom_rad=max(rlocs[bulge>disk])
bulge_ang=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi<bulgedom_rad,'ang'])
bulge_axrat=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi<bulgedom_rad,'axrat'])
bulge_box=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi<bulgedom_rad,'box'])

disk_ang=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi>bulgedom_rad,'ang'])
disk_axrat=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi>bulgedom_rad,'axrat'])
disk_box=mean(ellipses_box$ellipses[ellipses_box$ellipses$radhi>bulgedom_rad,'box'])

model_init=list(
  sersic = list(
    xcen   = c(ellipses_box$ellipses$xcen[1], ellipses_box$ellipses$xcen[1]),
    ycen   = c(ellipses_box$ellipses$ycen[1], ellipses_box$ellipses$ycen[1]),
    mag = c(fit1D[1]-2.5*log10(bulge_axrat), fit1D[4]-2.5*log10(disk_axrat)),
    re  = c(10^fit1D[2], 10^fit1D[5]),
    nser  = c(10^fit1D[3], 10^fit1D[6]),
    ang  = c(bulge_ang, disk_ang),
    axrat  = c(bulge_axrat, disk_axrat),
    box = c(bulge_box, disk_box)
  )
)

Usual ProFit bulge/disk setup stuff:

tofit=list(
  sersic=list(
    xcen= c(TRUE,NA), #We fit for xcen and tie the two togther
    ycen= c(TRUE,NA), #We fit for ycen and tie the two togther
    mag= c(TRUE,TRUE), #Fit for both
    re= c(TRUE,TRUE), #Fit for both
    nser= c(TRUE,TRUE), #Fit for both
    ang= c(FALSE,TRUE), #Fit for disk
    axrat= c(FALSE,TRUE), #Fit for disk
    box= c(FALSE,TRUE) #Fit for disk
  )
)

# What parameters should be fitted in log space:

tolog=list(
  sersic=list(
    xcen= c(FALSE,FALSE),
    ycen= c(FALSE,FALSE),
    mag= c(FALSE,FALSE),
    re= c(TRUE,TRUE), #re is best fit in log space
    nser= c(TRUE,TRUE), #nser is best fit in log space
    ang= c(FALSE,FALSE),
    axrat= c(TRUE,TRUE), #axrat is best fit in log space
    box= c(FALSE,FALSE)
  )
)

# The hard interval limits to use when fitting. This is not strictly required, but without
# this we cannot ensure the sampler does not enter unallowed values like negative sizes,
# Sersic indices and axial ratios etc:

intervals=list(
  sersic=list(
    xcen=list(lim=c(0,300),lim=c(0,300)),
    ycen=list(lim=c(0,300),lim=c(0,300)),
    mag=list(lim=c(10,30),lim=c(10,30)),
    re=list(lim=c(1,100),lim=c(1,100)),
    nser=list(lim=c(0.5,20),lim=c(0.5,20)),
    ang=list(lim=c(-180,360),lim=c(-180,360)),
    axrat=list(lim=c(0.1,1),lim=c(0.1,1)),
    box=list(lim=c(-1,1),lim=c(-1,1))
  )
)

Setup the basic Data:

Data=profitSetupData(image=image, sigma=sigma, segim=segim, psf=psf, modellist=model_init, tofit=tofit, tolog=tolog, intervals=intervals, magzero=0, algo.func='optim')

The inital guess bulge/disk/total plots:

profitLikeModel(Data$init,Data,makeplots=TRUE,whichcomponents=list(sersic=1))

profitLikeModel(Data$init,Data,makeplots=TRUE,whichcomponents=list(sersic=2))

profitLikeModel(Data$init,Data,makeplots=TRUE,whichcomponents=list(sersic='all'))

optimfit=optim(Data$init, profitLikeModel, method='BFGS', Data=Data, control=list(fnscale=-1))

Compare the fit model to the one estimated from the 1D fit:

profitRemakeModellist(optimfit$par, Data=Data)$modellist

And finally some bulge/disk/total plots:

profitLikeModel(optimfit$par,Data,makeplots=TRUE,whichcomponents=list(sersic=1))
profitLikeModel(optimfit$par,Data,makeplots=TRUE,whichcomponents=list(sersic=2))
profitLikeModel(optimfit$par,Data,makeplots=TRUE,whichcomponents=list(sersic='all'))