Stellar Content via Maximum a posteriori Ocvirk et al. (2006a) - - PowerPoint PPT Presentation

Stellar Content via Maximum a posteriori Ocvirk et al. (2006a) Ocvirk et al. (2006b)

WHAT DOES STECKMAP?

The observed spectrum is projected onto a temporal sequence of models of single stellar populations, so as to determine a linear combination of these models, that fit the observed spectra best (via a penalized chi2 ) The weighted of the different SSP indicate the stellar content The procedure is regularized using penalizing functions.

B0(λ, t, Z) = Z Mmax

Mmin

IMF(m)S(λ, m, t, Z)dm,

Basis: Unobscurespectral energy distribution of a galaxy:

Frest(λ) = Z

tmax

tmin

SFR(t)B0(λ, t, Z(t))dt

Where SFR(t) is the Star formation rate (mass of new stars born per unit of time)

The Luminosity Weighted Stellar Age Distribution, Λ(t) gives the contribution to the total emitted light of stars of age [t,t+dt]. It is related to the SFR by: Unobscure spectral energy distribution of a galaxy:

Λ(t) = SFR(t) ∆λ Z λmax

λmin

B0(λ, t, Z(t))dλ

Frest(λ) = Z tmax

tmin

λ(t)B(λ, t, Z(t))dt

If we add an extinction law:

Frest(λ) = fext(E, λ) Z tmax

tmin

SFR(t)B0(λ, t, Z(t))dt

PENALITATION (OR A PRIORY)

The function to minimize:

Qµ = χ2(s(x, Z, E)) + Pµ(x, Z)

THE MAIN CHARACTERISTICS

§It is non parametric, and thus provides properties such as

the stellar age distributio with minimal constraints on their shape.

§The ill-conditioning of the problem is taken into account

through explicit regularitation.

§Optimal interpretation of the data is achieved by the

proper setting of the smoothing parameter.

INSTALLING STECKMAP

http://astro.u-strasbg.fr/~ocvirk/. http://www.maumae.net/yorick/doc/. (1) Install Yorick $/HOME/Yorick à $HOME/Yorick/yorick-2.1/yorick/yorick

(2) Install STECKMAP tar -xvf STECKMAP.tar You have to setup the STECKMAPROOTDIR variable If you install STECKMAP in $HOME/Yorick export STECKMAPROOTDIR=$HOME/Yorick/ setenv STECKMAPROOTDIR $HOME/Yorick/

RUNNING STECKMAP

(1) Launch Yorick by typing ‘yorick´on the shell command line. (2) Once yorick is lauched, load STECKMAP by typing:

> include, "STECKMAP/Pierre/POP/sfit.i" You´ll find a couple of example data in Yorick/Pierre/POP/EXAMPLES/ They are provided in order to give the user a taste of what can be done and how to proceed.

RUNNING STECKMAP

There are basically three functions that you run in steckmap:

Øconvert_all (convert the file in a format that steckmap can read) ØbRbasis3 (include the SSP models you want to use) Øsfit (perform the actual fit)

CONVERT_ALL

ØfV=”spectrum_gal.fits” Øa=convert_all(fv,z0=redshift,SNR0=Signal-to-noise)

à convert_all can deal at the moment only with 1D and 2D provided spectra (no datacubes)

§ > info,convert_all (all the options)

Func convert_all(filelist,cut=,noplot=,log=,z0=,SNR0=,wav=,wavaxis=,xs=,xe=,hd u=,fsigm=,errorfile=) filelist can be a list but it’s usually more practical to convert and analyse spectra one by one.

CONVERT_ALL

§ hdu= if fits file contains multiple header data units, specify number of hdu to read § cut= filelist is cut at cut-th file, default is 10 § log= log=1 enforces log wave sampling in case fits header information is

inaccurate.

§ noplot= disables the plotting of the spectrum read (useful when remotely

running a batch of spectra on a machine without an active X11 window with nohup for instance. default is noplot=0, so plotting happens.

§ z0= if redshift is not provided in fits header, can be given by user as z0= § SNR0= same as z0 for global signal to noise ratio (Note that ideally it is better to

supply a noise spectrum via errorfile)

§ errorfile= specify a name for an error file in order to fill the sigm vector. This will

• nly work for 1D spectra right now.

§ wavaxis= possible values are 1 or 2. Useful if data is provided as 2d frame, typical

for long-slit spectroscopy. If no value is provided (default) we take as the wavelength axis as the axis with largest dimension.

§ xs=, xe= start and end of the stacking in the spatial direction, useful for long slit

spectroscopy.

BRBASIS3

§ To generate ta basis, use the function bRbasis3 Øb=bRbasis3([agemin[yr],agemax[yr]],basisfile=”BC03",nbins=30,w

avel=wavel) To see all the possible parameters run > help, bRbasis3 Or > info,bRbasis3

Code Reference Age range (yr) [Z/H] BC03 Bruzual & Charlot (2003) 105 -1.7x1010 [0.3,-2] MILES Vazdekis 2010 2x107 – 1.7x1010 [0.2,-1.3] PHR Leborgne et al. (2004) 2x107-1.7x1010 [0.2,-2.0] GD05 Gonzalez-Delgado et

• al. (2005)

2x107-1.7x1010 [0.2,-2.0]

BRBASIS3

§ nbins= Number of ages bins of the basis (it doesn’t need to coincide with those on the

basis)

§ wavel= Wavelength range of the models (by default the broadest available range is

taken.

§ R=The models can be broadened to an arbitrary spectral resolution to account for

instrumental spectral resolution

§ Basisfile = models to be used.

THE FITTING ENGINE: SFIT

§ > help,sfit § >x=sfit(a,b,kin=1,epar=3,noskip=1,sav=1,nde=40,L1="D3",RMASK=[[wav1,wav2],[wav1,

wav2]])

§ Sfit need to basic arguments, the models and the spectrum to fit; § If > spdata= convert_all (“myspectrum.fits”) § And if the models are b

X=sfit(spdata,b)

SFIT

SFIT

ØMask= [[4856,4866.],[6558.,6568.]] ØX=sfit(1,b,RMASK=mask)

ØMask= [[4856,4866.],[6558.,6568.]] ØX=sfut(1,b,RMASK=mask)

ØMask= [[4856,4866.],[6558.,6568.]] ØX=sfut(1,b,RMASK=mask)

DEPENDENCE OF THE SMOOTHING PARAMETERS

§ I invite you to play a litte bit with them. The default parameters usually are a good

balance between keeping the solution smooth while still fitting the data well.

§ Increasing mux, for instance, will yield a smoother solution at the price of slightly

larger chi2

§ On the other hand, lowering mux will improve the chi2 but will make the SAD very

unstable and sensitive to noise (you can test this making MC experiments)

§ It may be informative for you to play around with mux (10-2-102)

§ When the option sav=1 several outputs are saved.

Stellar content: res-SAD, res-MASS, res-SFR and res-AMR. They look like this (here for the res-MASS file

In order of appearance:

(1) Wavelength (in Angstrom) (2) The data (original data) (3) The best fitting model (4) The weight vector (5) If epar=3, then the non-parametric extinction curve