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How to make supernovae-redshift relations

Page history last edited by Tom 11 years, 9 months ago

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How to calculated the magnitude-redshift relation


Once IDL and iCosmo are set up, you can calculate the magnitude-redshift relation using the following 4 simple steps (an explanation is given below):


; (1) set fiducial parameters:



; (2) create a survey structure: 



; (3) create cosmology parameters structure:



; (4) calculate supernovae m(z) functions:





(1) Set Fiducial Parameters


Create a structure that contains all the fiducial values that are used in iCosmo.  At this stage users can input options here.  For this there are three input structures: cosmo_in, calc_in and expt_in:


cosmo_in: input cosmological parameter, the options are - 

H, Omega_B, Omega_m, Omega_L, w0, wa, n, Tau, Sigma8 and Curv 


expt_in: Input experiment parametersproperties of a survey. The options relevant to the supernovae calculation are: 

sv1_NS, sv1_SIGMAM, sv1_DELM, sv1_SNE_ZRAN, sv1_NAME, sv1_PROBES  (sv1 can also be changed to sv2 and sv3)


ns : the number of supernovae per square arcminute, depends on the total time of the survey and the efficiency of supernovae per galaxy

sigmam : the intrinsic scatter in apparent magnitudeof supernovae

delm : the experimental accuracy with with the magnitude of a given supernovae can be determined

zran : the minimum and maximum redshifts of the supernovae sample


To see the cosmological parameters:  help,fid.cosmo,/st

To see the calculation parameters:  help,fid.calc,/st

To see the parameters for survey:  help,fid.expt.sv1,/st


(2) Create a Survey Structure

Produces a structure with the survey parameters for the survey chosen by the user (help,sv,/st).  


(3) Create a Cosmology Structure


Calculates the basic cosmology parameters using the setting in the fiducial structure.  This routine produces a structure which in turn contains three structure (help,cosmo,/st):


     cosmo.const - cosmological constants such as Omega_m and sigma8

     cosmo.evol   - cosmological parameters that evolve with redshift such as co-moving distance

     cosmo.pk     - 3D matter powerspectrum (both linear and non-linear) for a set of redshift.


To see the const parameters: help,cosmo.const,/st  

To see the evol parameters:   help,cosmo.evol,/st

To see the pk parameters:      help,cosmo.pk,/st


(4) Calculate the supernovae m(z) 


You should now have a strucutre (sne) that contains the supernovae m(z) relation.  If you type, help,sne,/st , you will see the information contained in this structure.  In the example above we get;

IDL> help,sne,/st


** Structure <1d969d4>, 4 tags, length=3496, data length=3496, refs=1:

   MZ_BIN          DOUBLE    Array[18]

   Z_BIN           DOUBLE    Array[18]

   MZ              DOUBLE    Array[400]

   M0              DOUBLE           9.2254902

The m(z) has been calculated on a fine grid stored in sne.mz and in a binned structure which are the bins that would be used in the survey you have entered.


This means that:

(i)  mz_bin contains the unnormalised apparent magnitude of the supernovae in the survey redshift bins.

(ii) z_bin contains the information about the redshift bins used in the survey.  In our example if you type print,sne.Z_BIN  you should get:

IDL> print,sne.Z_BIN


      0.20000000      0.30000001      0.40000001      0.50000000      0.60000002

      0.69999999      0.80000001      0.89999998       1.0000000       1.1000000

       1.2000000       1.3000000       1.4000000       1.5000000       1.6000000

       1.7000000       1.8000000       1.9000000

To convert the supernovae magnitudes in sne.mz and sne.mz_bin to normalised supernovae add the constant sne.m0 i.e. mz_norm=sne.mz+sne.m0.




  • red - Commands you can type into IDL
  • green - What IDL print
  • blue - other, e.g. keywords


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