The Initial Mass Function of Massive Stars


Abstract:
The Initial Mass Function (IMF) of the bright end of the mass scale is a crucial parameter for determining the upper limit of stellar mass and its connection to the environment such as metallicity. The high mass stars, typically O- and B-type stars, are the luminous tracers of the young populations in galaxies. Although intrinsically few, their large fluxes make them easy to observe, both in our galaxy and other nearby galaxies. To determine the IMF it is necessary to know the mass of the stars (inferred from their position in colour-magnitude diagram) as well as their absolute magnitude, i.e. their exact distance and absorption. An efficient way of overcoming the problem of constraining the extinction as well as getting an exact estimation of the stars' distance is to consider the stars in stellar clusters. In order to address this science case using VO tools, we will suggest ways of selecting samples, construct the broad band spectral energy distribution of the selected stars and compare them to theoretical models available via the VO resources.


Step-by-Step

Launching the tools
Workbench running in the background, Aladin, Topcat, VOSpec. We will also use STILTS and the conesearch workflow.








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Finding and Loading
the Optically visible open clusters and candidates (Dias et al. 2002-2005) using Aladin







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Broadcast
the selected table to Topcat


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Define the subsample
The catalogue has 1697 entries. We will now selected distant, compact clusters with low reddening and a relatively large amount of stars-members:
  • Clusters with low reddening, E(B-V)<0.2 or $10<0.2
  • Distance > 500pc or $9>500
  • Angular size < 30 arcmin or $8<30
  • Clusters with over 30 known members or $16>30


There is a total of 12 open clusters with these characteristics. We change the name of the fourth column of the table ($4) from Cluster to Name (conesearch -see next step- needs this column) and save the subsample as a VOTable: working_sample.vot


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We will now use the Astrogrid conesearch Workflow to search for SDSS and 2MASS data. We will need the python script conesearch.py as well as the auxiliary file VOTable.py




For each entry of the catalogue (i.e. open cluster) conesearch creates a directory with three VOTables:
  • SDSS-DR4.vot, a catalogue with SDSS (from Data Release 4) datapoints withing the region of the cluster
  • 2MASS-PSC.vot, a catalogue with 2MASS datapoints (from the 2MASS Point Source Catalogue)
  • NED(sources).vot, a list of extragalactic sources from NED (not used in this case)

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Collect the theoretical models
Our aim is to compare the observed SEDs of hot star candidates with a series of theoretical models. We will first look for those models. One way of querying them is via the Spanish VO web pages. Via the Theoretical Models Web Server we will query the Kurucz stellar library and retrive model spectra of hot stars.









This query will return a tar file with models, in VOTable format, for each of the parameter combination.

Loop over the clusters
The following steps have to be repeated for each of the 12 selected open clusters:
  1. Extinction-corrected selected criteria
  2. Cross-correlation
  3. Hot star candidates selection
  4. Creation of observed SEDs
As an example, we will follow ste-by-step the case of NGC2420; the exact same procedure has to be followed in the case of all other open clusters

  • Extinction correction
    • Extinction correction: for NGC2420, E(B-V)=0.029 and thus E(U-B)=0.72*E(B-V)=0.021 (Turner et al., 1989, AJ, 98, 2399)
    • Colour conversion: u-g=0.75(U-B)+0.77(B-V)+0.72 (Jordi et al., 2006) => u-g<1.02
  • Cross-correlation
Load SDSS-DR4.vot and 2MASS-PSC.vot into Topcat; if the conesearch workflow failed to produce valid VOTables, the conesearch can be run from Topcat, as well, but around one position only.



Run the matching



1123 objects with SDSS and 2MASS datapoints


  • Hot star candidates selection
We use Topcat to create a u-g column





We then select objects with u-g<1.02 (see Extinction Correction)



There are 38 objects with u-g<1.02; 3 are galaxies according to the SDSS "Type" and are discared. 

Using Aladin we can construct and RGB image from three SDSS images (here u, g and i) and overplot the positions of the selected hot star candidates

  • Build observed SEDs table
    • The first step is to convert all the magnitudes into erg/sec/cm²/A. We will do it using Topcat. The SDSS AB magnitudes will be converted to fluxes using the function abToJansky. The 2MASS Vega magnitudes will be also converted to fluxes using this same function after subtracting the AB corrections  (0.933, 1.407 and 1.862 for J, H and K, respectively)


    • We then convert the Jy to erg/sec/cm²/A

                (We can do this in one step replacing flux_U by abToJansky(PSFMAG_U))
The conversion has to be done for each magnitude separately. We then save the table as a VOTable (in this example we call it NGC2420SDSS2MASS_new.vot)
    • We will now use STILTS to transpose the table (i.e. convert the columns to rows). STILTS is the library behind Topcat and is used in command-line. We call the transposed table NGC2420SDSS2MASS_new_transpose.vot


    • Each column of the transposed table now contains magnitudes and fluxes of a one object. We load NGC2420SDSS2MASS_new_transpose.vot and create a subsample keeping only the the rows with the fluxes





    • Finally, we create a new column and fill it add with the effective wavelength of each filter



  • Compare models and observed SEDs
As a last step, we will now compare model and observed SEDs in order to confirm that the selected objects are indeed massive hot stars. Ideally, this has to be done by SED fitting and standard chi² minimisation. Such tools are currently under construction. See, e.g., Yafit.

In a non-automated fashion, we can use Topcat or VOSpec.








The Workflow

If we wanted to schematically represent the workflow of all the steps we followed, it would look like this: