Stellar Density

NOTE: To attempt this exercise, some form of array manipulation software is required. If you have IDL or Supermango, these are highly recommended to use to complete the exercise. Excel or OpenOffice will work, but simply don't have the functionality to make the assignment easy to do. Because of this, and the fact that IDL/Supermango can be expensive, we recommend you use R. R can be downloaded from here. We have attached files at the end of the exercise for R, IDL, and Supermango, which contain solutions to all of the problems should you get stuck and need some help.

Datafile for assignment:
hwdata.dat
Save file for IDL !ONLY!-do not use if not using IDL: hwdata.sav

The data file hwdata.dat contains SDSS measurements for about 600,000 stars with b > 80? (i.e. within 10? from the north galactic pole) and 14 < r < 21. The data are listed as one line per star, with each line containing the following quantities:

  • ra dec: right ascension and declination (J2000.0) in decimal degrees
  • run: SDSS observing night identifier
  • Ar: the value of the r band ISM extinction used to correct photometry (adopted from the SFD maps; for bands other than r standard SDSS coefficients are used)
  • u g r i z: SDSS photometry (corrected for the ISM extinction)
  • uErr gErr rErr iErr zErr: photometric errors
  • pmL pmB: proper motion vector components in the longitudinal and latitudinal directions (mas/yr); set to 999.99 when no measurement is available
  • pmErr: mean proper motion error (mas/yr); set to 999.99 when no measurement is available

    • The goal of this project is to use paralax relations to calculate magnitudes and metallicities of stars, so that we can find the distances to them. We will compute absolute magnitude using a photometric parallax relation, and since b > 80, for these stars the distance is simply their height above the plane of the galaxy Z. Using Z = D , where D is computed from the absolute magnitude equation: r - Mr = 5 * log (D/(10pc)), attempt the following problems:

    1. For stars with 0.2 < g - r < 0.4, plot ln(Rho) vs. Z , where Rho is the stellar number density in a given bin (e.g. look at Figs. 5 and 15 in JuriŽ et al. 2008, ApJ, 673, 864 for similar examples). You can approximate Rho(Z) = N(Z)/V(Z ), where N(Z) is the number of stars in a given bin, and V(Z) is the bin volume (note that the solid angle is ~ 314 deg ). What is the Z range where you believe the results, and why?

    2. For subsample with 0.2 < g - r < 0.4, separate stars into low-metallicity sample, [F e/H ] < -1.0, and high-metallicity sample, [F e/H ] > -1.0. Compare their ln (Rho) vs. Z curves. What do you conclude?

    3. Add ln(Rho) vs. Z for stars with 0.4 < g - r < 0.6, 0.6 < g - r < 0.8, and 0.8 < g- r < 1.0 (you can rescale all curves to the same value at some ?ducial Z , or leave them as they are). Discuss the differences compared to the 0.2 < g - r < 0.4 subsample. Why do we expect larger systematic errors for 0.8 < g - r < 1.0 than for the adjacent bin with 0.4 < g - r < 0.6?

    4. For these low-metallicity and high-metallicity samples, plot and compare their differential r band magnitude distributions (i.e. the number of sources per unit magnitude, in small, say 0.1 mag wide, r bins). What do you conclude? How would you numerically describe these curves (i.e. what kind of functional form for the fitting functions would you choose)?

    5. What should be the faint r band limit for a survey to be able to map the ln ? vs. Z profile out to 100 kpc using main-sequence stars? Assume the same color distribution as for the SDSS sample. For a solid angle of 1 deg2 , how many stars with 0.2 < g - r < 0.4 would you expect with distances between 90 kpc and 100 kpc? Assume whatever additional information you need to solve this problem (not all required information is provided here).