Kurucz Model Stellar Atmosphere Lab

February 14, 2025

Overview

In this laboratory exercise, you will explore the relationships between different types of stars and their radiated spectral energy distributions, including how temperature and heavy-element abundances change stellar spectra, how reasonable blackbody radiation is as an approximation to "real" stellar radiation, and how the emergent spectrum translates into photometric "colors". Rather than observed stellar spectra, you will analyze detailed model spectra generated with the ATLAS stellar atmosphere code of Robert Kurucz and collaborators. The Kurucz models are available online for a large range of different types of stars, parameterized by "surface temperature" Teff (effective photospheric temperature), "surface gravity" g (gravitational acceleration at the photosphere, which differs for dwarfs and giants of the same spectral type), metallicity [M/H] (log heavy element abundance relative to Solar), and microturbulent velocity vturb. In this lab, we will adopt vturb = 2 km/s for all cases.

You will download and analyze the spectra on your own laptop computer, running Python code in the Jupyter Notebook environment installed for a previous lab assignment (probably launched from the Anaconda Navigator app). You may also need a text editor to modify text files occasionally. Ask your instructor if you need help with this.

An example plot command file is available in the directory linked below. You are welcome to copy it to your work area and modify it with a text editor for your own use. Please review it and ask if you have any questions.

A variety of reference materials on the relevant astrophysics, accessing the data, and using various software applications are linked below following the procedure instructions.

Laboratory Procedure

  1. Using Solar physical measurements (see below), determine which Kurucz model in the families listed below is the closest match to the Sun (spectral type G2 V). Report this choice and download the model spectrum to your computer.

  2. Plot up the Kurucz spectrum using Python (see examples below). Edit the Kurucz spectrum file to make sure that all the flux data conform to standard computer scientific notation (e.g., 9.87654E-321, not 9.87654-321) and all data columns are separated by at least one space.

  3. In another line type (dotted or dashed), overplot a blackbody curve for Teff  matching that of the chosen Kurucz spectrum, scaled appropriately to have the same area under the curve. (To compute this integral, find the sum of the flux in each spectral bin times the width of that bin, which can be found for bin i as half the difference between the center frequencies or wavelengths of bins i+1 and i-1.) Be careful of units, and make sure you choose the right form of the Planck function (per frequency or per wavelength). [Note: In order to avoid floating-point overflow/underflow errors, you may need to specify some constants like h, k, etc. as double-precision floating-point numbers, e.g., h = 6.626D-34 rather than 6.626E-34.]

  4. Is the blackbody spectrum a good fit to the stellar model spectrum? If not, is there a better one at another temperature? Explain why a Planck function is or is not a good fit to this model.

  5. Repeat all the steps above for a Vega-like A0 V star with 30% Solar metallicity (use Bradt's tabulated stellar parameters linked below; assume an isotropic A0 V star with the official Teff, ignoring Vega's own oblateness and the consequent bias in its observed Teff).

  6. Estimate the integrated Kurucz model flux for both the Solar-type and Vega-type stars in the U, B, and V photometric filters, assuming (somewhat simplistically) that the filters have perfect transmission within their respective passbands of 365 ± 34 nm, 440 ± 49 nm, and 550 ± 45 nm, and zero transmission outside these passbands (for real passband curves, see Carroll & Ostlie Fig. 3.10, linked below). Record your integrated fluxes fU,  fB, and  fV in a table.

  7. From these integrated fluxes, calculate and tabulate the U-B and B-V colors of the Solar-type star, adopting the convention that Vega, as a photometric color reference, has U-B = mU - mB = 0.0 and B-V = mB - mV = 0.0. Recall that from the definition of magnitude, m2 - m1 = -2.5 log10 (f2 / f1).

  8. Repeat the above analysis for a Solar-type star with 10% Solar metallicity (metal-poor Galactic thin disk Population I dwarf), including any graphs, discussions, and measurements (you don't need to repeat the steps for Vega). Comment on differences between the 10% and 100% metallicity spectra, and record any changes in UBV colors.

  9. Repeat the above analysis for a Solar-type star with 1% Solar metallicity (metal-poor Galactic thick disk Population II subdwarf), including graphs, discussions, and measurements. Describe any differences between the 1% and 10% metallicity spectra, and record any changes in UBV colors.

  10. Repeat the above analysis for a Solar-type star with 0.01% Solar metallicity (extreme metal-poor Galactic halo Population II subdwarf), including graphs, discussions, and measurements. Describe differences between the 0.01% and 1% metallicity spectra, and record any changes in UBV colors.

  11. Plot ``line blanketing vectors'' on a U-B vs. B-V color-color diagram, showing how the stellar model colors change from 0.01% to 1% to 10% to 100% Solar metallicity (put a big fat point at each metallicity and connect the points with lines). Compare these to Mihalas & Binney's Figure 3-11, linked below.

  12. Submit your completed work to your instructor, including all required plots and other results as specified by the questions above.

Software Links

Spectral Model Links

Astrophysics Links