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Cool Star with Molecular Lines

How individual TiO lines pile up into a bandhead

Hundreds of individual rotational TiO transitions (top) pile up at the blue edge of a vibrational band to form the sharp absorption "bandhead" (bottom) that dominates cool-star spectra. This is why molecular line lists are not optional below \(T_{\rm eff} \approx 4500\) K.

Cool stellar atmospheres (\(T_{\rm eff} \lesssim 4500\) K) are dominated by molecular opacity. This tutorial shows how to synthesize spectra for an M dwarf and a K giant, emphasizing the strong molecular bands that shape their spectral energy distributions.

What You Will Learn

  • How to ensure molecular data (TiO, H\(_2\)O, CN, etc.) are downloaded and enabled
  • How to select wavelength regions that capture key molecular features
  • The difference between M-dwarf and K-giant spectra at similar temperatures

Prerequisites

  • pykurucz installed and data downloaded with the full dataset (not --synthe-only)
  • Familiarity with the Stellar Parameters pipeline
  • numpy and matplotlib for plotting

Molecular data is required

Cool-star synthesis without molecular lines is physically meaningless. The --no-molecular-lines flag (or use_molecular_lines=False) should never be used for \(T_{\rm eff} < 4500\) K. pykurucz enables molecules by default when data/molecules/ is populated.

Step 1 — Verify Molecular Data

Before running, confirm that the molecular catalogs are present:

ls data/molecules/

You should see subdirectories such as tio/, h2o/, and Kurucz ASCII files for CN, CO, C\(_2\), etc. If these are missing, rerun the downloader:

python scripts/download_data.py

Disk space

The full download is ~5.2 GB. The --synthe-only option omits the gfpred29dec2014.bin predicted-line binary needed by atlas_py; for Stellar Parameters you need the full dataset.

Step 2 — Synthesize an M Dwarf

M dwarfs (\(T_{\rm eff} \approx 3000\)–\(4000\) K) show some of the strongest molecular bands in stellar astrophysics. We choose \(T_{\rm eff}=3500\) K, \(\log g=5.0\) — typical of a mid-M dwarf.

from pykurucz import synthesize

spec_path = synthesize(
    teff=3500,          # Mid-M dwarf temperature
    logg=5.0,           # High gravity (main sequence)
    mh=0.0,             # Solar metallicity
    am=0.0,
    vturb=2.0,
    wl_start=500.0,     # Optical red — TiO bandhead region
    wl_end=750.0,       # Extends into TiO γ and ε systems
    resolution=300_000,
    output_dir="results_cool",
    use_molecular_lines=True,  # Default, but explicit is clearer
    include_tio=True,
    include_h2o=True,
)

python pykurucz.py \
    --teff 3500 --logg 5.0 \
    --wl-start 500 --wl-end 750 \
    --output-dir results_cool

Runtime estimate

Cool stars have enormously more active lines than solar-type stars because of the dense molecular bands. The 250 nm window above at \(R=300\,000\) takes approximately 10–20 minutes on 8 cores. The atlas_py stage may also require a few extra iterations because the temperature structure is strongly affected by TiO opacity.

Step 3 — Synthesize a K Giant

K giants (\(T_{\rm eff} \approx 4000\) K, \(\log g \approx 1.5\)) have lower densities and therefore weaker collisional broadening, but their extended atmospheres produce deep molecular bands. We synthesize the same wavelength region for direct comparison.

from pykurucz import synthesize

spec_path = synthesize(
    teff=4000,          # K giant temperature
    logg=1.5,           # Low surface gravity (evolved star)
    mh=0.0,
    am=0.0,
    vturb=2.0,
    wl_start=500.0,
    wl_end=750.0,
    resolution=300_000,
    output_dir="results_giant",
)

python pykurucz.py \
    --teff 4000 --logg 1.5 \
    --wl-start 500 --wl-end 750 \
    --output-dir results_giant

Step 4 — Compare the Spectra

The two synthetic spectra reveal dramatically different molecular signatures despite the relatively small temperature difference.

Key features to look for (500–750 nm)

Feature Wavelength Molecule M dwarf (\(3500/5.0\)) K giant (\(4000/1.5\))
TiO \(\gamma\) bandhead ~495 nm (extends to 500+) TiO Extremely deep Strong
TiO \(\varepsilon\) 584–629 nm TiO Saturated bands Prominent
TiO \(\delta\) 705–730 nm TiO Deep Moderate
VO bands ~570, 620, 680 nm VO Visible in late M Weak or absent
CaH ~638, 675 nm CaH Moderate Weak

Why TiO dominates

Titanium is an iron-peak element with high solar abundance, and oxygen is the most abundant metal. In cool atmospheres TiO forms efficiently and has strong electronic transitions in the optical. The bandheads arise from closely spaced rotational lines that pile up at the band edge, producing nearly zero flux in late-type M dwarfs. See Molecular Equilibrium for the chemistry details.

Plotting comparison

import numpy as np
import matplotlib.pyplot as plt

# Load both spectra
wl_md, fl_md, ct_md = np.loadtxt(
    "results_cool/spec/t03500g5.00_mh+0.00_am+0.00_500_750.spec",
    unpack=True
)
wl_kg, fl_kg, ct_kg = np.loadtxt(
    "results_giant/spec/t04000g1.50_mh+0.00_am+0.00_500_750.spec",
    unpack=True
)

fig, ax = plt.subplots(figsize=(12, 5))

ax.plot(wl_md, fl_md / ct_md, lw=0.4, c="C0", alpha=0.9, label="M dwarf (3500/5.0)")
ax.plot(wl_kg, fl_kg / ct_kg, lw=0.4, c="C1", alpha=0.9, label="K giant (4000/1.5)")

ax.set_xlabel("Wavelength (nm)")
ax.set_ylabel(r"$F_\lambda / F_{\rm cont}$")
ax.set_ylim(0, 1.1)
ax.set_xlim(500, 750)
ax.legend(loc="lower left")
ax.set_title("Cool-Star Molecular Spectra Comparison")

# Annotate TiO bandheads
for wl0, label in [(516, "TiO γ"), (584, "TiO ε"), (705, "TiO δ")]:
    ax.axvline(wl0, color="gray", ls=":", lw=0.8, alpha=0.5)
    ax.text(wl0 + 2, 0.95, label, fontsize=8)

plt.tight_layout()
plt.savefig("cool_star_comparison.png", dpi=250)

You will see:

  • The M dwarf spectrum is almost completely blanketed by TiO bands, with the continuum barely visible between bandheads. The normalized flux drops to near-zero across broad wavelength intervals.
  • The K giant spectrum shows the same TiO bands but with more continuum peeking through, and overall deeper atomic lines relative to the molecular absorption because of the lower surface gravity (weaker pressure broadening).

Step 5 — Near-Infrared H\(_2\)O (Optional)

If you extend the synthesis into the J-band, H\(_2\)O becomes the dominant opacity source for very cool stars. This is more relevant for late-M and L-type objects.

from pykurucz import synthesize

spec_path = synthesize(
    teff=3500,
    logg=5.0,
    wl_start=900.0,   # Start of J-band
    wl_end=1400.0,    # J + H band
    resolution=100_000,  # Lower R saves time over such a wide range
    output_dir="results_cool_nir",
)

The output should show broad, shallow H\(_2\)O absorption troughs rather than the sharp TiO bandheads seen in the optical. At \(T_{\rm eff}=3500\) K the H\(_2\)O features are present but not yet as overwhelming as in late-M dwarfs.

Troubleshooting

Symptom Likely Cause Fix
Spectrum looks like a smooth continuum (no lines) Molecular data missing Run python scripts/download_data.py
Na D lines too shallow (~10% depth) MOLECULES OFF in atmosphere Ensure atlas_py ran with --enable-molecules (default in Stellar Parameters)
Runtime much longer than estimate Too many cores / memory contention Limit workers with n_workers=4

Next Steps