Lab 01: Building a Hertzsprung-Russell Diagram from Real Nearby and Bright Stars

Apparatus and Setup

You will use the real 20-star sample in ../data/nearby_bright_stars.csv (apparent V magnitude, parallax in milliarcseconds, effective temperature, and spectral type for the Sun plus 19 well-known nearby or bright stars; Sirius B values are independently verified against Bond et al. 2017, ApJ 840, 70; see ../reference-log.md for full provenance and spot-check notes on the remaining stars). No specialized instrument is required for this lab; it is a data-analysis lab using real published stellar parameters.

Materials and Data

Procedure

1. For each star with a measured parallax, compute distance d = 1/p(arcsec) in parsecs (the Sun has no meaningful stellar parallax; treat its distance as 1 AU = 4.848 × 10⁻⁶ pc for scale only, and do not plot the Sun's absolute magnitude derived this way — use its known M_V = 4.83 directly instead).
2. Compute each star's distance modulus (m − M) = 5log10(d) − 5, then its absolute magnitude M_V = m − (m−M).
3. Plot every star on a Hertzsprung-Russell diagram: T_eff (or spectral type, decreasing left to right) on the horizontal axis, M_V (brighter/more negative upward) on the vertical axis.
4. Identify which stars fall on the main sequence, which are giants/supergiants (well above the main sequence at their temperature), and which are white dwarfs (well below the main sequence at their temperature). Label at least one example of each from your plot.
5. For Sirius A and Betelgeuse, state which spectral-classification physics from Lecture 02 explains why each shows the line strengths it does at its respective T_eff.
6. Compute the luminosity ratio between Betelgeuse and Proxima Centauri using each star's absolute magnitude (L1/L2 = 10^((M2 − M1)/2.5)), and comment on how a red giant and a red dwarf can have such different luminosities despite similar surface temperatures (hint: revisit the Stefan-Boltzmann radius dependence from Lecture 01).

Analysis and Uncertainty

Distance-modulus uncertainty is dominated by parallax measurement precision; for a star with parallax uncertainty of a few percent, the resulting distance modulus uncertainty is of order 0.1 mag (a few percent in d translates to a few hundredths of a magnitude in 5log10(d)). State, for the star in your sample with the smallest parallax (largest relative uncertainty), why its derived absolute magnitude and hence its position on the H-R diagram is least certain.

Deliverables

• Completed distance/absolute-magnitude table for all 20 stars.
• One labeled Hertzsprung-Russell diagram with main sequence, giants/supergiants, and white dwarfs identified.
• Betelgeuse/Proxima luminosity-ratio calculation with a physical interpretation.
• A short (150-250 word) paragraph identifying which star in the sample has the least certain H-R diagram position and why.

Assessment Criteria

• Correct distance and absolute-magnitude arithmetic for all stars with parallax data.
• H-R diagram correctly separates main-sequence, giant/supergiant, and white-dwarf populations.
• Luminosity-ratio calculation shown with correct formula and units.
• Uncertainty discussion identifies the correct star and correct reasoning (smallest parallax, not simply "farthest star" without justification).

References and Provenance

• OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 18.1-18.2 and Chapter 19.1.
• Star sample: materials/ASTR230/data/nearby_bright_stars.csv, generated by materials/ASTR230/src/generate_astr230_content.py; provenance and spot-check status logged in materials/ASTR230/reference-log.md.