Apparatus and Setup
This lab reproduces the main-sequence turnoff age calculation for the Hyades open cluster (Lecture 09), using the cluster's live-verified distance, age, turnoff mass, and structural radii (fetched directly this session; see ../reference-log.md).
Materials and Data
| Quantity | Value |
|---|---|
| Distance | 47 pc |
| Independently measured (isochrone-fit) age | 625 Myr |
| Main-sequence turnoff mass | 2.3 M⊙ |
| Total cluster mass | 400 M⊙ |
| Core radius / half-mass radius / tidal radius | 2.7 / 5.7 / 10 pc |
Procedure
- Using L ≈ M^3.5, compute the predicted luminosity of a 2.3 M⊙ turnoff star.
- Using t_MS = 10 Gyr × M/L, compute the predicted main-sequence lifetime of a 2.3 M⊙ star from your Problem 1 luminosity.
- Compare your predicted lifetime to the cluster's independently measured age (625 Myr), computing the ratio explicitly, and state honestly (not as "excellent agreement") how large the discrepancy is.
- Using the cluster's total mass and tidal radius, estimate its mean mass density in M⊙/pc³, and compare this to its core-radius density (using the core radius instead of the tidal radius in the same formula), stating which is denser and by what factor.
Analysis and Uncertainty
State explicitly, using the ratio you computed in step 3, whether the fixed n=3.5 mass-luminosity exponent over- or under-predicts the true main-sequence lifetime for a 2.3 M⊙ star, and connect this to Lecture 07's discussion of the exponent's mass-dependence.
Deliverables
- Completed luminosity and lifetime predictions with full arithmetic.
- An honest, explicitly quantified statement of the discrepancy between the predicted lifetime and the cluster's measured age (no "excellent agreement" language for a discrepancy of this size).
- Both density estimates (core and tidal radius) with a comparison.
Assessment Criteria
- Correct mass-luminosity and lifetime arithmetic.
- Explicit, correctly computed discrepancy ratio, honestly characterized (not overstated as close agreement).
- Correct density arithmetic and comparison for both radii.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 21.1.
- Hyades cluster distance, age, turnoff mass, total mass, and structural radii: live-verified this session via a direct web fetch of Wikipedia's "Hyades (star cluster)" article, citing Perryman et al. (1998), A&A 331, 81; see
materials/ASTR330/reference-log.md. - Generated by
materials/ASTR330/src/generate_astr330_content.py.