Apparatus and Setup
This lab computes the Chandrasekhar mass from first principles (Lecture 12) and applies it to Sirius B, whose mass, radius, and temperature were independently live-verified in ASTR 230's production and carried forward through ASTR 310.
Materials and Data
| Quantity | Value |
|---|---|
| Sirius B mass | 1.018 M⊙ |
| Sirius B radius | 0.008098 R⊙ |
| Sirius B effective temperature | 25000 K |
| Fundamental constants | ħ = 1.0546e-34 J·s, c = 2.998e+08 m/s, G = 6.6740e-11 m³kg⁻¹s⁻², m_p = 1.6726e-27 kg |
Procedure
- Using M_Ch = (ω3&sup0;√3π/2)(ħc/G)^(3/2)/(μ_e m_p)² with ω3&sup0; = 2.018236 and μ_e = 2.0 (carbon-oxygen composition), compute the Chandrasekhar mass numerically, showing every substituted value.
- Compute Sirius B's mass as a fraction (percent) of your computed Chandrasekhar mass, and state whether this is consistent with Sirius B's continued existence as a stable white dwarf.
- Using the Stefan-Boltzmann law, compute Sirius B's luminosity from its measured radius and temperature, in solar luminosities.
- Using the schematic Mestel-type cooling estimate t_cool ≈ k_cool × (M/M⊙) × (L/L⊙)^(-5/7) with k_cool = 0.015, estimate Sirius B's cooling age, and compare it (order of magnitude only) to the commonly cited age of the Sirius system (a few hundred Myr).
Analysis and Uncertainty
State explicitly that the cooling-age estimate in step 4 uses a schematic calibration constant (k_cool), not a full white-dwarf cooling-track model, and explain why this is acceptable for an order-of-magnitude age estimate but not for a precision cooling-age measurement.
Deliverables
- The full Chandrasekhar-mass derivation with every substituted constant shown.
- Sirius B's mass-fraction-of-Chandrasekhar-mass calculation.
- Sirius B's Stefan-Boltzmann luminosity calculation.
- The cooling-age estimate with an explicit order-of-magnitude comparison to the Sirius system's commonly cited age.
Assessment Criteria
- Correct substitution and arithmetic in the Chandrasekhar-mass formula.
- Correct mass-fraction and luminosity calculations.
- Correct order-of-magnitude cooling-age estimate with an explicit, honestly qualified comparison.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 22.1-22.2.
- Sirius B mass, radius, and temperature: live-verified in ASTR 230's production (Bond et al. 2017, ApJ 840, 70); carried forward unchanged through ASTR 310 and this course.
- Generated by
materials/ASTR330/src/generate_astr330_content.py.