Apparatus and Setup
This lab uses Sirius B's independently measured mass, radius, luminosity, and temperature (Bond et al. 2017, ApJ 840, 70, combined with the Hipparcos parallax of 2.637 pc; see ../reference-log.md) to compute its density and compare it to the Chandrasekhar limit and to familiar densities.
Materials and Data
| Quantity | Value |
|---|---|
| Sirius B mass | 1.018 ± 0.011 M☉ = 2.0248e+30 kg |
| Sirius B radius | 0.008098 R☉ = 5.6338e+06 m (5,634 km) |
| Sirius B luminosity | 0.02448 L☉ |
| Sirius B effective temperature | 25,000 K |
| Chandrasekhar limit | 1.4 M☉ |
| Water density (comparison) | 1,000 kg/m³ |
| Earth's average density (comparison) | 5,510 kg/m³ |
Procedure
- Compute Sirius B's volume, V = (4/3)πR³, from its measured radius.
- Compute Sirius B's average density, ρ = M/V, in kg/m³ and convert to g/cm³.
- Compute the ratio of Sirius B's density to water's and to Earth's average density.
- Using Stefan-Boltzmann (L = 4πR²σT⁴), independently verify Sirius B's quoted luminosity (0.02448 L☉) from its measured radius and temperature. Report the percent agreement with the quoted value.
- State Sirius B's mass as a fraction of the Chandrasekhar limit, and explain what would need to happen (physically) for Sirius B to approach that limit, referencing Lecture 08's Type Ia supernova mechanism.
- A hypothetical second white dwarf has a measured radius of 0.0050 R☉ and the same average density you computed for Sirius B. Compute its implied mass, and state whether that mass is physically plausible for a white dwarf (compare to the Chandrasekhar limit).
Analysis and Uncertainty
Sirius B's mass carries a published uncertainty of ±0.011 M☉ (about 1%) and its radius carries an uncertainty of about ±0.6%. Propagate these into density uncertainty using σ_ρ/ρ = √[(σ_M/M)² + (3σ_R/R)²] (the factor of 3 arises because density depends on R³), and report the resulting percent uncertainty on the density you computed.
Deliverables
- Sirius B volume and density calculation (kg/m³ and g/cm³), with density uncertainty propagated.
- Density ratio to water and to Earth.
- Stefan-Boltzmann luminosity cross-check with percent agreement to the quoted value.
- Mass-to-Chandrasekhar-limit ratio and physical discussion.
- Hypothetical second-white-dwarf mass calculation and plausibility judgment.
Assessment Criteria
- Correct volume and density arithmetic with units at each step.
- Correct density-uncertainty propagation using the R³ scaling factor of 3.
- Stefan-Boltzmann cross-check computed correctly and compared quantitatively to the quoted luminosity.
- Physically sound discussion of the Chandrasekhar limit and the hypothetical white dwarf's plausibility.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 23.1.
- Sirius B measurements: Bond, H. E. et al. (2017), ApJ 840, 70; verified via live retrieval, logged in
materials/ASTR230/reference-log.md.