Apparatus and Setup
This lab builds a small exposure-time calculator using the CCD signal-to-noise equation of Lecture 06, applied to the Keck aperture and a representative modern CCD, for a range of target magnitudes.
Materials and Data
| Quantity | Value |
|---|---|
| Keck collecting area, system throughput | 76 m², 60% |
| Representative CCD read noise, dark current | 3.5 e⁻ rms, 0.001 e⁻/pix/s |
| V-band zero-point photon flux (standard published) | 9.00e+10 photons/m²/s |
| Dark-site V-band sky brightness (standard published) | 21.5 mag/arcsec² |
| V=18 target: source count rate, sky count rate | 243408.201 e⁻/s, 19483.414 e⁻/s |
Procedure
- Using the CCD equation, independently reproduce the SNR at 30 s and 300 s for the V=18 target (Lecture 06), and confirm your values against 2600.2 and 8222.6.
- Solve (by bisection or trial and error) for the exposure time reaching SNR=50 for the same V=18 target, and confirm your value against 0 s.
- Repeat step 2 for a target 2 magnitudes fainter (V=20), and compute the ratio of the two exposure times.
- State whether the ratio you found in step 3 is closer to the factor expected in the read-noise-limited regime (SNR ∝ t, so ratio ≈ flux ratio) or the background/source-limited regime (SNR ∝ √t, so ratio ≈ flux ratio squared), and justify your answer using the actual source and sky count rates in the data table.
Analysis and Uncertainty
The V-band zero-point photon flux and sky-brightness values used here are standard published order-of-magnitude values (Bessell 1998-class calibration), not independently re-verified this session; state explicitly why a real observing proposal would need site- and instrument-specific values (from an actual exposure-time calculator) rather than these representative figures.
Deliverables
- Independently reproduced SNR values at 30 s and 300 s.
- The SNR=50 exposure-time solutions for both target magnitudes.
- The exposure-time ratio with an explicit read-noise-limited-versus-background-limited classification.
Assessment Criteria
- Correct reproduction of the CCD-equation SNR values.
- Correct bisection or iterative solution for both SNR=50 exposure times.
- Correct regime classification supported by the actual count-rate numbers, not a guess.
References and Provenance
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 6 (astronomical instruments), descriptive only; this course exceeds that introductory treatment throughout.
- V-band zero-point flux and sky brightness: standard published order-of-magnitude values, not independently re-verified this session; Keck collecting area live-verified this session; see
materials/ASTR340/reference-log.md. - Generated by
materials/ASTR340/src/generate_astr340_content.py.