Lab 03: Interstellar Extinction and Dust Emission: Cygnus OB2 No. 12

Apparatus and Setup

This lab applies Lecture 05's Cardelli, Clayton & Mathis (1989) extinction-curve parametrization to the real, heavily reddened star Cygnus OB2 No. 12, computing extinction at multiple bands and propagating the correction to an intrinsic (dereddened) color, then extends into Lecture 06's modified-blackbody dust-temperature model.

Materials and Data

Cygnus OB2 No. 12: E(B-V)=3.10 mag, R_V=3.0, distance≈1400 pc (Massey & Thompson 1991, standard published, level 2). Cardelli, Clayton & Mathis (1989) diffuse-ISM optical/NIR parametrization coefficients (Lecture 05).

Procedure

1. Compute A_V for Cygnus OB2 No. 12 from its published E(B-V) and R_V.
2. Using the Cardelli parametrization, compute A(lambda)/A_V at V band (x=1/0.545 um^-1), B band (x=1/0.438 um^-1), and a representative near-infrared band, K (x=1/2.19 um^-1), and hence A_V, A_B, and A_K individually for this star.
3. Confirm A(V)/A_V evaluates to 1.000 (a self-consistency check on the parametrization implementation) and confirm A_K/A_V is much smaller than A_B/A_V (the physical basis for observing heavily reddened stars in the infrared).
4. Using a representative molecular-cloud dust temperature of 20 K and emissivity index beta=2, evaluate the modified-blackbody spectrum at three wavelengths (100, 250, and 850 micron) and identify which is closest to the emission peak.

Analysis and Uncertainty

Discuss how much your computed A_V would change if you had instead (incorrectly) assumed the diffuse-ISM average R_V=3.1 for Cygnus OB2 No. 12 rather than its own measured R_V=3.0 (a small correction in this case), and contrast this with how much larger an error the same substitution would cause for the anomalous HD 200775 sightline (R_V=5.0) discussed in the lecture.

Deliverables

• Computed A_V, A_B, A_K for Cygnus OB2 No. 12 with full derivations.
• The V-band self-consistency check result.
• The modified-blackbody wavelength evaluation and identified peak.
• The R_V-substitution error discussion for both stars.

Assessment Criteria

• Correct application of the Cardelli parametrization at all three bands with correct x=1/lambda values.
• Correct A_V=R_V E(B-V) arithmetic.
• Correctly reasoned R_V-substitution error comparison between the two real stars.

References and Provenance

• OpenStax Astronomy 2e (local extracted reference copy: references/openstax-astronomy-2e-extracted.txt) covers the interstellar medium in Chapter 20 ("Between the Stars: Gas and Dust in Space"): 20.1 The Interstellar Medium, 20.2 Interstellar Gas (including the 21 cm line and H II regions), 20.3 Cosmic Dust (extinction and reddening), 20.4 Cosmic Rays, 20.5 The Life Cycle of Cosmic Material, and 20.6 Interstellar Matter around the Sun. Chapter 20’s section numbering was cross-checked directly against its own embedded figure numbering this session (Figures 20.1 through 20.20 all appear under their matching section headers with no offset), so this citation is verified against the local extracted text rather than extrapolated by analogy. OpenStax’s treatment throughout Chapter 20 is descriptive and qualitative; nearly every quantitative derivation in this course (the 21 cm hyperfine radiative-transfer solution and HI column-density formula, the Jeans mass/length instability criterion, the free-fall collapse time, the Stromgren-sphere ionization-balance derivation, the Rankine-Hugoniot shock-jump conditions, and the cosmic-ray power-law spectrum) goes well beyond OpenStax Astronomy 2e’s introductory level; each lecture states explicitly where this course extends beyond the assigned reading.
• Cygnus OB2 No. 12 and HD 200775 parameters: standard published, level 2; see materials/ASTR360/reference-log.md.
• Generated by materials/ASTR360/src/generate_astr360_content.py.