Lecture 05: Interstellar Dust I: Extinction and Reddening

ASTR 360 The Interstellar Medium

Context and Why This Matters

Every optical/infrared observation of a star or nebula behind interstellar dust -- including the H II region diagnostics in Unit 6 and any real photometric distance/luminosity determination -- must be corrected for extinction and reddening; this lecture derives the physical basis for that correction from first principles.

Learning Goals

  1. Derive the relationships among optical depth, extinction in magnitudes, color excess E(B-V), and the total-to-selective extinction ratio R_V.
  2. Apply the Cardelli, Clayton & Mathis (1989) average Galactic extinction-curve parametrization to compute extinction at multiple wavelengths for a real, heavily reddened star.
  3. Explain, physically, why interstellar dust extinction is wavelength-dependent (grain-size-comparable-to-wavelength scattering) and why this produces reddening.

Opening Phenomenon

Cygnus OB2 No. 12, one of the intrinsically most luminous stars known in the Galaxy, appears in an ordinary optical image as a comparatively faint, deep-red point of light -- because 9.3 magnitudes of visual extinction, corresponding to a factor of 5248 in flux, lie along the line of sight through the Cygnus OB2 association’s dense foreground dust.

Terms Developed in Context

extinction

The wavelength-dependent loss of direct light from a beam through both absorption and scattering by intervening material. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. Extinction in magnitudes, A_lambda, is related to the optical depth tau_lambda of intervening dust by A_lambda = 1.086 tau_lambda (the factor 1.086 = 2.5/ln(10) converts from the natural-log-based optical depth to the base-2.5-per-magnitude convention).

It is tied to the lecture’s observables or evidence in this way: Interstellar dust both absorbs and scatters starlight out of the line of sight, dimming a star’s apparent brightness (extinction) by an amount that increases toward shorter (bluer) wavelengths, because interstellar grains are comparable in size to or smaller than optical wavelengths (Rayleigh/Mie-regime scattering is more efficient at shorter wavelengths) -- the same physical reason Earth’s sky is blue, applied to interstellar rather than atmospheric particles. A second connection is important for using the term in physical reasoning: The color excess E(B-V) = A_B - A_V isolates the wavelength-dependent part of extinction from any wavelength-independent flux normalization, and the total-to-selective extinction ratio R_V = A_V/E(B-V) characterizes the overall shape (steepness) of the extinction curve: a larger R_V means a "grayer" (less steeply wavelength-dependent) extinction law, physically associated with a larger typical grain size along that sightline. The observational interpretation is constrained by Because extinction is stronger at blue wavelengths than red, a reddened star’s observed color (e.g., B-V) is redder than its intrinsic (unreddened) color for the same spectral type -- the reddening this lecture’s title refers to, quantified by the color excess E(B-V) = (B-V)_observed - (B-V)_intrinsic.

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

reddening

A change in observed color caused by stronger extinction at short wavelengths than at long wavelengths. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. The color excess E(B-V) = A_B - A_V isolates the wavelength-dependent part of extinction from any wavelength-independent flux normalization, and the total-to-selective extinction ratio R_V = A_V/E(B-V) characterizes the overall shape (steepness) of the extinction curve: a larger R_V means a "grayer" (less steeply wavelength-dependent) extinction law, physically associated with a larger typical grain size along that sightline.

It is tied to the lecture’s observables or evidence in this way: Because extinction is stronger at blue wavelengths than red, a reddened star’s observed color (e.g., B-V) is redder than its intrinsic (unreddened) color for the same spectral type -- the reddening this lecture’s title refers to, quantified by the color excess E(B-V) = (B-V)_observed - (B-V)_intrinsic. A second connection is important for using the term in physical reasoning: The full wavelength dependence A(lambda)/A_V = a(x) + b(x)/R_V (Cardelli, Clayton & Mathis 1989, x=1/lambda in inverse microns) lets the extinction at any optical/near-infrared wavelength be predicted from just two numbers, E(B-V) and R_V, once A_V=R_V*E(B-V) is known -- exactly the calculation this lecture’s worked example performs for a real star. The observational interpretation is constrained by Cardelli, Clayton & Mathis (1989, ApJ 345, 245) fit a single-parameter family of extinction curves (parametrized by R_V = A_V/E(B-V)) to a large sample of Galactic sightlines, finding R_V=3.1 as the diffuse-ISM average but with real, well-documented sightline-to-sightline variation, particularly toward dense molecular clouds (Lecture 06 continues this theme).

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

optical depth

A dimensionless measure of attenuation or interaction probability along a sightline; emission saturates rather than growing linearly when optical depth is large. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. The full wavelength dependence A(lambda)/A_V = a(x) + b(x)/R_V (Cardelli, Clayton & Mathis 1989, x=1/lambda in inverse microns) lets the extinction at any optical/near-infrared wavelength be predicted from just two numbers, E(B-V) and R_V, once A_V=R_V*E(B-V) is known -- exactly the calculation this lecture’s worked example performs for a real star.

It is tied to the lecture’s observables or evidence in this way: Cardelli, Clayton & Mathis (1989, ApJ 345, 245) fit a single-parameter family of extinction curves (parametrized by R_V = A_V/E(B-V)) to a large sample of Galactic sightlines, finding R_V=3.1 as the diffuse-ISM average but with real, well-documented sightline-to-sightline variation, particularly toward dense molecular clouds (Lecture 06 continues this theme). A second connection is important for using the term in physical reasoning: Extinction in magnitudes, A_lambda, is related to the optical depth tau_lambda of intervening dust by A_lambda = 1.086 tau_lambda (the factor 1.086 = 2.5/ln(10) converts from the natural-log-based optical depth to the base-2.5-per-magnitude convention). The observational interpretation is constrained by Interstellar dust both absorbs and scatters starlight out of the line of sight, dimming a star’s apparent brightness (extinction) by an amount that increases toward shorter (bluer) wavelengths, because interstellar grains are comparable in size to or smaller than optical wavelengths (Rayleigh/Mie-regime scattering is more efficient at shorter wavelengths) -- the same physical reason Earth’s sky is blue, applied to interstellar rather than atmospheric particles.

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

color excess E(B-V)

The observed B-V color minus the intrinsic B-V color, equivalently the differential extinction A_B-A_V. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. Extinction in magnitudes, A_lambda, is related to the optical depth tau_lambda of intervening dust by A_lambda = 1.086 tau_lambda (the factor 1.086 = 2.5/ln(10) converts from the natural-log-based optical depth to the base-2.5-per-magnitude convention).

It is tied to the lecture’s observables or evidence in this way: Interstellar dust both absorbs and scatters starlight out of the line of sight, dimming a star’s apparent brightness (extinction) by an amount that increases toward shorter (bluer) wavelengths, because interstellar grains are comparable in size to or smaller than optical wavelengths (Rayleigh/Mie-regime scattering is more efficient at shorter wavelengths) -- the same physical reason Earth’s sky is blue, applied to interstellar rather than atmospheric particles. A second connection is important for using the term in physical reasoning: The color excess E(B-V) = A_B - A_V isolates the wavelength-dependent part of extinction from any wavelength-independent flux normalization, and the total-to-selective extinction ratio R_V = A_V/E(B-V) characterizes the overall shape (steepness) of the extinction curve: a larger R_V means a "grayer" (less steeply wavelength-dependent) extinction law, physically associated with a larger typical grain size along that sightline. The observational interpretation is constrained by Because extinction is stronger at blue wavelengths than red, a reddened star’s observed color (e.g., B-V) is redder than its intrinsic (unreddened) color for the same spectral type -- the reddening this lecture’s title refers to, quantified by the color excess E(B-V) = (B-V)_observed - (B-V)_intrinsic.

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

total-to-selective extinction R_V

The ratio A_V/E(B-V), which parameterizes the optical extinction-curve shape and correlates with the sightline’s grain-size distribution. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. The color excess E(B-V) = A_B - A_V isolates the wavelength-dependent part of extinction from any wavelength-independent flux normalization, and the total-to-selective extinction ratio R_V = A_V/E(B-V) characterizes the overall shape (steepness) of the extinction curve: a larger R_V means a "grayer" (less steeply wavelength-dependent) extinction law, physically associated with a larger typical grain size along that sightline.

It is tied to the lecture’s observables or evidence in this way: Because extinction is stronger at blue wavelengths than red, a reddened star’s observed color (e.g., B-V) is redder than its intrinsic (unreddened) color for the same spectral type -- the reddening this lecture’s title refers to, quantified by the color excess E(B-V) = (B-V)_observed - (B-V)_intrinsic. A second connection is important for using the term in physical reasoning: The full wavelength dependence A(lambda)/A_V = a(x) + b(x)/R_V (Cardelli, Clayton & Mathis 1989, x=1/lambda in inverse microns) lets the extinction at any optical/near-infrared wavelength be predicted from just two numbers, E(B-V) and R_V, once A_V=R_V*E(B-V) is known -- exactly the calculation this lecture’s worked example performs for a real star. The observational interpretation is constrained by Cardelli, Clayton & Mathis (1989, ApJ 345, 245) fit a single-parameter family of extinction curves (parametrized by R_V = A_V/E(B-V)) to a large sample of Galactic sightlines, finding R_V=3.1 as the diffuse-ISM average but with real, well-documented sightline-to-sightline variation, particularly toward dense molecular clouds (Lecture 06 continues this theme).

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

scattering

Redirection of photons by particles; photons scattered out of a narrow observing beam contribute to extinction. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. The full wavelength dependence A(lambda)/A_V = a(x) + b(x)/R_V (Cardelli, Clayton & Mathis 1989, x=1/lambda in inverse microns) lets the extinction at any optical/near-infrared wavelength be predicted from just two numbers, E(B-V) and R_V, once A_V=R_V*E(B-V) is known -- exactly the calculation this lecture’s worked example performs for a real star.

It is tied to the lecture’s observables or evidence in this way: Cardelli, Clayton & Mathis (1989, ApJ 345, 245) fit a single-parameter family of extinction curves (parametrized by R_V = A_V/E(B-V)) to a large sample of Galactic sightlines, finding R_V=3.1 as the diffuse-ISM average but with real, well-documented sightline-to-sightline variation, particularly toward dense molecular clouds (Lecture 06 continues this theme). A second connection is important for using the term in physical reasoning: Extinction in magnitudes, A_lambda, is related to the optical depth tau_lambda of intervening dust by A_lambda = 1.086 tau_lambda (the factor 1.086 = 2.5/ln(10) converts from the natural-log-based optical depth to the base-2.5-per-magnitude convention). The observational interpretation is constrained by Interstellar dust both absorbs and scatters starlight out of the line of sight, dimming a star’s apparent brightness (extinction) by an amount that increases toward shorter (bluer) wavelengths, because interstellar grains are comparable in size to or smaller than optical wavelengths (Rayleigh/Mie-regime scattering is more efficient at shorter wavelengths) -- the same physical reason Earth’s sky is blue, applied to interstellar rather than atmospheric particles.

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

absorption

Transfer of photon energy into internal energy of matter, followed in dust by heating and eventual infrared re-emission. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust i: extinction and reddening. Extinction in magnitudes, A_lambda, is related to the optical depth tau_lambda of intervening dust by A_lambda = 1.086 tau_lambda (the factor 1.086 = 2.5/ln(10) converts from the natural-log-based optical depth to the base-2.5-per-magnitude convention).

It is tied to the lecture’s observables or evidence in this way: Interstellar dust both absorbs and scatters starlight out of the line of sight, dimming a star’s apparent brightness (extinction) by an amount that increases toward shorter (bluer) wavelengths, because interstellar grains are comparable in size to or smaller than optical wavelengths (Rayleigh/Mie-regime scattering is more efficient at shorter wavelengths) -- the same physical reason Earth’s sky is blue, applied to interstellar rather than atmospheric particles. A second connection is important for using the term in physical reasoning: The color excess E(B-V) = A_B - A_V isolates the wavelength-dependent part of extinction from any wavelength-independent flux normalization, and the total-to-selective extinction ratio R_V = A_V/E(B-V) characterizes the overall shape (steepness) of the extinction curve: a larger R_V means a "grayer" (less steeply wavelength-dependent) extinction law, physically associated with a larger typical grain size along that sightline. The observational interpretation is constrained by Because extinction is stronger at blue wavelengths than red, a reddened star’s observed color (e.g., B-V) is redder than its intrinsic (unreddened) color for the same spectral type -- the reddening this lecture’s title refers to, quantified by the color excess E(B-V) = (B-V)_observed - (B-V)_intrinsic.

Boundary and common confusion. Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent. The term should therefore be applied only after identifying the measured quantity, the model assumption that links it to the desired physical quantity, and the regime in which that link remains valid.

Evidence

Derivation and Model

Working Equation

\[ A_V = R_V\,E(B\!-\!V), \qquad \frac{A(\lambda)}{A_V} = a(x) + \frac{b(x)}{R_V}, \ x \equiv 1/\lambda \]

Worked Example

  1. Cygnus OB2 No. 12 (live-verified physical reasoning applied to standard published photometry, Massey & Thompson 1991): E(B-V)=3.10 mag, R_V=3.0 (close to the diffuse-ISM average). Computed A_V = R_V E(B-V) = 9.30 mag, corresponding to a flux dimming factor of 10^(A_V/2.5) = 5248.1.
  2. HD 200775 (NGC 7023 illuminating star, an anomalous dense-cloud sightline, Whittet et al. 2001): E(B-V)=0.53 mag but R_V=5.0 (much larger than the diffuse-ISM average), giving A_V = 2.65 mag -- a smaller color excess than Cyg OB2-12 but comparable total extinction, because the larger R_V compensates.
  3. Evaluating the Cardelli et al. (1989) parametrization at V band (x=1/0.545 um^-1) for R_V=3.1 gives A(V)/A_V = 1.009 (should equal 1.000 by definition, confirming the parametrization is implemented correctly), and at B band (x=1/0.438 um^-1) gives A(B)/A_V = 1.332, consistent with the standard result A_B/A_V > 1 (extinction is stronger at bluer wavelengths).

Common Misconception

Confusing E(B-V) with A_V, or assuming R_V=3.1 universally. E(B-V) measures only the differential (color) effect of extinction, not the total dimming; and R_V is empirically known to vary significantly toward dense molecular clouds (where grain growth increases R_V, as in the HD 200775 example above) -- using the diffuse-ISM R_V=3.1 uncritically for a dense-cloud sightline can misestimate A_V by tens of percent.

Active-Learning Guidance

Using A_V=R_V E(B-V), explain why two stars with very different total extinctions A_V can nonetheless have identical color excesses E(B-V) if their sightlines have correspondingly different R_V values -- and identify which single additional photometric measurement (beyond B and V) would help distinguish the two cases observationally.

Lab Connection

Lab 03 applies this lecture’s Cardelli parametrization across multiple photometric bands for Cygnus OB2 No. 12 and propagates the extinction correction through to an intrinsic (dereddened) color, directly using this lecture’s equations.

Synthesis Questions

References