extinction
Definition: The wavelength-dependent loss of direct light from a beam through both absorption and scattering by intervening material.
Why it matters here: 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).
Relationship: 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.
Limitation or 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.
reddening
Definition: A change in observed color caused by stronger extinction at short wavelengths than at long wavelengths.
Why it matters here: 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.
Relationship: 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.
Limitation or 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.
optical depth
Definition: A dimensionless measure of attenuation or interaction probability along a sightline; emission saturates rather than growing linearly when optical depth is large.
Why it matters here: 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.
Relationship: 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).
Limitation or 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.
color excess E(B-V)
Definition: The observed B-V color minus the intrinsic B-V color, equivalently the differential extinction A_B-A_V.
Why it matters here: 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).
Relationship: 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.
Limitation or 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.
total-to-selective extinction R_V
Definition: The ratio A_V/E(B-V), which parameterizes the optical extinction-curve shape and correlates with the sightline’s grain-size distribution.
Why it matters here: 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.
Relationship: 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.
Limitation or 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.
scattering
Definition: Redirection of photons by particles; photons scattered out of a narrow observing beam contribute to extinction.
Why it matters here: 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.
Relationship: 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).
Limitation or 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.
absorption
Definition: Transfer of photon energy into internal energy of matter, followed in dust by heating and eventual infrared re-emission.
Why it matters here: 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).
Relationship: 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.
Limitation or 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.