Terms Developed in Context
grain alignment
A statistical orientation of nonspherical dust grains relative to the local magnetic field rather than a perfectly parallel arrangement of every grain. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. A dust grain reaches radiative equilibrium when the rate of starlight energy it absorbs equals the rate of infrared energy it re-emits; because small grains are inefficient infrared emitters at wavelengths much larger than their size (an effect captured by the frequency-dependent emissivity kappa_nu proportional to nu^beta), they must reach a higher equilibrium temperature than a perfect blackbody of the same absorbed power in order to balance the energy budget.
It is tied to the lecture’s observables or evidence in this way: Interstellar polarization was discovered independently by Hall (1949) and Hiltner (1949) through observations of systematically polarized starlight, immediately interpreted as evidence for both non-spherical dust grains and a large-scale Galactic magnetic field capable of aligning them. A second connection is important for using the term in physical reasoning: The resulting emitted spectrum, a modified blackbody S_nu = kappa_nu B_nu(T_dust), peaks at a wavelength that shifts to shorter wavelengths for warmer grains (an emissivity-modified Wien’s-law-like behavior) and can be used, given an assumed beta, to solve for T_dust directly from the observed peak or from multi-band photometry. The observational interpretation is constrained by The modern understanding of grain alignment (radiative torques from anisotropic starlight spinning up irregularly shaped grains, which then precess into alignment with the local magnetic field) is reviewed by Lazarian (2007, JQSRT 106, 225) and Andersson, Lazarian & Vaillancourt (2015, ARA&A 53, 501).
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
radiative torques
Torques exerted by anisotropic radiation on irregular grains that spin them up and help align their angular momenta with magnetic fields. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. The resulting emitted spectrum, a modified blackbody S_nu = kappa_nu B_nu(T_dust), peaks at a wavelength that shifts to shorter wavelengths for warmer grains (an emissivity-modified Wien’s-law-like behavior) and can be used, given an assumed beta, to solve for T_dust directly from the observed peak or from multi-band photometry.
It is tied to the lecture’s observables or evidence in this way: The modern understanding of grain alignment (radiative torques from anisotropic starlight spinning up irregularly shaped grains, which then precess into alignment with the local magnetic field) is reviewed by Lazarian (2007, JQSRT 106, 225) and Andersson, Lazarian & Vaillancourt (2015, ARA&A 53, 501). A second connection is important for using the term in physical reasoning: Because polarization angle traces projected magnetic-field direction and modified-blackbody fitting traces dust temperature and column density, the two observational techniques developed in this lecture are complementary tools this course will invoke again in Lecture 14’s magnetic-field diagnostics and throughout Unit 4’s molecular-cloud mass estimates. The observational interpretation is constrained by Cold dust grains re-radiate absorbed starlight predominantly in the far-infrared/submillimeter, where the observed spectral energy distribution is well described by a modified blackbody, S_nu proportional to kappa_nu B_nu(T_dust), with kappa_nu (the dust opacity) itself rising with frequency as a power law nu^beta (beta~1.5-2 typically) -- exactly the shape used by facilities like Herschel and ALMA to map dust temperature and column density in molecular clouds.
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
linear polarization
An imbalance between orthogonal electric-field components of light, described by a polarization fraction and a sky position angle. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. Because polarization angle traces projected magnetic-field direction and modified-blackbody fitting traces dust temperature and column density, the two observational techniques developed in this lecture are complementary tools this course will invoke again in Lecture 14’s magnetic-field diagnostics and throughout Unit 4’s molecular-cloud mass estimates.
It is tied to the lecture’s observables or evidence in this way: Cold dust grains re-radiate absorbed starlight predominantly in the far-infrared/submillimeter, where the observed spectral energy distribution is well described by a modified blackbody, S_nu proportional to kappa_nu B_nu(T_dust), with kappa_nu (the dust opacity) itself rising with frequency as a power law nu^beta (beta~1.5-2 typically) -- exactly the shape used by facilities like Herschel and ALMA to map dust temperature and column density in molecular clouds. A second connection is important for using the term in physical reasoning: A dust grain reaches radiative equilibrium when the rate of starlight energy it absorbs equals the rate of infrared energy it re-emits; because small grains are inefficient infrared emitters at wavelengths much larger than their size (an effect captured by the frequency-dependent emissivity kappa_nu proportional to nu^beta), they must reach a higher equilibrium temperature than a perfect blackbody of the same absorbed power in order to balance the energy budget. The observational interpretation is constrained by Interstellar polarization was discovered independently by Hall (1949) and Hiltner (1949) through observations of systematically polarized starlight, immediately interpreted as evidence for both non-spherical dust grains and a large-scale Galactic magnetic field capable of aligning them.
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
modified blackbody
Thermal emission represented by the Planck function multiplied by a frequency-dependent opacity or emissivity. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. A dust grain reaches radiative equilibrium when the rate of starlight energy it absorbs equals the rate of infrared energy it re-emits; because small grains are inefficient infrared emitters at wavelengths much larger than their size (an effect captured by the frequency-dependent emissivity kappa_nu proportional to nu^beta), they must reach a higher equilibrium temperature than a perfect blackbody of the same absorbed power in order to balance the energy budget.
It is tied to the lecture’s observables or evidence in this way: Interstellar polarization was discovered independently by Hall (1949) and Hiltner (1949) through observations of systematically polarized starlight, immediately interpreted as evidence for both non-spherical dust grains and a large-scale Galactic magnetic field capable of aligning them. A second connection is important for using the term in physical reasoning: The resulting emitted spectrum, a modified blackbody S_nu = kappa_nu B_nu(T_dust), peaks at a wavelength that shifts to shorter wavelengths for warmer grains (an emissivity-modified Wien’s-law-like behavior) and can be used, given an assumed beta, to solve for T_dust directly from the observed peak or from multi-band photometry. The observational interpretation is constrained by The modern understanding of grain alignment (radiative torques from anisotropic starlight spinning up irregularly shaped grains, which then precess into alignment with the local magnetic field) is reviewed by Lazarian (2007, JQSRT 106, 225) and Andersson, Lazarian & Vaillancourt (2015, ARA&A 53, 501).
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
dust emissivity index
The exponent beta in the approximate opacity law kappa_nu proportional to nu^beta at far-infrared and submillimeter wavelengths. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. The resulting emitted spectrum, a modified blackbody S_nu = kappa_nu B_nu(T_dust), peaks at a wavelength that shifts to shorter wavelengths for warmer grains (an emissivity-modified Wien’s-law-like behavior) and can be used, given an assumed beta, to solve for T_dust directly from the observed peak or from multi-band photometry.
It is tied to the lecture’s observables or evidence in this way: The modern understanding of grain alignment (radiative torques from anisotropic starlight spinning up irregularly shaped grains, which then precess into alignment with the local magnetic field) is reviewed by Lazarian (2007, JQSRT 106, 225) and Andersson, Lazarian & Vaillancourt (2015, ARA&A 53, 501). A second connection is important for using the term in physical reasoning: Because polarization angle traces projected magnetic-field direction and modified-blackbody fitting traces dust temperature and column density, the two observational techniques developed in this lecture are complementary tools this course will invoke again in Lecture 14’s magnetic-field diagnostics and throughout Unit 4’s molecular-cloud mass estimates. The observational interpretation is constrained by Cold dust grains re-radiate absorbed starlight predominantly in the far-infrared/submillimeter, where the observed spectral energy distribution is well described by a modified blackbody, S_nu proportional to kappa_nu B_nu(T_dust), with kappa_nu (the dust opacity) itself rising with frequency as a power law nu^beta (beta~1.5-2 typically) -- exactly the shape used by facilities like Herschel and ALMA to map dust temperature and column density in molecular clouds.
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
radiative equilibrium
An energy-balance state in which a grain’s absorbed radiant power equals its emitted thermal power. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. Because polarization angle traces projected magnetic-field direction and modified-blackbody fitting traces dust temperature and column density, the two observational techniques developed in this lecture are complementary tools this course will invoke again in Lecture 14’s magnetic-field diagnostics and throughout Unit 4’s molecular-cloud mass estimates.
It is tied to the lecture’s observables or evidence in this way: Cold dust grains re-radiate absorbed starlight predominantly in the far-infrared/submillimeter, where the observed spectral energy distribution is well described by a modified blackbody, S_nu proportional to kappa_nu B_nu(T_dust), with kappa_nu (the dust opacity) itself rising with frequency as a power law nu^beta (beta~1.5-2 typically) -- exactly the shape used by facilities like Herschel and ALMA to map dust temperature and column density in molecular clouds. A second connection is important for using the term in physical reasoning: A dust grain reaches radiative equilibrium when the rate of starlight energy it absorbs equals the rate of infrared energy it re-emits; because small grains are inefficient infrared emitters at wavelengths much larger than their size (an effect captured by the frequency-dependent emissivity kappa_nu proportional to nu^beta), they must reach a higher equilibrium temperature than a perfect blackbody of the same absorbed power in order to balance the energy budget. The observational interpretation is constrained by Interstellar polarization was discovered independently by Hall (1949) and Hiltner (1949) through observations of systematically polarized starlight, immediately interpreted as evidence for both non-spherical dust grains and a large-scale Galactic magnetic field capable of aligning them.
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.
spectral energy distribution (SED)
A source’s measured energy output or flux density as a function of wavelength or frequency. In this lecture, the term is not an isolated label: This concept is needed to reason about interstellar dust ii: polarization and thermal emission. A dust grain reaches radiative equilibrium when the rate of starlight energy it absorbs equals the rate of infrared energy it re-emits; because small grains are inefficient infrared emitters at wavelengths much larger than their size (an effect captured by the frequency-dependent emissivity kappa_nu proportional to nu^beta), they must reach a higher equilibrium temperature than a perfect blackbody of the same absorbed power in order to balance the energy budget.
It is tied to the lecture’s observables or evidence in this way: Interstellar polarization was discovered independently by Hall (1949) and Hiltner (1949) through observations of systematically polarized starlight, immediately interpreted as evidence for both non-spherical dust grains and a large-scale Galactic magnetic field capable of aligning them. A second connection is important for using the term in physical reasoning: The resulting emitted spectrum, a modified blackbody S_nu = kappa_nu B_nu(T_dust), peaks at a wavelength that shifts to shorter wavelengths for warmer grains (an emissivity-modified Wien’s-law-like behavior) and can be used, given an assumed beta, to solve for T_dust directly from the observed peak or from multi-band photometry. The observational interpretation is constrained by The modern understanding of grain alignment (radiative torques from anisotropic starlight spinning up irregularly shaped grains, which then precess into alignment with the local magnetic field) is reviewed by Lazarian (2007, JQSRT 106, 225) and Andersson, Lazarian & Vaillancourt (2015, ARA&A 53, 501).
Boundary and common confusion. Assuming dust temperature and gas temperature are always equal. They are well-coupled by gas-grain collisions only at the high densities found deep inside molecular clouds (as assumed above for Orion); in the much more tenuous diffuse ISM, dust and gas temperatures can differ substantially because the coupling collision rate is far lower there -- a genuine physical distinction, not a simplifying convenience to be applied everywhere. 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.