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Spectral Energy Distributions
and the
Signature of
Circumstellar Disks
The "Spectral Energy Distribution" or "SED"
is a time-worn representation of
photometric data from astronomical objects that is usually
plotted in units of
energy per time (i.e., as &lambda F&lambda or &nu
F&nu). It can also be plotted in Flux Density units (S&nu) or in units of luminosity density
(&nu F&nu 4 &pi D). An excellent primer on the SED signature of
circumstellar disks is found on the outreach web pages of
the Myers Legacy Team (Formation and Evolution of Planetary Systems
or "FEPS").
The simplest SED model is a scaled black-body
spectrum at an average temperature of the circumstellar dust.
See an example in the original discovery paper of dust around Vega:
- Aumann et al. 1984, Discovery of a Shell Around Alpha Lyrae,
ApJ, 278, L23 .
- Low, Hines, & Schneider 1999, NICMOS Observations of the Pre-Main-Sequence Planetary Debris System HD 98800, ApJ, 520, L45
Later models of "debris disk" emission relied on thermal equilibrium
and a temperature distribution determined only by the stellocentric
distances spanned by circumstellar dust grains, together with some
estimate of grain emissivity (a function of grain size and composition).
Sometimes these borrowed information from spatially resolved observations
as well.
- Backman, Gillett, &
Witteborn 1992, Infrared Observations and Thermal Models of the
&beta Pictoris Disk, ApJ, 385, 670
- Koerner et al. 1998, Mid-Infrared Imaging of a
Circumstellar Disk around HR 4796: Mapping the Debris of Planetary Formation,
ApJ, 503, L83
- Koerner et al. 1999,
A Single Circumbinary Disk in the HD 98800 Quadruple System, ApJ,
533, L37
Models of optically thick accretion disks cannot rely on simple
thermal equilibrium between stellar and grain radiation; radiative
transfer effects are important in conveying the energy from star to
the outer disk, since the star-to-grain line of sight is obscured
for most grains. Moreover, accretion disks have their own heat source!
Early work on viscous accretion disks predicted a power-law temperature
profile:
2-D Models of optically thick disks simply parametrized the density
and an effective
temperature profile as power laws and empirically fit the data.
-
Beckwith et al. 1990,
A Survey for Circumstellar Disks around Young Stellar Objects, AJ,
99, 924
- Koerner, Chandler, & Sargent 1995, Aperture Synthesis Imaging of the Circumstellar Dust Disk around DO Tauri, ApJ, 452, L69
The above often failed to derive temperature distributions that agreed with
theory. Explanations were given in terms of disk flaring, radiation
reflected back from an envelope, and
radiative transfer in the upper surface layers:
- Kenyon & Hartmann 1987,
Spectral Energy Distributions of T Tauri Stars: Disk Flaring and Limits
on Accretion,ApJ, 323, 714
- D'Alessio, Calvet, & Hartmann 1997,
The Structure and Emission of Accretion Disks Irradiated by Infalling Envelopes,ApJ, 474, 397
- Chiang & Goldreich 1997,
Spectral Energy Distributions of T Tauri Stars with Passive Circumstellar Disks
, ApJ, 490, 368,
A wealth of expanded physical detail can be put into SED models for
debris disks and accretion disks alike. These include realistic
grain size distributions, grain composition, radial and asymmetric structures
in the disk, inclusion of solid-state
spectral features, and modeling of the scattered light component.
It is rarely the case that photometric observations
alone can constrain all these parameters (!), but forthcoming high-resolution
images promise to help constrain these many-parameter models in a
meaningful way.
- Augereau et al. 1999, On the HR 4796 A circumstellar disk,
A&A, 348, 557
- Chiang et al. 2001, Spectral Energy Distributions of Passive T Tauri and Herbig Ae Disks: Grain Mineralogy, Parameter Dependences, and Comparison with Infrared Space Observatory LWS Observations, ApJ, 547, 1077
- Calvet et al. 2001, Evidence for a Developing Gap in a 10 Myr Old Protoplanetary Disk, ApJ, 568, 1008
- Schneider et al. 2003,
NICMOS Coronagraphic Observations of the GM Aurigae Circumstellar Disks,
ApJ, 125, 1467
- Aigen & Lunine 2003, Modeling the Infrared Emission from the HR 4796A Disk, ApJ, 590, 368
For a complete reference list on SED (and other) evidence for grain
growth in circumstellar dust (before 1997),
see Alyssa Goodman's excellent bibliography:
Relevant Review Articles:
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