Spectral Energy Distributions

The SEDs of the great majority of debris disks are remarkably similar, with shapes indicating that the material is at a temperature of about 70K. The SEDs encode the disk structure, since the equilibrium temperature of a grain is given by

Here, B(T, A) is the blackbody function for temperature T and at wavelength A, Qab (A) is the grain absorption coefficient at A, T* and Tg are the temperatures of the star and grain, respectively, R* is the stellar radius, and r is the distance of the grain from the star. The left side of this equation represents the energy absorbed by the grain from the star, and the right side that emitted by the grain. Applying this equation, the SEDs of the vast majority of debris disks indicate that the grain population is at tens to a couple of hundred AU from the star (depending on type). In fact, for stars of roughly solar type (late F to early K), Spitzer SEDs generally indicate little detectable debris emission at wavelengths short of 25 ¡m (Kim et

J Qaab (A) B (T„A) dA = 41 Qaab (A) B (Tg ,A) dA. (4.4)

al., 2005; Beichman et al., 2005), showing that these rings of debris are usually terminated at their inner edges with little material inside. The limits on the mass of interior material are very strong because at the higher equilibrium temperature for such grains they would be easily detectable. The most likely explanation for these inner clearings is the presence of massive planets (e.g., Liou & Zook (1999); Moro-Martín & Malhotra (2005)).

However, it is difficult to draw more specific conclusions from photometric-resolution SEDs, since a variety of models can be made consistent with the sparsely spaced measurements (Moro-Martín et al. (2005); see also Su et al. (2006)). Typically, a power law disk density behaviour similar to eq. 4.1 is assumed (but with alternative choices for the spectral index). This degeneracy of SED models is a significant obstacle to making further progress in understanding debris disk structure on a broad basis (Moro-Martín et al., 2005).

In general, the spectra of debris disks are featureless (Beichman et al., 2005; Chen et al., 2006), indicating that the particles are large enough to be optically thick (i.e., of order 10¡m or more). However, there are exceptions. The strong crystalline features in the 10-35 ¡m spectrum of HD 69830 show its excess is due almost entirely to a large population of extremely tiny, crystalline grains with very short lifetimes against loss or destruction (Beichman et al., 2006). Their presence in such numbers requires that they have been generated recently as part of a transient phenomenon such as a super-comet being deflected into an orbit approaching the star, or a collision in an asteroid belt more than an order of magnitude more densely populated than ours (Beichman et al., 2006). The discovery of a complex planetary system around this star, with three Neptune-mass members (Lovis et al., 2006), may help account for the peculiarities of its debris system. Song et al. (2005) have found similar properties in the infrared excess of BD +20.307, and they conclude that this star must also have its debris system dominated by a recent large collision.

A minority of systems also have very different SEDs, with strong excesses at 24 ¡m. The infrared outputs of many of these systems are likely to be dominated by recent massive collisions or other transient events. The best-studied example, Z Lep, has its debris concentrated within 3AU of the star (Chen & Jura, 2001; Moerchen et al., 2007). Wyatt et al. (2007a) conclude that its peculiar characteristics may well stem from a recent planetesimal collision. Wyatt et al. (2007b) show that, in addition to Z Lep, HD 69830 and BD +20.307, the hot dust around n Corvi and HD 72905 indicates the presence of planetesimals recently scattered inward from an outer belt of such bodies.

Objects with extreme excesses are also found in young clusters: up to eight in h and x Per at 13 Myr (Currie et al., 2007b); one or two in NGC 2547 at 25 Myr (Gorlova et al., 2007); and one in M47 at 100 Myr (Gorlova et al., 2004). A plausible explanation is that they represent collisions of very large bodies, perhaps analogous to the collision that formed our Moon.

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