Two-Temperature Debris Disks

Do Two-Temperature Debris Disks Have Multiple Belts? - Kennedy & Wyatt 2014

Background: The temperature of a dust grain in a debris disks depends both on the distance from the host star and on the optical properties of that dust grain (shape, composition, porosity, emissivity, etc). Since most debris disks are discovered by excess emission above the photosphere and not through direct imaging of the disk itself, it can be difficult to discern the physical structure of the disk. It is important to determine whether the system in question actually contains two spatially separated disks with a gap between them or a single disk with two different temperature grains, because a disk with a gap could be a signature of planet formation.

Possible interpretations of the 2-belt model:

1.  A gap between two spatially separated belts is carved out by a planet orbiting in the gap.
2.  A cold outer belt feeds material into a warm inner belt (e.g. comets from the outer belt pass close to the star and sublimate, leaving a cloud of hot debris behind).
3.  Poynting-Robertson drag causes particles from the outer belt to fall toward the star, creating a reservoir of hot dust.
4.  The emission is the result of a grains from a single belt with several different temperature populations.

Sample: The authors used 48 stars with two-temperature disks observed with Spitzer and Herschel.

SED Fitting: The authors fit the stellar photosphere to optical photometry (lam<10mu), and fit the dust to the mid- and far-IR photometry. They used a modified blackbody to fit the dust emission, which incorporates factors related to the surface area of the dust, the grain size of the dust, and the emissivity of the grains. For disks with two separate temperatures present, they calculate the ratio between the temperatures of the two belts and the ratio between the fractional luminosities of each belt.

Results:

Two-Temperature Systems: Most two-temperature disks have temperature ratios of 2-4. Systems with low temperature and luminosity ratios are difficult to detect, but probably do exist. Sun-like stars have warm components <220K, while A-type stars have warm components with T>220K. This makes sense if the temperature of the dust is correlated with the temperature of the star. This finding is in contrast to Morales et al. 2011, who found that warm dust temperatures tended to be ~200K, near the temperature required for the sublimation of icy bodies (comets).

Single-Temperature Systems: Some single-temperature systems actually show two components in images. Still, there is no evidence to suggest that all debris disks have two components - that is, there are several systems where a typical warm component was detectable, but not seen.

How common are two-temperature disks? ~30% of A-stars show two temperatures. Chen et al. 2014 found that 66% of debris disk systems had two temperature disks, but the authors believe that false positive warm excesses may have been included in that sample due to a calibration issue between IRS spectra and MIPS 24mu photometric points. The discrepancy might also be due to the fact that two-temperature disks are found more often around younger stars, and the Chen et al. sample was younger than the sample presented in this paper. Morales et al. 2011 quotes a double-belt frequency of 46%, while Ballering et al. 2013 quotes 33%.

Grain Models:

Grain Temperatures: Grain temperatures vary as a function of stellar luminosity (spectral type) and distance from the host star. The function of grain temperature as a function of grain size has two distinct regimes; one where the size of the particles is greater than the size of the peak wavelength of stellar emission (in which case the grains radiate efficiently at all wavelengths), and one where the size of the grains is less than the size of the peak wavelength. These two regimes are separated by a transition region that occurs near grain sizes ~2-10 microns for all spectral types. According to the models presented in this paper, there is some maximum temperature difference that can be achieved in a single belt of dust that depends on the minimum grain size. If the temperature difference exceeds that maximum, the two temperatures are probably indicative of two spatially separated belts.

Since early A-type stars are hotter and have a larger blowout radius for grains in orbit around them, the maximum temperature difference is much smaller. Thus is it unlikely that early A-type stars would show two-temperature SEDs from a single dust belt, while Sun-like stars could still host single belt systems with multiple temperature components.

Grain Compositions: The authors tested two grain models - one icy, and one rocky. They found that a population if many different grain sizes ranging from large to small can produce an overall spectrum that is modeled very well by a single-temperature blackbody. In order to create a spectrum that requires a two-temperature fit, they needed to increase the number of large grains. Again, this only works to create a two-temperature spectrum if we are looking at stars later than early-A, since we need some contribution from small grains.

The authors found that the ratio of fractional luminosities in the two-temperature model increased as the size distribution became steeper due to the decreasing contribution of large grains.

Single-Belt Model: Cool component is dominated by large blackbody-like particles, while the warm component is due to smaller grains. The large grains are large enough to emit like blackbodies at IR wavelengths, but small enough that they emit ineffectively at longer wavelengths. Thus, a simple blackbody curve will not be a best fit to the emission from the cold disk. This would also explain why the blackbody radius of the dust does not agree well with the radius observed in resolved images. Given the wide area of parameter space that would need to be covered by grains residing in a single belt in order to mimic a double-belt system, it seems likely that most two-temperature belts are created by bona-fide double-belts.

Evolution of Multiple Belt Systems:
    1.    Multiple belts arise from a single belt (belts evolve similarly)
    2.    Cold outer belt delivers material to warm inner belt (belts evolve similarly)
    3.    The two belts are truly separate (belts evolve separately)

If two spatially separated belts are evolving independently, the inner belt will start to decay in brightness first, since it will run out of material first.

The Effect of Planets: The warm dust may well be the result of the same sort of collisional evolution that we see in the cold dust. However, since there are undoubtedly planets in these systems, they should have some effect on the evolution of the dust. One theory is that icy planetesimals (comets) deposit their mass close to the Sun once they get close enough to sublimate. However, that picture suggests that all warm dust should be at approximately the sublimation temperature for ice (~150K). This is not the case for the sample in this paper.