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Astrophysics group
Brown dwarf discs Disc Fractions

Disc fractions

Disc fractions are commonly derived by applying empirically based cuts or selections to a photometric colour-colour diagrams (CoCoDs). Previously, JHK magnitudes have been used but more recently magnitudes from Spitzer's IRAC or MIPS cameras are used. Additionally the α value, the slope of the SED between two limiting wavelengths, has been used to classify objects as having associated discs. In Mayne and Harries (2010) we examined the behaviour of our modelled systems in CoCoDs using IR, IRAC and MIPS magnitudes. This allowed us to derive suggested disc selection criteria in colours derived from these systems. Furthermore, we examined the efficacy of example observational cuts when applied to our ("Ad-hoc") grid, which in the most part were found to be reliable.

Disc cuts

Our suggested disc candidate selection criteria are as follows:
Colour index
Disc selection
Number missed (# & %)
∝(3.6-8.0)0 > -2.20 26/4480=0.6%
([3.5]-[4.5])0 > +0.21 201/4480=4.5%
([3.5]-[5.8])0 > +0.50 12/4480=0.3%
([4.5]-[5.8])0 > +0.32 9/4480=0.2%
([4.5]-[8.0])0 > +0.45 7/4480=0.2%
([5.8]-[8.0])0 > +0.13 13/4480=0.3%
([8.0]-24)0 > -16.2 0/4480=0.0%
(24-70)0 > +9.90 2/4480=0.04%
(70-160)0 > -6.20 0/4480=0.0%

Colour-Colour Diagrams

The constructed CoCoDs for the all of the 1Myr models within the ("Ad-hoc") grid presented in Mayne and Harries (2010) are displayd below.

For all of the above figures the left hand panels show the typical accretors and the right hand panels the extreme accretors. Additionally, the top panels of each figure separate the systems, by colour coding, by accretion and the bottom panels by inclination. The naked stars systems are included as black crosses and the brown dwarf disc systems as dots. As can be see from the IR CoCoDs (top figure) the naked and disc star locus overlaps slightly. This suggests that empirically placed cuts may well include some naked stars, or exclude some disc systems, the latter being less problematic as the fractions are quoted as lower limits. Additionally, throughout all the figures it is clear that as the accretion rate moves to the extreme case the systems are much farther removed in CoCoD space from the naked stars. For the top two figures there is no clear correlation of CoCoD position with inclination or accretion rate, except perhaps for the extreme accretors where increasing the accretion rates moves the disc systems farther from the naked star locus. It is also clear that CoCoDs constructed from the IRAC bands, of which the middle figure is representative, are well suited to selecting brown dwarf disc systems as they are well separated from the naked star locus. Finally, for the longer wavelength MIPS channels there is clear, and intriguing stratification of the CoCoD position with accretion rate and inclination. This is due to the temperature, and therefore radial distance from the star, of the regions that these bands probe. Essentially, in the outer disc the structure, temperature and emission is a much finer function of the input variables. Whether this stratification could be used in practice to distinguish specific characteristics of brown dwarf disc models is doubtful.
We have also examined observational cuts used to identify brown dwarf disc candidates when applied to our model ("Ad-hoc") grid. These include cuts in CoCoDs and the α value, for the latter we have adopted the limiting wavelengths of 3.6 and 8.0μm (Kennedy and Kenyon, 2009).

The above figure shows observational cuts used (in descending order, i.e. top to bottom) in Luhman et al. (2005), Luhman et al. (2008), Monin et al. (2010) (who apply the criteria of Gutermuth et al, 2008) and Kennedy and Kenyon (2009). The first three figures (from top down) show cuts applied to IC348, σ Orionis and Taurus. For all the above figures, the left panels show all models with typical accretion rates and the right panels all models with extreme accretion rates.
As is shown in the above figures the observational cuts used in Luhman et al. (2005) and Luhman et al. (2008) would miss some typically accreting systems (which are mostly edge-on systems). The cuts of Gutermuth et al. (2008) applied by Monin et al. (2010) to Taurus would miss almost none of the disc systems. Additionally, for the α value cut some typically accreting systems would again be missed. Finally, in all cases none of the naked systems will be erroneously included in the sample.

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