Brown dwarf discs › Classification of Accreting Brown Dwarf Disc systems
Accreting Brown Dwarf and Disc, Spectra and Photometry
Accretion VeilingAs discussed in the disc structure page (and Mayne and Harries, 2010) accreting brown dwarfs can be seperated into two classes based on accretion rate. This separation is based on dust sublimation (as discussed in disc structure) and accretion veiling. As the accretion rate is increased the accretion flux (a black body curve at the temperature of the accretion hot spot) begins to dominate the stellar photosphere. This happens at an accretion rate of around log Ṁ=-9, the same boundary as found for the dust sublimation separation.
The above figure shows the SEDs for a typical brown dwarf system for different accretion rates (blue, black and red lines are logṀ=-8, -9 and -12, respectively), periods (5 and 0.5 days are the bottom and top panels, respectively) and areal coverages (1 and 10% are the right and left panels, respectively). It is clear that for all systems as the accretion rate is increases passed logṀ=-9 the photospheric features are lost and the stellar spectrum is heavily veiled. Practically, this means that classification using spectral features would be exceedingly difficult for systems we have classed as extreme accretors with logṀ>-9. Additionally, as the flux in the optical bands greatly increases, as we move from typical to extreme accretors, the magnitude will also become much brighter. This will in turn lead to difficulty in classifying, or selecting, brown dwarfs with extreme accretion rates correctly. The addition of a disc to the systems acts to therefore complicate the spectral and photometric classification.
As discussed on the disc structure pages brown dwarf discs are highly flared, under vertical hydrostatic equilibrium, when compared to their higher mass counterparts (i.e. CTTS). This leads to obscuration of the central star at lower inclinations. Additionally, as the vertical size of the outer disc increases with increasing flux the inclination at which the obscuration begins will lower with accretion rate (see discussion on disc structure pages).
The above figure shows the total SEDs for a typical brown dwarf and disc system at all the modelled inclinations, with the top and bottom panel showing systems with accretion rates of logṀ=-12 and -7, respectively. The dashed lines in the top and bottom panels indicate the inclination at which obscuration occurs, 71° and 56°, respectively. This shows that the higher accretion rate leads a larger vertical height in the outer disc and therefore occultation at earlier inclinations. This suggests that not only are accreting brown dwarf systems at face-on inclinations hard to classify (as described above) but also these systems will be obscured over a larger range of close to edge-on inclinations. This drop in flux will lead to a fall in magnitude with inclination.
The above figure shows the MV and MJ magnitudes (top and bottom panels, respectively). The solid lines (and crosses) denote the systems with rotation rates of 0.5 days, and the dashed lines (and cross) 5 days (only for the highest accretion rate). Additionally, the accretion rates of logṀ=-12, -9 and -7 are shown as black, red and blue lines respectively. The vertical dotted lines indicate the inclinations of 71° and 56°. Finally, the inset panel shows a magnification of the area of interest. As discussed above for accretion rates of Ṁ > -9 we see a large increse in flux (over the photospheric flux), this can be ssen in the top panel of the above figure as the MV brightens significantly with accretion rate. Additionally, for the higher accretion rates increasing the period increases the distance (from the star) and therefore potential energy of the infalling material, resulting in a brighter magnitude. This effect is less noticable in the longer wavelength, bottom panel, MJ magnitude. Finally, we can see that the occultation starts at earlier inclinations for the higher accretion rate models.
Photometric SpreadsBroadband photometric surveys are often used to derive important parameters which are subsequently used as key constraints for theoretical models. In particular, for accreting brown dwarf disc systems changes in the photometric magnitudes (and colours) leads to movement away from the naked star locus in a Colour-Magnitude-Diagram (CMD) or Colour-Colour-Diagram (CoCoD). For our model ("Ad-hoc") grid this movement way from the naked star locus is likely to result in many of the systems being unlikely to be selected in a photometric sample. These objects can often appear in a position indicative of a background, redenned, population of CTTS, or at best a brown dwarf population at a different age (or for individual systems different masses). Therefore, the inclusion of accretion (current) and a circumstellar disc results in the derivation of ages and masses being unreliable when applied, using isochrones, to our model ("Ad-hoc") grid. Furthermore, the separation from the naked star locus is a function of accretion rate. This is due to the extra flux from the accretion hot spot (see above discussion) and the subsequent effect of this flux on the disc structure (as explained on the disc structure page). Importantly, this suggests that there may exist a population of brown dwarf disc systems with elevated accretion rates which are not selected or classified as brown dwarfs. In turn this suggest a bias in any mass to accretion rate relationship.
Age and Mass Derivation
Age and Mass derivation is most often performed using optical and
IR Colour-Magnitude-Diagrams (CMDs) respectively, constructed from
stellar populations and subsequent fitting of isochrones. Using our Isochrones and Mass Tracks, constructed
using the photometric magnitudes (in our defined system, detailed in
calibration pages), we have constructed
similar CMDs for our model population. Justification for the colours
and magnitudes selected can be found in Mayne and
As suggested we have separated our model ("Ad-hoc") grid into two
The above figures show MV, (V-I)0 and MJ, (J-K)0 CMDs, of all of our models, with the left panels showing the typical accretors and the right panels the extreme accretors. The top panles then separate the photometric points into accretion rates and the lower panels in to inclination classes. The solid green line is a 1Myr isochrone of Siess et al (2000) adjusted to a distance modulus of 7 (≈ 250pc) and AV=2, to simulate a background CTTS population. The black lines are our isochrones for naked brown dwarfs with accretion rates of -12 and -9 in the left panel and -6 and -9 in the right panel (solid and dashed lines respectively in both cases) of the (top) optical CMD. For the bottom IR CMDs the same isochrones are present, with the same symbols except for the accretion rate of -6 which lies significantly blueward of the CMD scale.The above figures show that even for typical accreting systems (left panels) the models have little chance of being assigned the correct mass or age.
Mass to Accretion Rate RelationshipThis has important implications for the proposed mass to accretion rate relationship (Ṁ ∝ M≈ 2, Muzerolle et al. 2003, Natta et al. 2004 and Natta et al 2006). The figures above show that as the accretion rate increases the brown dwarf disc systems move increasingly far from the naked star locus. In the extreme accretor case the stars lie well removed from the naked star locus. Therefore, if one were to apply photometric selections to our models they are likely to derive a mass to accretion rate relationship even though one is not present. This suggests that current surveys of brown dwarf populations, used to assert a relationship of this sort may be subject to an intrinsic bias against low mass high accretion rate systems.