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Astrophysics group
Brown dwarf discs Science Overview

Accreting Brown Dwarf and Disc, Spectra and Photometry

Science Overview

Physical Model

To model what a young accreting brown dwarf disc system might look like requires several assumptions and simplifications. The problem can be broken down into the main elements which affect the total flux emitted from the system:

(1) The stellar interior and atmosphere.

As young stars evolve they contract and the stellar interior changes temperature. This change in temperature and radius leads to a change in the surface gravity of the star and its luminosity as a function of wavelength (or its spectrum). The flux emitted from the star must then pass through the stellar atmosphere, which for young, cool, brown dwarfs is complicated by the presence of many molecular species, resulting in a chacteristic spectrum differing from a simple Black Body. To model the light which is emitted by the star itself we have adopted the stellar interior "DUSTY00" models and the "AMES-Dusty" atmosphere models of Chabrier et al (2000), which are available online. These models allow us to generate (through interpolation) the Spectral Energy Distribution (SED, flux as a function of wavelength) for a brown dwarf disc at a given age and mass.

(2) The accretion stream.

Young brown dwarfs, and indeed higher mass stars, often retain gravitationally bound material from the pre-natal stellar envelope (the dust and gas from which the star is formed), which forms a circumstellar disc. At the disc inner edge (i.e. closest point to the star) this material is channelled down onto the stellar surface along magnetic field lines (a process similar to that causing the 'Northern lights'). This material is heated by the star and also liberates large amounts of gravitational energy as it hits the stellar surface, generating accretion hot spots. The luminosity or flux from the accretion stream must also be estimated. First, we calculate the potential energy lost as the material falls from orbit onto the stellar surface, given an accretion rate, or rate of mass flow. Then, by adopting an areal coverage, or accretion spot size, we calculate an effective temperature for the spot. Assuming that the accretion hot spot emits as a blackbody then allows us to generate a flux coming from the accretion hot spot. This is added to the intrinsic, photospheric, stellar flux. Although this is a rather simplistic accretion model, it does in fact match the reverse process by which accretion rates are most often estimated. An excess flux, above photospheric, is found and then used, via a black body emission curve, to estimate an accretion rate.

(3) The circumstellar disc.

This combined stellar and accretion flux is then used as a "NAKED" system for our analysis, systems without a disc. The final step for our "DISC" systems is to model the circumstellar disc. For this we must adopt a disc mass, stellar rotation rate, a vertical structure (analytic or defined by vertical hydrostatic equilibrium) and an outer radius. The rotation rate is required as this will dictate the co-rotation radius, where the Keplerian (or orbital) velocity of the disc is equal to that of the stellar surface. At this point the specific angular momentum (angular momentum per unit mass) of the disc material will be equal to that of material on the stellar surface and hence the material can fall or accrete onto the star without having to shed excess angular momentum. Effectively, this means that faster rotating objects will have discs existing closer to the stellar surface. Subsequent movement of the inner edge of the dust disc is controlled by dust sublimation (note: the inner edge of the gas disc does not change position as it is not sublimated at high temperatures). Either the dust sublimation is controlled by the temperature and density calculated for the dust in the inner regions of the disc, i.e. variable dust sublimation is used, or an inner radius is prescribed using the effective temperature of the star and a semi-empirical relationship. The vertical structure then defines the scaleheight and density of the disc as a function of radius from the star. If this is defined analytically the disc will remain static in terms of density and height. However, in the case of vertical hydrostatic equilibrium the vertical structure of the disc (and therefore density) can change as the temperature and pressure balance within the disc change. Finally, the outer radius simply defines the radial extent of the disc. For our initial models we have set this at a large value (300au). Once these parameters are adopted the disc is modeled using the TORUS radiation transfer code. This models the temperature and density distribution within the disc. Additionally, we include a sophisticated treatment of dust sublimation at the inner edge, this leads to a change in the shape and density profile of the inner disc. For cases where the co-rotation radius is close to the central star some of the dust will be destroyed due to the higher temperatures reached and therefore the inner edge will be pushed outwards. The TORUS code then produces SEDs of the final disc systems at a user selected inclination.
Therefore in summary, by adopting stellar models and likely limiting values of stellar age, mass and rotation period, accretion stream rate and areal coverage and a disc mass, we have produced a grid of both naked and disc brown dwarf systems spectra. Which can be explored using our Model Browser.

Model Grid Parameter Space

To allow our model grids to be useful for comparison to current data of young brown dwarf systems we must select reasonable values for our input parameters.
We have two grids available, termed the "Ad-hoc" grid and "Semi-emp" grid. For the "Ad-hoc" grid literature results for typical brown dwarf populations were used to select reasonable ranges for our parameter space, but the selections were made to explore the effects of accretion. The details of these selections are explained in
Mayne and Harries (2010). For the "fitting grid" the structure and sublimation radius of the disc are set analytically and the parameter space is designed to cover ranges conducive to the derivation of stellar parameters. The full parameter list can be found at the calibration pages.


Once the model spectra have been produced these data must be transfered into the 'observable plane'. Effectively, real data taken by astrophysics observers is obtained using specific telescopes, equipped with broadband imaging equipment or spectrographs. These instruments have their own specific calibration requirements and limitations. For surveys of young brown dwarf populations scientific quantities such as the stellar mass and age are used to constrain and possibly reject theoretical models. These surveys are generally photometric, therefore, to enable us to understand any implications our model grid has for observations we must simulate these observations. These simulated observations come in two, related, types which are, broadband magnitudes and monochromatic fluxes. To create these observable quantities some further assumptions and calibration is required, for instance the response of a given telescope as a function of wavelength is required to model what one of our spectra would 'look' like if observed through it. This information is detailed on the calibration page. The derived observables in the form of isochrones and mass tracks are available using our Isochrone and Mass Track tool.

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