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Astrophysics group
 
Brown dwarf discs Calibration and convergence Information

Accreting Brown Dwarf and Disc, Spectra and Photometry

TORUS model

We have used the TORUS radiative transfer code which is described in Harries (2000), including the subsequent refinements i.e. addition of Adaptive-Mesh-Refinement (AMR) introduced in Harries et al (2004) . TORUS uses the criterion of Lucy (1999) in a radiative equilibrium algorithm. The code can also calculates Vertical hydrostatic equilibrium for the disc, as described in Tannirkulam et al (2007). The code also includes a treatment of dust sublimation where the initial temperatures in the grid are derived and the grid is then progressively filled to increasing optical depth limits and temperatures re-calculated, with the dust reaching the dust sublimation temperature being destroyed at each step.

Grid Description:

These webpages describe and allow access to models and results from different grids. The details of the parameter coverage and physics included in each grid can be found in the table below:

Ad-hoc: STATUS=COMPLETE

A grid designed to explore the effects of accretion on disc structure, including variable dust sublimation and vertical hydrostatic equilibirum (as well as analytical structures). SEDs derived using isotropuc scattering. The results of this grid have been published in Mayne and Harries (2010) and are discussed throughout these pages using the term "Ad-hoc" grid.
Input parameter
Values (number of values)

Stellar parameters
Stellar Interior Model Dusty-'00 Chabrier et al (2000)
Stellar Atmosphere Model AMES-Dusty Chabrier et al (2000)
Age (Gyrs) 0.001 and 0.01 (2)
Mass (Msol) 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07 and 0.08 (8)
Rotation period (days) 0.5 and 5 (2)
Accretion rate (log(Macc/Msolyr) -12, -11, -10, -9, -8, -7 and -6 (7)
Areal coverage (%) 1 and 10 (2)
Disc parameters
Disc mass (M*) (0.0) 0.01 and 0.001 (2,3)
Disc outer radius (AU) 100 and 300 (2)
Vertical hydrostatic equilibrium (or analytic structure) yes and no (2)
Dust sublimation Variable dust sublimation (1)
Scattering Isotropic (1)
α (β) (for analytic models) 2.00 (1.00), 2.10 (1.10) and 2.25 (1.25)
Inclinations (deg) (for non-zero disc mass) 0, 27, 39, 48, 56, 64, 71, 77, 84 and 90 (10)
Total Models 448 (naked stars, 448 SEDs), 17,92 (vertical hydro, 17,920 SEDs), 5376 (analytic models, 53760 SEDs). 72128 SEDs total.

Semi-Empirical: STATUS=COMPLETE

A grid designed for the derivation of stellar parameters. Disc structures use analytically described density distributions and dust sublimation radii, SEDs are derived using full Mie phase scattering. This grid is currently in preparation and is termed the "Semi-emp" grid.
Input parameter
Values (number of values)

Stellar parameters
Stellar Interior Model M*<0.02Msol: Dusty-'00 Chabrier et al (2000).
M*>=0.02Msol: BACH98 Baraffe et al (1998).
Stellar Atmosphere Model Teff<1400K:AMES-Cond Chabrier et al (2000)
1400K< Teff<2500K: AMES-Dusty Chabrier et al (2000)(1) Teff>2500K: NextGen Hauschildt et al (1999)
Age (Gyrs) 0.001, 0.002, 0.003, 0.004, 0.005, 0.006, 0.007, 0.008, 0.009 and 0.01 (10)
Mass (Msol) 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.10, 0.20, 0.30, 0.40, 0.50, 0.60, 0.70, 0.80, 0.90, 1.00, 1.10, 1.20, 1.30 and 1.40 (23)
Rotation period (days) 1 and 5 (2)
Accretion rate (log(Macc/Msolyr) -12 (1)
Areal coverage (%) 10 (1)
Disc parameters
Disc mass (M*) (0.0) 0.01 and 0.001 (2,3)
Disc outer radius (AU) 50 and 100 (2)
Vertical hydrostatic equilibrium (or analytic structure) no (1)
Dust sublimation Analytical sublimation radius (1)
Scattering Full Mie phase (1)
α (β) (for analytic models) 2.00 (1.00), 2.10 (1.10) and 2.25 (1.25)
Inclinations (deg) (for non-zero disc mass) 0, 27, 39, 48, 56, 64, 71, 77, 84 and 90 (10)
Total Models 460 (naked stars, 460 SEDs). 55200 for disc systems, 55660 SEDs total.
(1) Between 1700 and 1400K the AMES-Settl atmospheres are being introduced but currently experimental.

Broadband Photometry and Monochromatic Fluxes

In addition to the magnitudes and colours derived and analysed in Mayne and Harries (2010), which are accesible through the Isochrones and Mass Tracks tool, we have derived magnitudes for several other filter sets. We have also derived monochromatic fluxes for each of the filters used.

Magnitudes

(Table of response function sources)

The magnitudes are defined using:
M=-2.5Log10(Number of e-)-Zeropoint.

If you would like magnitudes or fluxes for another filter set please email: nathan@astro.ex.ac.uk. The filters are named as SET_BAND, so a Bessell U filter is named bessell_U.

Integration and Zeropoints

(Table of zeropoints)

Dependent on whether the responses used are in e-/Photon or in e-/(Unit Energy), integration was performed over either photons or energy (as described in Bessell et al. 2000, in λ space).
Zeropoints either came from literature sources or were derived using a Vega spectrum.

Monochromatic fluxes

(Table of assumed SED shape and effective/central λ's)

Derivation of monochromatic fluxes requires a knowledge of the assumed SED shape used for each filter set. Each quoted monochromatic flux is essentially the value of the flux at a given central or effective λ derived by taking the integrated flux and distributing it over an assumed SED shape (across the filter response). Effectively this means integration over the filter response for our input SEDs must be modified allowing quotation of a monochromatic flux comparable to observation. Essentially, we are asking what would an observer (with no knowledge of the underlying SED) quote as a monochromatic flux for this filter. For our data we have two main cases:

(1) Flat=λ Fλ ∝ Constant
(2) 10,000K BB=λ4 Fλ ∝ Constant

We adopt (1) as a default and quote fluxes derived in this fashion if no other assumption is explicit. Integration then proceeds (dependent on the form of the response function) across the filter response modified for each case, with a similar process as explained in Appendix A of Thomas Robitaille's thesis.

Basically, as,

E=∫ U(λ) Fλ[actual]R(λ)dλ/(∫ Rλdλ) = ∫ U(λ) Fλ[assumed]R(λ)dλ/(∫ Rλdλ),

where U(λ)=1 for a R(λ) in e-/(Unit energy) or λ/(hc) for R(λ) in e-/Photons,

and λ Fλ[assumed] ∝ Either case (1) or (2) above≡ λ0F λ0[quoted].

Meaning the assumed SED shape must be substituted into the flux integration. Therefore to quote monochromatic fluxes for each filter requires the assumed SED shape and effective/central λ.

Details, values and tables.

  • The filter prefix names and response function sources (and units) are all listed in this table.

  • The suffix names, zeropoints (and source), assumed SED shapes, effective/central λ's and bandwidths are also available in this table.

    File Format for fitting Spectra

    If uploading Spectras for fitting please use a two column (ascii) space separated file, with wavelength in the first and flux in the second column (uncertainties, if included then should be placed in the third column). Fluxes and wavelengths must be in one of the supported units (see Fitting tool options). Comment lines must be preceded by a # and appear at the top of the file (not interspersed in the data). NOTE, this option can now be used to include a collection of monochromatic fluxes.


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