DRIFT-PHOENIX Atmosphere Models – Creating new worlds

As it was promised, here comes a review on the DRIFT-PHOENIX model atmospheres, which are used by our group. (See posts: 14 Mar, 30 Apr)

DRIFT-PHOENIX is a computer code that simulates the structure of an atmosphere including the formation of clouds. The code is part of the PHOENIX-code family (Hauschildt & Baron 1999; Baron et al. 2003) which is described by one of his main authors, Peter Hauschildt, as “… a general-purpose state-of-the-art stellar and planetary atmosphere code. It can calculate atmospheres and spectra of objects all across the HR-diagram ranging from main sequence stars, giants, white dwarfs, stars with winds, TTauri stars, over novae and supernovae, to brown dwarfs and extrasolar giant planets.”

DRIFT is a separate code that was coupled with PHOENIX (Dehn 2007; Helling et al. 2008a; Witte et al. 2009). DRIFT describes the formation of mineral clouds and allows to predict cloud details, like the size of the cloud particles and their composition (Woitke & Helling 2003, 2004; Helling & Woitke 2006; Helling et al. 2008b).

I. STELLAR ATMOSPHERE PART


The modelling of a stellar atmosphere structure is a standard task in astrophysical research. It is determined by three global parameters:

  • the effective temperature, T_eff [K], (represents the total flux of a star)
  • the surface gravity, log(g) [cm/s],
 (relates the mass and radius of an objects and, in many cases, serves as a reasonable age indicator)
  • a set of element abundances (H, He, O, C, Mg, Fe, Si, …), the so-called metallicity [M/H] 
(relies on primordial element abundances combining stellar nucleosythesis with the age of the universe before an object has formed, but also involves other dynamic effects like altitude-dependent gravitational settling or electromagnetic enrichment/depletion)

Given these global parameters, the atmosphere structure is the coupled solution of

(1) the hydrostatic equilibrium which provides the local gas pressure, p_gas [dyn cm^2],
(2) the energy transfer through radiation and convection which yields the local gas temperature, T_gas [K],
(3) the chemical equilibrium which provides the number densities of those ions, atoms, and molecules that compose the atmospheric gas.

The energy transfer through radiation is described by the radiative transfer equations, and the convective energy transfer is described by the Mixing Length Theory. Both produce a flux of energy through the atmospheric gas and the total flux through the atmosphere needs to be conserved as no heat nor radiation can be created inside the atmosphere itself. Radiation is transported through absorption and re-emission by the atmospheric gas. It is, therefore, essential to know how many absorbing ions, atoms and molecules are in the atmosphere (see (3)), and with which efficiency they absorb and re-emit photons. These chemical abundances, however, change with temperature and pressure, and are therefore interwoven with (1) and (2). The solution to this can only be found by an iterative numerical procedure. The solution to the problem is found if the iterative procedure fulfills some prescribed criteria to a certain precision.

The absorption and re-emission of photons by the atmospheric gas as part of a model atmosphere requires a set of material constants (wavelength dependent absorption coefficients for each individual atom and molecule and equilibrium constants for gas-phase chemistry). Without them, the atmosphere structure can not be calculated.

A more detailed insight into the theory of stellar atmospheres can be acquired from standard text books, like e.g. Mihalas (1978).

II. CLOUD FORMATION PART

In contrast to Earth, extra-solar atmospheres may not contain any condensation seeds. The cloud formation module DRIFT includes, therefore, a description of the formation of seed particles and their subsequent growth to macroscopic particles. DRIFT models the formation of (TiO2)_N-seed particles, and the mantle growth by the 7 [s]olids TiO2[s], Al2O3[s], Fe[s], SiO2[s], MgO[s], MgSiO3[s], Mg2SiO4[s] made of 6 elements and grown by 32 surface reactions (Witte et al. 2009). The cloud particles are composed of mixed materials, and their sizes change with atmospheric height. If a cloud forms, the atmospheric gas is reduced by those elements that are turned into the cloud particle. The cloud particles start to fall through the atmosphere. During this journey, they will grow in size but also change it’s material composition. The distance of their fall determines the cloud height.

Figure 1. Nucleation (seed formation), dust growth (and evaporation), gravitational settling (rain-out) and element replenishment are processes involved into the formation of a cloud. The inner part of an atmosphere is typically warmer than the outer part in a brown dwarf, and no cloud particles can form. Atmospheres of brown dwarfs and giant gas planets are convective (”boiling”) which provides the mechanisms for element replenishment. Original figure in Woitke & Helling (2004).

Figure 1. Nucleation (seed formation), dust growth (and evaporation), gravitational settling (rain-out) and element replenishment are processes involved into the formation of a cloud. The inner part of an atmosphere is typically warmer than the outer part in a brown dwarf, and no cloud particles can form. Atmospheres of brown dwarfs and giant gas planets are convective (”boiling”) which provides the mechanisms for element replenishment. (Woitke & Helling 2004)

The processes describing the cloud formation are (Woitke & Helling 2003, 2004; Helling & Woitke 2006; Helling et al. 2008a) (Fig. 1)

(4)  nucleation, growth & evaporation,
(5)  gravitational settling of cloud particles,
(6)  element conservation for those element involved in cloud formation, 
incl. convective element replenishment.

Process (4) requires the knowledge of the local gas temperature and of the number densities of those gas species involved into the cloud particle formation. Process (5) requires the knowledge of the local gas density (gas pressure), and process (6) requires the local gas velocity. In return, process (6) feeds back into the local gas-phase chemistry (3) with reduced element abundances, and (4)−(6) provide details for the opacity calculations as input for (2). Also the cloud formation part requires a set of material constants (e.g. material densities, molecular cluster data for nucleation) which are needed to calculate the cloud structure.

The text book by Gail & Sedlmayr (2014) provides a detailed derivation of the basic theory of dust formation in astrophysical objects. Helling & Fomins (2013) summarise additional developments for gravitational dominated atmospheres.

III. MODEL OUTPUT

A model atmosphere simulation provides detailed information for all the complexes (1)−(6). To keep the amount of numerical data sensible, only a subset of information is included into any output files. Table 1 summarises the most common output quantities. The easiest way to compare model results with observations of an astrophysical objects, like a brown dwarf, is compare the spectral energy distribution (Fig. 3), also called the spectrum, with the observed spectrum. The spectrum is the wavelength-dependent flux, F_λ, plotted versus the wavelength, λ.

Screen Shot 2014-06-30 at 17.08.56

Figure 2. Left: Drift-Phoenix (T_gas(z), p_gas(z))-structures for solar metallicity, log(g)=3.0 and effective temperatures, T_eff, as indicated. Right: Typical composition of clouds made of mixes of minerals that change throughout the cloud. The change in grain size is indicated (big grains / small grains).

Figure 2. Left: DRIFT-PHOENIX (T_gas(z), p_gas(z))-structures for solar metallicity, log(g)=3.0 and effective temperatures, T_eff, as indicated. Right: Typical composition of clouds made of mixes of minerals that change throughout the cloud. The change in grain size is indicated (big grains / small grains).

DF_Spec_metal

DRIFT-PHOENIX synthetic spectra for varying initial element abundances mimicking objects from the early universe for [M/H]=-6.0. The global parameters are given for each of the model results shown. (Witte et al. 2009).

4. DRIFT-PHOENIX MODEL ATMOSPHERE GRID

A model grid is a whole set of model atmospheres calculated for a whole set of global parameters (T_eff , log(g), [M/H]). The most up-to-date DRIFT-PHOENIX model atmosphere grid was presented in Witte et al. (2011). It contains an updated equilibrium chemistry (ACES). It spans over the following global parameter:

  • T_eff = 1000K . . . 3000K (in steps of 100K),
  • log(g)= 3.0 . . . 5.5 (in steps of 0.5),
  • [M/H]= −0.6 . . . + 0.3 (in steps of 0.3).

This set of global parameter (T_eff , log(g), [M/H]) allows combinations typical for:

  • M-dwarfs: Teff > 2700K, solar metallicity,
  • brown dwarfs: Teff < 2700K, log(g)≥4.5 for old brown dwarfs and log(g)<4.5 , for young brown dwarfs, solar metallicity and lower,
  • giant gas planets: Teff < 2700K, log(g)≤3.0, solar metallicity

The grid contains 527 model atmospheres in total ([M/H]=0.0: 148, [M/H]=-0.3: 130, [M/H]=+0.3: 121, [M/H]=-0.6: 128).

5. WHICH PAPERS TO CITE IF USING DRIFT-PHOENIX

Hauschildt & Baron (1999); Baron et al. (2003); Woitke & Helling (2003, 2004); Helling & Woitke (2006); Helling et al. (2008a, 2008b); Witte et al. (2009, 2011)

 

The PHOENIX code:

 http://www.hs.uni-hamburg.de/EN/For/ThA/phoenix/index.html

DRIFT-PHOENIX models are stored here:

http://svo2.cab.inta-csic.es/theory/newov/index.php

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