From Brown Dwarfs to Planets: Chemistry and

Cloud Formation

from 24 Oct 2006 through 27 Oct 2006

The workshop is sponsored by: University Leiden , Lorentz Center , Netherlands Organization for Scientific Research , Koninklijke Nederlandse Akademie van Wetenschappen , The Netherlands Research School For Astronomy , Scottish Universities Physics Alliance , European Space Agency

The Netherlands Research School For Astronomy

Test Case Study

abstract deadline: 4 September 2006 (abstract template) (list of abstracts + talk .pdf-files ! )

deadline test case delivery: 6 September 2006

What about?

The whole workshop idea is motivated by the present situation in substellar atmosphere modelling: different model approaches yield partially very satisfying results and the increasing observational power will need an ever increasing understanding of the models applied. We further encounter the need for massive grids of model atmospheres e.g. in the frame of "automated derivation of stellar atmosphere parameters" (Bailer-Jones et al. 1996, Recio-Blanco et al. 2006 astro-ph/0604385). Such methods need to be able to rely on atmospheric models for which a certain trust-range is available.

--> workshop main page
--> workshop program

Obviously, the physical state of the atmosphere is determined by its interaction with the interior and the objects evolution. For now, we consider this as known and concentrate on the atmosphere. It is also clear that the modelling quality of the atmosphere depends on material data (eg opacity data, equilibrium constants) and numerical treatment. In this test cases we will focus on the part of the stellar/planetary atmosphere problem dealing with chemistry and cloud formation.

Other examples:

* hydrocode comparison in disc-planet system

* radiative transfer code comparison

* Also the Lorentz Center did host at least one other workshop of our kind:
Benchmarking of PDR models

Literature related to the workshop idea:

* Calibrating models of utralow-mass stars
Reiners 2005, AN 326, No. 10, 930-933

* CFD: A Castle in the Sand?
Kleb & Wood, 34th AIAA Fluid Dynamics Conference, AIAA Paper 2004-2627

The first test case study of chemistry and cloud formation in

brown dwarf and planetary atmospheres

Below you find the questionnaire, the test models, a read_in_routine, and the element abundances which you can down load.

Questionnaire (click!)

Test models: (log g = 5.0, solar metalicity)
-- For details see Part II
-- ASCII files download here:
Teff=1800K
Teff=1400K
Teff=600K

Read_in_routine (click & adopt for your use!)

Element abundances (click!)
[Grevesse and Noels (1993) solar photosphere abundances]

Part I: fully iterated 1D static, model

Atmosphere model representatives will calculate a fully iterated 1D static,
model for a given set of stellar parameters (Teff, log g, element abundances)
and provide ASCII output of the local (T( p), rho(p), vconv(p)) and
general dust properties including the local dust-to-gas ratio, particle
number density, mean particle size and size distribution, and dust chemical
composition as function of local pressure p.

Given parameters:
Teff = 1800K, 1000K
log g = 5.0
element abundances eps_i^gas (see *1)

For each temperature compute two models: one with no dust opacity but with
dust included in the chemical equilibrium and one with normal dust opacity

Wanted output quantities for both test case models in ASCII format:
local T [K], p [dyn/cm2], rho_gas [g/cm3], vconv [cm/s], Fconv [erg/cm2/s]
local dust-to-gas ratio rho_d/rho_gas          (see *2 - for definition)
local mean particle size and size distribution (see *3 - for definition)
local chemical dust composition               (see *4 - for definition)
   --> provide mass & volume fractions

It would be a good idea to bring the complete model output with you to the
workshop.

The motivation for this exercise is that we start from the full solution of
the stellar atmosphere problem and see if there are differences. The idea
is now to find reasons for possible differences and according to the
workshop's topic, we will look in how far the treatment of dust and clouds
may cause differences. This leads logically to part II:

Part II: decouple the dust and cloud complex from the stellar atmosphere problem

We decouple the dust and cloud complex from the stellar atmosphere problem.
Provide the same dust parameters listed above for a pre-calculated atmosphere
model structure. The model structures will be provided by Matthias Dehn from
the Phoenix code team (Hamburger Sternwarte, Teff=1800, 1400K) and by Mark Marley
from the Marley & Ackerman code (NASA, Teff=600). In this state, the exact
details of how this models run is not of importance since we all will use
the their profiles as an input and hence, "start" from the same conditions.

Given quantities:
temperature-pressure structure T(p) [K] [dyn/cm2]
convective flux Fconv(p)             [erg/cm2/s]
convective velocity vconv(p)        [cm/s]
element abundances eps_i inside the deep, well-mixed,
dust-free convection zone

If your code needs more, let us know!

Wanted output quantities in ASCII format as function of local pressure p:
dust-to-gas ratio rho_d/rho_gas                 (see *2 - for definition)
mean particle size <a> and
    size distribution f(a,p)                         (see *3 - for definition)
chemical dust composition                  (see *4 - for definition)
     --> provide mass & volume fractions
number of dust particles per cm3
element abundances in the gas phase eps_i^gas (see *1 - for definition)

Definition (*1)

Note, there are newer element abundances provided by Asplund et al. (2005),
however, other authors cannot support these revised values (e.g. Ayres et al.
2006, astro-ph/0606153). We stick to the conventional and use
Grevesse and Noels (1993) solar photosphere abundances (attached).

The element abundances are normalized to hydrogen:
log_10 (12.0 - eps_i^\prime) = eps_i^gas
               with i the chemical elements (O, Si, Fe, ....).

definition: element abundances in gas phase eps_i^gas

eps_i^gas = ( sum_k n_k^gas * \nu_i^k ) / (sum_k n_k^gas * \nu_H^k)

sum_k	-	sum over all gas species k
n_k^gas	-	number density of gas species k	1/cm3
\nu_i^k	-	stoichiometric factor of gas species k containing element i
\nu_H^k	-	stoichiometric factor of gas species k containing element hydrogen (H)

example: SiO_2 : \nu_Si^SiO2 = 1, \nu_O^SiO2=2

Definition (*2)

definition: dust-to-gas ratio

rho_d/rho_gas

dust-to-gas ratio

Calculate dust mass density

in case of particles of fixed size:
rho_d = sum_s (n_s * M_d) (Eq. 1)

in case of particles of different sizes:
rho_d = sum_s ( int_a ( f_s(a) * M_s(a) ) da) (Eq. 2)

rho_d	-	dust mass density	[g/cm3]
rho_gas	-	gas mass density	[g/cm3]
n_s	-	number of dust particles of kind s per cm3	[1/cm3]
M_d	-	mass of dust particle of kind s of given size a	[g]
s	-	dust species (e.g. TiO2[s], Mg2SiO4[s], ...)
f_s(a)	-	grain size distribution	[1/cm3 * 1/cm]
a	-	grain size	[cm]
M_s(a)	-	mass of dust particle of size a and kind s	[g]
int_a	-	integral over grain size space

Definition (*3)

definition: mean particle size <a> [cm]

radius weighted mean size:
<a> = ( sum_s int_a ( f_s(a) * a) da ) / ( sum_s int_a f_s(a) da )       [cm]   (Eq. 3)


surface weighted mean size:
<a>_A = ( sum_s int_a ( f_s(a) * V_s(a)) da )   / ( sum_s int_a ( f_s(a) * A_s(a)) da ) [cm]   (Eq. 4)

      = ( sum_s int_a ( f_s(a) * a * a2) da )
       / ( sum_s int_a ( f_s(a) * a2    ) da )   in the chem. homogeneous case

for fixed particles size a = a_0 [cm]: f(a) = delta(a - a_0) => <a>=a

f_s(a)	-	size distribution of grains of kind s and size a	[1/cm3 * 1/cm]
V_s(a)	-	total dust volume of kind s and size a	[cm3]
A_s(a)	-	total surface of dust kind s and size a	[cm2]
a	-	grain size	[cm]
sum_s	-	sum over all kinds s of dust
int_a	-	integral over grain size space

definition: size distribution f(a,p) [1/cm3 * 1/cm]
total grain size distribution at pressure p in the atmosphere
= number of dust particles per size at pressure p
Ideally, one would have as many size distributions has one has layers
in the atmospheric model.

Definition (*4)

definition: chemical dust composition
in mass fraction of kind s : m_s / sum_s m_s = m_s / M_tot

in volume fractions: V_s / sum_s V_s = V_s / V_tot

m_s	-	total dust mass of dust of kind s	[g/cm3]
M_tot	-	total dust mass	[g/cm3]
V_s	-	total dust volume of dust of kind s	[cm3/cm3]
V_tot	-	total dust volume	[cm3/cm3]

Note: -- mass and volume are given per cm3 of atmospheric matter
-- V_s is not the volume of one particle but all volume
of dust kind s in all the dust present