FROM COMPLETE LINERIZATION TO ALI AND BEYOND (how a somewhat younger generation built upon Dimitri’s work). Ivan Hubeny University of Arizona. Collaborators: T. Lanz, D. Hummer, C. Allende-Prieto, L.Koesterke, A. Burrows, D. Sudarsky. Introduction.
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FROM COMPLETE LINERIZATION TO ALI AND BEYOND(how a somewhat younger generation built upon Dimitri’s work)
Ivan Hubeny
University of Arizona
Collaborators: T. Lanz, D. Hummer, C. Allende-Prieto, L.Koesterke,
A. Burrows, D. Sudarsky
Motto: One picture is worth 1000 words, but one spectrum is worth 1000 pictures!
The Numerical Problem
A model stellar atmosphere is described by a system of highly-coupled,
highly non-linear set of equations
The number of unknowns and cost of computing a model atmosphere increases quickly with
the complexity of the atmospheric plasma.
Transfer equation
Formal solution
Rate equation (def of S)
==>
Ordinary Lambda Iteration:
Accelerated Lambda Iteration:
and iterate as:
Define
FS = Formal Solution - uses an old source function
Ordinary Lambda Iteration
Accelerated Lambda Iteration
acceleration operator
(future)
OIV
SXI
Assumption:Boltzmann distribution inside each superlevel
FeIV
NLTE line blanketing: lines & frequencies
Fe III
Transition 1-13
Absorption
cross-section
OS
Sorted cross-section
ODF
- Formulated by Rybicki 1971, JQSRT 11, 589 for a two-level atom
- Suggested extension for LTE model atmospheres by Mihalas 1978 (SA2)
- Implemented for cool atmospheres by Hubeny, Burrows, Sudarsky 2003
original
Rybicki
Outer structure: depths
Inner structure: state parameters (intensities)
Block tri-diagonal
Inner matrices diagonal + added row(s)
Execution time scales:
-- linearly with ND
-- cubically with NF !
Outer structure: intensities
Inner structure: depths
Block diagonal + added row(s)
Inner matrices tri-diagonal
Execution time scales:
-- linearly with NF !
-- cubically with ND (only once)
------------------------ filled within the last month
OSTAR 2002; BSTAR 2006 GRIDS
Lanz & Hubeny, ApJS 146, 417; 169,83
Temperature structure for various metallicities
Comparison to Kurucz models
50,000 K
40,000K
30,000 K
Teff = 25,000
log g = 3
Hubeny, Burrows, Sudarsky 2003
Thermal Inversion: Water in Emission (!)
Strong Absorber at Altitude (in the Optical)
Hubeny, Burrows, & Sudarsky 2003
Burrows et al. 2007
OGLE-Tr-56b
Burrows, Hubeny, Budaj, Knutson, & Charbonneau 2007
r.h.s. lives in the comoving frame
l.h.s. lives in the lab frame
Hubeny & Burrows 2007
example: the energy equation
backward time differencing - implicit scheme
intensity at the end of timestep - expressed through an approximate lambda operator
lLinearizarion of the source function
moments of the specific intensity at the end of timestep
1) 1-D STATIONARY ATMOSPHERES
-- Can convection be described within a 1-D static picture?
-- Technical improvements in the modeling codes (more efficient formal solvers; even more efficient iteration procedure - Newton-Krylov; multigrid schemes; AMR; etc.)
2) 3-D SNAPSHOT OF HYDRO SIMULATIONS (i.e. with radiation-hydro split)
3) FULL 3-D RADIATION HYDRO