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A historical perspective on theoretical studies of brown dwarfs

Peter H. Hauschildt
Department of Physics & Astronomy
and
Center for Simulational Physics
The University of Georgia
Athens, GA 30602

Overview

1.

Disclaimer

2.

Introduction

3.

The Past

4.

The Path

• input physics
• enabling technologies

5.

Conclusions

Disclaimer

This talk will feature glaring omissions, possible misinterpretations and my subjective view on the topic. All errors and blunders are solely mine.

Introduction

• Publication rate on ``brown dwarfs'' follows the general increase in the astronomical literature ... almost.

  
  

• I will concentrate on theoretical studies of the interior/evolution and atmospheres of brown dwarfs.

The Past

Progress comes from two sides:

• the ``planetary community'' extending their models up in mass.
• the ``stellar community'' extending their models down in mass.

Interior & evolutionary modeling of brown dwarfs:

The beginning:

• Kumar, 1963: electron degeneracy stops collapse of low mass objects before H-burning temperatures are reached ($\approx 0.1\hbox{$\,$M$_\odot$}$).
• Peebles, 1964; Hubbard 1968: thermal cooling models of giant planets.
• Grossman, Graboske et al, 1970-1974: evolution of low mass stars (mass limit set to $\approx 0.085\hbox{$\,$M$_\odot$}$).
• Tarter, 1975: cooling of brown dwarfs based on extrapolated sequences
• Alexander, 1975: low temperature Rosseland opacities
• Stevenson, 1975-1978: thermodynamics and evolution of brown dwarfs.

The ???:

• D'Antona & Mazzitelli, 1982-1986: evolution of low mass stars and brown dwarfs.
• Hubbard & McFarlane, 1983-1986: equation of state for giant planets.
• Nelson, Rappaport & Joss, 1982-86: evolution of brown dwarfs from early stages to ages of $\gt 10\,$Gyr.
• Alexander et al, 1983, 1994: updated (molecules and grains) low temperature opacities.
• Lunine, Hubbard & Marley, 1986: evolutionary sequence of BDs with grey atmospheres used as boundary conditions.
• Burrows, Hubbard, Lunine, Saumon, Marley 1989-: continuously improved evolutionary models.

The Present:

• Chabrier, Saumon, van Horn: 1990-1995: non-ideal EOS for conditions in low mass stars, BDs and giant planets.
• Saumon et al, 1994: evolution/interior coupled to zero-metallicity non-grey atmospheres.
• Baraffe, Chabrier, 1995: evolutionary sequences coupled to finite metallicity, non-grey AH95 model atmospheres.
• CNRS/WSU/UGA collaboration, 1996; Tucson group, 1996: Gl229B models.

Model atmospheres for brown dwarfs

• Mould, 1975/1976: convective model atmospheres for $\hbox{$\,T_{\rm eff}$}\ge 3000\hbox{$\,$K}$based on ATLAS.
• Lunine et al, 1986: grey atmosphere models for giant planets.
• Allard, 1990; Kui 1991: model atmospheres for $\hbox{$\,T_{\rm eff}$}\le 3000\hbox{$\,$K}$ based on Wehrse's low $\hbox{$\,T_{\rm eff}$}$ white dwarf code.
• Brett & Plez, 1993: low $\hbox{$\,T_{\rm eff}$}$ models based on Gustafsson's MARCS code.
• Saumon, 1994: zero-metallicity models for brown dwarfs and giant planets.
• Allard & Hauschildt, 1995: model atmospheres for low mass stars based on the general PHOENIX code.
• Allard et al, Marley et al, Tsuji et al, 1996: model atmospheres for substellar objects (Gl229B).
• Allard, Hauschildt & Baron, 1998: unified (NLTE, wind, ...) model atmospheres from $\hbox{$\,T_{\rm eff}$}\le 1,000\hbox{$\,$K}$ to $\hbox{$\,T_{\rm eff}$}\gt 200,000\hbox{$\,$K}$.

The Path: Input Physics (interiors)

• stars with $M<0.3\hbox{$\,$M$_\odot$}$ are convective from the center to the upper atmosphere, simplifying the interior models but complicating the atmosphere models.
• structure of the object depends critically on the atmosphere and its thin radiative layer.
• nuclear process well understood (deuterium burning, Li burning).
• but screening factors are nasty ...

• Equation of State for low temperature, dense material.

  1.

  electron degenerate

  2.

  pressure ionization

  3.

  non-ideal

• early work: Salpeter (1961), Hubbard (1973-), Stevenson (1975-).

  
  

• State-of-the-art: Saumon, Chabrier & van Horn, 1995: consistent pressure ionization of H and He, tested with experimental results (Livermore).

The Path: Input Physics (atmospheres)

• Standard classical ``stellar atmosphere'' problem (at least, that is the usual assumption):

  1.

  plane parallel

  2.

  hydrostatic

  3.

  LTE

  4.

  radiative plus convective energy equilibrium

• The Problems:

  1.

  convection into optically thin layers (no real theory).

  2.

  complex equation of state (molecules, dust).

  3.

  highly non-grey opacities.

  4.

  poorly known opacities (molecules, dust).

  5.

  100's of millions of lines need to be handled (TiO, water vapor).

  6.

  strongly depth dependent line broadening (van der Waals) but mostly unknown interaction constants.

  
  

  7.

  non-ideal EOS effects occur near the bottom of BD atmospheres.

  8.

  illumination.

  9.

  radiative transfer.

  10.

  non-LTE.

• State-of-the-art: unified model atmospheres employing direct opacity sampling with large EOS, dust formation and opacities, and, for hotter BDs, NLTE effects for various elements (Allard, Hauschildt & Baron, 1998).

Enabling technologies

• mainframe era: serial scalar processors with virtual memory, 1965-1980's
  • allowed more detailed calculations than were previously possible.
  • numerical algorithms developed for simulations.
  • line opacity included as ODF's and similar techniques (table interpolation).
  • allowed direct processing of a few 10k lines with detailed profiles.
  • NLTE possible for $\approx 10-20$ atomic levels.
  • CPU performance and virtual memory limitations severely restricted what could be done.

• vector computer era: serial vector processors, mid 1980's-early 1990's
  • vast increase in raw CPU performance.
  • required moderate algorithmic changes.
  • allowed direct processing of a few 1M lines with detailed profiles.
  • NLTE possible for $\approx 100$ atomic levels with early ALI RT methods.
  • memory (no VM on Crays!) and IO restrictions limit calculations.

• parallel computer era: parallel vector or superscalar processors, 1990's-
  • vast increase in number of available CPUs per machine (>64), architectural design not yet fully evolved.
  • requires significant algorithmic changes.
  • allowed direct processing of a few 100M lines with detailed profiles.
  • NLTE possible for at least 10,000 atomic levels with latest ALI algorithms.
  • allow more physically accurate treatment within the simulations.
  • memory and IO restrictions significantly reduced, this makes much more detailed and accurate calculations possible.

Conclusions

• Breakthroughs are typically made when the physics that is included in the models was improved, either explicitly or implicitly.
• explicit: EOS, better line lists for molecular lines, dust condensation and opacities.
• implicit: progress in ``enabling technologies'' (computer and algorithms) allows a progressively more accurate treatment of the input physics, leading to better results.
• synergy effects help driving the theory towards better results.
• In the future:
  • NLTE.
  • NLCE.
  • better treatment of dust.
  • more complete opacities (which means more lines in many cases).
  • true 3D models (fun but hard).
  • ...