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Chapter 14 – Chemical Analysis

Chapter 14 – Chemical Analysis. Review of curves of growth How does line strength depend on excitation potential, ionization potential, atmospheric parameters (temperature and gravity), microturbulence Differential Analysis Fine Analysis Spectrum Synthesis. The Curve of Growth.

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Chapter 14 – Chemical Analysis

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  1. Chapter 14 – Chemical Analysis • Review of curves of growth • How does line strength depend on excitation potential, ionization potential, atmospheric parameters (temperature and gravity), microturbulence • Differential Analysis • Fine Analysis • Spectrum Synthesis

  2. The Curve of Growth • The curve of growth is a mathematical relation between the chemical abundance of an element and the line equivalent width • The equivalent width is expressed independent of wavelength as log W/l Wrubel COG from Aller and Chamberlin 1956

  3. Curves of Growth Traditionally, curves of growth are described in three sections • The linear part: • The width is set by the thermal width • Eqw is proportional to abundance • The “flat” part: • The central depth approaches its maximum value • Line strength grows asymptotically towards a constant value • The “damping” part: • Line width and strength depends on the damping constant • The line opacity in the wings is significant compared to kn • Line strength depends (approximately) on the square root of the abundance

  4. The Effect of Temperature on the COG • Recall: • (under the assumption that Fn comes from a characteristic optical depth tn) • Integrate over wavelength, and let lnr=Na • Recallthat the wavelength integral of the absorption coefficient is • Express the number of absorbers in terms of hydrogen • Finally,

  5. The COG for weak lines Changes in log A are equivalent to changes in log gfl, qc, or kn For a given star curves of growth for lines of the same species (where A is a constant) will only be displaced along the abcissa according to individual values of gfl, c, or kn. A curve of growth for one line can be “scaled” to be used for other lines of the same species.

  6. A Thought Problem • The equivalent width of a 2.5 eV Fe I line in star A, a star in a star cluster is 25 mA. Star A has a temperature of 5200 K. • In star B in the same cluster, the same Fe I line has an equivalent width of 35 mA. • What is the temperature of star B, assuming the stars have the same composition • What is the iron abundance of star B if the stars have the same temperature?

  7. The Effect of Surface Gravity on the COG for Weak Lines • Both the ionization equilibrium and the opacity depend on surface gravity • For neutral lines of ionized species (e.g. Fe I in the Sun) these effects cancel, so the COG is independent of gravity • For ionized lines of ionized species (e.g Fe II in the Sun), the curves shift to the right with increasing gravity, roughly as g1/3

  8. Effect of Pressure on the COG for Strong Lines • The higher the damping constant, the stronger the lines get at the same abundance. • The damping parts of the COG will look different for different lines

  9. The Effect of Microturbulence • The observed equivalent widths of saturated lines are greater than predicted by models using just thermal and damping broadening. • Microturbulence is defined as an isotropic, Gaussian velocity distribution x in km/sec. • It is an ad hoc free parameter in the analysis, with values typically between 0.5 and 5 km/sec • Lower luminosity stars generally have lower values of microturbulence. • The microturbulence is determined as the value of x that makes the abundance independent of line strength.

  10. Microturbulence in the COG 5 km/sec 0 km/sec Questions – At what line strength do lines become sensitive to microturbulence? Why is it hard to determine abundances from lines on the “flat part” of the curve of growth?

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