Chapter 16 – Chemical Analysis Review of curves of growth –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  Line strength depends (approximately) on the square root of the abundance How does line strength depend on excitation potential, ionization potential, atmospheric parameters (temperature and gravity), microturbulence Differential Analysis Fine Analysis Spectrum Synthesis

Determining Abundances Classical curve of growth analysis Fine analysis or detailed analysis –computes a curve of growth for each individual line using a model atmosphere Differential analysis –Derive abundances from one star only relative to another star –Usually differential to the Sun –gf values not needed – use solar equivalent widths and a solar model to derive gf values Spectrum synthesis –Uses model atmosphere, line data to compute the spectrum

Jargon [m/H] = log N(m)/N(H) star – log N(m)/N(H) Sun [Fe/H] = -1.0 is the same as 1/10 solar [Fe/H] = -2.0 is the same as 1/100 solar [m/Fe] = log N(m)/N(Fe) star – log N(m)/N(Fe) Sun [Ca/Fe] = +0.3 means twice the number of Ca atoms per Fe atom

Solar Abundances from Grevesse and Sauval

Basic Methodology for “Solar-Type” Stars Determine initial stellar parameters –Composition –Effective temperature –Surface gravity –Microturbulence Derive an abundance from each line measured using fine analysis Determine the dependence of the derived abundances on –Excitation potential – adjust temperature –Line strength – adjust microturbulence –Ionization state – adjust surface gravity

Using stellar Fe I lines to determine model atmosphere parameters derived abundance should not depend on line strength, excitation potential, or wavelength. If the model and atomic data are correct, all lines should give the same abundance

Adjusting for Excitation Potential For weak lines on the linear part of the COG, curves of growth can be shifted along the abcissa until they line up, using the difference in excitation potential If the temperature is right, all the curves will coincide  log A = log (gf/g’f) + log / ’ – log  /  l –  ex (  –  ’)

Using a good model The temperature distribution of the model - the T(  ) relation, can make a difference in the shape of the COG The differences depend on excitation potential because the depth of formation depends on excitation potential

The COG for Fe II lines depends on gravity Fe II lines can be used to determine the gravity The iron abundance from Fe II lines must also match the iron abundance from Fe I lines

Strong lines Strong lines are sensitive to gravity and to microturbulence The microturbulence in the Sun is typically 0.5 km s -1 at the center of the disk, and 1.0 km s -1 for the full disk For giants, the microturbulence is typically 2-3 km s -1

Spectrum Synthesis Compute the line profile to match the observed spectrum Vary the abundance to get a good fit. Jacobson et al. determination of the sodium abundance in an open cluster giant Model profiles are shown for 3 different oxygen abundances

Spectrum Synthesis II (Jacobson) Oxygen abundance determinations Matching the line profile for 3 different values of the oxygen abundance, with  [O/H] = 0.5 dex Note CN lines also present near the [O I] line. The strength of CN also depends on the oxygen abundance –When O is low, CN is stronger… Why? [O I]

Interesting Problems in Stellar Abundances Precision Abundances –Solar iron abundance –Effects of 3D hydro –Solar analogs Stellar Populations –SFH of the Galactic thin/thick disk –Population diagnostics –Migrating stars –Merger remnants –Dwarf spheroidals –Galactic Bulge Nucleosynthesis –Abundance anomalies in GC –Extremely metal poor stars –Peculiar red giant stars Metallicity and Planets Evidence for mixing and diffusion

Planets and Metallicity What does this tell us about planet formation? What about 2 nd order effects (O/Fe, Mg/Fe, Ca/Fe)??? Fisher & Valenti 2005

Iron in the Solar Neighborhood [Fe/H] is not a good indicator of the age of the disk Why Iron? Fe is abundant Fe is easy Fe is made in supernovae

Ultra Metal-Poor Stars Ultra metal-poor stars are rare in the halo Most metal poor star known is ~ [Fe/H] = -6 Surveys use Ca II K line Science Magazine

Alpha-process Elements: Edvardsson et al. Pilachowski et al. McWilliam et al. Excesses at low metallicity  /Fe ratio originally set by SN II production Later, SN Ia produce a different Ca/Fe ratio

How to Make Heavy Metals: neutron-capture processes  r-process –High neutron flux –Type II Supernovae (massive stars) –No time for b-decay –Eu, Gd, Dy, some Sr, Y, Zr, Ba, La…  s-process –Low neutron flux –B-decay before next n-capture –No Eu, Gd, Dy Main s-process Low mass stars Double shell burning Makes SrYZr, Ba, etc. Weak s-process Massive stars He-core and shell Burning Lower neutron flux makes SrYZr only

n-capture Synthesis Paths Ba La Cs Xe pps,r s r r p s ss r-process path s-process path

r- and s-Process Elements

Heavy Metal Abundances Note:  Scatter  Deficiencies at low metallicity  Excesses at intermediate metallicity

r-Process vs. s-Process Transition from r-process only to r+s process at log  (Ba)=+0.5 Corresponds to [Fe/H] ~ -2.5 S-process nucleosynthesis begins to contribute to galactic chemical enrichment At lower metallicities only r-process contributes

n-capture Abundances in BD+17 o 3248 Scaled solar-system r-process curve: Sneden 2002

Solar-System s-process Abundances DON’T Fit Sneden (2002), Burris et al. (2000)

BD Is Typical of Very Metal Poor Stars Sneden et al. (2000); Westin et al. (2000); Cowan et al. (2002)

Abundance Dispersions in Globular Clusters

Star Formation History in DSps CMD for the Carina dwarf spheroidal galaxy from Smecker-Hane Note at least two epochs of star formation Abundance differences?

S FH in Omega Centauri The globular cluster Omega Cen also shows interesting structure in its CMD indicating multiple epochs of star formation Epochs of star formation reflected in metallicity distribution function Pancino et al Lee et al 1999, Nature 402, 55