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--- anlyplot [2014/05/09 15:04]
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-====== TALENT ======
+====== EXERCISES ======
-===== Training in Advanced Low Energy Nuclear Theory:  EXERCISES =====
+**[[RXNnetworkEX|Reaction Networks]]**, **[[NuclPhysInput|Nucl Physics Input]]**, **[[HydroEX|Hydro]]**, **[[BBNEX|BBN]]**, **[[AnlyPlot|Abundances, Analysis and Plotting]]**
-[[http://www.nucleartalent.org|{{:talent.png?650|Nuclear TALENT}}]]
-**[[RXNnetworkEX|Reaction Networks]]**, **[[HydroEX|Hydrodynamics]]**, **[[BBNEX|BBN]]**, **[[AnlyPlot|Abundances, Analysis and Plotting]]**, **[[NuclPhysInput|Nucl Physics Input]]**
 ==== Abundances, Analysis and Plotting ====
 <box left 80% orange|**(Pre-Course Assignment)**>
-**Analyze and plot abundances:**
+**Analyze and plot Solar Abundances:**
    -	Grab the solar system abundances and plot them
+    * Cite the data source (Anders & Grevesse, Lodders, Asplund, etc)
     *	Vs mass number (A)
     *	Vs atomic number (Z)
-   -	Subtract the solar s-process abundances from solar
-    *	Plot the remaining abundance pattern
+**Analyze and plot Stellar Abundances**
-   -	Grab stellar abundances from the [[http://saga.sci.hokudai.ac.jp/wiki/doku.php|SAGA Database]] for a handful of stars
+   - Grab stellar abundances from the [[http://saga.sci.hokudai.ac.jp/wiki/doku.php|SAGA Database]] for a handful of stars
-    *	Plot abundances in [A/H] notation
+$\ \ \ \ \ \ [A/B]= \log_{10}(A/B)_{star} - \log_{10}(A/B)_\odot$
-    *	Translate [A/H] notation into mass fraction abundances
+   * Plot
+     - [Ca/H], [Ge/H], [Zr/H], [Sr/H], [Ba/H], [La/H], [Nd/H], [Eu/H] vs [Fe/H]
+         * Are these elements correlated with metallicity?
+         * Do they have the same correlation?
+     - [Ca/Fe], [Ge/Fe], [Zr/Fe], [Sr/Fe], [Ba/Fe], [La/Fe], [Nd/Fe] vs [Eu/Fe]
+         * Are these elements correlated with Eu?
 </box>
-<box left 80% blue|**(During-Course Assignment)**>
-**Abundance Measures**
-There is a whole thicket of abundance measures that one finds
-in the literature, which can unfortunately lead to confusion. The following are some
-exercises to get you used to the different notations and to translating among them.  (I have cribbed Brian Fields' first question from his first homework from his [[http://courses.atlas.illinois.edu/fall2009/astr/astr596npa/|Nuclear and Particle Astrophysics]] course.)
-   * Given the mass density $\rho_i$ of nuclide species $i$, what is $n_i$, the number density in $i$? Express this both with and without including the nuclear binding energy of $i$. Show that ignoring the binding energy introduces a $< 1\%$ error in $n_i$. Of course, neutral matter will also contain electrons; show that neglecting the electron contribution to the mass densities also gives a $< 1\%$ error–thus, we can take $\rho$ to be the total matter density as well as the baryonic density. Using these approximations, express $\rho_i$ in terms of $n_i$ and $A_i$, the mass number.
-   * One way to define an abundance is the mass fraction $X_i \equiv \rho_i/\rho$, where $\rho = \Sigma_j \rho_j$ is the total baryonic mas density summed over all species. Show that $X_i$ is unaffected by a bulk, chemically homogeneous expansion of the gas, and that the mass fractions obey $\Sigma_i X_i = 1$ (this also means that any given $0 \leq X_i \leq 1$, i.e., that these are really fraction).
-   * Another useful measure is the mole fraction $Y_i = n_i/n_B$. What is the relationship between $Y_i$ and $X_i$? That is, find an expression for $X_i$ in terms of $Y_i$ and physical/nuclear constants. Show that $\Sigma_i Y_i \neq 1$ in general. In general, is $\Sigma_i Y_i \leq 1$ or $\geq 1$? Prove your answer.
-   * It is sometimes useful to define the electron fraction $Y_e = n_e/n_B$, where $n_e$ is the number density of electrons, with each nuclide species $i$ contributing $Z_i$ electrons (assuming electrical neutrality). Find an expression for $Y_e$ in terms of the set of $Y_i$. What are the upper and lower limits to $Y_e$? What astrophysical systems have compositions for which $Y_e$ approaches these limits? Estimate $Y_e$ for the Earth, assuming that nuclei of heavy elements typically have half protons and half neutrons.
-   * Mass fractions are not in practice easy to measure directly. A more useful observable is $y_i = {\mathcal A}_i/H = n_i/n_H$. This is usually what observers mean when they say “abundance.” Like $X_i$, this is dimensionless, but the “normalization” condition does not hold (show this). What is the connection between ${\mathcal A}_i/H$ and $X_i$? That is, express $X_i$ in terms of the set of {$y_i$} ≡ {${\mathcal A}_i/H$}, and express $y_i$ in terms of $X_i$ and $X_H$. Explain why mass fractions are seldom reported by observers.
-   * Geologists and cosmochemists of course use different abundance scales, often setting Si to some arbitrary fiducial value like $10^2$ or $10^6$. Using your handy table of abundances from Anders & Grevesse (1989 Geochim. et Cosmochim. Acta) compute the solar values of: D/H, He/H, O/H, and La/H. Using the table and $Z_\odot \simeq 0.02$, what is the inferred $Y_\odot$?
-</box>

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