/
notebook.tex
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/
notebook.tex
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% Default to the notebook output style
% Inherit from the specified cell style.
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
% Nicer default font (+ math font) than Computer Modern for most use cases
\usepackage{mathpazo}
% Basic figure setup, for now with no caption control since it's done
% automatically by Pandoc (which extracts  syntax from Markdown).
\usepackage{graphicx}
% We will generate all images so they have a width \maxwidth. This means
% that they will get their normal width if they fit onto the page, but
% are scaled down if they would overflow the margins.
\makeatletter
\def\maxwidth{\ifdim\Gin@nat@width>\linewidth\linewidth
\else\Gin@nat@width\fi}
\makeatother
\let\Oldincludegraphics\includegraphics
% Set max figure width to be 80% of text width, for now hardcoded.
\renewcommand{\includegraphics}[1]{\Oldincludegraphics[width=.8\maxwidth]{#1}}
% Ensure that by default, figures have no caption (until we provide a
% proper Figure object with a Caption API and a way to capture that
% in the conversion process - todo).
\usepackage{caption}
\DeclareCaptionLabelFormat{nolabel}{}
\captionsetup{labelformat=nolabel}
\usepackage{adjustbox} % Used to constrain images to a maximum size
\usepackage{xcolor} % Allow colors to be defined
\usepackage{enumerate} % Needed for markdown enumerations to work
\usepackage{geometry} % Used to adjust the document margins
\usepackage{amsmath} % Equations
\usepackage{amssymb} % Equations
\usepackage{textcomp} % defines textquotesingle
% Hack from http://tex.stackexchange.com/a/47451/13684:
\AtBeginDocument{%
\def\PYZsq{\textquotesingle}% Upright quotes in Pygmentized code
}
\usepackage{upquote} % Upright quotes for verbatim code
\usepackage{eurosym} % defines \euro
\usepackage[mathletters]{ucs} % Extended unicode (utf-8) support
\usepackage[utf8x]{inputenc} % Allow utf-8 characters in the tex document
\usepackage{fancyvrb} % verbatim replacement that allows latex
\usepackage{grffile} % extends the file name processing of package graphics
% to support a larger range
% The hyperref package gives us a pdf with properly built
% internal navigation ('pdf bookmarks' for the table of contents,
% internal cross-reference links, web links for URLs, etc.)
\usepackage{hyperref}
\usepackage{longtable} % longtable support required by pandoc >1.10
\usepackage{booktabs} % table support for pandoc > 1.12.2
\usepackage[inline]{enumitem} % IRkernel/repr support (it uses the enumerate* environment)
\usepackage[normalem]{ulem} % ulem is needed to support strikethroughs (\sout)
% normalem makes italics be italics, not underlines
% Colors for the hyperref package
\definecolor{urlcolor}{rgb}{0,.145,.698}
\definecolor{linkcolor}{rgb}{.71,0.21,0.01}
\definecolor{citecolor}{rgb}{.12,.54,.11}
% ANSI colors
\definecolor{ansi-black}{HTML}{3E424D}
\definecolor{ansi-black-intense}{HTML}{282C36}
\definecolor{ansi-red}{HTML}{E75C58}
\definecolor{ansi-red-intense}{HTML}{B22B31}
\definecolor{ansi-green}{HTML}{00A250}
\definecolor{ansi-green-intense}{HTML}{007427}
\definecolor{ansi-yellow}{HTML}{DDB62B}
\definecolor{ansi-yellow-intense}{HTML}{B27D12}
\definecolor{ansi-blue}{HTML}{208FFB}
\definecolor{ansi-blue-intense}{HTML}{0065CA}
\definecolor{ansi-magenta}{HTML}{D160C4}
\definecolor{ansi-magenta-intense}{HTML}{A03196}
\definecolor{ansi-cyan}{HTML}{60C6C8}
\definecolor{ansi-cyan-intense}{HTML}{258F8F}
\definecolor{ansi-white}{HTML}{C5C1B4}
\definecolor{ansi-white-intense}{HTML}{A1A6B2}
% commands and environments needed by pandoc snippets
% extracted from the output of `pandoc -s`
\providecommand{\tightlist}{%
\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\DefineVerbatimEnvironment{Highlighting}{Verbatim}{commandchars=\\\{\}}
% Add ',fontsize=\small' for more characters per line
\newenvironment{Shaded}{}{}
\newcommand{\KeywordTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\DataTypeTok}[1]{\textcolor[rgb]{0.56,0.13,0.00}{{#1}}}
\newcommand{\DecValTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\BaseNTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\FloatTok}[1]{\textcolor[rgb]{0.25,0.63,0.44}{{#1}}}
\newcommand{\CharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\StringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\CommentTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textit{{#1}}}}
\newcommand{\OtherTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{{#1}}}
\newcommand{\AlertTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\FunctionTok}[1]{\textcolor[rgb]{0.02,0.16,0.49}{{#1}}}
\newcommand{\RegionMarkerTok}[1]{{#1}}
\newcommand{\ErrorTok}[1]{\textcolor[rgb]{1.00,0.00,0.00}{\textbf{{#1}}}}
\newcommand{\NormalTok}[1]{{#1}}
% Additional commands for more recent versions of Pandoc
\newcommand{\ConstantTok}[1]{\textcolor[rgb]{0.53,0.00,0.00}{{#1}}}
\newcommand{\SpecialCharTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\VerbatimStringTok}[1]{\textcolor[rgb]{0.25,0.44,0.63}{{#1}}}
\newcommand{\SpecialStringTok}[1]{\textcolor[rgb]{0.73,0.40,0.53}{{#1}}}
\newcommand{\ImportTok}[1]{{#1}}
\newcommand{\DocumentationTok}[1]{\textcolor[rgb]{0.73,0.13,0.13}{\textit{{#1}}}}
\newcommand{\AnnotationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\CommentVarTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\VariableTok}[1]{\textcolor[rgb]{0.10,0.09,0.49}{{#1}}}
\newcommand{\ControlFlowTok}[1]{\textcolor[rgb]{0.00,0.44,0.13}{\textbf{{#1}}}}
\newcommand{\OperatorTok}[1]{\textcolor[rgb]{0.40,0.40,0.40}{{#1}}}
\newcommand{\BuiltInTok}[1]{{#1}}
\newcommand{\ExtensionTok}[1]{{#1}}
\newcommand{\PreprocessorTok}[1]{\textcolor[rgb]{0.74,0.48,0.00}{{#1}}}
\newcommand{\AttributeTok}[1]{\textcolor[rgb]{0.49,0.56,0.16}{{#1}}}
\newcommand{\InformationTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
\newcommand{\WarningTok}[1]{\textcolor[rgb]{0.38,0.63,0.69}{\textbf{\textit{{#1}}}}}
% Define a nice break command that doesn't care if a line doesn't already
% exist.
\def\br{\hspace*{\fill} \\* }
% Math Jax compatability definitions
\def\gt{>}
\def\lt{<}
% Document parameters
\title{template\_AST3001-assignment1-SOLVED}
% Pygments definitions
\makeatletter
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\let\PY@bc=\relax \let\PY@ff=\relax}
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\def\PY@toks#1+{\ifx\relax#1\empty\else%
\PY@tok{#1}\expandafter\PY@toks\fi}
\def\PY@do#1{\PY@bc{\PY@tc{\PY@ul{%
\PY@it{\PY@bf{\PY@ff{#1}}}}}}}
\def\PY#1#2{\PY@reset\PY@toks#1+\relax+\PY@do{#2}}
\expandafter\def\csname PY@tok@w\endcsname{\def\PY@tc##1{\textcolor[rgb]{0.73,0.73,0.73}{##1}}}
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\expandafter\def\csname PY@tok@cs\endcsname{\let\PY@it=\textit\def\PY@tc##1{\textcolor[rgb]{0.25,0.50,0.50}{##1}}}
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\def\PYZcb{\char`\}}
\def\PYZca{\char`\^}
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\def\PYZsh{\char`\#}
\def\PYZpc{\char`\%}
\def\PYZdl{\char`\$}
\def\PYZhy{\char`\-}
\def\PYZsq{\char`\'}
\def\PYZdq{\char`\"}
\def\PYZti{\char`\~}
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\def\PYZlb{[}
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% Prevent overflowing lines due to hard-to-break entities
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% Setup hyperref package
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breaklinks=true, % so long urls are correctly broken across lines
colorlinks=true,
urlcolor=urlcolor,
linkcolor=linkcolor,
citecolor=citecolor,
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% Slightly bigger margins than the latex defaults
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\begin{document}
\maketitle
\section{Welcome to Assignment 1 for
AST3001.}\label{welcome-to-assignment-1-for-ast3001.}
For those unfamiliar with Jupyter Notebook, each window can be run by
simply pressing 'shift'+'enter' keys. To add another cell to run more
code, simply click the insert button at the top of the browser, and
'Insert Cell Above/Below'. You can find some tutorials at this website:
https://github.com/jupyter/jupyter/wiki/A-gallery-of-interesting-Jupyter-Notebooks.
Any issues or quetions please email swebb@swin.edu.au with the subject
title containing 'AST3001 assignment - '
ENJOY!
First let's start by loading all our modules for this session, because
we are running on an online interactive session we'll need to install
the modules first (note: when running python on your local computer you
won't need to do this).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}1}]:} \PY{o}{!}pip install astropy
\PY{o}{!}pip install matplotlib
\PY{o}{!}pip install numpy
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Requirement already satisfied: astropy in /anaconda3/lib/python3.6/site-packages (3.0.5)
Requirement already satisfied: numpy>=1.10.0 in /anaconda3/lib/python3.6/site-packages (from astropy) (1.16.1)
\textcolor{ansi-yellow}{WARNING: You are using pip version 19.2.1, however version 19.2.2 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.}
Requirement already satisfied: matplotlib in /anaconda3/lib/python3.6/site-packages (3.1.1)
Requirement already satisfied: pyparsing!=2.0.4,!=2.1.2,!=2.1.6,>=2.0.1 in /anaconda3/lib/python3.6/site-packages (from matplotlib) (2.2.0)
Requirement already satisfied: cycler>=0.10 in /anaconda3/lib/python3.6/site-packages (from matplotlib) (0.10.0)
Requirement already satisfied: kiwisolver>=1.0.1 in /anaconda3/lib/python3.6/site-packages (from matplotlib) (1.0.1)
Requirement already satisfied: numpy>=1.11 in /anaconda3/lib/python3.6/site-packages (from matplotlib) (1.16.1)
Requirement already satisfied: python-dateutil>=2.1 in /anaconda3/lib/python3.6/site-packages (from matplotlib) (2.6.1)
Requirement already satisfied: six in /anaconda3/lib/python3.6/site-packages (from cycler>=0.10->matplotlib) (1.11.0)
Requirement already satisfied: setuptools in /anaconda3/lib/python3.6/site-packages (from kiwisolver>=1.0.1->matplotlib) (40.6.2)
\textcolor{ansi-yellow}{WARNING: You are using pip version 19.2.1, however version 19.2.2 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.}
Requirement already satisfied: numpy in /anaconda3/lib/python3.6/site-packages (1.16.1)
\textcolor{ansi-yellow}{WARNING: You are using pip version 19.2.1, however version 19.2.2 is available.
You should consider upgrading via the 'pip install --upgrade pip' command.}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}2}]:} \PY{k+kn}{from} \PY{n+nn}{astropy}\PY{n+nn}{.}\PY{n+nn}{io} \PY{k}{import} \PY{n}{fits}
\PY{k+kn}{import} \PY{n+nn}{matplotlib}\PY{n+nn}{.}\PY{n+nn}{pyplot} \PY{k}{as} \PY{n+nn}{plt}
\PY{k+kn}{import} \PY{n+nn}{numpy} \PY{k}{as} \PY{n+nn}{np}
\PY{k+kn}{from} \PY{n+nn}{spec\PYZus{}tools} \PY{k}{import} \PY{o}{*}
\PY{k+kn}{import} \PY{n+nn}{subprocess}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} inline
\end{Verbatim}
Great. For this assignment we will be looking at a star HD122563 and
comparing it to a Solar twin star HD147513.
The aim of this assignment is to get an idea of concepts such as
spectral type and features, radial velocity and metallicity.
\section{Prep: First we need to read in our
data}\label{prep-first-we-need-to-read-in-our-data}
We can do this using a pre-defined function called 'open\_file'. This
function takes the id of the star as an argument, and assigns the
wavelength and flux arrays to the output of this function. Simply 'run'
the code box below by selecting the box and pressing 'shift'+'enter'
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}14}]:} \PY{n}{star\PYZus{}id} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD122563}\PY{l+s+s1}{\PYZsq{}}
\PY{n}{wave}\PY{p}{,}\PY{n}{flux} \PY{o}{=} \PY{n}{open\PYZus{}file}\PY{p}{(}\PY{n}{star\PYZus{}id}\PY{p}{)}
\PY{n}{solar\PYZus{}twin} \PY{o}{=} \PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD147513}\PY{l+s+s1}{\PYZsq{}}
\PY{n}{sol\PYZus{}wave}\PY{p}{,}\PY{n}{sol\PYZus{}flux} \PY{o}{=} \PY{n}{open\PYZus{}file}\PY{p}{(}\PY{n}{solar\PYZus{}twin}\PY{p}{)}
\end{Verbatim}
Now we've read in the data, we can plot the flux and wavelength of these
spectra using the matplotlib functions below. Again simply select the
box and press 'shift'+'enter'
Use the zoom to rectangle icon Above the plot to zoom in on some
spectral features. Note - The home button resets to the original view
Alternatively, you can remove the '\#' from the bottom lines to zoom
into sections the following command to automatically zoom in on a
wavelength range.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}15}]:} \PY{o}{\PYZpc{}}\PY{k}{matplotlib} notebook
\PY{c+c1}{\PYZsh{}Plots a figure and a set of axes for which we can use to plot our data.}
\PY{n}{fig}\PY{p}{,}\PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{l+m+mi}{1}\PY{p}{,}\PY{l+m+mi}{2}\PY{p}{,}\PY{n}{figsize}\PY{o}{=}\PY{p}{(}\PY{l+m+mi}{10}\PY{p}{,}\PY{l+m+mi}{5}\PY{p}{)}\PY{p}{)} \PY{c+c1}{\PYZsh{} this is making a figure for us to put two plots in}
\PY{c+c1}{\PYZsh{}Plot spectrum for HD122563}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{wave}\PY{p}{,}\PY{n}{flux}\PY{p}{)}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}ylim}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mf}{1.1}\PY{p}{)}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{0}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD122563}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{}Do the same for HD147513}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{sol\PYZus{}wave}\PY{p}{,}\PY{n}{sol\PYZus{}flux}\PY{p}{)}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}ylim}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mf}{1.1}\PY{p}{)}
\PY{n}{ax}\PY{p}{[}\PY{l+m+mi}{1}\PY{p}{]}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD147513}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{} FOR HDHD122563 \PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}}
\PY{c+c1}{\PYZsh{} ax[0].set\PYZus{}xlim(3950,4000)}
\PY{c+c1}{\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{} FOR HD147513 \PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}\PYZsh{}}
\PY{c+c1}{\PYZsh{}ax[1].set\PYZus{}xlim(3950,4000)}
\end{Verbatim}
\begin{verbatim}
<IPython.core.display.Javascript object>
\end{verbatim}
\begin{verbatim}
<IPython.core.display.HTML object>
\end{verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}15}]:} Text(0.5, 1.0, 'HD147513')
\end{Verbatim}
\section{PART 1 - FINDING SPECTRAL
TYPE}\label{part-1---finding-spectral-type}
Using the plots above, let's look at how do these two spectra differ
qualitatively.
Question 1: What is the spectral type of HD147513? Comparitively, what
is the spectral type of HD122563? Hint: What significant spectral
features come and go with OBAFGKM spectral types? Make reference to
these spectral features to justify your answer.
The solar twin is a G type star, HD122563 is a metal poor red giant
star approx F8
Question 2: Name two things that contribute to the width/profile of an
absorption line?
1. the number of atoms, more atoms the more photons that are absorbed
and the boarder/wider the absorbtion line. 2. Lines can be
widened/boarden from doppler shift.
\section{Part 2 - RADIAL VELOCITY}\label{part-2---radial-velocity}
Let's use this plot to measure the radial velocity of the star. You can
zoom in on a line feature (by setting the appropriate x-range limits)
and then compare the observed wavelength for the line feature with the
rest wavelength of that feature to find the radial velocity of the star.
Hold the cursor over the plot to see the wavelength of the absorption
feature. We can use the rest frame Balmer series lines to compare to
calculate the radial velocity of this star.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}16}]:} \PY{o}{\PYZpc{}}\PY{k}{matplotlib} notebook
\PY{n}{fig}\PY{p}{,}\PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{wave}\PY{p}{,}\PY{n}{flux}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}ylim}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mf}{1.1}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD122563}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} You can use the following command to automatically zoom in on a wavelength range }
\PY{c+c1}{\PYZsh{} or use the zoom to rectangle button below}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xlim}\PY{p}{(}\PY{l+m+mi}{4330}\PY{p}{,}\PY{l+m+mi}{4350}\PY{p}{)}
\end{Verbatim}
\begin{verbatim}
<IPython.core.display.Javascript object>
\end{verbatim}
\begin{verbatim}
<IPython.core.display.HTML object>
\end{verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}16}]:} (4330, 4350)
\end{Verbatim}
H \(\beta\) = 4861.36 Angstrom
H \(\gamma\) = 4340.46 Angstrom
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}17}]:} \PY{c+c1}{\PYZsh{}Compute the radial velocity here:}
\PY{c+c1}{\PYZsh{}remove hashes and enter relevant values to run the code and print the radial velocity}
\PY{c+c1}{\PYZsh{} Try doing this for all three lines to get an average and standard deviation as an estimate of the error.}
\PY{n}{c} \PY{o}{=} \PY{l+m+mf}{2.99793e5}
\PY{n}{lamb\PYZus{}obs} \PY{o}{=} \PY{l+m+mf}{4339.96}
\PY{n}{lamb\PYZus{}rest} \PY{o}{=} \PY{l+m+mf}{4340.46}
\PY{n}{V\PYZus{}rad} \PY{o}{=} \PY{n}{c} \PY{o}{*} \PY{p}{(}\PY{n}{lamb\PYZus{}obs} \PY{o}{\PYZhy{}} \PY{n}{lamb\PYZus{}rest}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{n}{lamb\PYZus{}rest}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{n}{V\PYZus{}rad}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
-34.53470369500007
\end{Verbatim}
This equation can be re-arranged to apply a shift to the observed
spectrum to achieve a rest wavelength state. Hint: make sure you use the
correct sign to the radial velocity to produce the correct redshift or
blueshift as appropriate. You can check you've made the correct
adjustment by re-plotting the spectrum in the window above. If you make
a mistake and what the original spectrum, just reload the file using:
wave,flux = open\_file(star\_id1)
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}18}]:} \PY{c+c1}{\PYZsh{}Make the radial velocity correction to the wavelength array}
\PY{n}{wave\PYZus{}new} \PY{o}{=} \PY{n}{wave} \PY{o}{+}\PY{o}{\PYZhy{}} \PY{n}{wave}\PY{o}{*}\PY{n}{V\PYZus{}rad}\PY{o}{/}\PY{n}{c}
\PY{o}{\PYZpc{}}\PY{k}{matplotlib} notebook
\PY{n}{fig}\PY{p}{,}\PY{n}{ax} \PY{o}{=} \PY{n}{plt}\PY{o}{.}\PY{n}{subplots}\PY{p}{(}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{plot}\PY{p}{(}\PY{n}{wave\PYZus{}new}\PY{p}{,}\PY{n}{flux}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}ylim}\PY{p}{(}\PY{l+m+mi}{0}\PY{p}{,}\PY{l+m+mf}{1.1}\PY{p}{)}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}title}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{HD122563}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\PY{c+c1}{\PYZsh{} You can use the following command to automatically zoom in on a wavelength range }
\PY{c+c1}{\PYZsh{} or use the zoom to rectangle button below}
\PY{n}{ax}\PY{o}{.}\PY{n}{set\PYZus{}xlim}\PY{p}{(}\PY{l+m+mi}{4330}\PY{p}{,}\PY{l+m+mi}{4350}\PY{p}{)}
\end{Verbatim}
\begin{verbatim}
<IPython.core.display.Javascript object>
\end{verbatim}
\begin{verbatim}
<IPython.core.display.HTML object>
\end{verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{outcolor}Out[{\color{outcolor}18}]:} (4330, 4350)
\end{Verbatim}
Question 3: Radial velocities stretch and shift the spectrum along the
wavelength axis. What happens to a spectrum when the source is spinning
rapidly?
redshifted
\section{PART 3 - METALLICITY}\label{part-3---metallicity}
Metallicity is a measure of how many 'metals' or heavy elements are in a
star compared to Hydrogen. Metal enrichment happens over many
generations of stars and so the Sun is quite metal rich compared to
older stars that are found for example in the Galactic bulge or halo. In
this section we are going to measure the metallicity of HD122563 and
compare it to the Solar value.
Question 4: Iron content compared to Hydrogen is used as a proxy for
metallicity. Explain why this is a reasonable approximation.
We compare Iron to Hydrogen to see the relative depletion of hydrogen
in the stars, the more heavry elements (higher fraction of Iron) the
longer the star has been undergoing fusion on the main sequence
In this part we are going to measure the equivalent width (EW) of iron
lines to calculate the {[}Fe/H{]} which is an abbrieviated notation for
the Fe/H ratio compared to the Solar value on a log scale. You can
measure EW using plot\_n\_measure\_EW function.
Remember: EW = \(\int{(1 - F_{\lambda}/F_0)d\lambda}\) (where \(F_0\) is
the flux of the continuum).
The function below returns the measured EW for a spectrum, you can call
it on the following line to measure the EW of the Ca II line shown in
the plot. For those interested you can use this as a quantitative
measure to compare HD122563's Na line against the Sun's.
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}33}]:} \PY{n}{plot\PYZus{}n\PYZus{}measure\PYZus{}EW\PYZus{}spectrum}\PY{p}{(}\PY{n}{wave}\PY{p}{,}\PY{n}{flux}\PY{p}{,}\PY{p}{[}\PY{l+m+mf}{5889.0}\PY{p}{,}\PY{l+m+mf}{5890.6}\PY{p}{]}\PY{p}{)}
\PY{n}{midpoint} \PY{o}{=} \PY{p}{(}\PY{l+m+mf}{5889.959}\PY{o}{+}\PY{l+m+mf}{5895.937}\PY{p}{)} \PY{o}{/}\PY{l+m+mi}{2}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{midpoint wavelength: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{midpoint}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{verbatim}
<IPython.core.display.Javascript object>
\end{verbatim}
\begin{verbatim}
<IPython.core.display.HTML object>
\end{verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Equivalent Width = 0.2 A
midpoint wavelength: 5892.948
\end{Verbatim}
To find a list of potential iron lines, let's load a line list file
using the function 'read\_n\_display', which takes the filename as an
argument, reads the file and prints it to the screen. The sample line
list is called: 'example.ew'
The line list file has columns that have various characteristics of that
line feature. For now let's focus on the first two columns, the
wavelength of the line in angstroms and the element of the feature
(atomic number).
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}34}]:} \PY{n}{read\PYZus{}n\PYZus{}display}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{example.ew}\PY{l+s+s1}{\PYZsq{}}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
3302.369 11.0 0.00 -1.745 XXX.X
3302.979 11.0 0.00 -2.050 XXX.X
5889.959 11.0 0.00 0.108 XXX.X
5895.937 11.0 0.00 -0.194 XXX.X
3829.360 12.0 2.71 -0.227 XXX.X
4057.505 12.0 4.35 -0.900 XXX.X
5172.691 12.0 2.71 -0.393 XXX.X
5183.604 12.0 2.72 -0.167 XXX.X
5528.416 12.0 4.35 -0.498 XXX.X
5711.102 12.0 4.35 -1.724 XXX.X
3943.998 13.0 0.00 -0.638 XXX.X
3961.525 13.0 0.01 -0.340 XXX.X
3853.660 14.0 6.85 -1.341 XXX.X
3905.523 14.0 1.91 -1.041 XXX.X
4102.936 14.0 1.91 -2.470 XXX.X
5645.611 14.0 4.93 -1.630 XXX.X
4289.364 20.0 1.88 -0.300 XXX.X
4302.536 20.0 1.90 0.276 XXX.X
4318.650 20.0 1.90 -0.210 XXX.X
4425.437 20.0 1.88 -0.358 XXX.X
4435.677 20.0 1.89 -0.519 XXX.X
4454.774 20.0 1.90 0.260 XXX.X
4578.551 20.0 2.52 -0.558 XXX.X
5581.975 20.0 2.52 -0.710 XXX.X
5588.752 20.0 2.53 0.210 XXX.X
5590.113 20.0 2.52 -0.710 XXX.X
5594.464 20.0 2.52 -0.050 XXX.X
5601.290 20.0 2.53 -0.690 XXX.X
5857.452 20.0 2.93 0.230 XXX.X
4314.080 21.1 0.62 -0.100 XXX.X
4320.742 21.1 0.60 -0.250 XXX.X
5526.785 21.1 1.77 0.020 XXX.X
5667.149 21.1 1.50 -1.240 XXX.X
5669.038 21.1 1.50 -1.120 XXX.X
5684.195 21.1 1.51 -1.080 XXX.X
3924.529 22.0 0.02 -0.937 XXX.X
3958.210 22.0 0.05 -0.176 XXX.X
4512.739 22.0 0.84 -0.480 XXX.X
4518.027 22.0 0.83 -0.324 XXX.X
4533.242 22.0 0.85 0.476 XXX.X
4534.779 22.0 0.84 0.280 XXX.X
4548.765 22.0 0.83 -0.354 XXX.X
4555.488 22.0 0.85 -0.488 XXX.X
4981.735 22.0 0.85 0.504 XXX.X
4999.503 22.0 0.83 0.250 XXX.X
5022.869 22.0 0.83 -0.434 XXX.X
5039.957 22.0 0.02 -1.130 XXX.X
5173.742 22.0 0.00 -1.118 XXX.X
5210.384 22.0 0.05 -0.883 XXX.X
5866.452 22.0 1.07 -0.840 XXX.X
3900.540 22.1 1.13 -0.440 XXX.X
4300.043 22.1 1.18 -0.770 XXX.X
4312.879 22.1 1.18 -1.160 XXX.X
4395.032 22.1 1.08 -0.660 XXX.X
4399.765 22.1 1.23 -1.270 XXX.X
4417.714 22.1 1.17 -1.430 XXX.X
4443.806 22.1 1.08 -0.710 XXX.X
4468.495 22.1 1.13 -0.620 XXX.X
4501.275 22.1 1.12 -0.750 XXX.X
4533.969 22.1 1.24 -0.770 XXX.X
4563.762 22.1 1.22 -0.960 XXX.X
4571.974 22.1 1.57 -0.520 XXX.X
4583.412 22.1 1.16 -2.870 XXX.X
4589.949 22.1 1.23 -1.780 XXX.X
4762.767 22.1 1.08 -2.710 XXX.X
4865.613 22.1 1.12 -2.810 XXX.X
4911.193 22.1 3.12 -0.340 XXX.X
5185.900 22.1 1.89 -1.460 XXX.X
3545.198 23.1 1.10 -0.390 XXX.X
3592.023 23.1 1.10 -0.370 XXX.X
4274.804 24.0 0.00 -0.230 XXX.X
4289.723 24.0 0.00 -0.360 XXX.X
4545.957 24.0 0.94 -1.380 XXX.X
4600.758 24.0 1.00 -1.260 XXX.X
4613.365 24.0 0.96 -1.680 XXX.X
4616.128 24.0 0.98 -1.180 XXX.X
4626.177 24.0 0.97 -1.320 XXX.X
4652.162 24.0 1.00 -1.030 XXX.X
5206.042 24.0 0.94 0.019 XXX.X
5208.449 24.0 0.94 0.159 XXX.X
5298.273 24.0 0.98 -1.160 XXX.X
5345.799 24.0 1.00 -0.980 XXX.X
5348.322 24.0 1.00 -1.290 XXX.X
5409.789 24.0 1.03 -0.720 XXX.X
4754.040 25.0 2.28 -0.085 XXX.X
4783.425 25.0 2.30 0.042 XXX.X
5394.670 25.0 0.00 -3.503 XXX.X
3441.991 25.1 1.78 -0.273 XXX.X
3460.330 25.1 1.81 -0.540 XXX.X
3488.676 25.1 1.85 -0.860 XXX.X
3749.485 26.0 0.91 0.161 XXX.X
3787.879 26.0 1.01 -0.859 XXX.X
3841.047 26.0 1.60 -0.045 XXX.X
3865.528 26.0 1.01 -0.982 XXX.X
3886.287 26.0 0.05 -1.076 XXX.X
3887.049 26.0 0.92 -1.144 XXX.X
3891.923 26.0 3.42 -0.734 XXX.X
3895.656 26.0 0.11 -1.670 XXX.X
3899.711 26.0 0.09 -1.531 XXX.X
3902.948 26.0 1.56 -0.466 XXX.X
3906.484 26.0 0.11 -2.243 XXX.X
3916.730 26.0 3.23 -0.604 XXX.X
3920.263 26.0 0.12 -1.746 XXX.X
3922.916 26.0 0.05 -1.651 XXX.X
3930.305 26.0 0.09 -1.491 XXX.X
3949.954 26.0 2.18 -1.251 XXX.X
4271.158 26.0 2.45 -0.349 XXX.X
4271.768 26.0 1.49 -0.164 XXX.X
4282.404 26.0 2.18 -0.779 XXX.X
4294.114 26.0 1.49 -1.110 XXX.X
4299.223 26.0 2.42 -0.405 XXX.X
4307.902 26.0 1.56 -0.072 XXX.X
4325.765 26.0 1.61 0.006 XXX.X
4337.046 26.0 1.56 -1.695 XXX.X
4375.934 26.0 0.00 -3.031 XXX.X
4383.547 26.0 1.49 0.200 XXX.X
4404.752 26.0 1.56 -0.142 XXX.X
4415.123 26.0 1.61 -0.615 XXX.X
4427.317 26.0 0.05 -3.044 XXX.X
4430.616 26.0 2.22 -1.659 XXX.X
4442.340 26.0 2.20 -1.255 XXX.X
4447.718 26.0 2.22 -1.342 XXX.X
4459.107 26.0 2.18 -1.279 XXX.X
4461.656 26.0 0.09 -3.210 XXX.X
4489.744 26.0 0.12 -3.966 XXX.X
4494.565 26.0 2.20 -1.136 XXX.X
4531.149 26.0 1.49 -2.155 XXX.X
4592.651 26.0 1.56 -2.449 XXX.X
4602.946 26.0 1.49 -2.220 XXX.X
4625.048 26.0 3.24 -1.348 XXX.X
4871.317 26.0 2.87 -0.362 XXX.X
4872.137 26.0 2.88 -0.567 XXX.X
4891.491 26.0 2.85 -0.112 XXX.X
4918.998 26.0 2.87 -0.342 XXX.X
4920.509 26.0 2.83 0.068 XXX.X
4957.599 26.0 2.81 0.233 XXX.X
5166.286 26.0 0.00 -4.195 XXX.X
5171.600 26.0 1.49 -1.793 XXX.X
5192.343 26.0 3.00 -0.421 XXX.X
5194.944 26.0 1.56 -2.090 XXX.X
5198.713 26.0 2.22 -2.135 XXX.X
5217.387 26.0 3.21 -1.162 XXX.X
5227.188 26.0 1.56 -1.228 XXX.X
5232.941 26.0 2.94 -0.057 XXX.X
5269.539 26.0 0.86 -1.321 XXX.X
5324.181 26.0 3.21 -0.103 XXX.X
5393.171 26.0 3.24 -0.715 XXX.X
5405.782 26.0 0.99 -1.844 XXX.X
5410.910 26.0 4.47 0.398 XXX.X
5415.200 26.0 4.39 0.642 XXX.X
5424.066 26.0 4.32 0.510 XXX.X
5434.527 26.0 1.01 -2.122 XXX.X
5445.042 26.0 4.39 -0.030 XXX.X
5473.901 26.0 4.15 -0.790 XXX.X
5497.518 26.0 1.01 -2.849 XXX.X
5501.466 26.0 0.96 -3.047 XXX.X
5506.781 26.0 0.99 -2.797 XXX.X
5569.623 26.0 3.42 -0.486 XXX.X
5572.842 26.0 3.40 -0.275 XXX.X
5576.087 26.0 3.43 -0.940 XXX.X
5586.756 26.0 3.37 -0.144 XXX.X
5624.542 26.0 3.42 -0.755 XXX.X
5662.512 26.0 4.18 -0.573 XXX.X
5701.556 26.0 2.56 -2.216 XXX.X
5762.975 26.0 4.21 -0.470 XXX.X
5956.705 26.0 0.86 -4.608 XXX.X
3255.901 26.1 0.99 -2.498 XXX.X
3277.348 26.1 0.99 -2.191 XXX.X
3281.291 26.1 1.04 -2.678 XXX.X
4416.817 26.1 2.77 -2.430 XXX.X
4491.401 26.1 2.84 -2.600 XXX.X
4508.300 26.1 2.84 -2.280 XXX.X
4555.888 26.1 2.82 -2.170 XXX.X
4576.333 26.1 2.83 -2.900 XXX.X
4583.831 26.1 2.81 -1.740 XXX.X
4923.929 26.1 2.89 -1.206 XXX.X
5018.442 26.1 2.89 -1.350 XXX.X
5197.571 26.1 3.23 -2.230 XXX.X
5234.621 26.1 3.22 -2.220 XXX.X
5534.847 26.1 3.25 -2.640 XXX.X
3842.045 27.0 0.92 -0.763 XXX.X
3845.466 27.0 0.92 0.009 XXX.X
3873.114 27.0 0.43 -0.666 XXX.X
3807.145 28.0 0.42 -1.180 XXX.X
3858.299 28.0 0.42 -0.967 XXX.X
4401.550 28.0 3.19 0.084 XXX.X
5578.719 28.0 1.68 -2.640 XXX.X
5587.849 28.0 1.94 -2.140 XXX.X
5592.280 28.0 1.95 -2.590 XXX.X
5892.883 28.0 1.99 -2.340 XXX.X
3247.540 29.0 0.00 -0.056 XXX.X
3273.959 29.0 0.00 -0.360 XXX.X
4607.331 38.0 0.00 0.283 XXX.X
3774.334 39.1 0.13 0.220 XXX.X
3788.697 39.1 0.10 -0.060 XXX.X
3818.350 39.1 0.13 -0.974 XXX.X
3832.887 39.1 0.18 -0.330 XXX.X
3950.351 39.1 0.10 -0.484 XXX.X
4398.013 39.1 0.13 -1.000 XXX.X
4883.688 39.1 1.08 0.070 XXX.X
5123.210 39.1 0.99 -0.830 XXX.X
5200.413 39.1 0.99 -0.570 XXX.X
5205.734 39.1 1.03 -0.340 XXX.X
3836.761 40.1 0.56 -0.060 XXX.X
4317.315 40.1 0.71 -1.380 XXX.X
4554.033 56.1 0.00 0.140 XXX.X
4934.076 56.1 0.00 -0.160 XXX.X
5853.685 56.1 0.60 -0.908 XXX.X
3964.260 59.1 0.22 -0.400 XXX.X
4061.090 60.1 0.47 0.290 XXX.X
3538.522 66.1 0.00 -0.020 XXX.X
3810.730 67.1 0.00 0.190 XXX.X
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}35}]:} \PY{c+c1}{\PYZsh{}\PYZsh{}\PYZsh{} Enter your code here \PYZsh{}\PYZsh{} }
\PY{c+c1}{\PYZsh{}\PYZsh{} HINT : You will need to play around with moving the star and stop of each }
\PY{c+c1}{\PYZsh{} absorbtion line to get the fit only over the absorbtion line }
\PY{n}{plot\PYZus{}n\PYZus{}measure\PYZus{}EW\PYZus{}spectrum}\PY{p}{(}\PY{n}{wave}\PY{p}{,}\PY{n}{flux}\PY{p}{,}\PY{p}{[} \PY{l+m+mf}{3886.6} \PY{p}{,}\PY{l+m+mf}{3887.049}\PY{p}{]}\PY{p}{)}
\PY{n}{midpoint} \PY{o}{=} \PY{p}{(} \PY{l+m+mf}{3886.287} \PY{o}{+} \PY{l+m+mf}{4583.831}\PY{p}{)} \PY{o}{/} \PY{l+m+mf}{2.0}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{midpoint wavelength: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{midpoint}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{} hint: use plot\PYZus{}n\PYZus{}measure\PYZus{}EW\PYZus{}spectrum(wave,flux,[,]) function to get your EW and }
\PY{c+c1}{\PYZsh{} midpoint of lambda that you will need below }
\end{Verbatim}
\begin{verbatim}
<IPython.core.display.Javascript object>
\end{verbatim}
\begin{verbatim}
<IPython.core.display.HTML object>
\end{verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Equivalent Width = 0.1 A
midpoint wavelength: 4235.059
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}37}]:} \PY{n}{EW\PYZus{}1\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{0.2}
\PY{n}{lambda\PYZus{}HD122563\PYZus{}1} \PY{o}{=} \PY{l+m+mf}{4235.059}
\PY{n}{EW\PYZus{}2\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{0.1}
\PY{n}{lambda\PYZus{}HD122563\PYZus{}2} \PY{o}{=} \PY{l+m+mf}{5574.4645}
\PY{n}{EW\PYZus{}3\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{0.1}
\PY{n}{lambda\PYZus{}HD122563\PYZus{}3} \PY{o}{=} \PY{l+m+mf}{4919.753}
\end{Verbatim}
Pick 3 to 5 Fe lines from the line list (lines where the 2nd column has
the number 26) and measure their EWs using HD122563 spectrum below.
\subsection{Part 3 Finding abundances}\label{part-3-finding-abundances}
We can now use these EW to calculate a value called Epsilon which is
descriebed below:
\begin{equation*}
\epsilon = 12 + log\left(\frac{N_{Fe}}{N_H}\right)
\end{equation*}
This value Epsilon can be used to detemined the stars elemental
abundance. We first need to find the column density of atoms for Iron
(Fe). The column density will be the value of N which we will step
through how to find below
** Before starting the following please have a read through
http://spiff.rit.edu/classes/phys440/lectures/curve/curve.html **
We will now take the measured EW from above and detemine how many atoms
are present in that line (the value of N) using the below figure, The Y
axis is log(EW /lambda), (EW written above as W) \textbf{This is your
measured EW} And the X axis is log Nf(lambda/5000 Angstroms) where N is
the column density.
\textbf{Note} the line can be descibed by three eqautions as shown
overlaid the plot. The value of N is the eqaution of the X axis
\subsection{Step 1. Find the value of
Y:}\label{step-1.-find-the-value-of-y}
\begin{equation*}
Y = log10(\frac{EW}{\lambda})
\end{equation*}
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}38}]:} \PY{c+c1}{\PYZsh{}\PYZsh{} Example on Na}
\PY{c+c1}{\PYZsh{}\PYZsh{} USE THE BELOW EQUATION \PYZsh{}\PYZsh{} }
\PY{c+c1}{\PYZsh{} y = np.log10(EW/central wavelength) }
\PY{n}{Y} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log10}\PY{p}{(}\PY{l+m+mf}{0.2}\PY{o}{/}\PY{l+m+mf}{5892.948}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y value for Na: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{Y}\PY{p}{)}\PY{p}{)}
\PY{c+c1}{\PYZsh{}\PYZsh{} Do the same for your 3 to 5 Fe lines below below, where you place }
\PY{c+c1}{\PYZsh{}\PYZsh{} your EW and lambda for each line: }
\PY{n}{y\PYZus{}Fe\PYZus{}1\PYZus{}HD122563} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log10}\PY{p}{(}\PY{n}{EW\PYZus{}1\PYZus{}HD122563} \PY{o}{/}\PY{n}{lambda\PYZus{}HD122563\PYZus{}1} \PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y value for Fe line 1: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{y\PYZus{}Fe\PYZus{}1\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\PY{n}{y\PYZus{}Fe\PYZus{}2\PYZus{}HD122563} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log10}\PY{p}{(}\PY{n}{EW\PYZus{}2\PYZus{}HD122563} \PY{o}{/}\PY{n}{lambda\PYZus{}HD122563\PYZus{}2} \PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y value for Fe line 2: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{y\PYZus{}Fe\PYZus{}2\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\PY{n}{y\PYZus{}Fe\PYZus{}2\PYZus{}HD122563} \PY{o}{=} \PY{n}{np}\PY{o}{.}\PY{n}{log10}\PY{p}{(}\PY{n}{EW\PYZus{}3\PYZus{}HD122563} \PY{o}{/}\PY{n}{lambda\PYZus{}HD122563\PYZus{}3} \PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{Y value for Fe line 2: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{y\PYZus{}Fe\PYZus{}2\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
Y value for Na: -4.469302613187371
Y value for Fe line 1: -4.325829469344172
Y value for Fe line 2: -4.746203154076228
Y value for Fe line 2: -4.69194329922472
\end{Verbatim}
\subsection{Step 2 Find the value of
X:}\label{step-2-find-the-value-of-x}
Go back to the plot above, and find what the approximate value of x is
along the line of growth. See example for Ca II below:
** We find the approximate X value is 15.35. **
\#\# TO DO: Find X value for Fe
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}39}]:} \PY{c+c1}{\PYZsh{}\PYZsh{} Save your values for X\PYZus{}Fe below as variables to use later }
\PY{n}{X\PYZus{}Fe\PYZus{}1\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{13.9}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X value for Fe line 1: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{X\PYZus{}Fe\PYZus{}1\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\PY{n}{X\PYZus{}Fe\PYZus{}2\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{12.05}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X value for Fe line 2: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{X\PYZus{}Fe\PYZus{}2\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\PY{n}{X\PYZus{}Fe\PYZus{}3\PYZus{}HD122563} \PY{o}{=} \PY{l+m+mf}{12.25}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{X value for Fe line 3: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{X\PYZus{}Fe\PYZus{}3\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}
\end{Verbatim}
\begin{Verbatim}[commandchars=\\\{\}]
X value for Fe line 1: 13.9
X value for Fe line 2: 12.05
X value for Fe line 3: 12.25
\end{Verbatim}
\subsection{Step 3 Find the value of
N:}\label{step-3-find-the-value-of-n}
This value of N is in atoms per cm\^{}2 (This value for f will not be
completely accuate for all lines of Fe but will do for the propose of
this assignment, we are using the oscillator strength specficlly of the
Fe II transistion at 321.045nm. Oscillator numbers for ions can be found
here http://vizier.u-strasbg.fr/viz-bin/VizieR-3?-source=VI/69/catalog,
where the value of \(gf\) is log(f))
\#\# TO DO: Find N value for Fe
\begin{Verbatim}[commandchars=\\\{\}]
{\color{incolor}In [{\color{incolor}44}]:} \PY{c+c1}{\PYZsh{} Fill in the values for X and Lambda below to find your value of N for HD122563, use the example}
\PY{c+c1}{\PYZsh{} code of Na as a template }
\PY{c+c1}{\PYZsh{} N = (10**(X))/((f)*((lambda)/(5000)))}
\PY{c+c1}{\PYZsh{} N = (10**(15.35))/((1.19)*((3933.8)/(5000)))}
\PY{n}{f} \PY{o}{=} \PY{l+m+mf}{0.020}
\PY{n}{N\PYZus{}Fe\PYZus{}HD122563\PYZus{}1} \PY{o}{=} \PY{p}{(}\PY{l+m+mi}{10}\PY{o}{*}\PY{o}{*}\PY{p}{(}\PY{n}{X\PYZus{}Fe\PYZus{}1\PYZus{}HD122563}\PY{p}{)}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{p}{(}\PY{n}{f}\PY{p}{)}\PY{o}{*}\PY{p}{(}\PY{p}{(}\PY{n}{lambda\PYZus{}HD122563\PYZus{}1}\PY{p}{)}\PY{o}{/}\PY{p}{(}\PY{l+m+mi}{5000}\PY{p}{)}\PY{p}{)}\PY{p}{)}
\PY{n+nb}{print}\PY{p}{(}\PY{l+s+s1}{\PYZsq{}}\PY{l+s+s1}{N value for Fe line 1: }\PY{l+s+s1}{\PYZsq{}} \PY{o}{+} \PY{n+nb}{str}\PY{p}{(}\PY{n}{N\PYZus{}Fe\PYZus{}HD122563\PYZus{}1}\PY{p}{)}\PY{p}{)}