\documentclass[12pt]{article} \newcommand{\sigline}{\rule[-0.8mm]{60mm}{0.2mm}} \newcommand{\scoreline}{\rule[-0.8mm]{15mm}{0.2mm}} \newcommand{\mybox}{\fbox{\parbox[c][3mm]{4mm}{\ \ }}\ \ } \newcommand{\ip}{\textsf{Instruction Packet}} \newcommand{\ret}{$<$\tectsf{return}$>$} \newcommand{\ctrl}{$<$\textsf{Ctrl}$>$} \newcommand{\ie}{\textit{i.e.},\ } \newcommand{\eg}{\textit{e.g.},\ } \newcommand{\ea}{\textit{et~al.}\ } \newcommand{\teff}{T_{\mbox{{\small eff}}}} \newcommand{\lappxe}{\ ^{<}_{\sim}\ } \newcommand{\gappxe}{\ ^{>}_{\sim}\ } \newcommand{\jbar}{\overline{J}} \newcommand{\apj}{ApJ} \newcommand{\apjl}{ApJ} \newcommand{\apjs}{ApJS} \newcommand{\aj}{AJ} \newcommand{\ana}{A\&A} \newcommand{\anas}{A\&AS} \newcommand{\baas}{BAAS} \newcommand{\pasp}{PASP} \newcommand{\mnras}{MNRAS} \setlength{\topmargin}{-0.5in} \setlength{\oddsidemargin}{0.0in} \setlength{\textwidth}{6.5in} \setlength{\textheight}{9.0in} \setlength{\parskip}{20pt} \setlength{\parindent}{0pt} \pagestyle{plain} % \begin{document} \begin{center} \large \textbf{(1) Cover Page}\\*[5mm] Proposal to the PHYS-4007/5007 Computational Physics\\ Research Project Proposal\\*[10mm] \LARGE \textbf{Put your proposal title here.}\\*[18mm] \end{center} \begin{tabbing} XXXXXXXXXXXXXXXXXXXXXXXXXXXX \= \kill \> \\ \> \\ PRINCIPAL INVESTIGATOR: \> \sigline \\ \> Type your name here \\ \> \\ NAME AND ADDRESS OF THE \> East Tennessee State University \\ ORGANIZATION: \> Department of Physics and Astronomy \\ \> Johnson City, TN 37614 \\ \> \\ SUBMISSION DATE: \> 15 October 2021 \\ \> \\ CLASS STATUS AND MAJOR: \> Senior in Physics ($\ll$ edit this) \\ \> \\ MACHINE ARCHITECTURE: \> Intel Core 2, 64-bit CPU \\ \> \\ OPERATING SYSTEM: \> Ubuntu Linux \\ \> \\ PROGRAMMING LANGUAGE: \> Python 3.x ($\ll$ edit this) \\ \> \\ \> \\ \> \\ GRANT OFFICIAL SIGNATURE: \> \sigline \\ \> Dr.\ Donald G. Luttermoser \\ \> East Tennessee State University \\ \> \end{tabbing} % \newpage \begin{center} \Large \textbf{Put your proposal title here.}\\*[10mm] \large \textbf{(2) Proposed Science Program Summary} \end{center} % This should be a single paragraph ranging between 100 to 200 words summarizing your proposed research. % \newpage \begin{center} \Large \textbf{(3) Scientific Justification} \end{center} This section should give some background of the proposed science and why it is important to the scientific community. You you limit this section to no more than 4 printed pages. Below is some sample paragraphs from a NASA proposal I wrote a many years ago. Clip out what I write in this section and write your own justification based on whatever you want to research. I encourage you to make this look as professional as you can, but don't put too much effort into it. Late-type, giant stars (spectral types M, S, and C) on the asymptotic giant branch (AGB) all vary in brightness. These stars are of fundamental importance to the chemical history and evolution of the Galaxy (\eg Richer 1989; Jura 1989). Three primary variable classes have been defined. (1) The Mira (\textit{M\,}) variables are stars that show evidence for pulsations in their spectra and light curves. These red giant stars display relatively regular light variation greater than 2.5 magnitudes over periods from 200 to 500 days. Emission lines are seen in their spectra (\eg Fe~II lines and the hydrogen Balmer lines) which vary in flux over the pulsation cycle. Phase-dependent velocity measurements of these emission line features indicate the presence of shock waves propagating through the outer envelopes of these stars (Willson 1976). (2) The semiregular (\textit{SR\,}) variables are stars that vary somewhat less regularly and/or have light variations less than 2.5 magnitudes. This class is further subclassified into 4 separate classes: \textit{SRa} variables are giant stars that are distinguished from the genuine Mira stars by their smaller amplitude (SRa's will be included in the Mira classification from this point forward); \textit{SRb} variables are giants that have a somewhat regular period that becomes inoperative from time to time; \textit{SRc} are supergiants that vary almost completely irregularly with small light amplitude changes; \textit{SRd} are warmer versions (\ie spectral class F-K) of the SRb variables. The semiregular variables do not show the hydrogen Balmer emission lines (except SRa) that are seen in the Mira-type variables. (3) The irregular (\textit{L\,}) variables have no hint of a regular period in their light variations. These variables come in 2 subclasses: \textit{Lb} variables are giant stars and \textit{Lc} variables are supergiant stars. Over the past decade, considerable effort has been made to deduce the \textit{outer} atmospheric structure of the late-type, variable stars. The Mira variables have been modeled by a variety of groups, most notably by Wood (1979), Bowen (1988), and Drinkwater \& Wood (1985). These authors calculated their models with detailed hydrodynamics, but made gross (and probably incorrect) approximations to the transfer of radiation. Meanwhile the modeling of semiregular and irregular variables have been based on the hydrostatic approximation with the transfer handled by detailed non--LTE (NLTE) calculations (\eg Luttermoser \ea 1989; Luttermoser \& Johnson 1992; Luttermoser, Johnson, \& Eaton 1994). Such semiempirical modeling of these SR and L variables have demonstrated that macroscopic gas velocities in the emitting region (\ie the chromosphere) are supersonic (see Luttermoser \ea 1989), thus making the hydrostatic approximation invalid. Finally, Luttermoser, Johnson, \& Eaton (1994) were \underline{unable} to fit the UV spectrum of g~Her with a one-component, hydrostatic, plane-parallel chromospheric model. We propose to investigate the underlying atmospheric structure of semiregular variable giants through detailed NLTE radiative transfer and hydrodynamics. For this program, we have selected the two bright semiregular (SRb), oxygen-rich, giant stars R~Lyr (M5 III) and g~Her (M6 III). Both have a substantial data base of IUE observations with a \underline{total} of 38 high- and 15 low-dispersion, long-wavelength spectra for R~Lyr and 11 high- and 40 low-dispersion spectra for g~Her to date. AGB stars are of fundamental importance, not only to stellar evolution, but also to the chemical evolution of the Galaxy. During their AGB phase, low mass ($M \lappxe 4.0~M_{\odot}$) stars have mass loss rates from $10^{-7} - 4 \times 10^{-5} \dot{M}_{\odot}$ (\eg Wannier \& Sahai 1986). Due to their great number, these stars are the primary source of carbon and s-processed elements in the Galaxy. Thus a detailed analysis of the temperature-density structure of their stellar atmospheres becomes apparent. Besides their large mass-loss rates, these stars show evidence for enhanced temperature regimes ($10^{4} \gappxe T \gappxe \teff$) in their outer atmospheres through the appearance of UV emission lines of singly ionized metals, especially the Mg~II h \& k lines near 2800~\AA, the Fe~II UV1 multiplet near 2600~\AA, and the Fe~II UV62,63 multiplet near 2750~\AA. Typically the C~II] UV0.01 intersystem lines are also seen. These features are important to the analysis of the atmospheric structure of late-type stars for the following reasons: \begin{itemize} \item High-dispersion spectra of the Mg II $h$ and $k$ resonance lines are a very sensitive diagnostic of temperature reversals in the atmospheres of stars due to their high opacity in relatively low-temperature regimes ($\sim$5000~\AA ). \item The Fe~II multiplets are a major source of cooling in these types of stellar atmospheres (Judge \& Neff 1990). \item The line strengths of the C~II] UV0.01 multiplet are sensitive to the electron density of the emitting region (Stencel \ea 1981; Lennon \ea 1985). \end{itemize} \newpage \begin{center} \Large \textbf{(4) Plan of Work} \end{center} This section should describe how you plan to carry out the proposed research. Keep this section fairly short (1 or 2 paragraphs up to no more than 2 printed pages). Here are some sample paragraphs. We will obtain the relevant IUE spectra of both R~Lyr and g~Her from the archive. We will require two high dispersion spectra taken on approximately the same day, one short exposure so that the Mg~II lines are not overexposed and one long exposure to bring out the weaker C~II] lines. We have searched the IUE archives and have found 4 long-wavelength, high-dispersion, large-aperture images for g~Her and 5 for R~Lyr that meet our requirements. These are listed in Table 1. We are using observations that are spread out over time to check whether the C~II] features change with time (as they should if formed in outward propagating shocks). Spectra will be reduced with the standard IUE data reduction procedures using IDL on the machines at East Tennessee State University (ETSU). Once these data are in hand, we will begin with the classical chromospheric models. We will take the published plane-parallel, chromospheric model of g~Her (Luttermoser, Johnson, \& Eaton 1994) and reconverge it in spherical symmetry. We will then take the g~Her chromospheric model and attach it the a radiative equilibrium model representative of R~Lyr. This chromospheric model, also in spherical symmetry, will be modified until the best fit is obtained with the IUE spectra. All of the calculations will be performed with the NLTE radiative transfer code PANDORA (see Vernazza, Avrett, \& Loeser 1981) which is written in Fortran 77. Should these models be unable to fit both the Mg~II and C~II] multiplets, we can claim without a doubt that the ``classical'' chromospheric model is not a valid representation of the UV emitting region of semiregular variables. Finally, we will generate representative hydrodynamic models for both R~Lyr and g~Her. Bowen (1988) has describes the hydrodynamic code that we will use, I will add a new and improved treatment of dust formation. We will set up PANDORA runs for at least eight different phases throughout the pulsation cycle of these stars. We will not be able to ascertain the exact phase of the pulsation cycle of these stars corresponding to the dates that the IUE observations were taken, since we have no coincident photometry. This will not be a problem however, since we are choosing eight equally spaced phases from the hydrodynamic models --- we should have enough phase coverage to confirm or reject a given model. Luttermoser \& Johnson (1992) have described the difficulties involved in the solution of the transfer equation in these cool, low density environments. % Table 1 \protect\begin{table} \caption{\textbf{Program Data Base of IUE Images}} \begin{center} \begin{tabular}{clcr} \hline & & Exposure & Observation \\ Star & \ \ \ \ Image & Time ({\it min\,}) & Date\ \ \ \ \ \ \\ \hline\hline R~Lyr & LWP \,\ 9596 & 385 & 28 Nov 1986 \\ & LWP 19097 & 20 & 31 Oct 1990 \\ & LWP 19098 & 100 & 31 Oct 1990 \\ & LWP 25278 & 20 & 6 Apr 1993 \\ & LWP 25279 & 60 & 6 Apr 1993 \\ \hline g~Her & LWP \,\ 6575 & 15 & 4 Aug 1985 \\ & LWP \,\ 6576 & 360 & 4 Aug 1985 \\ & LWP 13442 & 40 & 16 Jun 1988 \\ & LWP 13443 & 880 & 17 June 1988 \\ \hline \end{tabular} \end{center} \protect\end{table} From these calculations, we will be able to determine whether the hydrostatic chromospheric models or the hydrodynamic models better represent the outer atmosphere of these stars. It will also help clarify the differences between the atmospheric structure of the semiregular variables to the Mira variables. We have had considerable experience with NLTE radiative transfer calculations of Mira--type models (see Luttermoser \& Bowen 1992; Luttermoser, Bowen, \& Willson 1994) and with semiempirical chromosphere models (see Luttermoser \ea 1989; Luttermoser, Johnson, \& Eaton 1994). This past work, coupled with results from this program, will give us valuable insight of the physical processes in the atmospheres of late-type AGB stars. \newpage \begin{center} \Large \textbf{(5) References} \end{center} % Put your own references in place of mine, but follow the format I have used here. \begin{description} \item Bookbinder, J.A., Brugel, E.W., \& Brown, A. 1989, \apj, 342, 516 \item Bowen, G.H. 1988, \apj, 339, 299 \item Brugel, E.W., Beach, T.E., Willson, L.A., \& Bowen, G.H. 1987, in {\it IAU Colloquium No. 103, The Symbiotic Phenomena}, ed.\ M. Friedjung (Dordrecht: Reidel), p.67 \item Drinkwater, M.J., \& Wood, P.R. 1985, in {\it Mass Loss from Red Giants}, ed.\ M. Morris \& B. Zuckerman (Dordrecht: Reidel), p.257 \item Eaton, J.A., \& Johnson, H.R. 1988, \apj, 325, 355 \item Johnson, H.R., \& Luttermoser, D.G. 1987, \apj, 314, 329 \item Judge, P.G., \& Neff, D.H. 1990, in {\it Sixth Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun}, ed.\ G. Wallerstein, ASP Conf.\ Series, v.9, p.57 \item Judge, P.G., \& Stencel, R.E. 1991, \apj, 371, 351 \item Jura, M. 1989, in {\it IAU Colloquium 106: The Evolution of Peculiar Red Giant Stars}, ed.\ H.R. Johnson \& B. Zuckerman (Cambridge: Cambridge University Press), p.339 \item Lennon, D.J., Dufton, P.L., Hibbert, A., \& Kingston, A.E. 1985, \apj, 294, 200 \item Luttermoser, D.G., \& Bowen, G.H. 1992, in {\it Seventh Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun}, ed.\ M.S. Giampapa \& J.A. Bookbinder, ASP Conf.\ Series, v.6, p.558 \item Luttermoser, D.G., Bowen, G.H., \& Willson 1994, \apj, (submitted) \item Luttermoser, D.G., \& Johnson, H.R. 1992, \apj, 388, 579 \item Luttermoser, D.G., Johnson, H.R., Avrett, E.H., \& Loeser, R. 1989, \apj, 345, 543 \item Luttermoser, D.G., Johnson, H.R., \& Eaton, J.A. 1994, \apj, (to appear Feb.\ 10) \item Richer, H. 1989, in {\it IAU Colloquium 106: The Evolution of Peculiar Red Giant Stars}, ed.\ H.R. Johnson \& B. Zuckerman (Cambridge: Cambridge University Press), p.35 \item Stencel, R.E., Linsky, J.L., Brown, A., Jordan, C., Carpenter, K.G., Wing, R.F., \& Czyzak, S. 1981, \mnras, 196, 47P \item Vernazza, J.E., Avrett, E.H., \& Loeser, R. 1981, \apjs, 45, 635 \item Wannier, P.G., \& Sahai, R. 1986, \apj, 311, 335 \item Willson, L.A. 1976, \apj, 205, 172 \item Wood, P.R. 1979, \apj, 227, 220 \end{description} \end{document}