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| en:praktikum:wrstern [2014/12/14 00:22] – created, Part 1 msteinke | en:praktikum:wrstern [2024/10/09 08:09] (current) – Adjusts name of laboratory computer rhainich |
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| FIXME **This page is not fully translated, yet. Please help completing the translation.**\\ //(remove this paragraph once the translation is finished)// | |
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| ====== D3 - Spectral analysis of a Wolf-Rayet star====== | ====== D3 - Spectral analysis of a Wolf-Rayet star====== |
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| | ===== Task ===== |
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| ==== Task ==== | Determine the temperature $T_*$, radius $R_*$, luminosity $L$, mass loss rate $\dot{M}$, the mass fraction of hydrogen $X_{\mathrm{H}}$, and the stellar wind's terminal velocity $v_{\infty}$ of the Wolf-Rayet star BAT99 58 (Brey 47) in the Large Magellanic Cloud (LMC) by comparison with synthetic spectra calculated with the PoWR stellar atmosphere code. |
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| Determine the temperature $T_*$, radius $R_*$, luminosity $L$, mass loss rate $\dot{M}$, the mass fraction of hydrogen $X_{\mathrm{H}}$ and the stellar wind's terminal velocity $v_{\infty}$ of the Wolf-Rayet star BAT99 58 (Brey 47) in the Large Magellanic Cloud (LMC) by comparison with PoWR models. | ===== General ===== |
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| ==== General ==== | As you already learnt in D2 (Determine the mass loss rate of OB stars), hot and massive stars have strong mass loss by stellar winds. This can be seen in their spectra that, in case of the Wolf-Rayet (WR) stars, are entirely dominated by emission lines formed in the wind. These stars are seen as late evolutionary stages of very massive O-type stars that might be at the transition between (central) hydrogen and helium burning. |
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| As you already learnt in D2 (Determine the mass loss rate of OB stars), hot and massive stars have strong mass loss by stellar winds. This can be seen in their spectra which are, in case of the Wolf-Rayet (WR) stars, entirely dominated by emission lines that form in the wind. These stars are seen as late evolutionary stages of very massive O-type stars that may be at the transition between (central) hydrogen and helium burning. | To derive stellar parameters, the observed spectrum is compared to model spectra (synthetic spectra). By means of the Potsdam models of expanding stellar atmospheres (PoWR) one can analyze spectra of hot stars ($T_* > 10\,\mathrm{kK}$), which holds true for WR stars. According to the dominance of nitrogen or carbon lines in the spectrum a distinction is made between WR stars of the nitrogen (WN) and carbon (WC) sequence, while the former are subdivided into **late types** (WNL) and **early types** (WNE) depending on their atmosphere's hydrogen content. In this experiment a WN type star of the LMC shall be examined. |
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| To derive stellar parameters from the observed spectrum they are compared to model spectra (synthetic spectra). With help of Potsdam Models of expanding stellar atmospheres (PoWR) can analyze spectra of hot stars ($T_* > 10\,\mathrm{kK}$) which holds true for WR stars. According to the dominance of nitrogen or carbon lines in the spectrum a distinction is made between WR stars with nitrogen (WN) and carbon (WC), while the former are subdivided into **late types** (WNL) and **early types** (WNE) depending on their atmosphere's hydrogen content. In this experiment a WN type star of the LMC shall be examined. | ==== Preparation ==== |
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| === Preparation ==== | |
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| Find the [[http://www.astro.physik.uni-potsdam.de/PoWR.html|grid models]] at the main page of the [[http://www.astro.physik.uni-potsdam.de|Astrophysics Department of the Uni Potsdam]]. Get an impression of the parameters that enter into the models, e.g. the range of temperatures and the so called transformed radius $R_{\mathrm{t}}$. Learn the principles of line-driven winds. | Find the [[http://www.astro.physik.uni-potsdam.de/PoWR.html|grid models]] at the main page of the [[http://www.astro.physik.uni-potsdam.de|Astrophysics Department of the Uni Potsdam]]. Get an impression of the parameters that enter into the models, e.g. the range of temperatures and the so called transformed radius $R_{\mathrm{t}}$. Learn the principles of line-driven winds. |
| Then copy the WRplot script ''lmcstars.plot'' and the accopanying file for the line identifications ''ident.dat'' from the directory ''~/skripte/d3/'' to the laboratory course computer ''a12'' into your working directory. | Then copy the //WRplot// script ''lmcstars.plot'' and the accompanying file for the line identifications ''ident.dat'' from the directory ''~/scripts/d3/'' into your working directory on the laboratory course computer ''columba''. |
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| ==== Course ==== | ===== Realization ===== |
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| === Observational data === | ==== Observational data ==== |
| There are visual observational data for the star that are already linked in the previously mentioned WRplot script. Additional UV observations from the International Ultraviolet Explorer (IUE) can be downloaded from the [[http://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html|MAST archive]]. There are spectra in different wavelength ranges (SWP: 1150–1980 $\mathrm{\AA}$ and LWP or LWR: 1850–3350 $\mathrm{\AA}$). Search in the MAST archive for UV data of this star (note: the search radius should be limited to a few arcseconds) and save the downloaded fits files in your working directory. To ease the further handling, convert the fits files (the spectra) to X-Y tables (ASCII-Format, text files), e.g. with the program fitsviewer: | There are visual observational data for the star that are already linked in the previously mentioned //WRplot// script. Additional UV observations from the International Ultraviolet Explorer (IUE) can be downloaded from the //[[http://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html|MAST]]// archive. There are spectra in different wavelength ranges (SWP: $1150-1980\,\unicode{x212B}$ and LWP or LWR: $1850-3350\,\unicode{x212B}$). Search in the MAST archive for UV data of this star (note: the search radius should be limited to a few arcseconds) and save the downloaded fits files in your working directory. To ease the further handling, convert the fits files (the spectra) to X-Y tables (ASCII format), e.g. with the program //fitsview//: |
| fv filename.fits | fv filename.fits |
| and display all data tables (Table -> All). Mark and delete unneeded datasets and export the remaining data as text file (choose a descriptive filename) with fixed column width. Add the reference number of the selected observation as comment line (starting with an asterisk, *). | Display all data tables by clicking on ''Table'' and then ''All''. Mark and delete unneeded datasets and export the remaining data as a text file (choose a descriptive filename) with fixed column width. Add the reference number of the selected observation as comment line (starting with an asterisk, *). Alternatively, search for the star directly in the [[https://archive.stsci.edu/iue/search.php|IUE database]]. On the results page, click on the ''Data ID'' to get to the preview window, where you can download the spectra as ASCII files. |
| Alternatively, download the IUE spectra directly from the [[https://archive.stsci.edu/iue/search.php|IUE database]]. Search for the star and the results page will display the spectra and allow to download the spectra as ASCII files. | |
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| Furthermore, use [[http://simbad.u-strasbg.fr/simbad/|Simbad]] and [[http://vizier.u-strasbg.fr/viz-bin/VizieR|VizieR]] to obtain the photometry of the star. This means the u, v und b small band magnitudes ([[http://adsabs.harvard.edu/abs/1968MNRAS.140..409S|Smith et al. 1968]]) as well as the 2MASS IR broad band magnitudes (J, K and H). Copy these values. If needed look for photometry in the literature. | Furthermore, use //[[http://simbad.u-strasbg.fr/simbad/|Simbad]]// and //[[http://vizier.u-strasbg.fr/viz-bin/VizieR|VizieR]]// to obtain the photometry of the star. This means the u, b, and v small band magnitudes ([[http://adsabs.harvard.edu/abs/1968MNRAS.140..409S|Smith et al. 1968]]) as well as the 2MASS IR broad band magnitudes (J, K, and H). Copy these values to the //WRplot// script. If needed look for photometry in the literature. |
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| === Fit the spectrum === | ==== Fit the spectrum ==== |
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| Im Prinzip ist das wrplot-Skript direkt benuztbar. Es gilt nur noch die Variablen und Parameter anzupassen, die bisher mit einem Fragezeichen versehen sind. Wählen sie sich ein Modell und das entsprechende Gitter, tragen sie die ermittelten Photometriedaten | In principle the //WRplot// script can be used right away, just some variables and parameters (those that are seeded with q ''?'') need to be specified. Choose a model and the corresponding grid, copy the values for the photometry and enter the path of the observational data. Create the so-called masterplot by running the script |
| ein und passen sie die Pfade an, die die Beobachtungsdaten betreffen. | |
| Wenn sie das Skript mit | |
| wrpdf lmcstars.plot | wrpdf lmcstars.plot |
| ausführen erhalten sie einen sogenannten Masterplot mit dem Namen ''lmcstars.pdf''. Dieser enthält 5 Paneele und eine Kopfzeile, die Informationen über das gewählte Modell, Temperatur, Radius, Geschwindigkeit, | which creates the file ''lmcstars.pdf''. It contains five panels and a headline with information on the model, its temperature, radius, velocity, abundances, and the model number. The uppermost panel shows the spectral energy distribution (SED) in a double logarithmic plot (absolute flux over wavelength). The observation is in blue, the chosen model in red, the blue boxes mark the photometry. The other panels show the normalized line spectrum (flux over wavelength) in the same color coding. |
| chemische Häufigkeiten und Modellnummer enthält. | |
| Das oberste Panel ist die Spektrale Energieverteilung (SED), die doppelt logarithmisch den absoluten | |
| Fluss über der Wellenlänge darstellt. Dabei wird die Beobachung blau und das gewählte Modell rot abgebildet. Die blauen Kästchen entsprechen den Flussmarken der Photometriewerte. Die weiteren Plots enthalten das normalisierte Linienspektrum über der Wellenlänge in Angström ($\mathrm{\AA}$) in gleicher Farbcodierung. | |
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| Es gilt nun, das Modell auszuwählen, welches die bestmögliche Übereinstimmung mit dem beobachteten | The task is to select the model that shows the best possible accordance with the observed spectrum. Pay attention to the identified spectral lines: Their form, height, and width should be reproduced by the model spectrum. By changing the model number (variable ''MODEL''), the temperature (the first two digits of the model number) and/or the transformed radius (the last two digits of the model number) can be changed. First check if the hydrogen lines $\mathrm{H_{\alpha}}$, $\mathrm{H_{\beta}}$, and $\mathrm{H_{\gamma}}$ can (roughly) be reproduced. If the hydrogen lines are very different, change the grid. |
| Linienspektrum aufweist. Dabei ist im wesentlichen darauf zu achten, dass die bezeichneten Spektrallinien | For the LMC there are three model grids available that differ in their hydrogen content (and their helium content, thus): 40, 20, 0% hydrogen mass fraction. Change between the model grids by setting the appropriate path (variable ''PATH''): |
| in Form, Höhe und Breite wiedergegeben werden. Durch die Veränderung der Modellnummer (Variable ''MODEL'') können sie im Gitter entsprechend höhere/tiefere Temperaturen und/oder transformierte Radien wählen. | |
| Mit einem Blick auf die Linien $\mathrm{H_{\alpha}}$, $\mathrm{H_{\beta}}$ und $\mathrm{H_{\gamma}}$ kann festgestellt werden, ob ggf. das Gitter gewechselt werden muss. Dies kann nötig sein, wenn speziell | |
| die Linien $\mathrm{H_{\alpha}}$, $\mathrm{H_{\beta}}$ und $\mathrm{H_{\gamma}}$ durch das synthetische Spektrum noch nicht gut dargestellt werden. | |
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| Für die LMC sind drei Modellgitter verfügbar, die sich in ihrem Wasserstoffgehalt (und dementsprechend auch dem Heliumgehalt) unterscheiden. Ein Wechsel des Modellgitters kann durch die Anpassung des verwendeten Pfads (Variable ''PATH'') erreicht werden. Diese lauten jeweils: | |WNs with 40% hydrogen (WNL) | ''~/scripts/d3/models/wnl40/'' | |
| | |WNs with 20% hydrogen (WNL) | ''~/scripts/d3/models/wnl20/'' | |
| | |WNs without hydrogen (WNE) | ''~/scripts/d3/models/wne/'' | |
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| |WNs mit 40% Wasserstoff (WNL) | ''~praktikum/skripte/d3/models/wnl40/'' | | For some standard grid models, additional versions with different wind velocities ($v_{\text{inf}}$) are available. Once a model has been found that reproduces the normalized line spectrum continue with the SED fit. For this purpose, adjust the reddening (variable ''EBVSMITH'') and apply a shift to the luminosity (variable ''shift''). Their starting values could be ''shift=0'' and ''EBVSMITH=0.1''. The line strength of the normalized emission spectrum depends on the temperature and the transformed radius, so the luminosity can be scaled up/down in a certain interval by means of the ''shift'' variable without affecting the normalized spectrum. The model SED should reproduce the general trend of the observations, while going through the center of the photometry boxes. This ensures a correct model flux. |
| |WNs mit 20% Wasserstoff (WNL) | ''~praktikum/skripte/d3/models/wnl20/'' | | |
| |WNs ohne Wasserstoff (WNE) | ''~praktikum/skripte/d3/models/wne/'' | | |
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| Für einige Standardgittermodell sind zusätzliche Versionen mit angepassten Windendgeschwindigkeiten ($v_{\text{inf}}$) verfügbar. Hat man ein Modell gefunden, welches das normalisierte Linienspektrum gut wiedergibt, kann man nun die spektrale Energieverteilung (engl.: spectral energy distribution, kurz SED) fitten. Hierfür müssen die Parameter Rötung (Variable ''EBVSMITH'') und Leuchtkraft (Variable ''shift'') angepasst werden, als Startwert bieten sich folgende Werte an ''shift=0'' und ''EBVSMITH=0.1''. Da die Linienstärke des normalisierte Emissionsspektrum bei gleicher Oberflächentemperatur und gleichem transformierten Radius unabhängig von den einzelnen in $R_t$ eingehenden Parametern erhalten bleibt, kann die Leuchtkraft über die ''shift''-Variable in einem gewissen Rahmen skaliert werden ohne das Emissionslinienspektrum abzuändern. Die Modell-SED sollte sowohl den allgemeinen Verlauf der Beobachtungsdaten reproduzieren, als auch etwa die Mitte der jeweiligen Photometriekästchen durchlaufen. Damit kann ein akkurater Flussverlauf für das Modell gewährleistet werden. | ==== Determine the stellar parameters ==== |
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| === Bestimmung der Sternparameter === | The stellar parameters can be obtained from the properties of the selected model. These parameters are described on the PoWR homepage. Following the Stefan-Boltzmann law: |
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| Die Bestimmung der stellaren Parameter erfolgt aus den Informationen des gewählten Modells, dessen Parameter auf der Webseite vorgestellt und erläutert werden. Nach dem Stefan-Boltzmann Gesetz gilt | $L \propto R_{*}^2$ and $L \propto T^4$, |
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| $L \propto R_{*}^2$ bzw. $L \propto T^4$, | both combined: |
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| zusammenfassend also: | |
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| $L \propto R_{*}^2 \cdot T^4$. | $L \propto R_{*}^2 \cdot T^4$. |
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| Der Sternradius ist bei konstanter Leuchtkraft also proportional zu $T^{−2}$. Durch Addition des ''shift''-Parameters zur Leuchtkraft des Modells kann diese an die wahre Leuchtkraft des Stern angepasst werden. | The stellar radius (at constant luminosity) is proportional to $T^{−2}$. By adding the ''shift'' parameter to the luminosity, the model luminosity can be adjusted to the true luminosity of a star. |
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| Über den transformierten Radius ist die Massenverlustrate mit der Leuchtkraft verbunden und es gilt | The mass loss rate is connected to the luminosity via the transformed radius: |
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| $R_t \propto \dot{M}^{−\frac{2}{3}}$ sowie $R_t \propto R_{*}$ | $R_t \propto \dot{M}^{−\frac{2}{3}}$ and $R_t \propto R_{*}$ |
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| $\Rightarrow \dot{M} \propto L^{−\frac{3}{4}}$. | $\Rightarrow \dot{M} \propto L^{−\frac{3}{4}}$. |
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| Mit den vorhergehenden Beziehungen ergibt sich somit der Zusammenhang | So, in total: |
| $\dot{M}^{\frac{2}{3}} \propto T^{−2} \cdot R_t$. | $\dot{M}^{\frac{2}{3}} \propto T^{−2} \cdot R_t$. |
| ==== Auswertung ==== | |
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| Es ist ein praktikumsübliches Protokoll anzufertigen. | ===== Report ===== |
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| | A usual laboratory course report is to be handed in. |
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| [[praktikum:index|Übersicht: Praktikum]] | [[en:praktikum:index|Overview: Laboratory Courses]] |