Equivalent Width Abundance Analysis In Moog Eric J. Bubar Department of Physics and Astronomy, Clemson University, Clemson, SC 29630-0978 ebubar@clemson.edu ABSTRACT In this cookbook I give in depth steps on how use the MOOG computer software to perform a standard spectroscopic abundance analysis using the abfind routine. Subject headings: Equivalent Widths, abfind 1. Model Atmospheres The following description requires use of a model atmosphere to establish the relevant thermodynamic properties (temperature structure, electron density, etc.) for calculating abundances in. For late type (F, G and K) stars, an appropriate choice for model atmospheres, commonly utilized in the literature, are the 1D plane-parallel model atmospheres of Robert Kurucz Broadly, these model atmospheres break the photosphere of a star (the outer atmosphere where the majority of visible wavelength spectral lines are formed) into many, subsequent layers. Within a given layer the equations of hydrostatic equilibrium hold (pressure balances with gravity) and energy transport is through radiative processes. Perhaps the most essential assumption in these model atmospheres is that of local thermodynamic equilibrium (LTE). In LTE, the transfer equation is solved assuming a blackbody source function and the properties of a small volume of gas are determined by the thermodynamic equilibrium values determined from the local temperatures and pressures. Typically these model atmospheres are created based on the four fundamental physical parameters that are used to describe a star; temperature, surface gravity, metallicity, and microturbulent velocity. 2. Equivalent Widths The abfind package of MOOG uses equivalent widths to force fit abundances using a curve of growth method. Consequently, you need to measure equivalent widths for lines of the elements that you want abundances for. The best choice is going to be lower EXCITATION POTENTIAL lines (χ nu 5-ish ev). You want to find nice clean lines that don t appear to be blended and have shapes that you can fit nicely using SPECTRE. Once you have a measured a bunch of lines for your given element, you need to create a linelist in the MOOG abfind package format.
2 3. Linelist You will need to put all of your line equivalent widths into a MOOG format linelist. MOOG is kind of picky about spacing so your list must look the same as the sample list found in the MOOG manual. Make sure that the first line in your file is a commented piece of text. I like to at least put the number of total lines that are in the file on this top line. Starting on the second line of the linelist file, the various columns each give different parameters. COLUMN 1: Wavelength of the line that you measured. COLUMN 2: The ATOMIC NUMBER and IONIZATION STATE of the line that you measured in decimal form. For example, a line of neutral iron would be denoted as 26.000. The 26 gives the atomic number (in this case iron). The decimal tells MOOG that the ionization state of the line is coming next. The 000 gives the ionization state, in this case neutral. If I wanted singly ionized iron, I would enter in 26.100, where the.100 tells MOOG this is a singly ionized state. COLUMN 3: This is the lower EXCITATION POTENTIAL of the line. This tells you the energy you need to give the atom to ionize to the desired state. COLUMN 4: This is the log(gf) or gf value. This basically just tells you what the probability is that a specified transition will occur for a given line. This is the important part for MOOG and is most likely the largest source of uncertainty. Getting lines with good, reliable log(gf) s or gf s is half the battle for the stellar spectroscopist. COLUMN 5: This is the dissociation energy. For my purposes the only number i ve used thus far is 2.2. I believe it becomes much more important for molecular lines, but I like atoms! COLUMN 6: The final column is the equivalent width of the line that you measured in SPECTRE. This will be used for the curve of growth. 4. Check For Trends: Plot of EXCITATION POTENTIAL versus REDUCED EQUIVALENT WIDTH This next step, i m told, is not really performed by a lot of spectroscopists out there, but I trust my mentor, and do what he tells me. I m going for QUALITY here, not QUANTITY, so lets be rigorous so that people will learn to trust our word. It is important to check and see if the lines you measured have any trends that connect the EXCITATION POTENTIAL to the REDUCED EQUIVALENT WIDTH. If they do, there could be problems later on when you ll be guessing, checking and iterating to converge on a solution. The first step is to create a plot of the EXCITATION POTENTIAL versus the log of the REDUCED EQUIVALENT WIDTH. You say, but Eric, I only have an equivalent width!. No problem, the reduced equivalent with is simply the Equivalent Width you measured, divided by the wavelength of the line that you measured that width at. To give a little bit of physical explanation for why we re doing this lets think about the quan-
3 tities we re plotting. Okay, the EXCITATION POTENTIAL tells how much energy you need to ionize (or EXCITE) an electron to a given state from the ground state. In general, the HIGH EX- CITATION POTENTIAL LINES form deeper in the atmosphere of the star, where temperatures are high enough to excite atoms to the higher EXCITATION POTENTIAL states. Now, if the line forms deeper, its likely that it might be a little bit weaker just from having to travel through more stuff in the stellar atmosphere before it reaches us. Conversely, a LOWER EXCITATION POTENTIAL LINE doesn t need as much energy to form, so it can form in lower temperature regions, i.e. closer to the stellar surface. Consequently it travels through less stuff so it may be a stronger line. For these reasons you may naturally expect: 1) Lower EXCITATION POTENTIAL lines may form closer to the stellar surface and thus be stronger. - and - 2) Higher EXCITATION POTENTIAL lines may form deeper in the bowels of the stellar atmosphere and thus may be intrinsically weaker. Now, hopefully you can see that there may be a slightly intrinsic trend for lower EXCITATION POTENTIAL lines to give larger equivalent widths, and vice versa, so you need to see if your line choices embellish this effect. If this is the case, you may have problems down the road when fiddling with your spectroscopic parameters. The goal is to get a list of lines that show no such trend so that down the line you will be able to figure out your temperatures and your mictroturbulent velocities separately. You will see down the line what I m talking about, but if you must know now: We will be creating plots of [Fe/H] versus EXCITATION POTENTIAL and [Fe/H] versus log of the REDUCED EQUIVALENT WIDTH. MOOG basically gives us our abundances, (from which we find [Fe/H]) and the EXCITATION POTENTIALS and REDUCED EQUIVALENT WIDTHS are known values from our linelist. The plot of [Fe/H] versus EXCITATION POTENTIAL will be used to determine TEMPERATURE and the plot of [Fe/H] versus log of REDUCED EQUIVALENT WIDTH will be used to find MICROTURBULENT VELOCITY. If there is a trend between these two different abscissa (i.e. x-coordinates, EXCITATION POTENTIAL and REDUCED EQUIVA- LENT WIDTH) then changes in temperature will effect the plot for finding MICROTURBULENCE and vice versa and we have a big mess/headache when trying to spectroscopically determine our best fit solutions. INSERT A PLOT OF EXCITATION POTENTIAL VERSUS REDUCED EQUIV- ALENT WIDTH
4 5. Solar Differential Analysis If you are calculating exact abundances, then you don t need this section. However, its most likely that you want to do a differential analysis with respect to the Sun. What you want to do then, is measure a bunch of lines for a given element in your star s spectrum. Then, get a good solar spectrum that has similar resolution and S/N as your spectrum and measure the same lines as you measured in your star. Then, first run MOOG on the linelist you create of your measured SOLAR lines. Use a model atmosphere with the known parameters of the Sun (T= 5777,[g]=4.44,[Fe/H]=0.00,vt=1.10) in your MOOG run. The results of this run will be kept constant, because we KNOW that these are the basic physical parameters of the Sun and we don t want to fiddle with these. We will now do some MOOG running and a little bit of country folk music (i.e. fiddling). 6. Running MOOG Okay, we ve either removed lines that give a trend in EXCITATION POTENTIAL versus REDUCED EQUIVALENT WIDTH or we have found that there are no such trends. This means we re ready to run MOOG! Take your super-terrific pure linelist and we ll make a parameter file for running the ABFIND routine to get abundances.
5 Sample Parameter File for Running ABFIND abfind standard out /local/ebubar/moogout/test std.out summary out /local/ebubar/moogout/test sum.out model in /local/ebubar/models/pttmodels/t4748 g4.45 m0.20 vt1.01.atm lines in /local/ebubar/moogin/linelist/bd392587 fe1.lst terminal x11 atmosphere 1 molecules 2 lines 3 flux/int 0 damping 0 units 0 obspectrum 0 plot 4 strong 0
6 You can read about what these things mean in the MOOG manual, but basically i m taking a model atmosphere of my star, i m inputting my good linelist, and will output a plot of the results. Once you run moog, you will utilize the second output file for determining what parameters you need to fiddle with. The file that is called summary out is what you will utilize to create your plots of [Fe/H] versus EXCITATION POTENTIAL and [Fe/H] versus log of the REDUCED EQUIVALENT WIDTH. 7. Fiddler on the Roof Now is the fun part. You get to fiddle with your model atmosphere parameters until you start to remove the correlations The idea is to remove the correlations in both the plots of [Fe/H] versus EXCITATION PO- TENTIAL and [Fe/H] versus log of REDUCED EQUIVALENT WIDTH. When I do this, I run MOOG with my model atmosphere parameters for my star. Then, I take that output file and use SUPERMONGO to read in both the abundances for the star and for the Sun. Subtract the Sun abundance from the star abundance and you have the metallicity! In this same SUPERMONGO file I create my relevant plots. 7.1. [Fe/H] versus EXCITATION POTENTIAL If this plot has some slope to it, you need to change your TEMPERATURE. As you fiddle with the temperature in your model atmosphere your least squares fit will either get better or worse. You will keep adjusting the temperature until you flatten the trend. You should aim for an RMS of 0.05-ish and a Correlation coefficient of better than 0.005-ish. 7.2. [Fe/H] versus log of REDUCED EQUIVALENT WIDTH If this plot has some slope to it, you need to change your MICROTURBULENT VELOCITY. As you fiddle with the microturbulent velocity in your model atmosphere your least squares fit will either get better or worse. Keep adjusting the MICROTURBULENCE until you flatten the trend. You should again aim for an RMS of 0.05-ish and a Correlation coefficient of better than 0.005-ish.
7 7.3. Fe II for MICROTURBULENCE Lets now say you were able to measure lots of Fe II lines (bully for you!). You can use these lines to determine the microturbulent velocity parameter. Again, make plots of EXCITATION POTENTIAL versus log(reduced EQUIVALENT WIDTH). Check for trends and strange lines. Of course, you may have been just fine with getting a great fit with just the Fe I lines. That is quite excellent as well. Therefore, this step may not even be a necessary one. In that case, you ll be jumping ahead to find logg. But if you want to use Fe II to find microturbulence and there are strange trends in existence, you may have to deal with strange lines in the method described below. 7.3.1. Dealing with Strange Lines Do you see some line that looks odd in one of your trend plots? This is entirely possible (and likely). The first step is to return to your measurements and make sure that they are correct. Perhaps you transposed wrong or were having a bad measuring day. If the line measurement still looks fine, then its time to get a little more involved. Look to see if there are any other lines of significant strength around your alleged Fe II line. Its possible you have measured a blended line feature. You can use MOOG to create synthetic spectra of the lines in your region of interest. A great way to do this is to get all the lines from VALD for your region of interest. Then put these in a MOOG format linelist and plug it in to create a synthetic spectrum. Once you have a synthetic spectrum, check the FIRST output file that you get from running that MOOG synthesis. Look a good ways down and you should see a listing of all the wavelengths from your linelist along with various columns. One of these columns is labeled strength. This column gives a magical number that gives the relative strength of each of the lines that are in your linelist. If you see a line near your Fe II line that is either stronger or comparable in strength when using this magical line strength column, then your line is likely blended and perhaps isn t actually an Fe II line at all! This spectral synthesis method is a good way to check lines that may otherwise have escaped your notice as being blended. Of course its also always possible that in your fervor to find as many good lines as possible you included blended lines by mistake, with the good intentions of improving your results. It happens. You just want to check lines that appear to be giving wonky/inconsistent results because there really is physics underlying all of this black magic and it should be consistent. Of course, you may have inconsistencies, and thats perfectly fine. In fact, thats when you ll most likely discover something new and exciting! 7.4. Fe II for LOG(G) Okay, so you got a beautiful fit by fiddling with Temperature and Microturbulence (correlation coefficients are less than 0.005). Now, we re going to take these pristine results and fiddle with
8 log(g) and wipe out all that hard work. You need to get the metallicity of your star based on your Fe II line equivalent widths ([Fe II/H]). You should just take an average of all your Fe II abundances (you won t have enough Fe II lines measured to try and remove correlations with EXCITATION POTENTIAL or REDUCED EQUIVALENT WIDTH) to get some FINAL abundance [Fe II/H]. Now, for solar-type stars (i.e. F, G, and K), singly ionized Fe lines are sensitive to changes in the pressure (and thus gravity), while neutral lines are essentially independent of surface gravity effects (not really true in a strict sense, but approximately its good enough). So, we ll assume you have determined a temperature from removing the correlation in [Fe I/H] versus EXCITATION POTENTIAL (aka EXCITATION BALANCE) and a microturbulence by removing the correlation in [Fe I/H] versus REDUCED EQUIVALENT WIDTH (equivalent width balance). In doing this, you should have converged to a single abundance for the star (i.e. an average [Fe I/H]. Now, you need to adjust the surface gravity (logg) until the abundance you derive from Fe II lines ([Fe II/H]) matches with that from Fe I lines ([Fe I/H]). The pain in this comes from the parameters all being interdependent. As you change the gravity, your temperature, microturbulence and metallicity solutions will likely fall apart (sometimes by a lot, sometimes by a little). The trick now is to iterate on the parameters until you get a solution over all parameters. In summary, you need to do this: 7.5. Summary 1) Tweak the temperature in order to remove the correlation in [Fe I/H] versus EXCITATION POTENTIAL (EXCITATION BALANCE) 2) Tweak the microturbulent velocity in order to remove the correlation in [Fe I/H] versus RE- DUCED EQUIVALENT WIDTH (line strength balance or equivalent width balance) 3) Tweak surface gravity in order to force [Fe II/H] to be equal to [Fe I/H] which you have from steps 1 and 2. Once you satisfy these three steps, you have performed your standard spectroscopic abundance analysis. Congratulations! Now start the whole messy process over again with another star and watch as you rip your hair trying to converge to unique solutions.