Bayesian Analysis for Stellar Evolution with Nine Parameters
Contents
1. from a one hour exposure the S N is scaled by sqrt exptime These exposure times can be set in the base9 yaml file under exposures for each individual filter Additional options for scatterCluster are available in the yaml file The bright and faint end cut off mags allow you to narrow the portion of the CMD that you wish to retain The relevantFilt option specifies which band is the reference filter in this case O U 1 B etc The base9 yaml options brightLimit and faintLimit refer to the bright and faint end cut 11 off magnitudes for the reference filter indicated You can also clip on S N with limitS2N and decide to cut out field stars if they were simulated by simCluster Additionally scatterCluster will determine which filters you are using based on the header in the simCluster output file Again the integer seed may be set at the command line to allow you to start from the same input file but create multiple simulated observations of that file with different initial seed values linux gt scatterCluster Seed 1564704505 The output file of scatterCluster looks like linux gt head 2 hyades hyades scatter out id U B V R I J H K sigU sigB sigV sigR sigIl sigJ sigH sigK massi massRatio stage Cmprior useDBI 1 3 065 3 016 2 691 2 509 2 328 2 128 1 985 1 977 0 010 0 010 0 010 0 010 0 010 0 010 0 010 909 010 1 555 0 000 1 9 999 1 Notice now that the output includes the estimated errors for each band sig The format of t2. linux head 2 hyades hyades res logAge Y FeH modulus absorption logPost 8 843553 0 288468 0 016795 0 180626 0 013647 198 263339 After the column headers there is one record for each iteration of each of the cluster parameters of interest If everything goes well all you really need to do is plot histograms for any column of interest These are the posterior parameter distributions You can also calculate moments of these columns if you d like and look at correlations among the columns e g by plotting logAge vs modulus D sampleMass and sampleWDMass These modules are useful for anyone interested in the masses of some or all of the stars in their database Running them is unnecessary if you are only interested in the cluster parameters The module sampleMass reports the primary mass and secondary mass ratio at all iterations for every star in the database and sampleWDMass reports the primary mass for the subset of database stars that are being fit as WDs Running these programs is quite simple linux sampleWDMass Seed 1690745648 Warming up generator Done Generated 10000 values Reading models Done sampledPars at age 8 78411 sampledPars at last age 8 74765 Part 2 completed successfully Running sampleMass is effectively identical These output files names end with wdMassSamples wdMassSamples membership massSamples and massSamples membership These correspond to the WD mass outputs from sampleWDM
3. membership probability for every stellar object BASE 9 is provided as open source code on a version controlled web server The executables are also available as Amazon Elastic Compute Cloud images This manual provides potential users with an overview of BASE 9 including instructions for installation and use Table of Contents We Introd ction Pet Em 3 IL Skip the install and go to the cloud iissiscsccesstedsecincdstisssssicitescarescdinctenstususeodesrsuncesicnastendenenenane 5 TED Tri Cea ithe ris E 6 A Installing gcc gsl and cmake on a Mac running OS X 10 7 10 9 eee 6 B Installing gcc gsl and cmake on a Linux machine eene 8 em iDridenpdi lupe 8 ION EIEIDAIAMIIDLENPRM S G S X 9 IV Running BASES Lucem circi d tinci enden a canc o Bates enc ase n dde d caua 9 wing 10 B scatterCluster iiec aevo nie in eren ien RE cur D RE DELL anale MENS One n CEN EE a Rr c eoa 11 EID ddiirde E 13 D sampleMass and sampleWDMAass renes ener tnn natntn teinte ntn te te tn ananas tasa tasas se asa sa sonans 15 ETA CEM EU 16 F Hyades Test reete T ie Leere itle E 17 G How long does all of this take eeeeeessseseeeeeeseee nennt tn rne tetntn tnnt te t
4. of models you do not know if the posterior distributions will be Gaussian shaped or more complex so we suggest you take the conservative approach and initially assume complex posterior distributions and run BASE 9 for 10 000 uncorrelated iterations The parameter thin sets the increment between saved iterations We recommend that this parameter be left equal to 1 to keep the adaptive sampling routine efficient If the output of singlePopMcmc is correlated see below then each new iteration or step is not independent and you need substantially more than 10 000 iterations to draw robust inferences In situations like this we recommend that the output file be thinned afterwards i e that the user uses every n record where n is large enough to keep the output uncorrelated Under the cluster options there are five parameters for which means and standard deviations can be set the metallicity prior Fe H the distance modulus prior distMod the absorption prior Av the helium prior Y and the carbon fraction prior for a C O WD carbonicity Note that carbonicity only works with the Montgomery models and is not yet supported because we are currently testing it If you only have weak priors that is fine If you do not want to sample on one or more of these parameters you can set the sigma for that parameter to 0 0 and this will turn of sampling for that parameter Under starting the parameter logClusAge is a starting value for the log of the a
5. own research and educational purposes BASE 9 may be the code for you if 1 you are dissatisfied with deriving cluster level parameters by over plotting isochrones on your data and iteratively adjusting parameters 2 you wish to recover more than just an average and error bar for each parameter and instead wish to characterize the probability distributions for these parameters 3 you wish to take fuller advantage of ancillary data such as proper motion membership probabilities spectroscopic mass estimates or distances from trigonometric parallaxes This manual is designed to help you install and run BASE 9 If you use BASE 9 in your research please cite von Hippel T Jefferys W H Scott J Stein N Winget D E DeGennaro S Dam A amp Jeffery E 2006 Inverting Color Magnitude Diagrams to Access Precise Star Cluster Parameters A Bayesian Approach ApJ 645 1436 and if you find the following helpful please also cite DeGennaro S von Hippel T Jefferys W H Stein N van Dyk D A amp Jeffery E 2009 Inverting Color Magnitude Diagrams to Access Precise Star Cluster Parameters A New White Dwarf Age for the Hyades ApJ 696 12 van Dyk D A DeGennaro S Stein N Jefferys W H amp von Hippel T 2009 Statistical Analysis of Stellar Evolution Annals of Applied Statistics 3 117 Depending on how you use BASE 9 this part is under your control the software also relies on the stellar evoluti
6. sudo apt get install cmake cmake curses gui linux sudo apt get install libgslO dev libgsl ldbl A similar process will work with the yum tool on Fedora RHEL linux sudo yum install gcc gcc c cmake git linux sudo yum install gsl gsl devel boost boost devel RHEL 5 amp 6 repositories have an old gcc version The devtoolset package will install an alternate up to date build environment at opt lt distro gt devtoolset 2 linux sudo yum install devtoolset 2 toolchain The scl utility can create a shell referencing these alternate build tools where BASE 9 can be built linux scl enable devtoolset 2 bash C Unpacking BASE 9 Create a directory where you wish to install and run the software then download the newest code release from https github com argiopetech base tags and the newest stellar evolution files from https github com argiopetech base models tags and extract them to the appropriate directory e g tar xzf base 9 4 2 tar gz gt cd base 9 4 2 Note that your computer may uncompress the gz file for you on download in which case the above command would instead be gt tar xvf base 9 4 2 tar cd base 9 4 2 D Installing Boost BASE 9 has an included script to install Boost The install location can be changed by modifying the CMAKE INSTALL PREFIX variable linux cd contrib linux cmake DCMAKE INSTALL PREFIX usr local linux sudo make Ubuntu users can save some time o
7. Bayesian Analysis for Stellar Evolution with Nine Parameters BASE 9 v9 4 3 User s Manual Ted von Hippel Elliot Robinson Elizabeth J effery Rachel Wagner Kaiser Steven DeGennaro Nathan Stein David Stenning William H Jefferys and David van Dyk Embry Riddle Aeronautical University Daytona Beach FL USA ted vonhippel erau edu Argiope Technical Solutions Ft White FL USA elliot robinson argiopetech com Brigham Young University Provo UT USA ejeffery byu edu University of Florida Gainesville FL USA rawagnerkaiser gmail com Studio 42 Austin TX USA studiofortytwo yahoo com University of Pennsylvania Philadelphia PA USA nathanmstein gmail com University of California Irvine CA USA dstennin Quci edu University of Texas Austin TX USA and University of Vermont Burlington VT USA bill astro as utexas edu Imperial College London London UK d van dyk imperial ac uk BASE 9 is a Bayesian software suite that recovers star cluster and stellar parameters from photometry BASE 9 is useful for analyzing single age single metallicity star clusters binaries or single stars and for simulating such systems BASE 9 uses Markov chain Monte Carlo and brute force numerical integration techniques to estimate the posterior probability distributions for the age metallicity helium abundance distance modulus and line of sight absorption for a cluster and the mass binary mass ratio and cluster
8. CMC iterations will increase the run time but somewhat less than linearly because some of the time is spent during the burnin You will see substantial increases in runtime if you have much larger data sets and or if you have to increase the total number of calculated iterations 17 V Diagnostics of run quality The following two plots show examples of poor and good sampling In the first extreme case the age sampling is highly correlated and one would need to use post run thinning probably by a factor of 100 This means that one would need to run the code for 100x as many interations The metallicity sampling displays only minor correlation and if all other parameters looked this uncorrelated then this run would be sufficient In this particular case both plots were generated from the same singlePopMcmc run and because no single parameter is reliable until all parameters are essentially uncorrelated this run did not reliably determine the metallicity or any other posterior distribution 10 095 10 09 loqfaqe 10 085 10 08 10 075 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 iteration Fe 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 iteration 18 VI Example uses of BASE 9 In Section IV we outlined how to use the outputs of BASE 9 Here we provide additional examples from our papers and on going work The first figure of this section taken from DeGennaro et al 2009 shows Hyad
9. OS etc If you do follow this route after installing Xcode you will need to specifically install the command line tools with a window that will look similar to the one below Click on the install button to the right of command line tools and it will appear as follows when done eoo Downloads Po Sop 1D 4 General Behaviors Fonts amp Colors Text Editing Key Bindings Locations Downloads Documentation _ Check for and install updates automatically Check and Install Now Wil iOS 6 0 Simulator 573 4 MB Install Wi iOS 5 1 Simulator 614 5 MB Install Wil iOS 5 0 Simulator 554 1 MB Install Command Line Tools Installed This will install clang and for Xcode 4 6 GCC 4 2 Download gsl from http www gnu org software gsl Use the ftp site to obtain the source code then mac gt cd Downloads mac gt tar xzf gsl 1 15 tar gz mac gt cd gsl 1 15 mac gt configure mac gt make mac gt sudo make install Download cmake from http www cmake org cmake resources software html Choose the dmg version of the code for the correct operating system if you want to let Mac installation guide you through the process We suggest placing the cmake build into usr local bin by choosing that directory when prompted B Installing gcc gsl and cmake on a Linux machine The simplest way to install on Ubuntu is via the apt get tool linux sudo apt get install gcc linux
10. PopMcmc to converge it is helpful to have this parameter set to 1 for stars that are likely to be cluster members and if there are many field stars it is helpful if the bulk of them can be set to 0 at this point 12 C singlePopMcmc The singlePopMcmc module is the workhorse of our software suite This routine along with its many subroutines runs a Markov chain Monte Carlo sampler using a variety of standard Bayesian techniques as well as a few techniques newly developed by us The approach and mathematics are presented by DeGennaro et al 2009 van Dyk et al 2009 and Stein et al 2013 This code was designed to run on photometry formatted in the same manner as the output of scatterCluster It can also be run just as easily on the simulated photometry from simCluster scatterCluster The singlePopMcmc module has a variety of values and options set in the base9 yaml file Under the singlePopMcmc group the stage2IterMax and stage3Iter set the length of the burnin for singlePopMcmc The runIter option lets you choose the number of iterations of the Markov chain Monte Carlo The rule of thumb is that one typically wants 10 000 well sampled points from a Markov chain Monte Carlo in order to draw robust inferences on the posterior distribution At the other extreme the Central Limit Theorem dictates that approximately 30 uncorrelated samples are sufficient for a normal distribution Before running a particular dataset against a specific set
11. are available VI VIM Emacs and nano are pre installed III Installation BASE 9 is written in C and designed to run on a variety of UNIX and Linux based operating systems It is currently tested on MacOS X 10 7 through 10 9 e Ubuntu 10 04 through 12 04 RHEL 5and6 Gentoo 13 0 e FreeBSD 9 and 10 To compile the code you will need gcc 4 7 or clang 3 2 C C language compilers gsl the gnu science library cmake a cross platform build system and Boost a peer reviewed portable C library To install these software packages you may need help from your system administrator though we provide some guidance here The best place to put all of this code is in the usr local bin directory If you don t have that directory on your machine already you can create it as follows gt sudo mkdir usr local gt sudo mkdir usr local bin Note that the sudo command gives you super user or root permission for that one command after you enter your password at the prompt assuming that your account has been allowed to invoke the command A Installing gcc gsl and cmake on a Mac running OS X 10 7 10 9 Download the compiler One way to do that is via downloading Xcode 4 6 or later from http connect apple com This requires that you have a developer account but you can register for that for free Also it will give you 1 GB of code and tools most of which you will only need if you intend to develop for iPhones Mac
12. ass the membership likelihood of those masses the mass and secondary mass ratio outputs from sampleMass and the membership likelihood of those pairs 15 sampleWDMass output files consist of the same number of columns as there are WDs and the same number of rows as there are in the results res file Each item in a row corresponds to the mass of a WD ordered as in the database given the sampled parameters in the results file The membership file shares this format though the values correspond to the likelihood that the given star is a member of a cluster with the given parameters sampleMass output files are similar to sampleWDMass output files but have two columns per star in the database For every 0 indexed star k in the database column 2k corresponds to that star s primary mass and 2k 1 to that star s secondary mass ratio The membership file is identical to that of sampleWDMass though the values correspond to the likelihood that the given unresolved binary is a cluster member sampleWDMass has no configurable parameters sampleMass takes two parameters in the YAML file deltaMass and deltaMassRatio These values are used as starting step sizes for the adaptive MCMC process used to obtain mass and mass ratio We recommended that you change these parameters only if you are manipulating the code for diagnostic purposes E makeCMD The final module of our software suite makeCMD is a small module that calculates a mean fit isoc
13. e Bayesian Analysis of Stellar Evolution Seed 1570065938 Reading models Done Model boundaries are 7 800 10 250 log years Binaries are OFF Running Stage 1 burnin Complete acceptanceRatio 0 090 Running Stage 2 adaptive burnin Acceptance ratio 0 350 Trying for trend Acceptance ratio 0 600 Retrying Acceptance ratio 0 380 Trying for trend Acceptance ratio 0 520 Retrying Acceptance ratio 0 280 Trying for trend Acceptance ratio 0 180 Retrying Acceptance ratio 0 400 Trying for trend Acceptance ratio 0 440 Retrying Acceptance ratio 0 320 Trying for trend Acceptance ratio 0 500 Retrying Acceptance ratio 0 240 Trying for trend Leaving adaptive burnin early with an acceptance ratio of 0 220 iteration 1300 OOo cocococ Starting adaptive run Preliminary acceptanceRatio 0 300 The singlePopMcmc routine creates multiple output files In this case it created rw r r 1 comp staff 57955 Nov 3 17 27 hyades hyades res rw r r 1 comp staff 50317 Nov 3 17 25 hyades hyades res burnin The burnin files provide the sampling patterns during the burnin process and may be useful for diagnostic purposes especially if singlePopMcmc is not sampling well see below The res burnin files look like 14 linux gt head 2 hyades hyades res burnin logAge Y FeH modulus absorption logPost 8 821886 0 280626 0 086646 0 010790 0 011206 174 520334 And the res files have the same format
14. es CMDs with three sets of stellar evolution models placed at their average fit values as determined by a previous version of the code BASE 8 Because these stellar models do not provide good fits to the lower main sequence the following figure shows the derived age from BASE 8 for each of the three input models and for a range of lower main sequence cut offs In this way DeGennaro et al were able to argue that their derived parameters were stable over an appropriate range of data and were able to quantitatively point to where problems emerged in the models 10 12 14 16 1 0 0 5 00 05 1 0 U B 19 log age o Yale Yonsei o DSED Girardi 6 8 10 12 Faintest MS Magnitude This next figure taken from Jeffery E J 2009 Ph D Dissertation University of Texas at Austin compare the age information resident in just the main sequence turn off stars black dashed line compared to that resident in the white dwarfs Data from the main sequence was included in both BASE 8 runs and this provides the primary constraints on metallicity distance and reddening This is useful for studying the information content in the MSTO vs WD regions 0 08 0 06 0 06 0 04 0 04 0 02 0 02 0 0 0 6 z 0 04 P 0 04 0 03 T 0 02 0 02 0 01 0 01 10 10 2 104 106 108 Distance Modulus Figure 5 16 A comparison of MCMC results for cluster parameters of NGC 2360 from fitting the MSTO vs WDs The dashed black
15. following papers Jeffery E J von Hippel T Jefferys W H Winget D E Stein N amp DeGennaro S 2007 New Techniques to Determine Ages of Open Clusters Using White Dwarfs ApJ 658 391 Jeffery E J von Hippel T DeGennaro S Stein N Jefferys W H amp van Dyk D 2011 The White Dwarf Age of NGC 2477 ApJ 730 35 II Skip the install and go to the cloud BASE 9 executables are available as Amazon Elastic Compute Cloud EC2 images Up to date instance IDs are listed in the release descriptions at http github com argiopetech base releases An Amazon Web Services AWS account is required to use these instances To run your code on EC2 1 Log in to your AWS account 2 Navigate to EC2 3 Navigate to the Instances pane 4 Click Launch Instance 5 Choose Community AMIs 6 7 8 9 1 Enter the AMI code for the version of BASE 9 you would like to run Select Review and Launch then Launch Wait for the instance to launch use rsync scp to copy your data to the public IP of the instance 0 Login to your instance with SSH The default user name is ec2 user There is no root password by default BASE 9 executables are in usr local bin should be in the path Current models appropriate for the installed version of BASE 9 are in usr local share base models The instance operating system is the newest release of FreeBSD 10 The tcsh csh sh and bash shells
16. ge in years e g 9 0 for a 1 billion year old cluster This is not a prior but just tells singlePopMcmc where to start searching for a fit We have found that although convergence may depend on starting with a roughly reasonable age the actual posterior age distribution does not depend on what that value is assuming it does converge The msRgbModel lets you choose which set of models to use with your data the filters available in the models must match the filters of your observed or simulated scattered cluster This allows you to derive cluster parameters for a range of models as well as to create simulated clusters under one set of models and use singlePopMcmc to derive the cluster and stellar parameters under another set of models The latter experiments might be useful for instance if you wanted to test the sensitivity of basic cluster or stellar parameters to a given model 13 ingredient With ancillary data for cluster or stellar parameters this might allow you to constrain model ingredients Again we mention that the seed can be set inline with seed when singlePopMcmc is called If singlePopMcmc appears to be unable to converge on reasonable cluster values rerun it with a different initial seed Changing the seed also allows you to start a new MCMC chain if you ran a prior calculation with too few iterations To run singlePopMcmc using a properly prepared input base9 yaml file type the following linux singlePopMcmc verbos
17. he output file is otherwise the same as the input file for scatterCluster In this case only the id mass1 and stage1 values are kept from the output of simCluster The photometry values here UBVRIJHK are derived from the photometry values in the simCluster output file but are different in that they are scattered by adding a Gaussian random deviate with sigma sigU sigB etc This section of the output file is all one needs to plot realistic CMDs for proposals and possibly to prepare for observing projects The scatterCluster output file contains additional information however and is formatted to be ingested by singlePopMcmc so that it can be used to test singlePopMcmc and so that you can test the precision and accuracy that you would expect to recover from real data based on a given set of cluster parameters observational errors and the number of stars available The massRatio column lists the ratio by mass of the secondary to primary stars which in these examples are both 0 since there were no secondaries The CMprior column is set by default in scatterCluster to 0 99 but the file can easily be edited to set a different prior probability that any particular star is a cluster member The final column is just a 0 or 1 switch off or on of whether to use a particular star during the burnin process See DeGennaro et al 2009 and van Dyk et al 2009 for a discussion of what the burnin entails and why it is used To make it easiest for single
18. hours Modifying the IFMR You can do this by editing or adding a few lines of code in ifmr cpp Less than 8 hours Change the IMF You will need to create a subroutine where a random mass value can be drawn from your IMF distribution This currently takes place in drawFromIMF cpp Note that you will also have to normalize the IMF for the Bayesian routine to work properly and that this takes place in densities cpp and is stored in logMassNorm Less than 16 hours Incorporating another set of stellar evolution models see instructions at the top of msRgbEvol cpp and possibly wdCooling cpp and or gBergMag cpp Less than a week Sampling a new variable e g stellar rotation alpha element enhancement This takes place primarily in singlePopMcmc MpiMcmcApplication cpp and base9 densities cpp 22
19. hrone This is helpful for runs that do not converge as well as for situations where the posterior distribution of some key parameter may be multimodal To run makeCMD linux makeCMD Seed 1574116425 Reading models Done Warning F435W is not available in the selected WD Atmosphere model This is non fatal if you aren t using the WD models The output of makeCMD looks like linux head 2 hyades hyades cmd Mass U B V R I J H K F435W F475W F550M F555W F606W F625W F775W F814W 0 150000 16 170454 14 623905 13 035403 11 950929 10 490719 9 196773 8 640356 8 386555 14 666132 13 907510 12 768529 13 128038 12 587469 12 243942 10 744691 10 477001 Because makeCMD uses the values of means under cluster in the base9 yaml one can enter the mean or median values from the singlePopMcmc posterior distributions into the yaml file 16 prior to running makeCMD The output file from makeCMD can then be used to overplot what essentially amounts to the average fit isochrone from among the posterior parameter distributions Note that this is not a best fit isochrone but rather a representative example drawn from that distribution In fact isochrones created from summary statistics such as mean or median parameters may not be truly representative if the distributions are substantially non Gaussian because that simultaneous combination of parameters may fit the data with low probability F Hyades Test We have created a script hyades csh which i
20. it both as a DA and as a DB helium atmosphere We also try two different initial final mass relations from Salaris et al 2009 and Williams Bolte amp Koester 2009 The clouds of points show acceptable fits and the error bars indicate the mean and standard deviation for each of the four cases Clearly these distributions are non Gaussian and publishing just the means and standard deviations could lead readers to misunderstand the results This kind of analysis can also point the way toward future observational work For this star a trigonometric parallax could potentially rule out much of the age range yielding a precise age If this star were a DB a much more accurate trig parallax would be required to meaningfully constrain the age This is not a general statement about WDs but a result for this star with the available photometry griz HK 21 J0003 0111 DA grizJHK 100 T T T co o T distance pc o o T Salaris DA Williams DA 7 Salaris DB Williams DB 40 20 4 age Gyr J0003 0111 DA grizJHK T T W ZAMS mass N I F on o N age Gyr VII Modifying the code to extend its capabilities We continue to upgrade BASE 9 for our on going projects If you wish to add capability to BASE 9 we will be happy to suggest to you how best to go about this and try to estimate the work involved Here is an example list of how involved a variety of tasks are likely to be Less than 2
21. lines are the posterior distributions from fitting the MSTO while the blue dotted lines are from fitting the WDs 20 The next figure also from Jeffery 2009 indicates how one can study the sensitivity of a given result to the observations of an individual star For the open cluster NGC 2360 the posterior age distribution is given by the black line During some iterations however a particular WD is fit as a field star and the remaining WDs yield the posterior age distribution indicated in red During the iterations when this particular WD is included in the fit the posterior age distribution is as indicated in blue The final age posterior distribution is a linear combination of these two distributions based on the fraction of time this particular WD was included in the fit 9 Log Age Figure 5 7 Age distribution of NGC 2360 with and without the inclusion of WD5 The solid black line is the complete age posterior distribution The dotted blue line is the age distribution when WD5 is included as a cluster member The red dashed line is the distribution when WD5 is excluded as a field star This indicates the importance of this star in determining the location of the WD cooling sequence and hence measuring the age via MCMC The next figure shows unpublished work based on applying BASE 8 to an individual WD In this particular case we know that the WD has a hydrogen atmosphere type DA yet for demonstration purposes we analyze
22. n this step by running linux sudo apt get install libboost dev E Installing BASE 9 Once you have all of the above software in place you are ready to install BASE 9 The following instructions should work identically for all platforms Change directories into the BASE 9 source directory and simply run build sh sudo build sh This will if you have properly installed all libraries build and install the BASE 9 executables and install them in the default location generally usr local bin Alternatively if you do not have the ability to run sudo on your machine you may use build local sh to build and install the executables locally The executables will be installed in the BUILD bin directory IV Running BASE 9 In the following subsections we describe how to run stand alone portions of the BASE 9 modules from the command line There are various reasons why you might want to run one or another of these or some but not all so we detail how to run each one As of BASE 9 2 0 all settings have been moved into a YAML format configuration file A sample configuration file with reasonable initial settings can be found in the base 9 4 2 conf directory under the name base9 yaml A sample cshell script can be found at scripts hyades csh Individual settings can be changed on a run by run basis via the command line options Run any of the BASE 9 applications with the command line flag help to view a description of available
23. nn nns a tasa tasas se ssa ta tna nnn 17 V Diagnostics of run quality icuanreninks iin saarkia nda kel Cl kv a dude eS d UD dd aud 18 VI Example uses of BASE O 15 ereinenianiniic nbn rdc nao ecc ce n ni EO Dni 19 VII Modifying the code to extend its capabilities eee 22 I Introduction Bayesian Analysis for Stellar Evolution with Nine Parameters BASE 9 is a Bayesian software suite that recovers star cluster and stellar parameters from photometry BASE 9 is useful for analyzing single age single metallicity star clusters binaries or single stars and for simulating such systems This document assumes you are working with base 9 4 3 We will endeavor to update this manual as we update the code or as libraries or operating systems meaningfully change BASE 9 uses a Markov chain Monte Carlo MCMC technique along with brute force numerical integration to estimate the posterior probability distribution for up to six cluster and three stellar properties The cluster properties are age metallicity helium abundance distance modulus line of sight absorption and parameters of the initial final mass relation IFMR The stellar properties are primary mass secondary mass if a binary and cluster membership probability The MCMC technique is used for the cluster quantities and numerical integration is used for the stellar quantities BASE 9 is freely available source code that you may use as is or modify for your
24. ompanion if applicable The 20 column lists the stage of stellar evolution for that particular star 1 MS or RG 3 WD gt 3 for evolved stars above the WD mass limit The final two columns are the cluster membership prior which is essentially 1 for simulated stars and the flag 0 or 1 whether to use the star during the burn in stage With these final columns the output file is formatted for input into scatterCluster You should be able to plot reasonable looking CMDs isochrones from this file for a wide range of cluster parameters stellar models and filters B scatterCluster The scatterCluster module adds Gaussian random errors to the photometry output created by simCluster To specify the appropriate amount of error to add for your particular simulation adjust the virtual exposure time in the base9 yaml file We use exposure times of 1 hour in each filter to generate a scattered cluster with the above file The algorithm for adding noise to the cluster photometry is rudimentary and only meant for simple purposes such as preparing for an observing proposal or for creating test files for the Markov chain Monte Carlos singlePopMcmc routine The algorithm is an approximation to the results one would obtain in one hour with the KPNO 4m Mosaic UBVRI or Flamingos JHK assuming dark time seeing 1 1 arcsec airmass 1 2 Signal to noise for the Spitzer bands if included are naively set to be the same as for the K band For departures
25. on models of Dotter A Chaboyer B Jevremovic D Kostov V Baron E amp Ferguson J W 2008 The Dartmouth Stellar Evolution Database ApJS 178 89 3 Girardi L Bressan A Bertelli G amp Chiosi C 2000 Evolutionary tracks and isochrones for low and intermediate mass stars From 0 15 to 7 Msun and from Z 0 0004 to 0 03 A amp AS 141 371 Yi S Demarque P Kim Y C Lee Y W Ree C H Lejeune T amp Barnes S 2001 Toward Better Age Estimates for Stellar Populations The Y2 Isochrones for Solar Mixture ApJS 136 417 the white dwarf atmosphere models of Bergeron P Wesemael F amp Beauchamp A 1995 Photometric Calibration of Hydrogen and Helium Rich White Dwarf Models PASP 107 1047 as updated and made available at http www astro umontreal ca bergeron CoolingModels the white dwarf interior models of Althaus L G amp Benvenuto O G 1998 Evolution of DA white dwarfs in the context of a new theory of convection MNRAS 296 206 Montgomery M H Klumpe E W Winget D E amp Wood M A 1999 Evolutionary Calculations of Phase Separation in Crystallizing White Dwarf Stars ApJ 525 482 The paper describes the stellar evolution code that M Montgomery used in 2012 to calculate the WD sequences specifically for use with BASE 9 Renedo I Althaus L G Miller Bertolami M M Romero A D Corsico A H Rohrmann R D amp Garcia Berro E 2010 New C
26. ooling Sequences for Old White Dwarfs ApJ 717 183 Wood M A 1992 Constraints on the age and evolution of the Galaxy from the white dwarf luminosity function ApJ 386 539 the Initial Mass Function of Miller G E amp Scalo J M 1979 The initial mass function and stellar birthrate in the solar neighborhood ApJS 41 513 and the Initial Final Mass Relations of Salaris Salaris Maurizio Serenelli Aldo Weiss Achim Miller Bertolami Marcelo 2009 Semi empirical White Dwarf Initial Final Mass Relationships A Thorough Analysis of Systematic Uncertainties Due to Stellar Evolution Models ApJ 692 1013 Weidemann V 2000 Revision of the initial to final mass relation A amp A 363 647 Williams K A Bolte M amp Koester D 2009 Probing the Lower Mass Limit for Supernova Progenitors and the High Mass End of the Initial Final Mass Relation from White Dwarfs in the Open Cluster M35 NGC 2168 ApJ 693 355 or a fitted IFMR parameterized as lines broken lines or low order polynomials as described by Stein N M van Dyk D A von Hippel T DeGennaro S Jeffery E J amp Jefferys W H 2013 Combining Computer Models in a Principled Bayesian Analysis From Normal Stars to White Dwarf Cinders Statistical Analysis and Data Mining 6 34 For a further discussion of what BASE 9 and its precursor BASE 8 has been used for to date and some indications of how it might be useful in your research see also the
27. s set up to run on a Hyades data set Hyades UBV testphot It is a cshell script If you have problems with this script you may be using a shell other than the cshell or tshell e g the Bourne shell You can invoke the cshell as follows Bourne shell gt csh New prompt indicating you are now running csh gt hyades csh This will allow you to test your code installation and plot results then compare to the DeGennaro et al results Note that you will not obtain an exact correspondence to the results of DeGennaro et al because we have updated the Hyades data set since that publication Because of the relative depth of the Hyades which is significant compared to its distance we have now corrected the cluster stars to lie at the mean cluster distance using individual proper motions from Hipparcos and the cluster converging point method Because of the way we have corrected distances this data set is converted to absolute magnitude space we otherwise always use apparent magnitudes and for this one test case you will find a distance modulus of approximately 0 0 G How long does all of this take In our tests it took 147 minutes to run hyades csh which in turn ran s inglePopMcmc for 152 Hyades stars in three photometric bands for 10 000 iterations on a early 2011 Macbook Pro 2 3 GHz Intel with 8 GB RAM laptop computer Increasing the number of filters or number of stars will increase the computation time linearly Increasing the number of M
28. settings The following examples assume you have installed the BASE 9 executables in a directory that is in your PATH e g usr local bin If this is not the case you may need to use absolute pathnames e g home me base 9 4 2 BUILD bin singlePopMcmc A simCluster The first tool that you are likely to use within BASE 9 is simCluster This module simulates a stellar cluster for a particular set of models see references in the Introduction and user specified values of various cluster parameters that have been set in the base9 yaml file the base 10 log of the cluster age metallicity the helium mass fraction only for some Dotter et al models the distance modulus absorption in the V band the percent of cluster stars that are binaries the upper mass limit for creating a white dwarf WD and the fraction of WDs that have helium atmospheres DBs We recommend leaving these last two parameters at 8 solar masses and 0 as we have not yet fully implemented and tested them An additional parameter the seed to the random number generator is necessary as the mass of each star is determined by randomly drawing from the IMF This allows you to specify multiple clusters with the same parameters but different random seeds if you wish to test the effects of for instance cluster size on the number of WDs or the clarity of the main sequence turn off MSTO This seed can be set via the seed option in the command line To run simCluster simply t
29. ype its name linux simCluster Seed 1559729633 Reading models Done Properties for cluster logClusAge 8 796 Fe H 0 07 Y 0 29 modulus 0 00 Av 0 01 WDMassUp 8 0 fractionBinary 0 00 Totals nSystems 100 nStars 100 nMSRG 98 nwWD SQ nNSBH 0 massTotal 62 72 MSRGMassTotal 55 10 wdMassTotal 1 66 The above output is diagnostic and reiterates the settings in the base9 yaml file The stored output of simCluster is placed in a filename specified by the user with the outputFileBase 10 option in the base9 yaml file The file contents from the output of simCluster should look like the following linux gt head 2 hyades sim out id U B V R I J H K sigU sigB sigV sigR sigIl sigJ sigH sigK massi massRatio stage Cmprior useDBI 1 3 061 3 031 2 694 2 501 2 320 2 127 1 983 1 965 0 000 0 000 20 000 0 000 0 000 20 000 20 000 0 000 1 555 0 000 1 9 999 1 There are more columns than can be presented cleanly on a page but hopefully this is clear enough The first column lists identification numbers for each star system single star or binary This is meant to be useful in tracking down particular stars The next eight columns list the U through K band magnitudes or ugriz through K of the primary star Columns 10 through 17 give the photometric uncertainties for each filter entry for a simulated cluster these are zero The 18 and 19 columns give the mass of the primary star and the mass of its c
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