Sensitivity Studies: A How to with r-Java 2.0

Modifying Data

There's two ways to change the data in the program: directly modifying the data in the tables or by importing modified data tables. The method you choose is going to be based on how many values you want to change and how convenient that is. For simple changes of one or two properties it is easiest to just directly change that in the data table itself. All you have to do is double click on the cell and modify the value (then hit enter). In my experience, this is most useful for changing things like masses or beta-decay rates of one or two isotopes. The second and more flexible method is to export the data then manipulate the data with a spreadsheet program or script. This allows for changing several variables simultaneously or performing more complicated changes. The data comes in three sets of tables which can be imported and exported from the data panel in the program. 


For example, if you wanted to see the effect of increasing the neutron capture cross section of isotope X, you would have to modify the cross sections of X and (according to detailed balance) change the photo-dissociation rates of isotope Y (for the reaction X + n -> Y). In order to accomplish this, it is easiest to export the data table, open it in a spreadsheet and the multiply all the neutron capture cross sections by your chosen amount and then multiply all the photo-dissociation rates by the corresponding inverse factor. Since these are temperature dependent rates, all of the temperature cross-section interpolation points need to be multiplied.


Another example change could be if you wanted to investigate the effect of beta-decay rates in a region of the chart of nuclides. Perhaps there is evidence for much faster beta-decay rates for isotopes below the N=82,Z=50 closed shell and you would like to investigate a factor of 10 increase to these rates. This can be done by either manually modifying the rates in the table or with a short script which modifies the exported nuclear data table.

If you have access to other nuclear datasets and want to investigate the effect of different mass models, the datasets can be replaced in the program. The input format is the same as the exported data files which is explained further in comments of the exported data. Any new sets of data can be imported by importing data files which conform to the import/export format of the r-Java program. If you are going to do this; however, you must import the nuclear data table first before the nuclear and neutron capture data. 

Analyzing the Data


Assessing the sensitivity of the generated data is somewhat of a difficult problem. The easiest way of comparing two r-process simulations is by graphically comparing their abundance pattern (as a function of mass number, Y vs. A). Simulations that reproduce the characteristic r-process peaks are usually the goal of r-process simulation, but if we want a quantitative analysis of how certain underlying nuclear processes affect the r-process then we need a quantitative metric. Without any automated tools built into the current released version of the code, the type of data analysis is limited to what can be accomplished from final isotopic distributions and the types of statistics you can perform to compare them.


In the works of Mumpower and Surman (for example, Mumpower et. al. 2012) they use the sum of the relative or absolute differences as an indication of sensitivity. For the types of changes (changing one cross section at a time) they performed that is a reasonable value because the overall distribution does not change drastically. In our example, the distributions are orders of magnitude different for some data points and the overall distribution has a different shape. When comparing these datasets there is an issue of scaling the two distributions if we want to compare the sum of differences. If we compare only the isotopes in the mass range 120<A<210 then we get sensitivity factors of 63 and 40 for the "Times 0.1" and "Times 10" respectively (if we add the relative differences). This indicates that the r-process is more sensitive to neutron capture rate decreases than increases (when they are global increases/decreases). Since the abundances are arbitrarily scalable; however, we should see how that affects our results. For our three relatively different distributions this turns out to have a significant impact on our results. If we scale all the datasets to (A=195, Y=1.0)we get the opposite results: we get sensitivity factors of 56 and 283 which gives the opposite conclusion. So this presents a challenge for comparing these datasets using a simple sum or differences approach.


As we move forward in development of the new version of the code (SiRop) we intend to include utilities to assist in these types of calculations. In order to include the best and most relevant statistics we need some help from potential users of the code to help identify what we should be including and coding up for the newest and future versions of our r-process code. The type of data and statistical calculations required to assess nuclear sensitivity is still an open question in r-process simulations and we would input to help us build a better application which can best serve the users of our code.