Welcome to the Eclipsing Time Variation Calculator.
These are the instructions to use this tool based on the Applegate Mechanism.
Source Parameters
Once you get here you will be prompted with an initial form to enter the necessary values to perform such calculations. You can either input your own parameters or select one of the test sources provided in the section
Test Sources.
We encourage you to test this first using one of the sources in the list, check the default parameters and then proceed along with yours.
As you will notice, there are two default values already assigned for the k_{1} and k_{2} parameters which are provided by the theory authors (see Theory section). These values are computed assuming ratios λ=ρ_{shell}/ ρ_{core} and ξ=R_{star}/ R_{core} with radii and densities in the same but arbitrary units. You can change these numbers according to your preferences, and also can use the tool provided in the main page to compute them using your own data.
Calculating k_{1} and k_{2} parameters
The k_{1,2} numbers comes from mathematical convenience at the time of obtaining the final formula for evaluating the minimum energy required for the secondary star in a close binary system to trigger the Applegate Mechanism.
These parameters are actually functions of the λ and ξ ratios (k_{1,2}(λ,ξ) = k_{1,2}(R_{star},R_{core},ρ_{shell},ρ_{core})) assuming the two-zone model for the density distribution inside the secondary (magnetically active one) star. This way, in order to evaluate your own k_{1,2} functions you must know the expected proportions (or the actual values) of the inner and outer densities and radii.
As a test, the default ratios given in the Theory section are λ=0.96/100 ξ=4/3. You can use them and test this tool obtaining roughly the default values.
Once those values are obtained, you must close such window and proceed by the regular way using your new numbers.
Understanding Results
Once you have entered all the required and clicked in the button Calculate Energy Required for Applegate Mechanism then three results will be given, listing the one obtained through the equation proposed by Tian et al. (2009) considering the core and the shell of the secondary star rotating as rigid bodies, the one obtained by Voelschow et al. (2016) considering a constant density profile and the one obtained by the same author but this time considering a two-zone model for the density distribution, respectively.
It is also possible, in the introduced two-zone model, to fall into a critical condition in which no real-valued results are generated as solution, in this case, a message is displayed indicating such situation: "Imaginary Value. No physical solution exists".
You will also find there a button to go back and perform a new calculation, and a message indicating the time it took to evaluate the solution for these three models.
Please contact us in case of any doubt, problem or suggestion, we will be pleased to solve it. The contact information is found at the header and the Contact section also.