What the LISA Calculator does:

The LISA Calculator models gravitational waves emitted by circular binary systems, as well as the motion and resonse¹ of LISA. Using a Fisher Information Matrix approach² the uncertainties of the various binary parameters are determined. The motion of LISA in the Calculator uses the adiabatic approximation³. The LISA transfer functions are included, so the approximation is valid to 500 mHz.

The Calculator covers three regimes of circular binary behavior: monochromatic, mildly chirping, full chirp. In the monochromatic regime the parameter uncertainties that will be reported are: polar location (&theta), azimuthal location (&phi), frequency, amplitude, inclination (&iota), polarization (&psi), initial orbital phase (&phi_o). The mildly chirping regime includes all the angular parameters of the monochromatic regime, but the three variables time to coalescence (t_c), luminosity distance (D_l), and chirp mass (M_c) have replaced the two variables frequency and amplitude. The full chirp regime reports all the parameters of the mildy chirping regime, plus the reduced mass (&mu). The Calculator will determine from the input parameters which of the three regimes the binary system is in, and display its respective parameter uncertainties.

What the LISA Calculator does not do:

The 2PN assumptions used in the code for the LISA Calculator does not allow for highly relativistic orbits. The Calculator will warn the user if the input binary enters such a regime, and will either take no data (if the input binary starts in the highly relativistic regime) or take data only up until the binary is passing into that regime (the user is given a warning that this occurred, along with the actual time of observation the Calculator used).

As the gravitational waves are modeled for circular binaries, eccentric orbits are not included in the analysis.

Also, the spin effects of the binary constituents are not included in the analysis.

Updates:

LISA Calculator 1.1.01:

   - The distance range for the LISA Calculator has been extended to z = 100.

LISA Calculator 1.1:

   - The LISA Calculator has been switched over to one-sided noise. This will change the SNR and uncertainty values by a factor of sqrt(2).

   - A bug was corrected that slightly affected sky (solid) angle uncertainty.

LISA Calculator 1.0:

   - The LISA Calculator has been switched over to A and E time-delay interferometry variables⁴. The T channel is not being used due to numerical instabilities below the transfer frequency of the detector.

   - A bug was corrected that affected noise levels of non-standard LISA configurations.

   - Values for azimuthal location (&phi), polarization (&psi), and initial orbital phase (&phi_o) are no longer limited to the range [0°, 360°].

   - Values for polar location and inclination are still limited to the ranges [-90°,90°] and [0°, 180°], respectively. If the values entered are not in these ranges they will be transformed into the corresponding value in the ranges.

   - If the uncertainty of a parameter is greater than the possible range of the parameter (e.g. an uncertainty in &phi of 3&pi), that parameter is listed at "Undeterminable" and is removed from the analysis.

Thanks to all the beta testers whose suggestions were such a great help. Thanks especially to Shane Larson for his repeated attempts to break the LISA Calculator and telling us all about them.