About the CLHT Detectability Calculator:

This observer tool aims at answering the question "Can LISA Hear This?" and is developed to provide a simple Signal-to-Noise-Ratio (SNR) calculator for the LISA mission. It takes as input gravitational-wave source parameters like masses, distance, orbital period, and gives as outputs:

• LISA's response and its sensitivity curve
• an estimate of the total SNR of the source
• a plot of the cumulated SNR as a function of time
• an estimate of source parameter uncertainties (under development, not yet implemented).

CLHT is based on pieces of software written in Python and developed in the framework of the LISA Data Challenge. It uses two fundamental blocks:

• 1. Waveform generators that compute LISA's response to a given gravitational-wave source expressed in the frequency domain. For example, galactic binary waveforms are generated using the FastGB code developed by Cornish & Littenberg, and the massive black hole binary waveforms are generated with a Fourier-domain inspiral-merger-ringdown code developed by Marsat & Baker.
• 2. A sensitivity model calculator computing the power spectral density of LISA's noise, as described in the LISA Science Requirement Document.

These two blocks allow the user to plot the frequency-domain response to a given source along with the instrument sensitivity, as it will be measured by LISA through the time-delay interferometry channels. As a result, the output values are not sky-averaged, and reflect the exact parameters of the source, assuming an arbitrary starting orbital phase for the constellation and for the source.

How do I use the CLHT tool?

In order to perform a calculation, the user must specify the following:

• 1. The gravitational-wave source parameters. This can be done by using the "Parameter suggestions" scroll-down menu. One can either:
  • select a typical pre-defined source like "stellar-origin binary" or "massive black hole binary" or
  • choose "User-specified values", where 5 custom parameters can be filled-in. Note that only binary sources are considered.

  The parameters that can be tuned are:

  • 1) & 2) the masses of the two orbiting objects in the source frame
  • 3) their luminosity distance in megaparsecs (or equivalently, their redshift)
  • 4) their orbital period in seconds (or equivalently, their orbital separation)
  • 5) the observation time in years (time during which the source is observed by LISA).
• 2. The sky-localization and the orientation of the source with respect to LISA. 4 parameters can be tuned:
  • 1) the inclination angle of the source orbital plane (degrees)
  • 2) the polarization angle of the gravitational wave (degrees)
  • 3 & 4) sky location, for which 3 choices are possible:
    • User-specified: the values of the ecliptic longitude and latitude in degrees (must be filled-in by the user).
    • Favorable: this mode preselects a combination of latitude and longitude that is optimal in terms of SNR.
    • Unfavorable: this mode preselects a combination of latitude and longitude that is unfavorable in terms of SNR.

These last two modes are crude approximations where the direction of propagation of the gravitational wave is chosen approximately perpendicular to (in the favorable case) or within (in the unfavorable case) the plane defined by the constellation triangle. In the case of massive black hole binaries, the sky location is chosen so that the favorable or unfavorable configuration happens at the time of merger.

What does the CLHT tool generate?

The outputs of the tool are 3-fold:

• 1. A plot of LISA's TDI response to the gravitational wave emitted by the source as a function of frequency, along with the TDI noise sensitivity. Both signal and noise are averaged over the 3 quasi-orthogonal TDI channels A, E, T;
• 2. The value of the total SNR of the source cumulated over the entire observation time;
• 3. A plot of the cumulated SNR as a function of time.