Impact of missing data on the construction of LISA time-delay-interferometry Michelson variables

We investigate the impact of missing input data on the construction of second-generation time-delay-interferometry (TDI) variables, which enable data analysis for the Laser Interferometer Space Antenna (LISA). TDI relies on the introduction of precise time delays into the raw interferometric data streams before they are combined to suppress otherwise dominant laser phase noise. We show that a single missing sample, corresponding to 0.25 s of data, will result in an effective data gap of approximately 90 s in the second-generation TDI output if further measures are not taken. This additional gap is largely independent of the initial gap duration, but it increases linearly with the order of the fractional-delay filter used for the computations. For a realistic gap scenario, incorporating both planned and unplanned data interruptions consistent with a target duty cycle of approximately <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mn>84</a:mn> <a:mi mathvariant="normal">%</a:mi> </a:math> , we find that frequent, short-duration gaps (e.g., a total of 1000 per year, each of which has a duration of approximately <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mn>100</d:mn> </d:math> s) could result in an additional loss in the TDI variables of about one day per year, corresponding to a reduction of approximately <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:mn>0.3</f:mn> <f:mi mathvariant="normal">%</f:mi> </f:math> in duty cycle. This amounts to a loss of approximately one day of LISA data suitable for the global fit per year.