LISA spacecraft maneuver design to estimate tilt-to-length noise during gravitational wave events

The Laser Interferometer Space Antenna (LISA) mission aims to observe gravitational waves featuring a three-spacecraft interferometer constellation with an arm length of 2.5 Mio km. In support of maximizing LISA’s scientific return, the paper presents the design of coordinated spacecraft constellation maneuvers tailored for high-precision estimation of tilt-to-length (TTL) coupling noise under the influence of gravitational wave events. Tilt-to-length coupling couples the angular jitter of the three LISA spacecraft and their optomechanical assemblies to longitudinal measurement noise of the interferometers. The effect is a fundamental limitation of LISA’s sensitivity and spaceborne long-arm interferometers, in general. The limitation can be avoided by estimating tilt-to-length coupling noise and correcting the scientific measurements. Former research allows limited conclusions to be drawn about the feasibility of accurate tilt-to-length coupling estimation because only the effect of system-internal noise sources has been addressed. Since tilt-to-length coupling noise in LISA is estimated and corrected based on science instrument measurements, the calibration shall be robust against the disturbing impact of gravitational wave events. The paper quantifies the deterioration of tilt-to-length parameter observabilities in the view of stellar and galactic events without maneuver execution. Then the developed maneuver design method is shown to provide accurate estimation results in the more realistic scenario. Although the approach temporarily reduces the number of independent scientific signals, the scientific operation mode of the spacecraft constellation can be maintained.

Figure 1

Illustration of the LISA Constellation.

Figure 2

TTL-induced path length change.

Figure 3

Schematic sequence of TTL noise correction through TDI separation.

Figure 4

Determination of the maximum maneuver relation error ($L=2.5\mathrm{Mio}\mathrm{km}$).

Figure 5

Closed-loop system ($y={\mathrm{\Theta }}_i$, $H_i$, ${\mathrm{\Phi }}_i$, ${\delta }_{ij}$).

Figure 6

LSD of Eq. (9) ($C_{\mathrm{RX},13,\eta }=C_{\mathrm{TX},13,\eta }=C$, ${\lambda }_{13}={\lambda }_{31}=\lambda$, $L=2.5\mathrm{Mio}\mathrm{km}$).

Figure 7

Filter composition for test signal design and generation of TTL contribution in diagnostic TDI variables.

Figure 8

Frequency behavior of the filter composition.

Figure 9

$K_2$-normalized LSD of $d_{{\mathrm{\Theta }}_2}$ and ${\mathrm{\Theta }}_2$.

Figure 10

Thruster demand and maneuver strength.

Figure 11

Allowable plant error.

Figure 12

Sources of gravitational waves for the spaceborne detectors LISA and eLISA [24], © 2015 Cambridge University Press [27].

Figure 13

Estimation performance without TDI separation and maneuver execution.

Figure 14

Tolerable gravitational wave strength for precise TTL factor estimation with TDI separation.