Anisotropic overlap reduction functions for arbitrary equal-arm TDI channels: A fully analytic framework and efficient evaluation
Abstract
We establish a unified analytic framework for anisotropic overlap reduction functions (ORFs) of arbitrary finite-delay time-delay interferometry (TDI) channels in a static, reciprocal, equal-arm equilateral constellation. The construction combines the polynomial constraints for laser-noise cancellation, constellation symmetries, and directional-projection integration. A free basis of the admissible channel module separates channel generation from angular integration; two families of elementary angular kernels then generate all channel-pair intensity ORFs. The channel algebra is independent of gravitational-wave polarization, and the intensity-kernel reduction applies to tensor, vector, breathing, and longitudinal sectors. Tensor multipoles illustrate the framework here. Complete propagation effects are retained at arbitrary fixed finite angular order, with explicit examples through ℓ=5. Prepared frequency batches, shared multiprecision expressions, and local expansions at removable delay points provide stable evaluation. In the prepared-batch benchmark, the analytic implementation is approximately 50 to 5000 times faster than optimized sky quadrature at matched error tolerances. Independent multiprecision sky integrations also validate prescribed mixed error targets down to 10−100 in the tested cases. The resulting kernels and generation rules supply reusable inputs for anisotropic multichannel background models.
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BibTeX
@misc{zhou2026anisotropic,
title = {{Anisotropic overlap reduction functions for arbitrary equal-arm TDI channels: A fully analytic framework and efficient evaluation}},
author = {Kun Zhou and Jin Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40548},
eprint = {2610.40548},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40548},
}
RIS
TY - UNPB
TI - Anisotropic overlap reduction functions for arbitrary equal-arm TDI channels: A fully analytic framework and efficient evaluation
AU - Kun Zhou
AU - Jin Li
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40548
UR - https://arxiv.org/abs/2610.40548
AB - We establish a unified analytic framework for anisotropic overlap reduction functions (ORFs) of arbitrary finite-delay time-delay interferometry (TDI) channels in a static, reciprocal, equal-arm equilateral constellation. The construction combines the polynomial constraints for laser-noise cancellation, constellation symmetries, and directional-projection integration. A free basis of the admissible channel module separates channel generation from angular integration; two families of elementary angular kernels then generate all channel-pair intensity ORFs. The channel algebra is independent of gravitational-wave polarization, and the intensity-kernel reduction applies to tensor, vector, breathing, and longitudinal sectors. Tensor multipoles illustrate the framework here. Complete propagation effects are retained at arbitrary fixed finite angular order, with explicit examples through ℓ=5. Prepared frequency batches, shared multiprecision expressions, and local expansions at removable delay points provide stable evaluation. In the prepared-batch benchmark, the analytic implementation is approximately 50 to 5000 times faster than optimized sky quadrature at matched error tolerances. Independent multiprecision sky integrations also validate prescribed mixed error targets down to 10^−100 in the tested cases. The resulting kernels and generation rules supply reusable inputs for anisotropic multichannel background models.
ER -