A Linearized Approach to Radial-Velocity Extraction. II: Shot-Noise-Limited Precision via Spectral Factorization
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911447269769216 |
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| author | Shahaf, Sahar Zackay, Barak |
| author_facet | Shahaf, Sahar Zackay, Barak |
| contents | We generalize the short-time Fourier transform (STFT) formalism for radial velocity extraction to cases where the underlying spectral components are unknown. The method factorizes a spectroscopic time series into principal spectra and time-dependent kernels, enabling simultaneous recovery of both. In Fourier space, each inverse-wavelength slice is decomposed by singular value decomposition, and radial velocity shifts are inferred from phase differences between epochs. In the high-SNR regime, this provides a linearized and statistically tractable estimate of differential velocities. The method is validated on synthetic and SOAP simulations and applied to EXPRES observations of HD 34411 and $τ$ Ceti, recovering coherent signals and reaching the instrumental precision limit of ~30 cm/s. Apart from p-mode modulation, the residuals show no significant long-term correlations and allow the detection of signals with semi-amplitudes down to ~50 cm/s with $\lesssim10$ cm/s uncertainty. The framework thus enables extreme-precision radial velocity measurements in the presence of spectral variability, representing a step toward detecting and characterizing Earth-like planets around solar-type stars. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_23040 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Linearized Approach to Radial-Velocity Extraction. II: Shot-Noise-Limited Precision via Spectral Factorization Shahaf, Sahar Zackay, Barak Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics We generalize the short-time Fourier transform (STFT) formalism for radial velocity extraction to cases where the underlying spectral components are unknown. The method factorizes a spectroscopic time series into principal spectra and time-dependent kernels, enabling simultaneous recovery of both. In Fourier space, each inverse-wavelength slice is decomposed by singular value decomposition, and radial velocity shifts are inferred from phase differences between epochs. In the high-SNR regime, this provides a linearized and statistically tractable estimate of differential velocities. The method is validated on synthetic and SOAP simulations and applied to EXPRES observations of HD 34411 and $τ$ Ceti, recovering coherent signals and reaching the instrumental precision limit of ~30 cm/s. Apart from p-mode modulation, the residuals show no significant long-term correlations and allow the detection of signals with semi-amplitudes down to ~50 cm/s with $\lesssim10$ cm/s uncertainty. The framework thus enables extreme-precision radial velocity measurements in the presence of spectral variability, representing a step toward detecting and characterizing Earth-like planets around solar-type stars. |
| title | A Linearized Approach to Radial-Velocity Extraction. II: Shot-Noise-Limited Precision via Spectral Factorization |
| topic | Earth and Planetary Astrophysics Instrumentation and Methods for Astrophysics |
| url | https://arxiv.org/abs/2512.23040 |