AC18
Stellar Activity and Radial Velocity
A missing patch of light can move a spectral line. Follow that mechanism into orbital inference, then compare activity and planet posteriors on an actual HARPS campaign.
L1
A star can fake a wobble
A rotating dark patch can shift a stellar absorption line. Follow the missing light before deciding that a repeating velocity means a planet.
L2
The speed hidden in a line
Derive Doppler velocity, orbital semi-amplitude and minimum mass, then see exactly where inclination and stellar mass enter the inference.
L2
Follow a spot’s missing light
Derive a rotating surface’s flux, line centroid and photocenter from one set of light weights, including a worked missing-patch example.
L3
A posterior for two explanations
Build a joint Gaussian-process model for velocity and activity, derive its derivative covariance and retain uncertainty when orbit and activity compete.
L3
Replay the HARPS campaign
Refit all 71 published CoRoT-7 HARPS observations with Kepler, activity and joint posteriors, retaining source units, weights and failure diagnostics.
L4
Earth-mass signals and active stars
Read pinned primary papers on joint activity inference, a sampling ghost and GJ 1002, following covariance, instrument offsets and posterior assumptions.
Sources and calculation scope
- Dumusque, Boisse & Santos — SOAP 2.0, arXiv:1409.3594v1
11 September 2014 version. Sections 2.1–2.3, Equations 1–7 and Figure 1: surface-profile integration, flux contrast and convective blueshift. Our identical Gaussian local profiles are a simpler independent mechanism model.
- Haywood et al. — CoRoT-7, arXiv:1407.1044v1
3 July 2014 version. Sections 2–3 and 4.2, Equations 1–12 and Table A1. All 71 HARPS2012 numerical rows are retained; the tutorial does not reproduce the full contemporaneous-photometry analysis.
- Rajpaul et al. — joint activity processes, arXiv:1506.07304v1
24 June 2015 version. Sections 3.1–3.4 and 4.1–4.2, Figures 3–4, Appendix A.2. Derivative covariance signs follow a lag equal to first time minus second time; kernel-width normalizations must be kept with their equations.
- Rajpaul, Aigrain & Roberts — Ghost in the time series, arXiv:1510.05598v1
20 October 2015 version. Sections 2–3 and Figures 1–3: sampling-window and synthetic-content tests. The Alpha Centauri B analysis is a source guide, not our reproduced dataset.
- Suárez Mascareño et al. — GJ 1002, arXiv:2212.07332v2
25 January 2023 arXiv version; manuscript dated 26 January. Sections 2.1–2.2 and 4.1–4.4, Table 2, Table B.1, Figures 9–10. Multiple instrument states and minimum-mass interpretation are reading targets; no original figures are republished.
- IAU 2015 Resolution B3 — nominal conversion constants
Official adopted table: nominal solar and terrestrial gravitational parameters and nominal solar radius are exact conversion constants, not uncertainty-free measurements of the real Sun and Earth.
- Rasmussen & Williams — Gaussian Processes for Machine Learning, Chapter 2
Authors’ 2006 Chapter 2, Sections 2.1–2.2 and 2.7: Gaussian conditioning, normalized marginal densities and linear basis functions. The importance sampler and surface quadrature are independently authored here.
- GJ 1002 — published A&A 670, A5 (2023)
Publisher version and DOI 10.1051/0004-6361/202244991 confirm publication status. Its older abstract retains a 20.202-day typo; the pinned arXiv v2 and parameter tables give 21.202 days. The guide reads the corrected author manuscript and preserves this version distinction.