---
title: "Stellar Activity and Radial Velocity"
description: "Follow a rotating active region, derive Doppler velocities, fit real HARPS observations and read the assumptions behind an orbital signal."
canonical_url: "https://sandboxphysics.com/stories/rv-activity/"
language: "en"
page_type: "story"
alternate_languages:
  zh-CN: "https://sandboxphysics.com/zh/stories/rv-activity/"
last_modified: "2026-10-28"
---

AC18

# Stellar Activity and Radial Velocity

Sandbox Physics · 2026-10-28

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.

1. L1

   ## [A star can fake a wobble](https://sandboxphysics.com/stories/rv-activity/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.

2. L2

   ## [The speed hidden in a line](https://sandboxphysics.com/stories/rv-activity/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.

3. L2

   ## [Follow a spot’s missing light](https://sandboxphysics.com/stories/rv-activity/a-spots-missing-light/)

   Derive a rotating surface’s flux, line centroid and photocenter from one set of light weights, including a worked missing-patch example.

4. L3

   ## [A posterior for two explanations](https://sandboxphysics.com/stories/rv-activity/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.

5. L3

   ## [Replay the HARPS campaign](https://sandboxphysics.com/stories/rv-activity/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.

6. L4

   ## [Earth-mass signals and active stars](https://sandboxphysics.com/stories/rv-activity/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.

[Move an active region](https://sandboxphysics.com/labs/binary-star-mass/)

## Sources and calculation scope

1. [Dumusque, Boisse & Santos — SOAP 2.0, arXiv:1409.3594v1](https://arxiv.org/pdf/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.

2. [Haywood et al. — CoRoT-7, arXiv:1407.1044v1](https://arxiv.org/pdf/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.

3. [Rajpaul et al. — joint activity processes, arXiv:1506.07304v1](https://arxiv.org/html/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.

4. [Rajpaul, Aigrain & Roberts — Ghost in the time series, arXiv:1510.05598v1](https://arxiv.org/pdf/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.

5. [Suárez Mascareño et al. — GJ 1002, arXiv:2212.07332v2](https://arxiv.org/pdf/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.

6. [IAU 2015 Resolution B3 — nominal conversion constants](https://www.iau.org/common/Uploaded%20files/IAUGA2015-Resolution-B3-recommended-nominal-conversion.pdf)

   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.

7. [Rasmussen & Williams — Gaussian Processes for Machine Learning, Chapter 2](https://gaussianprocess.org/gpml/chapters/RW2.pdf)

   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.

8. [GJ 1002 — published A&A 670, A5 (2023)](https://www.aanda.org/articles/aa/pdf/2023/02/aa44991-22.pdf)

   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.