--- title: "A star can fake a wobble" description: "A rotating dark patch can shift a stellar absorption line. Follow the missing light before deciding that a repeating velocity means a planet." canonical_url: "https://sandboxphysics.com/stories/rv-activity/a-star-can-fake-a-wobble/" language: "en" page_type: "story" alternate_languages: zh-CN: "https://sandboxphysics.com/zh/stories/rv-activity/a-star-can-fake-a-wobble/" last_modified: "2026-10-28" --- [Stellar Activity and Radial Velocity](https://sandboxphysics.com/stories/rv-activity/) AC18 · L1 # A star can fake a wobble Sandbox Physics · 2026-10-28 Cover a small part of a spinning star and its spectrum can appear to move, even when the star has no companion. The missing light carries a preferred velocity. That is enough to shift the average. ## Before you begin No spectroscopy is required. Think of a spectrum as light sorted by wavelength, with dark notches where atoms absorb it. ## The notch is made of many voices One edge of a rotating star approaches us while the other recedes. Each small patch contributes an absorption notch at a slightly different wavelength. A distant telescope usually receives all those contributions together. Those contributions merge into one broadened notch. A companion pulls the whole star around their shared center of mass. Its motion shifts every local contribution together. That is the useful Doppler signal. But a dark region on the receding side removes some redshifted light. The combined notch moves toward the blue without the star’s center of mass making that motion. Open the Lab and choose “A spot without a planet.” There is no companion in this preset. Watch the region cross the visible disk: the flux falls, the line becomes slightly uneven and its centroid changes. Drag the region toward the other side. The sign changes because a different part of the rotational velocity field loses light. Reading: Dumusque, Boisse & Santos — SOAP 2.0, arXiv:1409.3594v1 · Haywood et al. — CoRoT-7, arXiv:1407.1044v1 ## Two clues do not always tell the same story A cool spot changes brightness. A magnetically active bright region can instead suppress convective blueshift: rising bright gas normally contributes a net blueshift, and magnetic activity reduces it. That makes a local contribution redder. A real active region can do both. Brightness alone therefore cannot predict every activity velocity. The Lab keeps these mechanisms separate. Its dark-region contrast changes the light weights; its advanced convective-shift control changes local line centers. “Bright magnetic region” shows why a small or reversed brightness variation need not mean a small velocity variation. The active-area indicator below the scene is a synthetic area proxy. It is not a measured calcium index or a thermometer. The photocenter offers another clue. Remove light from the right side and the brightness-weighted apparent position moves left. The Lab computes that displacement and the spectrum from the same surface. A companion also moves the star in the sky, but the animation magnifies that tiny orbit. The plotted angular positions keep their actual model units. Reading: Dumusque, Boisse & Santos — SOAP 2.0, arXiv:1409.3594v1 · Rajpaul et al. — joint activity processes, arXiv:1506.07304v1 ## Repetition starts an investigation A rotating region can repeat. Its shape and the observing schedule can also place power at a harmonic or an alias. A neat sinusoid usefully describes a pattern. Independent observations must then test its orbital interpretation. Real observations help by combining velocities with activity indicators, photometry and, when available, astrometry. Those measurements share a star; they do not necessarily respond to it in the same way. Our real example contains 71 published HARPS measurements of CoRoT-7. The campaign lasts about 25 days, roughly one stellar rotation. Later chapters compare three declared statistical models on exactly those rows. They do not turn this short interval into an independent planet discovery. The known short orbital period is supplied as external information, and the stellar-activity model remains an approximation. If you want the original double-lined binary mass experiment, choose “Binary orbit.” That mode keeps the original paired velocities and resolved geometry. It answers a different question: how orbital velocities and the inclination connect to two masses. Reading: Haywood et al. — CoRoT-7, arXiv:1407.1044v1 · Rajpaul, Aigrain & Roberts — Ghost in the time series, arXiv:1510.05598v1 ## Exercises and explanations 1. A dark region moves onto the receding half of the star. With convection switched off and no companion, which way should the measured centroid move? Read the explanation Toward the blue, or negative velocity in our away-positive convention. Removing positive-velocity absorption leaves a negative weighted average. At the disk center the rotational contribution is close to zero, so the darkest moment need not be the largest velocity shift. 2. A velocity varies while the brightness is almost steady. Has activity been ruled out? Read the explanation No. A region may alter convective line shifts much more than its continuum brightness. Different viewing angles and several regions can also cancel some photometric variation. You need a model for the indicators and their uncertainties, rather than a rule that steady light guarantees a planet. ## Try the prediction ### [Make a false wobble](https://sandboxphysics.com/labs/binary-star-mass/) 1. Choose “A spot without a planet,” then pause and drag the visible region across the disk. 2. Compare the measured centroid, the gray companion-only reference and the apparent-position track. The reference remains at zero while the surface signal changes. 3. Switch to the bright-region preset and ask which part of the dark-spot explanation still works. [Next: The speed hidden in a line](https://sandboxphysics.com/stories/rv-activity/the-speed-hidden-in-a-line/) ## 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.