How much of a star can be covered in starspots?

Question

Many stars, including the Sun, periodically display starspots, cooler areas of the surface associated with higher local concentrations of the stellar magnetic field. They can sometimes be a couple thousand Kelvin cooler than the surrounding regions of the stellar photosphere. My reasoning is that because surface flux from a star is proportional to $T^4$, with $T$ the photospheric temperature, if a large portion of the star was covered by starspots, we could see a significant reduction in flux, and I'm trying to use such a star in my universe.

The thing is, I don't know just how dramatic the effect could be. I can't say that I know much about starspots, and while Wikipedia claims that up to 30% of the surface of a star can be covered,

• The claim is not backed up by a citation.
• It's not clear if that's the theoretical limit or just the maximum value found in observations.
• Wikipedia doesn't say in what type of stars this dramatic coverage is seen.
• Another site claims a limit of at least 66%.

Therefore, what is the upper limit for the amount of a star's surface that can be covered by starspots at a given time? I'm hoping for main sequence stars of between $0.5M_{\odot}$ and $3M_{\odot}$, but I would be okay if we need to go outside those boundaries to cover a significant portion of the surface.

As a note, when I say "starspot", I'm looking for a region roughly $\sim1000\text{ K}$ to $2000\text{ K}$ cooler than the normal stellar photosphere outside the period of starspot activity. In other words, the spot is not necessarily substantially cooler than the regions around it at a given time, if it happens to be in a large region of magnetic activity, but it's cooler than the same location would be if there was no magnetic activity at all.

Answer 1

I will take a swipe at this.

1. Starspots are created by magnetic flux tubes that extend out past the surface of the star.

2. The center of the tube has decreased convection because the magnetic fields inside the flux tube suppress convection. Decreased convection means decreased heat transferred to outermost visible layer. That layer cools, and thus darkens: the spot.

3. Bigger flux tube = bigger center = bigger star spot.

4. I figured the theoretical maximum size of a flux tube would be one that encompassed the entire star, from axis to axis. The diameter of such a tube could be the diameter of the star and could produce a bihemispheric starspot occupying nearly all of the star surface. Maybe there would be a bright band at the equator. Could such a thing exist?

5. Flux tubes are caused by vortices in the star stuff. A single giant flux tube would mean the star stuff was rotating as a piece rather than countless small eddies as in our sun.

I went looking. I found this. Emphasis mine.

Doppler Imagery of the Spotted RS Canum Venaticorum Star HR 1099 (V711 Tauri) from 1981 to 1992 https://iopscience.iop.org/article/10.1086/313195/fulltext/36316.text.html

We believe that these starspots are not measuring photospheric differential rotation. Instead, like solar coronal holes, their relatively low degree of shearing and nearly solid body rotation may be enforced by a multikilogauss, axisymmetric, nearly current-free quasi-potential global magnetic field. Our Doppler images also agree very closely with the Zeeman-Doppler imagery of Donati et al. and support their finding that regions around the edge of the polar spot and within bright spots show largely monopolar fields of at least 300700 G strength. The large, permanent cool polar spots, the very low observable differential rotation and shearing of starspots, and the evidence of strong, essentially unipolar magnetic fields associated with them leads us to believe that HR 1099 and other rapidly rotating RS CVn stars harbor quite strong (multikilogauss) axisymmetric global magnetic dipole fields. These fields have historically been largely hidden from view by their high degree of rotational symmetry, by being concentrated in the low surface brightness dark spots, and by these stars' high degree of rotational line broadening. We propose that the starspots on HR 1099 and other rapidly rotating RS CVn stars are, by analogy with solar coronal holes, large unipolar, magnetic regions that are tightly frozen into multikilogauss, axisymmetric global dipole fields in these stars. Since the large cool polar spots, the signature of these dipoles, are not present on more slowly rotating RS CVn stars, we believe that they must be dynamo-induced fields rather than remnant fossil fields.

So: they describe a single giant, long-lived star-spanning flux tube created as a product of rapid stellar rotation, and this associated with the largest known starspots. Yay!

I took away also that these very rapidly rotating stars might often be binaries, and owe their rapid rotation to the influence of their partner. Not sure how that factors into your fiction.