# How much of a star can be covered in starspots?

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.

• Visually or actually? I mean, once enough surface is "cold", it won't appear black anymore, or not?
– L.Dutch
Commented Dec 4, 2019 at 15:24
• Sunspots are not "dark", they are just less luminous than the rest of the Sun. And I would say that no more than 50% of the apparent surface can be covered in less luminous spots, for the obvious reason that above this you won't have less luminous spots but rather more luminous spots... Commented Dec 4, 2019 at 15:26
• @AlexP Well, that's true if you think about a starspot as being cool relative to the area around it, but I was thinking about its temperature/flux relative to times when the star is not undergoing such magnetic activity. After all, that's the whole motivation behind the question - figuring out if this is a viable method of dimming. Commented Dec 4, 2019 at 15:29
• @AlexP I'm not sure that follows. Given that the baseline of 'normal' is set by the mass of the star and its composition, even if >50% of the star is in a less luminous mode, you can still define which is the normal luminosity and which is a temporary aberation due to the 'spot' activity, no matter how extensive. Commented Dec 4, 2019 at 15:30
• Tongue in cheek: 50%. Beyond 50%, then the "sun spots" are the brighter glowing bits, and cover less than 50% of the surface. Commented Dec 6, 2019 at 18:13

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.

• This seems like it could be a start, but looking at the images, the starspot only seems to extend down by about 40°, in general - it doesn't give the extensive coverage you're claiming. Commented Dec 4, 2019 at 15:52
• I did not mean to claim anyone had observed giant bihemispheric spots. I was proposing a theoretical maximum suitable for hard SF, extrapolating from the mechanism that generates known large spots. Commented Dec 4, 2019 at 16:02
• Well, okay, but I'm not sure that's it quite the rigorous upper limit I'm looking for - it's not really backed up by anything hard science-y. It's kinda like saying, well, I assume that a rocky planet must be less massive than a galaxy - sure, that's true, but there's almost certainly a smaller lower limit based on more physics. I hope I'm not being too unclear. Commented Dec 4, 2019 at 16:04
• Just as a heads-up, I've removed the hard-science tag from the question. Commented Dec 4, 2019 at 19:31
• I would say it's backed up by hard science--just not all the hard science that might be available. I do hope someone posts an answer with stronger limits, but I appreciate Willk's attempt to be helpful.
– Qami
Commented Dec 4, 2019 at 20:01