Re: is there a emulation of the sun?

By an "emulation of the Sun", do you mean a map or atlas? Or do you mean 
a computer model? The simple answer to the former is "no, it is not 
possible to develop a permanent map of the surface of the Sun". The much 
more complex answer to the second is, yes, there are lots of computer 
models that try to understand the structural features of the sun.

With regard to the map, the surface of the Sun is far from static. The 
Sun is basically a giant fusion explosion that has been occurring for the 
past 4.5 billion years and will continue to occur for another 4.5 billion 
years. The energy of the Sun comes from the smashing together of hydrogen 
nuclei under the influence of the immense heat and gravitation at the 
core. This energy takes a few million years to travel outwards through 
the Sun's mass but eventually it reaches the upper surface region. 

In the last 20% of its journey to the surface - in the subsurface region -
the "gas pressure" has decreased sufficiently to allow convection cells 
to form. Convection cells can be seen in a number of everyday phenomena - 
including a cup of coffee. But the place that most of us are familiar 
with seeing them is in a pot of water just before it boils. They provide 
the streaming effect and flows that are visible. The Sun is much the 
same. And just as the flows in a pot of water are essentially random, so 
to are they on the Sun.

This means that the surface of the Sun is in a constant state of turmoil 
and mapping the surface would have to be a very dynamic procedure. In 
some regions, matter is rising to the surface from the interior. In other 
regions, it is falling back towards the core. Because of the size of 
these regions and that mass of the Sun, the cells have a much longer life 
span than the cells in a pot of water, but they do collapse and new cells 
form.

With regard to Sunspots, they are a manifestation of both the convection 
of matter to the surface and, more importantly, of the Sun's magnetic 
field. In a Sun spot, there is a contraction of the magnetic field - a 
sort of bunching up of field lines - that results in "magnetic pressure". 
The result of this is that there is both "gas pressure" and "magnetic 
pressure" inside a Sun spot. This means that the temperature does not 
have to be as high. The ideal gas law (although not strictly applicable) 
tells us that the gas pressure is related directly to temperature. 
Decreasing the gas pressure results in a decrease in the temperature. And 
this is exactly what a Sun spot is -  a region where the surface layer of 
the Sun is only about 4000 degree celsius instead of the normal 5500 
degrees celsius. In effect, the concentration of the magnetic field 
inside a Sun spot allows the gas inside the spot to be cooler than the 
surroundings. This is why they appear darker than the rest of the surface.

Predicting where a Sun spot will occur is still something that scientists 
can not do. And this is, I think, the crux of your question. Sun spots 
are NOT permanent features of the surface of the Sun. They come and go, 
depending upon the magnetic field of the Sun. There is an apparent 11 
year cycle (although it actually reanges from 9 to 12 years), which 
repeats itself on both sides of the Sun equator (hence, it is really a 22 
year cycle) but each spot is uniquely formed and last for only a short 
portion of that cycle. Indeed, they typically do not last for a full 
revolution of the Sun! But they are, in essence, simply a convection cell 
that has a bit of a lifespan due to the confluence of magnetic field 
lines.

Having said that, if you would like to know which Sun spot is which, 
there is a website (http://www.spaceweather.com) sponsored by 
Science@NASA that does a really (REALLY) superb job of providing 
information on the Sun - what it is doing, which Sun spots are visible, 
the number assigned to each spot, where you can find it. I should note 
that each spot as it emerges or is first detected is given a unique 
number. Right now, Sun spots 631 and 632 are visible. The next one to 
appear will be labelled 633. But it is impossible to map Sun spots long 
term as when and where the next one will appear is anyone's guess.

I should also point out that NO ONE SHOULD EVER LOOK AT THE SUN DIRECTLY. 
Always use an indirect method - either through projection onto a surface 
or by using safety approved filters. This is critically important when 
trying to observe Sun spots.

I hope that this helps. I didn't talk about the computer modeling of the 
Sun but there is a lot of really interesting work being done to try and 
understand the dynamics of the Sun and maybe develop a predictive model 
of where Sun spots are likely to occur. This is a huge topic of research!