All Parameters are Equal,
but Some Parameters are More Equal than Others

Derek L. Buzasi

Valdosta State University

Wes may claim that the panels were chosen for our experience and vast knowledge and ability to retain information, but I think I was chosen more for my ignorance, as a tabula rasa, to see what the meeting ends up writing on me.

I'm going to approach this a little differently than Tom did, and address three subjects. First, parameters: how do we pick solar analogs, what are good parameters, what are not so good parameters. I'm shamelessly going to try to bias you before the rest of today's meetings in favor of my favorite parameters. Then I have a few other issues that are just nearer and dearer to my heart.

So, what are my biases as far as parameters are concerned? I think good parameters are quantities you can interpret directly, i.e., without extensively using models. I'll give you an example of something I think does not fit that criterion, and that's abundance analysis. Keep in mind that I'm trying to strike a balance between two points here: (1) what parameters would we like to use in selecting solar analogs, and (2) what parameters is it at present practical to use in selecting solar analogs? I don't think abundances are the best parameters to use, because in my experience, different people get different answers for the same object. In a broad sense, abundances are fine, obviously at the Pop I vs. Pop II level, but when you get to finer distinctions I become more suspicious.

I also have a bias in favor of relative over absolute quantities, although my view on that has been softened a bit. For example, bolometric magnitude is not usually my favorite quantity, because it's contaminated by distance, which typically we do not know very well. Now we know our distances a little better, I've softened on that one. Of course, you'd also like to pick parameters that are independent as much as you can, but isn't that always the trick.

So, what do I think are bad parameters -- I've kept this hidden at the bottom of the page so people don't scream at me [laughter]. You can scream at me later. Well, I don't think energy distribution is a good parameter, simply because based on the work I've seen from Wes and other people, I don't think our knowledge of the energy distribution of the Sun is good enough for us to be using it as a parameter for picking a solar analog. Abundances are too model dependent. I'm not keen on photometric variability, because based on the work I've seen from Richard Radick, the photometry really only shows you the spots very well, and it's not so good at detecting plage and faculae. So I'm suspicious there.

Giampapa: Um, Derek, aren't your bad parameters exactly what you'd like to have for your solar analog?

Yes, indeed they are. But just because you'd like to have them doesn't make them good parameters! If you'd like to have them, but you can't measure them, they're meaningless.

Cayrel: But you have to stick with them, and study them, or they'll never be good parameters. So you have to study them.

I'm not saying they shouldn't be studied. I'm just saying that at this point they should not be the deciding parameter for picking a solar analog.

Cayrel:For future projects they will be vital.

Right. But I'm talking about now, not the future. Indeed you should look at these things, because in the future they may turn out to be better and you may understand them better. I just saying that right now, for example, if you've done a careful study of a star, and it looks like the Sun in every way, and somebody comes up with an abundance study for it that differs somewhat from the solar value, I don't think that's enough of a reason to kick it out.

What are better parameters? Well, B-V is differential, so I like it; it's easy to measure, so it's a good place to start. The MK spectral type is always a good reality check. The HK index seems to be a good activity proxy, although some people could argue that, and in fact I'm still trying to convince myself, although the poster by Henry and Baliunas was very impressive in showing that. Spectroscopic variability, particularly the work in Jeff Hall's poster showing this ``many-line index'' -- that's not really a good word for it, but I'm not sure what to call it -- looks very nice. I'm very happy about that, especially what he did in terms of breaking it up into spot-sensitive and non-spot-sensitive lines, because that gives you the possibility of seeing stars that are similar to the Sun in the sense of spot and plage activity at the same time.

Kinematics and location: I have a question mark there, because it's so far from my area of expertise that I hesitate to make any statements about it one way or the other.

Rotation: I like rotation, and I'll talk more about it in a minute. I like it because it's fundamental, with no model dependency at all. Not easy to measure, but fundamental.

Now just a few comments on things I've heard people talking about. First, the Sun defines the envelope of acceptable parameters. A lot of people have said this, and I want to repeat it. We need to not ask too much from our solar analogs. We can't demand that a star look exactly like the Sun because the Sun doesn't always look exactly like the Sun.

Next, and I know this is an un-American thing to say, but not all parameters are created equal. We need to decide how to weight these things. I've taken a stab at it here by saying ``these are good parameters'' and ``these are bad parameters,'' but that doesn't mean I like them all equally. You can try to weight them in several different ways. I weight highly those that are fundamental, and that you can just go out and measure. MK spectral type: no problem, you go get a low-dispersion spectrum and look at it. B-V: no problem, you can do lots of stars accurately. Kinematics and location: same story. So these are probably good basic parameters to start with, just to whittle your list down, and then you move on to the other, more elusive parameters.

Okay, let me talk about rotation for a minute. There's a saying that when you have a hammer, everything looks like a nail, and since I've started working on rotation over the past few years, well, now everything is tied to rotation as far as I'm concerned. So here's a figure.

FIGURE 1: Dotted lines indicate the envelope of acceptable values for rotation as a function of mass under the constraint imposed by requiring surface activity levels to be comparable to that of the Sun, while dashed lines indicate a similar envelope constrained by dynamo period. The solid line marks the dividing line beyond which stellar surface activity (in the form of active latitudes) is dominated by the Coriolis effect. The result of all of these constraints is that only stars lying within the filled region are acceptable solar analogs: this corresponds to stars hotter than spectral type K0.

What I've tried to do here is use a simple Parker dynamo to examine activity level and cycle period as a function of mass and rotation. I require that activity levels and cycle periods be comparable to the solar case, using the solar history over the last few hundred years. I also required that the surface latitudes of activity be comparable to those on the Sun. What does that mean? If you generate activity at the base of the convection zone, and it rises to the surface as flux tubes (a la Tom), and if the star is rotating, which of course it is, the flux will be diverted by the Coriolis effect and it will be pushed toward the poles. In the Sun, this is not a big effect. In a rapidly rotating M-dwarf, it's a huge effect. It becomes more sensitive to rotation as you move down the main sequence. So you put all this together, and you get sort of a box that defines the acceptable range occupied by solar analogs. Not solar twins, but decent solar analogs. Now, a lot of people have extended the concept of the solar analog of spectral type K2 or even K5. I disagree. I think anything later than about G9 is not a good solar analog.

Finally, just a few comments on 18 Sco, which is looking like the Holy Grail of this workshop so far. A few warnings I've noticed: first, the color is not necessarily the best match among the stars to the solar color. Second, Jeff Hall's ``many-line index'' for this star indicates it might be more active than the Sun. How important are these differences? I don't know. But, they're certainly worth considering, and I've haven't heard them discussed at this workshop yet.