The summer night sky is full of stars—bright stars like Vega and Arcturus, middling stars like Polaris (the North Star) and Mizar (the star in the “bend” of the Big Dipper’s handle), and dim stars like Rho Leo (a faint star in the constellation of Leo, the lion) and Alcor (the faint companion of Mizar). When we look at these stars, what are we seeing? Astronomers say that the sun is a star. Are the stars then suns? How do we even know what these stars are? In the posts from two weeks ago and from last week we laid the groundwork for answering these questions. We looked at the stellar magnitude system and the things that affect a star’s magnitude. Now let’s finally answer the questions.
Let’s begin with Vega. Vega is magnitude 0.0—one step brighter on the magnitude scale than the summer star Spica, which is magnitude 1.0. Vega’s parallax is 0.130 arc seconds. Reading off the parallax chart from last week, we find a parallax of 0.130 arc seconds corresponds to the star being 1,500,000 AU distant (1,500,000 times more distant than the sun).
So suppose Vega were in the place of the sun—that is, suppose somehow we could magically replace the sun with Vega, which would make Vega 1,500,000 times closer than it currently is. According to the magnitude and distance chart, making Vega 1,500,000 times closer would make it about 31 steps of magnitude brighter.
Vega is 0.0, and smaller numbers on the magnitude scale mean brighter (a 1 is brighter than a 5, a 0 is brighter than a 1, a minus 1 is brighter than a 0, a minus 5 is brighter than a minus 1, etc.), so making Vega 1,500,000 times closer would make it a minus 31. The sun, by contrast, is minus 27. So, were Vega in the place of the sun it would be four magnitude steps brighter than the sun. Four magnitude steps means 2.5×2.5×2.5×2.5=39 times the sun’s luminosity. Vega seems to be much more powerful than the sun.
That makes sense. Vega is bluer than the sun, and therefore hotter. In fact, based on its color, Vega should be about 1.7 times hotter than the sun. Judging from the magnitude and temperature chart, being 1.7x hotter would only make Vega about 2 magnitudes brighter than the sun at the same distance.
So Vega must also be larger than the sun. According to the magnitude and size chart, to account for the remaining 2 magnitudes of brightness, Vega must be about 3.3 times the sun’s radius.
If we put Arcturus where the sun is, we make it 2,000,000x closer. According to the charts, that will make Arcturus about 32 steps brighter on the magnitude scale. Were Arcturus where the sun is, it would be magnitude negative 31.8—we’ll just say minus 32. That is five steps of magnitude brighter than the sun at the same distance. That makes Arcturus 100x more luminous than the sun.
But Arcturus is a golden yellow star. It is a little redder, and thus a little cooler, than the sun. Its color tells us that it is about 9/10 the sun’s temperature, so the sun is 10/9 its temperature. Were Arcturus the size of the sun, the sun would be the more luminous, but only by a magnitude or less according to the charts.
Therefore the reason Arcturus would be five magnitudes brighter than the sun were it at the same distance as the sun has to be because Arcturus is larger than the sun. According to the size and magnitude chart, that five magnitude (plus the half or so magnitude due to temperature) difference means Arcturus must be about 14 times the sun’s radius.
So, we have reasoned out that Vega must be about 39x more luminous than the sun, and 3.3x larger (in terms of radius). We have reasoned out that Arcturus must be about 100x more luminous than the sun, and 14x larger. Let’s “check” our answers using the Celestia computer app. Celestia gives the luminosity of stars and can show us what different stars would look like were they in the place of the sun.
According to Celestia, Vega is 49.1x as luminous as the sun, and about 3x as large, while Arcturus is 113x as luminous and 25x as large. So our calculations are in general agreement with Celestia. That’s not too bad, since Celestia’s values are no doubt based the work of astronomers who used more sophisticated and precise reasoning and measurements than these limited charts!
There are stars more powerful than Arcturus. Consider Antares, in the constellation of Scorpius.
According to Celestia, Antares is over 9000x as luminous as the sun, even though it is only about half as hot. The luminosity of Antares is owed to it being so huge that, were it in the place of the sun, the Earth would be deep inside it! Antares is bigger than Earth’s orbit.
Then there is Rho Leo, which doesn’t look like much in the sky, but that is only because it is so far away. Celestia says Rho Leo is almost 70,000x more luminous than the sun.
Don’t be surprised that so many of the stars visible in the summer sky are more powerful than the sun—luminous stars stand out. There are plenty of sun-like stars out there; they just do not stand out. Consider HIP 80337, a dim star in Scorpius.
According to Celestia, HIP 80337 is very sun-like: same size, same color, same luminosity. Put HIP 80337 in the place of the sun and it would look pretty much the same.
HIP 80337 has about the same parallax as Arcturus, and therefore is about the same distance. When you look at HIP 80337 you are seeing what the sun would look like if it were where Arcturus is.
Now consider Barnard’s Star. It is a summer star, but you cannot see it without a telescope, even though it is not half as distant as even Vega.
Like Antares, it is not very hot, but unlike Antares, it is small. According to Celestia, it is not even one half of one thousandth of the sun’s luminosity. Or consider the star 2MASS J18353790+3259545, near Vega. Celestia says its luminosity is just a tiny fraction of Barnard’s star! Were 2MASS J18353790+3259545 to be put in the place of the sun, it would look so small as to be almost star-like. It would glow red like a piece of charcoal, and provide less light than a full moon. Astronomers believe that small, dim, red stars like Barnard’s and 2MASS J18353790+3259545 comprise the vast majority of stars in the universe—we just can’t see them.
So now we know what some of the summer stars are. More importantly, we know how we know what the summer stars are. We see that the sun is definitely a star: HIP 80337 is a star, and the sun and HIP 80337 are pretty similar. But are the stars suns? Antares is giant compared to the sun; Rho Leo is blinding compared to the sun; 2MASS J18353790+3259545 is puny compared to sun. And the differences between these stars and the sun pale compared to the differences among themselves—consider 2MASS J18353790+3259545 versus Antares or Rho Leo. Perhaps the safest thing to say is that there is an incredible amount of diversity among the summer stars.
Next week is the final installment of Summer Stars.