Stellar Fingerprints

When you look at the night sky from your backyard, do you sometimes think that there is no order to all of those stars out there? If the star isn’t part of a well known constellation, is it nothing more than a point of light in a sea of other points of light? Nothing that distinguishes it from any other star?

Well, this just isn’t so. In fact, stars have characteristics such as temperature, luminosity (brightness), mass, galactic location, distance to the earth, and even age — all combined forming a stellar fingerprint that uniquely identifies a specific star.

You probably already know this, but did you ever stop to wonder how we came to know these unique characteristics of a star? After all, we can’t run up and stick a thermometer in a star, or run a tape measure from the star to Earth. So, how do we find get information about stars?

Finding the distance to a star

Well, this one had me the most curious, so this is the one I’ll take first. How do we measure the distance to a specific star? If the stars are nearby, we use stellar parallax

When you move towards objects that are near you, they seem to move in relation to the objects that are located much futher than you. You might notice this when you look at signs by the side of the road in comparison to the background detail when you’re traveling in a car. You can also notice this effect when you hold a pencil in front of you and view it through one opened eye and then another (see diagram).

This same effect seems to happen to stars that are close to the Earth. If you measure the angle to a star from a fixed point on the Earth, and then measure it again from the same point when the Earth is at the opposite position in its orbit around the sun (in 6 months time), you’ll find that the two measurements form a triangle where they intersect (see U of Oregon Diagram). If you half the triangle and then take the angle of one half, you’ll get a value in arcseconds (an arcsecond is 1/360 of a degree). You can then find the distance to the star using stellar parallex:

d = 1/p

The distance to the star (in parsecs, roughly equal to 3.26 light years) is equal to the inverse of the parallex angle of the star.

A light year is the distance light travels within a year — roughly 300,000 km/s

Using this approach we’ve been able to find the distances to several stars such as Proxima Centauri at 0.772 parallax (4.22 light years); Sirius B at 0.379 parallax (8.61 light years); and Epsilon Indi at 0.276 parallax (11.82 light years).

Of course, this approach works only for stars that are relatively close to the solar system, but once you have this information, you can use the distance in other calculations — such as to find the luminosity of a star.

Finding Luminosity

A star’s brightness is a measure of its luminosity.

Luminosity is the amount of light energy emitted by the star within a second, measured in watts (joules per second).

You might think that luminosity is directly related to the distance of the object from the Earth. Well, it is, but there are other factors involved such as the mass of the star and its temperature. If star A is further from the Earth than star B, but star A is much, much brighter, it can appear more bright to us than the closer star.

Still, the distance to the star can tell us its luminosity, with a simple formula:

L = 4pid2b
In this, the Luminosity is equal to the distance squared, multiplied by the brightness, and then multiplied by 4 times pi (pi approx equal to 3.1415926...). The brightness is the apparent brightness as its measured here on Earth (or wherever the viewpoint is), through techniques such as photometry. The brightness of a star is usually described by comparing it to Sirius A, the brightest star we see from Earth (and with a brightness of 1.0).

A simplified approach to finding luminosity is to plug the Sun's brightness, distance, and luminosity into the formula and then take the ratio of the two equations. By doing this, the value of 4pi falls out of the formula:

L/Lsun = (d/dsun)2 b / bsun

Luminosity can now be found by direct comparison between the star and the Sun.

For instance, if a star has a brightness of 5.2 x 10-12 compared to the sun, and it’s distance from earth is 5.2 x 106 that of the Sun to the Earth, you would use the following to find the luminosity:

Lstar/Lsun = (5.2 x 106)2 5.2 x 10-12 = 140

The star (Regulus) has 140 times the luminosity of the Sun, but appears dimmer because of its distance. You could use this same approach with any two stars — find the ratio of the stars and then solve for the unknown value:

L1/L2 = (d1/d2)2 b1/b2

With this, if you find out that star 1 is 3 times the distance of star 2 and appears twice as bright, you can figure the luminosity without having to use a calculator: star 1 has 18 times the luminosity as star 2.

Another characteristic you can find out about a star from the light it emits is its temperature, found next.

Finding a star’s temperature

Quiz time: which is hotter, a blue star or a red star?

The answer might surprise you — the blue star is hotter. The blue color is because most of the star’s radiation is in shorter wavelengths, hence in the blue to ultraviolet range. A cooler star has a longer wavelength, in the red to infrared range.

Wien’s Law states that as a star’s temperature increases, it’s color shifts to the blue.

You can find the temperature of a star by finding the wavelength of its maximum intensity, and using this value in the Wien’s Law equation:

wavelengthmax = .0029 / T

In the equation just shown, the maximum wavelength emission is equal to a constant value (.0029) divided by the temperature. The maximum wavelength emission can be found using instruments on Earth, so this value is used to find the star’s temperature:

T = .0029 / wavelength max

If a star has a maximum wavelength of 500 nm (5 x 10-7 m), its temperature would then be about 5800 degrees kelvin:

T = 0.0029 / 5 x 10-7

This is the temperature of our own Sun. Its color is due to the fact that the maximum wavelength emission is at 500nm, putting it within the yellow color range in the visible light spectrum.

You can find the maximum wavelength emission of any star using photometry, regardless of its distance from the Earth.

Of course, once you have a star’s temperature, and its luminosity, you can then find its radius.

Finding a star’s radius

Okay, let’s recap what we’ve been able to find out about distant stars.

We’ve been able to find their distance (if close enough to use stellar parallax), as well as their luminosity (regardless of distance). We can also find a star’s maximum wavelength emission, and we’ve used this to find the star’s color as well as temperature. One thing we haven’t found, yet, is a star’s size. We have found, though, the values necessary to find the radius of the star: its luminosity and it’s temperature.

A star’s luminosity is equal to its radius, squared, multiplied by its temperature to an exponent of 4:

L = 4piR2(const)T4

The (const) value in the equation is the Stefan-Boltzmann constant, a value of 5.67 x 10-8 W m-2 K-4. (Find other constants.)

You don’t have to remember this rather computationally instensive formula if you look at it as a measure of the ratio between the star and the Sun:

L/Lsun = (R / Rsun)2 (T / Tsun)4

Re-arranging this to search for the radius, you have:

R/Rsun = (Tsun / T)2 SQRT(L / Lsun)

For instance, the star Rigel has a temperature 3 times that of the Sun, and a luminosity 64,000 times that of the Sun (one very bright star). It’s radius in comparison to the Sun’s is:

RRigel/Rsun = (1/3)2SQRT(64,000) = 27.5

Rigel has a radius about 28 times that of our Sun. As the Sun’s radius is 6.96 x 105 km, Rigel’s radius would be about 1.9 x 107 km.

An so on…

There are other things we can find out about stars, but this should give you an idea of what we know, and what we can find out about a specific star. And we didn’t even have to leave our backyards to find it.

Just Shelley

New York, New York

It isn’t Fall without trees changing color, birds flying south for the Winter, and being in New York to speak at the Internet World conference — this time as part of the Webmaster Forum.

However, this time, I stayed in New York for a few days. What an adventure.

New York Cabbies

The cab that took me from Penn Station to my hotel was driven by a gentleman from Haiti who happened to have strong religious beliefs. I know he was religious because he kept playing religious tapes, and would slam on the brakes occasionally in order to jot something down in a notebook he kept by his seat. I knew he was Haitian as he would alternate this behavior with Haitian utterances under his breath as he literally tore through that town, determined to get me to my hotel at all due speed.

I didn’t know one could drive between cars in car lanes in New York. I also didn’t know that one could drive 60MPH down Park Avenue in the middle of the day. I do now. I also received a lesson in the finer points of car horn blasting in New York.

There’s the light tatoo on the horn that says “Yo!”. There’s the more emphatic tatooing that seems to say “Yo! Stupid!”.

There’s the single tap that just lets folks know you’re in the vicinity and to watch out. Compare this with the heavy hand on the horn that will get even the most diehard New Yorker’s attention. If the horn blower is a cab driver, people seem to understand that the cabby is just letting someone know that they are invading the driver’s personal territory, whatever that may be.

I also know that pedestrians in New York don’t walk in front of the cabs without looking at the driver’s face, first. How does this driver define territory…

Cab rides are a way to experience New York, but I can’t experience a new town or city from a car — I just don’t like cars. So, I decided to walk to Central Park. On foot. No cabs.

Walking to Central Park

I started my walk on Madison Avenue — established home of advertising agencies everywhere.

Madison Avenue doesn’t have the crowds other streets do in New York, thought there are a large number of gray and black suited people, all with cellphones glued to their ears (call them New York earrings).

The buildings along the way reminded me of some of the canyons I used to explore in Arizona, except those canyons were created by water flows over a millenium of time. New York canyons are built on man’s desire to one up nature. I did notice, though, when I crossed over to Fifth Avenue that the human tide is remarkably similar to a moving river. Woe to you going against that tide of affluent and determined shoppers.

(I particularly treasure a moment when two older, well dressed women walking behind me suddenly stopped in the middle of the sidewalk and murmured “Armani” in one breath. I consider this to be a quintessential New York moment.)

The Park

Central Park is a surpise after all the opulence of the surrounding stores and the shadows cast by the towering buildings elsewhere in downtown New York.

Part of the Park was closed off for renovation, but I walked every last bit of those sections that were open. And it was a long walk.

First, let me state categorically that I cannot BELIEVE that anyone would jog in the Park after dark. The place is full of nooks and crannies, dark corners, and bushes. Charming by day, sinister by night. A horse carriage ride, yes — but not a lonely stroll through the footpaths. I’d rather play tag with a grizzley. It would be safer.

Central Park is pretty, but the trees look a little tired, and more than a bit dusty. However, the bushes and lawns are very pretty, as are the little specialized areas such as the Dairy farm.

I found an old fashioned carousel and thought about taking a ride, but dignity intruded — dammit.

My favorite sections of the Park were rocky outcroppings with bits of mica scattered about, sparkling in the noon day sun. Something like the windows at Tiffany’s and Cartier’s I passed on the way, only I could touch the rocks at Central Park and not get arrested.

I actually saw a black squirrel; I’ve not seen one of that coloration before. I don’t have my books to check to see if this is a natural variation, or a protective adaption based on New York city smog. (I know, meow, meow — but Boston is a whole lot greener.)

I walked through some bushes at one point and found a group of people silently standing around a mosaic embedded in the cement. All the mosaic had on it was the single word “imagine” — I was in Strawberry Fields, the John Lennon memorial.

One word, and I stopped dead in my tracks. One moment, with a lifetime of memories, flooding in, all because of that one word.

Back from the Park

I was getting tired at this point, so back to the hotel.

Towards the end of my walk, I stood out in front of St. Patrick’s Cathedral, an incredible edifice of which New Yorkers take considerable pride. If you’ve been to New York, you know what it’s like to come upon the Cathedral after blocks and blocks of modern glass and steel.

I have to admit that when I first looked at St. Patrick’s, I thought of how much further we would be as a people if only we expended as much energy and resources on education as we did and still do on religion.

We could have cured cancer by now, eliminated all smog and pollution, perhaps be walking on some distant planet around some distant sun.

Then I walked into St. Patrick’s. I literally stopped in the middle of the Vestibule, overwhelmed by the absolute rightness of the interior of the church. The vaulted ceilings, the stained glass windows, the slight smoky air from thousands of votive candles lit by the faithful.

It then came to me that without faith — or perhaps human spirit — we wouldn’t even try to cure cancer, or walk on the moon, much less planets surrounding distant stars. And we wouldn’t have beauty such as that.

Maybe we didn’t do so bad with our time and our resources in the past, after all.

New York, New York

My last stop on my walk was Rockerfeller Center, located a couple of blocks from the hotel. As I approached the Center, I could hear the strains of the Sinatra song, “New York, New York” filling the air. I kid you not — there had just been an ice show at the center, which finished by playing New York’s anthem song.

I couldn’t end my walking tour of New York on a better note than that.