If it wasn’t for my atypical stellar atmosphere, I would be of no value to astronomers. I have a layer of ionized hydrogen and fully ionized helium, neither of which can lose energy to outer space. So these ions keep absorbing energy from my interior until I expand. This eventually lowers my density and allows electrons to recombine with ions and neutralize them. Now excitation can lead to loss of energy to outer space, eventually decreasing radiative pressure. This makes me shrink. Hydrogen and helium then reionize, and the cycle repeats itself.
Since temperature is related to luminosity, there are more ionized atoms associated with more luminous stars of my type. And the more there are, the longer it takes to go through a cycle. In chemistry, a correlation of concentration and color becomes more practical if it relies on prepared standard solutions of known concentrations. Similarly if it wasn’t for parallax measurements for nearby relatives, the relationship between luminosity and the logarithm of periods could not be calibrated.
A technique known as spatial scanning has allowed the Hubble Space telescope to extend the range of measurements for my type of star.
Spectroscopy lets astronomers determine whether I am metal-rich or not. Each of the two types has a different linear relationship.
So thanks to my star-type, astronomers have a way of measuring the distance of galaxies. Using these distances from spatial scanning and thanks to Hubble’s infrared camera, astronomers could correct the apparent brightness of my star-type to the values that would be observed if they all were located at a standard distance of 10 parsecs (1 parsec = 3.26 light years). When the observed brightness is plotted against the periods of various variable stars of my type, , the ratio of the brightness for the corrected curve to that of the galaxy in question is determined. The reduction in brightness factor is then square rooted because of the inverse square relationship between the distance of a star and its brightness. If the denominator of that result is then multiplied by ten parsecs, we get the distance to that galaxy or star cluster. Here’s an example involving the Large Magellanic Cloud.
Probably the best known star of my type is Polaris. It has a period of only four days. In contrast, the period of RS Puppis is about 40 days.
In the Hertzsprung-Russell diagram, I am on an instability strip.
Walking back from an errand yesterday morning, I was startled by the length of my shadow, almost 10 meters long. Yesterday, the first day of winter, marked the pinnacle of shadow-length. From today onward, as the days will begin to lengthen, as solar angles become more generous, concentrating solar radiation on less area, the march towards spring begins and shadows will shorten.
For a variety of reasons, on any day the halfway point between sunrise and sunset is most often not exactly 12 PM (It will only be so, after adjusting for daylight savings time, for a couple of days in January and for part of July and August). The so-called solar noon yesterday occurred at 11:52 PM at our longitude and latitude in Montreal, Canada. Like most people, I made sure I was out in the cold, standing upright on my deck with a tape measure to determine the length of my shadow.
At that time, my 75.0 inch frame, including the one inch hat, cast a shadow 196 ± 2 inches in length. (Using the actual solar angle corrected for atmospheric refraction it should have been a bit over 194.7 inches).
Using the fact that at a point directly south of us along the Tropic of Capricorn at a latitude of 23.5º South, the sun is at the zenith, so no shadow is cast. This is a situation similar to what Eratosthenes used to estimate the circumference of the Earth. But here we could also use the alternate and equal angles to derive an expression for latitude. Substituting h = 75.0″ and the measured shadow length = s = 196″, Montreal’s latitude works out to be 45.6º, pretty close to its accepted value of 45. 5º.
The nice thing about measuring the shadow at solar noon is that since the solar angle changes very slowly around midday, the shadow-length is relatively stable for several minutes. At about three in the afternoon I went out and measured my shadow, which was much longer than what was of course the shortest shadow of the day at solar noon. Fifteen minutes after 3 PM, the shadow had lengthened considerably. This not only happened because the sun does not sweep across the sky at a constant rate, but also because the tangent ratio is more sensitive to changes in smaller angles that occur shortly after sunrise and before sunset. Here is a plot to make what I just pointed out more obvious:
If you enjoy these types of experiments and calculations, and you want to verify your results, there is a great spreadsheet online with all sorts of astronomical calculations. They are set up so that you could easily adapt them for your own space and time coordinates. It is made available at no cost by the NOAA Earth System Research Laboratory. Using their formulas, here is a graph of maximum solar angles I created for all days of the upcoming year for Montreal , Canada. As elevation angles increase, it’s not only shadows that get amplified. Ultraviolet rays also intensify, and knowing which months of the year receive the most helps us take precautions for our skin’s sake.
The Stars in the Brazilian flag are not randomly drawn. For instance, in the lower left area of the circle are six stars from the Canis Major constellation. This morning while the rest of the family either snored or dreamed, I walked the dog at an early hour under relatively dark skies. Thanks to our dim streetlamps and a waning moon. I was able to observe the fourth brightest star of Canis Major, designated as delta (δ). Named as such because δ is the fourth letter of the Greek alphabet, it also has the common name of Wezen. Deceivingly it only seems dimmer than the very bright Sirius, the alpha-dog star, because Sirius is a lot closer to the Earth.
How do we know how far away Wezen is?
Hold a finger close and directly in front of your nose. Close one eye. Close the other eye while opening the first one. The finger seems to move against the background. If you hold the finger further away and repeat the exercise, the finger still seems to move, but not as much. Similarly for a given star, if it can be observed from two distant viewpoints along earth’s orbit around the sun, the star, will seem to be in slightly different positions against the background of more distant stars. If the distance between viewpoints is known and the angle of apparent movement is measured, simple trigonometry can help us calculate the distance between our sun and the star. The problem is that the angle is extremely small—after all, any star is a lot further away than your finger can possibly be by a factor significantly larger than the ratio of the orbit’s diameter to that of your eye-separation. A small uncertainty in angle can be amplified into a large error in distance, limiting us to measurements of only “neighborhood stars”. For more distant stars, other techniques involving Cepheid variables and type 1a supernovae have to be used. But thanks to Hipparcos, a scientific satellite of the European Space Agency (ESA) especially devoted to astrometry, parallax measurements have improved recently and are definitely accurate enough for a Milky Way star at Wezen’s distance.
Given that there are 3600 arc seconds in a degree and setting the sun-earth distance at 1 astronomical unit (AU), tan p = 1/d or d = 1 ÷ tan (2.03 × 10-3/3600) = 1.02 × 108 AU.
1 light–year = 63240 AU, so Wezen is about 1.02 × 108 AU ÷ 63 240 AU/light year = 1607 or about 1610 light years away.
How do you get absolute luminosity from distance and apparent brightness?
Due to that distance, which is far greater than the 8.61 light years that separates us from Sirius, Wezen’s apparent brightness is only 1.83. Compared to the number line, the stellar brightness scale runs backwards. The dimmest stars have the largest positive values and the brightest have pronounced negative values.
To get the true or intrinsic brightness ( absolute magnitude) of Wezen, we can use the following formula:
M = m – 5 log (d/10),
where m = apparent brightness and d = the star’s distance from our sun in parsecs. Since there are 3.26 light years per parsec,
M = 1.83 – 5 log(1607÷3.26÷10) = – 6.63
That’s a lot more intrinsically bright than Sirius, which has an M value of +1.42. It is Sirius’ proximity to us that makes it the 2nd brightest star in the sky after our sun and puts its apparent brightness at – 1.47. If you imagine them to be both at Sirius’ distance from Earth, by doing the math you realize that Wezen would have an apparent brightness of – 9.52, which would be almost as bright as a half-moon.
Using Two Measurements To Learn About Wezen’s Nature
Now if you rely on one other measurement for Wezen, something even more startling will be revealed. Its color is yellow, and with spectroscopic analysis of the lines from its excited atoms, it is classified as F8Ia, which gives away its surface temperature.
If you then plot absolute magnitude versus spectral class for various stars you get astronomy’s equivalent of the “periodic table”. It’s called the Hertzsprung–Russell diagram and it reveals a star’s stage in its evolution.
Using F8 as its x coordinate (each class has 10 subdivisions, zero through 9, so F8 is close to G’s lower bound) and its absolute magnitude of -6.63 as its y coordinate, we end up with a coordinate point on the supergiants line on the instability strip.
Our sun’s class of G2 and absolute magnitude of 4.83 place it on the main sequence, which is why we are still alive. Notice however that the sun’s spectral class is telling us that its surface is actually a little warmer than Wezen’s. If Wezen’s luminosity is so much greater than that of the sun, Wezen has to be a lot bigger, but its energy is spread thinly over its large surface area. But with more mass, gravity is a lot stronger, driving Wezen’s core temperature exponentially higher. This accelerates its rate of fusion. To make a long story short, Wezen is only 10 million years old and has already stopped fusing hydrogen, whereas the sun has celebrated its 4.6 billionth birthday. Moreover, the sun will also stay on the main sequence long enough to double its present age.
It seems that Wezen has already started to expand. As it fuses helium, it will become a red supergiant and eventually go supernova within a mere 100 000 years. When that happens, in our night sky, Wezen will appear almost as bright as Sirius and brighter than every other star. It’s comforting to think that maybe our descendants will walk with their dogs early one morning and marvel at it.