A “What Am I?” Puzzle

  1. 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.
  2. 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.
  3. A technique known as spatial scanning has allowed the Hubble Space telescope to extend the range of measurements for my type of star.

    14-104-hubble-parallax.png
    By applying spatial scanning to astronomical parallax,  NASA’s Hubble Space Telescope can be used to make precision distance measurements 10 times farther into our galaxy than previously possible. Image source: NASA/ESA, A.Feild/STScI
  4.  Spectroscopy lets astronomers determine whether I am metal-rich or not. Each of the two types has a different linear relationship.

    Luminosity
    The same period can correspond to different luminosities, depending on whether this type of variable star is metal- rich(Type I) or metal poor. A metal-rich star is a star that has a higher proportion of any element other than hydrogen or helium, even though the elements may not necessarily be metals from a chemical standpoint.
  5. 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.

    LMCDistance
    The blue data is for a group of variable stars whose brightness has been adjusted for a distance of 10 parsecs from the earth. The red data represents data for the brightness of variable stars in the Large Magellanic Cloud, which are 4940^2 dimmer. From this we can conclude that the Large Magellanic Cloud is 4940 *10 parsecs from the earth or 49400*3.26 =160 000 light years away. Source: http://hubblesite.org/hubble_discoveries/science_year_in_review/pdf/2006/cepheid_calibration.pdf
  6. 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.

    Heic1323a_-1243686232
    RS Puppis is one of the brightest stars of its type in the Milky Way Galaxy. Picture source: https://www.spacetelescope.org/news/heic1323/ The source describes how a light echo was used to determine its distance.
  7. In the Hertzsprung-Russell diagram, I am on an instability strip.H-Rv_E.jpg

For more What Am I blogs, see:

uvachemistry.com/2014/08/07/what-chemical-compound-am-i/

uvachemistry.com/2016/07/11/again-guess-whats-being-described

uvachemistry.com/2016/06/22/guess-whats-being-described

Sources:

Universe. William J. Kaufmann II. W.H. Freeman

NASA Cepheid Calibration http://hubblesite.org/hubble_discoveries/science_year_in_review/pdf/2006/cepheid_calibration.pdf

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Fun With Shadows on the Winter Solstice

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).shadows

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:

winterShadows

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.

solarNoon

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