- Review #1519 was about counting stars with visible light using the naked eye, a small backyard telescope, and the Hubble Space Telescope. This review counts stars using the infrared part of the spectrum.
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- The Wide-field Infrared Survey Experiment uses a 16 inch telescope that detects photons at 3,400 nanometers, 4,600 nm, 12,000 nm, and 22,000 nm. In 10 months of operation it images hundreds of millions of galaxies and asteroids in the infrared. The 10 month limit is caused by the coolant dissipating that is keeping the detectors at near absolute zero temperatures, 12 degrees Kelvin.
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- Analysis of the data starts with a question, how many stars are at each level of magnitude. Magnitude is a measure of a stars brightness. Each increase in magnitude corresponds to a decrease in brightness by a factor of 100^1/5, which is about 2.5 times. An increase of 5 magnitudes is a decrease in brightness by 100. The reference star is Vega which is set at magnitude zero.
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------------------Comparing the brightness of 2 stars , b1 / b2 = 100^(m2-m1)/5
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- The brightness of each star is proportional to its intrinsic Luminosity and inversely proportional to its distance squared.
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- The theory behind the question is that there are always more dimmer stars because looking backwards in time the Universe was more compact. Also, early stars were bigger and brighter but had shorter life spans. Dimmer stars live longer.
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- Next we plot graphs f the number of stars versus each level of magnitude. Number, N, as a function of magnitude, m. The mathematical equation that best fit the curve for the number of stars per square degree pre magnitude. Stars of a given magnitude are counted +½ and - ½ centered on the magnitude, m. The function is:
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------------------------- N (m) = 3 * m^3.5
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---------------------- N (12) = the number of stars per degree^2 at magnitude 12.
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--------------------- N = 3 *(12)^3.5 = 3 * (5,986) = 17,958 stars
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- The area of the sky is 41,252 degrees^2.
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-------------------- Total number of magnitude 12 stars in the sky = 741,000,000
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- Other plots were made for just the wavelength 3,400 nanometers. The faintest detectable is a star at magnitude 15 in the high ultraviolet and near X-ray wavelengths. The function that best matches the curve is :
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--------------------- N = 2.4*10^-6 * m ^7.4
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---------------------- N = 2.4*10^-6 * (15) ^7.4
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---------------------- N = 1,200 stars counted at magnitude 15 per degree^2
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- What would the count be for all the stars from magnitude 6 to magnitude 15? To get this we have to some up all the magnitudes at each level. This involves integration. The general formula is:
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---------------------- Integral x^a dx = x^(a+1) / ( a+1) + constant
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--------------------- Integral N from 6 to 15 = 2.4*10^-6 * [(15) ^8.4 - (6)^8.4] / 8.4
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-------------------- N = 0.2857 *1-^-6 * 7.568*10^9
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------------------ N = 2,163 stars per degree^2
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- The telescope field of view is 0.64 degrees^2. Therefore, the image would contain 1,385 stars.
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- Mapping the entire sky would yield 89,200,000 stars at these magnitudes and at the 3,400 nanometer wavelength.
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- Counting stars works much better than counting sheep. Trust me.
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707-536-3272, Thursday, December 6, 2012
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