Photometry: The measurement of the intensity, brightness, or other properties of light. Photons/sec

Count Photons Sounds simple, but -- what if the measuring equipment misses some because it is not 100% efficient? -- what if the atmosphere or telescope don’t transmit all of the photons? -- what if some photons are from something else like the sky which is not totally dark?

Comparison Sources Useful to compare an unknown source to a known reference -- this is what you did to measure the luminosity of the Sun which was compared to a known source, a 300-Watt light bulb But this scheme has it limitations, too: -- what about the temperature of the light bulb as compared to the Sun? -- is the Sun observed through the same air path as the light bulb? -- is your eye the most accurate recording device?

Compare an Unknown Star to a Known Star Another useful technique is to measure a star in comparison to another star, very convenient when looking for stars that vary like Cepheids Using a comparison star avoids the issues with instrument and atmospheric shortcomings Look through the same air path Also reduces problems due to different temperatures

“Blinking” to Find Varying or Moving Objects The homework has you using a simulated blink comparator to find variable stars Clyde Tombaugh used a blink comparator to discover Pluto

Extra Sources of Photons When measuring a star you most likely would be measuring it against a “background” that produces some photons (ie., the night sky isn’t completely dark due to scattered light from cities, etc) By measuring a region around the star, this level can be subtracted from the star to get the brightness of the star without any photons being included Star = Inner Disc ave – Outer Ring ave = 6454.59 – 2334.49 = 4120.1

Complete Measurement Take data on a pair of stars, one of which is the star of interest and the other of which is a known reference star (sometimes called a standard or comparison star) Correct each star’s data for background counts Compare the star of interest with the reference star Repeat many times if looking for variable stars Brightness Time

What to Believe Notice in the example from the previous slide that comparison star’s data is not always exactly the same value. Is it varying? Probably not – need to understand “noise” or uncertainty in a measurement. Brightness Time

Noise from Counting Anything that comes in indivisible units and has some probability of occurring is subject to “counting statistics”. For example, if you toss a coin 20 times, you would expect to get heads 10 times, but will you actually get 10 heads? -- sometimes, and sometimes not but if you repeat the experiment of tossing a coin 20 times, on average you will get 10 heads -- the spread in the number of heads is given by the square root of the average value Average = 10 heads so expect to get any where from 10 - 10 to 10+ 10 heads 6.8 to 13.2 ( 10 = 3.2) Any number is still possible, but some numbers of heads are very unlikely: Probability of getting 20 heads = (.5)20 = 9.5 x 10-7 or just under 1 in a million!

Other Examples of Counting Statistics Sports: A basketball player doesn’t make every free throw she tries. On average a player might make 85% of her throws but you must be careful when making claims about a single game performance. For example: A player tries 10 throws in a game. On average she would make 8.5 (but obviously you can’t have a half throw!). The square root of 8.5 is 2.9 so one should expect to see a number of throws made in the range of 8.5-2.9 to 8.5+2.9 or 5.6 to 11.4 so making only 6 throws wouldn’t be so unusual. Voter polls: Suppose 1000 people are sampled. The margin of error as a percentage will be 1000 /1000 x 100% = 3.2% . Two thirds of the time the true average will be within +/- the margin of error and 95% of the time it will be within 2 time the +/- margin of error.

Photon Counting Photons arrive in indivisible units and therefore are subject to counting statistics The variation in the reference star noticed earlier was due to the noise in counting photons -- if only 100 photons were counted, then the error would be 100 = 10 photons = 10% of the signal. Beware that there is also noise associated with counting the background photons! Notice that the averages of these two blank sky regions are not the same.