Spaced throughout this unit we showed that there are several methods that astronomers use to determine distances to astronomical objects.
Your mission is to find another technique used by astronomers to obtain the distance to objects and the approximate limits to the methods accuracy. Below are all the techniques that were covered in the web pages, ... so please don't use them (or repeat another student post)
Other techniques we already covered:
Stellar Parallax - Use the motion of the earth around the sun to produce a measurable parallax with nearby stars. The smaller the parallax, the farther the star is away. This technique is limited to a few hundred light years.
Cepheid Variables (as a standard candle) - Using the fact that the rate of pulsation is linked to the luminosity of a star, one can estimate the distance because you now believe you know the amount of light a star puts out, ... and can, therefore, place it at the correct distance to produce the amount of light you actually receive. It is like saying, I know that a distant light bulb is a 200 Watt bulb, .... therefore, it has to be xxx feet away to produce its observed brightness. This method is used to find the distance of globular clusters within our own Milky Way to galaxies which are close enough to spot individual Cepheid variable stars (usually limited to around 10 million light years).
Type 1a Supernovae (as a standard candle) - Since astronomers believe that this type of stellar explosion produces a consistent amount of light, we can play the same game we did with Cepheid variable stars. This method is most useful when a galaxy is too far away to make out individual Cepheid variable stars but it does require a bit of luck because you have to catch an un-obscured view of a random event. It is limited to a few billion light years.
Cosmic Expansion - The Hubble Law says that the universe is expanding and the farther away an object, the faster it is receding from us. A quasar with the largest redshift is, therefore, assumed to be the most distant. This method is limited to only the most distant objects, .... beyond a few million light years, ... and up to around 13 billion light years.
Here is a brief overview of some acceptable answers:
Spectrographic Parallax - This method may be known as "spectrograph parallax" but has nothing to do with parallax. It only works on main sequence stars (which can be determined by examining the spectrum) and it works like this. Look at the HR diagram again. You already know it plots absolute magnitude against temperature. If you look at some star and determine that it lies on the main sequence, then all you need is the temperature (which is fairly easy using Wein's Law) which you then use to determine its absolute magnitude. That is pretty important if you have read about Cepheid variables. You play the same game as described in the web pages to get the distance to that main sequence star. That is, compare the apparent magnitude to the absolute magnitude to get distance.
Standard Sirens - This one is so new the ink has not dried yet. In October 2017, gravity waves were detected from the merger of two neutron stars. Some really clever astronomers determined that it is possible to determine the distance to the event by measuring the strength of the incoming wave. In theory, the merger of neutron stars should produce a wave in gravity with a known amplitude. As that wave spreads out, the amplitude decreases at a known rate. This is very similar to the way we measure distances with type 1A supernova ... only using gravity waves instead of light. Learn more here.
Stellar Twins Method - This one is new ... so new a student in this class taught something to the teacher. As you know, stellar parallax is highly accurate but only works for nearby stars. The trick is to find two stars that have identical spectra and assume they are identical in every other aspect ... including luminosity. If you can get an accurate distance (using parallax) for one of the stars, it becomes a simple matter of playing the same game as used with Cepheids. That is, you can now estimate what the absolute magnitude of the twin is (since it has the same luminosity as the close twin) and compare that with the apparent magnitude you observe. From that you get the distance. As an analogy, lets say you take two identical automobile headlights and place one close to you and the other far away. If you have a great way of obtaining the distance to the close bulb (parallax), you can determine how much light it puts out (luminosity). Now the other light bulb puts out the same luminosity ... so ... if it appears fainter, you know it is because it is further away. However, if both lights appear to have the same brightness, both must be at the same distance from you. Learn more here.
Radar is used within our solar system to determine distance. By bouncing a radio signal off a planet, moon, asteroid, etc, all you have to do is measure the time it takes. More distant objects take longer to receive the echo.
Standard Rulers - The idea goes something like this .... If you think you know how large something actually is, you can place its distance based on how it appears to you. As an example, all stop signs have the same actual size (right?) so if you see a very small stop sign (small angular diameter), it must be far away. This technique has been tried with large elliptical galaxies (which are often found in a large cluster of galaxies) and even with very distant clumps of matter in the early universe.
The Faber–Jackson relation is a way to estimate the distance to elliptical galaxies. It was observed that individual stars move differently from one elliptical galaxy to the next (known as velocity dispersion). This happens to be linked to the overall luminosity of the entire galaxy. If you know the true brightness of the galaxy, it becomes a matter of placing it at the proper distance to display the light we receive (similar to the way it is applied with Cepheid variables).
The Tully–Fisher relation is a way of finding the distance to spiral galaxies. It was observed that the characteristics of the spiral galaxies rotation is directly linked to its overall luminosity. Again, if you think you know how bright the galaxy is, it is a simple matter to place it at the appropriate distance to produce the observed brightness.