# The Standard Candles of Astronomy, or How We Attempt to Measure Distance in Space

Updated on March 6, 2018

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

## Parallax

Using little more than trigonometry and our orbit, we can calculate the distance to nearby stars. At one end of our orbit, we record the position of the stars and then at the opposite end of our orbit we once again look at the same region. If we see any stars that have seemingly shifted, we know they are close by and that our movement gave away their close nature. Then, we use a triangle where the altitude is the distance to the star and the base is double our orbital radius. By measuring that angle from the base to the star at both points, we have the angle to measure. And from there, using trig, we have our distance. The only downside is that we can only use it for close objects, for they can have the angle measured accurately. After a certain distance, however, the angle becomes too uncertain to give a reliable measurement.

That became less of a problem when Hubble was brought into the picture. Using its high-precision technology, Adam Riess (from the Space Telescope Science Institute) along with Stefano Casertano (from the same institute) perfected a way to get parallax measurements as small as five-billionths of a degree. Instead of imaging a star over many exposures, they "streaked" a star by having Hubble's image detector trail the star. Small differences in the streaks can be caused by parallax motion and thus give scientists better data, and when the team compared the different 6-month snapshots, errors were eliminated and intel was gathered. When combining this with information from Cepheids (see below), scientists can better refine established cosmic distances (STSci).

## Cepheids and the Hubble Constant

The first major use of Cepheids as a standard candle was by Edwin Hubble in 1923 when he began to examine several of them in the Andromeda Galaxy (then known as the Andromeda Nebula). He took data on their brightness and period of variability and was able to find their distance from this based on a measured period-luminosity relationship that gave the distance to the object. What he found was at first too astounding to believe but the data wasn’t lying. At the time, astronomers thought our Milky Way was the Universe and that other structures we now know as galaxies were just nebula within our own Milky Way. However, Hubble found that Andromeda was outside the bounds of our galaxy. The floodgates were opened for a bigger playground and a larger Universe was revealed to us (Eicher 33).

However, with this new tool, Hubble looked at distances of other galaxies in hope of revealing the structure of the Universe. He found that when he looked at the redshift (an indicator of motion away from us, courtesy of the Doppler Effect) and compared it to the distance of the object, it revealed a new pattern: The further something is from us, the faster it is moving away from us! These results were formalized in 1929 when Hubble developed the Hubble Law. And to help talk about a quantifiable means for measuring this expansion was the Hubble Constant, or H­o. Measured in kilometers per second per mega parsec, a high value for H­­o implies a young Universe while a low value implies an older Universe. This is because the number describes the rate of the expansion and if it is higher then it has grown faster and therefore has taken less time to get into its current configuration (Eicher 33, Cain, Starchild).

You would think that with all our tools of astronomy we could fix down Ho with ease. But it is a tough number to track, and the method used to find it does seem to impact its value. HOLiCOW researchers used gravitational lensing techniques to find a value of 71.9+/- 2.7 kilometers per second per megaparsec that agreed with the large scale Universe but not on a local level. This may have to do with the object being used: quasars. The differences in light from a background object around it are key to the method as well as some geometry. But cosmic microwave background data gives a Hubble Constant of 66.93 +/- 0.62 kilometers per second per megaparsec. Maybe some new physics are at play here...somewhere (Klesman).

## RR Lyrae

Related to Cepheids are these old, yellow variable stars whose absolute magnitude is well known with very little changes in their period. Couple this with their low mass, a period of less than a day, and their population numbers being higher than Cepheids and you have a winning model for finding distances. Their high numbers arise from their age, with them being old and thus located in such objects as globular clusters and dwarf galaxies. Cepheids typically are not located in these so having the RR in them helps us get valuable distance data (Eicher 36).

The first work into RR Lyrae was done in the early 1890’s by Solon Bailey, who noticed that these stars resided in globular clusters and that those with the same period of variability tended to have the same brightness, which would then make finding the absolute magnitude similar to Cepheids. In fact, years later Harlow Shapley was able to tie Cepheids and RR scales together. And as the 1950’s progressed, technology allowed for more accurate readings, but two underlying problems exist for RR. One is the assumption about the absolute magnitude being the same for all. If false, then much of the readings are nullified. The second main problem is the techniques used to get period variability. Several exist, and different ones yield different results. Keeping these in mind, RR Lyrae data must be handled carefully (Ibid).

## Planetary Nebula

This technique arose from work done by George Jacoby of the National Optical Astronomy Observatories, who began to collect data on planetary nebulas in the 1980’s as more and more were found. By extending the measured values of composition and magnitude of planetary nebula in our galaxy to those found elsewhere, he could estimate their distance. This was because he knew distances to our planetary nebula courtesy of Cepheid variables measurements (34).

However, a major hurdle was getting accurate readings courtesy of dust obscuring light. That changed with the advent of CCD cameras, which act like a light well and collect photons that are stored as an electronic signal. Suddenly clear results were attainable and thus more planetary nebula were accessible and thus able to compare with other methods like Cepheids and RR Lyrae. The planetary nebula method does agree with them but offers an advantage they don’t have. Elliptical galaxies typically don’t have Cepheids nor RR Lyrae but they do have plenty of planetary nebula to see. We can therefore get distance readings to other galaxies otherwise unattainable (34-5).

## Spiral Galaxies

In the mid-1970’s, a new method for finding distances was developed by R. Brent Tully from the University of Hawaii and J. Richard Fisher of the Radio Astronomy Observatory. Now known as the Tully – Fisher relation, it is a direct correlation between rotation rate of the galaxy and the luminosity, with the specific wavelength of 21 cm (a radio wave) being the light to look at. According to the conservation of angular momentum, the faster something is spinning then the more mass is has at its disposal. If a bright galaxy is found then it too is thought to be massive. Tully and Fisher were able to pull all of this together after taking measurements of the Virgo and Ursa Major clusters. After plotting out the rotation rate, brightness, and size, trends appeared. As it turns out, by measuring the rotation rates of spiral galaxies and finding their masses from this, you can along with the measured magnitude of brightness compare it to the absolute and calculate the distance from there. If you then apply this to far away galaxies, then by knowing the rotation rate you can calculate the distance to the object. This method has high agreement with RR Lyrae and Cephieds but has the added benefit of being used well outside their range (37).

## Type Ia Supernova

This is one of the most common methods used because of the mechanics behind the event. When a white dwarf star accretes matter from a companion star, it eventually blows off the accumulated layer in a nova, and then resumes normal activity. But when the amount added surpasses the Chandrasekhar limit, or the maximum mass the star can maintain while being stable, the dwarf goes supernova and in a violent explosion destroys itself. Because this limit, at 1.4 solar masses, is consistent, we expect the brightness of these events to be virtually identical in all cases. The Type Ia supernova are also very bright and thus can be seen at further distances than Cehpeids. Because of the number of these happening is rather frequent (on a cosmic scale), we have lots of data on them. And the most frequently measured portion of the spectrum for these observations is Nickel-56, which is produced from the high kinetic energy of the supernova and has one of the strongest bands. If one knows the supposed magnitude and measures the apparent, a simple calculation reveals the distance (Eicher 38, Starchild).

## Baryon Acoustic Oscillations (BAOs)

In the early Universe, a density which encouraged a "hot fluid-like mix of photons, electrons, and baryons" existed. But so did clusters of gravitational collapse, which caused particles to clump together. And as that happened, pressure increased and temperatures rose until the radiation pressure from the combining particles pushed photons and baryons outward, leaving behind a less dense region of space. That imprint is what is known as a BAO, and it took 370,000 years after the Big Bang for electrons and baryons to recombine and allow light to travel freely in the Universe and thus also let the BAO spread unhindered. With theory predicting a radius for a BAO of 490 million light-years, one simply needs to measure the angle from the center to the outer ring and apply trig for a distance measurement (Kruesi).

## Which is Right?

Of course, this discussion of distance was too easy. A wrinkle does exist that is tough to overcome: different methods contradict Ho values of each other. Cepheids are the most reliable, for once you know the absolute magnitude and the apparent magnitude, the calculation involves a simple logarithm. However, they are limited by how far we can see them. And though Cepheid variables, planetary nebulas, and spiral galaxies give values supporting a high Ho (young Universe), Type Ia supernova indicate a low H (old Universe) (Eicher 34).

If only it was possible to find comparable measurements in an object. That is what Allan Sandage of the Carnegie Institution of Washington aimed for when he found Cepheid variables in galaxy IC 4182. He took measurements of them using the Hubble Space Telescope and compared that data to the findings from supernova 1937C, located in the same galaxy. Shockingly, the two values disagreed with each other, with Cepheids placing it at about 8 million light years away and Type Ia at 16 million light years. They aren’t even close! Even after Jacoby and Mike Pierce of the National Optical Astronomy Observatory found a 1/3 error (after digitizing the original Fritz Zwicky plates of 1937C), the difference was still too large to fix easily (Ibid).

So is it possible that the Type Ia are not as similar as previously thought? After all, some have been seen to decrease in brightness slower than others and have an absolute magnitude greater than the rest. Others have been seen decrease in brightness faster and therefore have a lower absolute magnitude. As it turns out, 1937C was one of the slower ones and therefore had a higher absolute magnitude than expected. With this taken into consideration and adjusted for, the error was reduced another 1/3. Ah, progress (Ibid).

## Works Cited

Cain, Fraser. “How Do We Measure Distance in The Universe.”universetoday.com. Universe Today, 08 Dec. 2014. Web. 14 Feb. 2016.

Eicher, David J. “Candles to Light the Night.” Astronomy Sept. 1994: 33-9. Print.

Klesman, Allison. "Is the Universe Expanding Faster Than Expected?" Astronomy May 2017. Print. 14.

Kruesi, Liz. "Precise Distances To 1Million Galaxies." Astronomy Apr. 2014: 19. Print.

Starchild Team. “Redshift and Hubble’s Law.” Starchild.gsfc.nasa.gov. NASA, n.d. Web. 14 Feb. 2016.

---. “Supernovae.” Starchild.gsfc.nasa.gov. NASA, n.d. Web. 14 Feb. 2016.

STSci. "Hubble stretches stellar tape measure 10 times farther into space." Astronomy.com. Kalmbach Publishing Co., 14 Apr. 2014. Web. 31 Jul. 2016.

© 2016 Leonard Kelley

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Leonard Kelley

5 months ago

Thank you for those kind words, Umesh. I am glad you enjoyed it!

• Umesh Chandra Bhatt

5 months ago from Kharghar, Navi Mumbai, India

I have some interest in amateur astronomy. I found this article very informative and interesting. Fathoming the depths in the deep universe is definitely a challenge.

Thanks for posting the article here.

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