Why care so much about finding distances in astronomy? If you know the distance to a star, you can determine its luminosity and mass. You can then discover a correlation between luminosity, mass, and temperature for main sequence stars that our physical theories must account for. Finding distances to stellar explosions like planetary nebulae and supernovae enables you to find the power needed to make the gaseous shells visible and how much was needed to eject them at the measured speeds. Stellar distances and distances to other gaseous nebulae are necessary for determining the mass distribution of our galaxy. Astronomers have then been able to discover that most of the mass in our Galaxy is not producing light of any kind and is in a dark halo around the visible parts of the Galaxy.
Finding distances to other galaxies enables you to find their mass, luminosity, and star formation history among other things. You are better able to hone in on what is going on in some very active galactic cores and also how much dark matter is distributed among and between galaxy cluster members. From galaxy distances, you are also able to answer some cosmological questions like the large-scale geometry of space, the density of the universe needed to stop the expansion (called W [``Omega'']), age of the universe, and whether or not the universe will keep expanding. The cosmological questions will be discussed fully in the next chapter on cosmology. This is only a quick overview of the reasons for distance measurements and is by no means an exhaustive list of reasons why distance measurements are so important.
Now let's take a look at the distance scale ladder. The bottom foundational rung of the ladder is the most accurate and the most certain of all the distance determination methods. Each rung depends on the rung below and it is less certain than the previous one.
The entire main sequence of a cluster is used in the same way to find the distance to the cluster. You first plot the cluster's main-sequence on a color-magnitude diagram with apparent magnitudes, not absolute magnitude. You find how far the unknown main sequence needs to be shifted vertically along the magnitude axis to match the calibrated main sequence. The amount of the shift depends on the distance.
The age of the cluster affects the main sequence. An older cluster has only fainter stars left on the main sequence. Also, stars on the main sequence brighten slightly at a constant temperature as they age so they move slightly vertically on the main sequence. You must model the main sequence evolution to get back to the Zero-Age Main Sequence. This method assumes that all Zero-Age main sequence stars of a given temperature (and, hence, mass) start at the same luminosity. These methods can be used to find distances out to 50 kiloparsecs.
RR-Lyrae have the same time-averaged luminosity (about 49 solar luminosities or an absolute magnitude MV = +0.6). They pulsate with periods < 1 day. Cepheids pulsate with periods > 1 day. The longer the pulsation, the more luminous they are. There are two types of Cepheids: classical (brighter, type I) and W Virginis (fainter, type II). They have different light curve shapes. The period-luminosity relation enables us to find distances out to 4 megaparsecs (40 megaparsecs with the Hubble Space Telescope).
The Rung 5 methods can be used to measure distances out to 50 to 150 megaparsecs depending on the particular method.
The Hubble Law relates a galaxy's recession (expansion) speed with its distance: speed = Ho × distance. Measuring the speed from the redshift is easy, but measuring the distance is not. You can calibrate the Hubble Law using galaxies out to 500 megaparsecs.
Rung 4 is a critical one for the distance scale ladder. With the Hubble Space Telescope, astronomers were able to use the Cepheid period-luminosity relation out to distances ten times further than what could be done on the ground. Previous ground measurements of the Hubble constant were 50 to 100 km/sec/Mpc. Using the Hubbble Space Telescope, astronomers observing Cepheids in the visible band in the Key Project constrained its value to between 64 and 80 km/sec/Mpc with a best value of 72 km/sec/Mpc. More recently, the Hubble Constant has been narrowed even further to between 70.6 and 77.8 with a best value of 74.2 km/sec/Mpc by using Cepheid period-luminosity relation in the near-infrared. The earlier measurement of 72 km/sec/Mpc had an uncertainty (error margin) of +/- 8 km/sec/Mpc and the newer near-infrared work reduces the uncertainty by more than two times to +/- 3.6 km/sec/Mpc. The value of 1/Ho is a rough upper limit on the age of the universe (assuming constant recession speeds!), so the new measurements imply an universe age of about 14 billion years. The favorite model for how the recession speeds have changed over the history of the universe gives an age of about 13.7 billion years with this value for the Hubble constant. This agrees with the ages derived for the oldest stars (found in globular clusters) of about 12 to 13 billion years. Also, the greater precision of the newer measurement of the Hubble Constant provides increased constraints on the nature of the "dark energy" discussed in the cosmology chapter.
An entirely independent way of determining the Hubble Constant (Ho) of the Hubble Law was made possible when we detected in mid-August 2017 the gravitational waves coming from the merger of two neutron stars in an elliptical galaxy NGC 4993, 130 million light years away (see also the article in Physical Review Letters). The amplitude of the gravitational waves enables us to determine the distance of the source independent of the distance scale ladder. The merger of the neutron stars created an explosion that could be seen with ground and space-based telescopes from gamma rays to radio waves. The telescope data give us the redshift due to the Hubble expansion that when coupled with the direct distance measurement from the gravitational wave data gives us a Hubble Constant value of 70 km/sec/Mpc (with an uncertainty of +12 and -8 km/sec/Mpc).
The Sombrero Galaxy is one of the most photographed galaxies and this exquisitely beautiful picture from the Hubble Space Telescope shows why. There are number of beautiful objects that draw people to take up astronomy as a profession or a life-long hobby and the Sombrero Galaxy is one of them. Seeking to understand what these objects are made of, how they behave, and how they formed gives us a greater appreciation for the art that surrounds us. Visible in even small telescopes at the southern edge of the Virgo cluster of galaxies, the Sombrero Galaxy is a spiral galaxy more massive than the Milky Way seen nearly edge-on from a distance of about 28 million light years away.
This image also provides a nice illustration of the parts of a spiral galaxy and its history. The oldest stars are in the spherical bulge & stellar halo retaining their randomly-oriented eccentric orbits of the original gas cloud from which the galaxy formed about 13 billion years ago. The stellar halo also sports almost 2000 globular clusters (the Milky Way has only about 150 globular clusters). The more massive stars in the spherical component added heavier elements (dust) to the newly-formed disk in which younger generations of stars are still forming. These younger stars have added to the dust layer that now outlines the disk and spiral arms. The fortunate slight tilt of the disk to our line of sight allows us to easily distinguish the near side of the disk from the far side. The disk star orbits are closely aligned to each other to make the very thin disk characteristic of spiral galaxies. A billion solar-mass black hole lies at the heart of the bright core.
Select the image to go to the webpage in the Hubble Heritage Team's website from which this image came. Larger versions of this image are available from the Hubble Site for the general public.
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last updated: October 29, 2017