Various Techniques for Measuring Astronomical Distances Alex Blanton 1

Introduction A very common tool for knowing the distance to a star is the distance modulus. Through knowing of the Galaxies motion, a celestial body can be determined by calculating its galactic position. Through the expansion of the Universe, Edwin Hubble was able to find a relationship through velocity and distance on inter galactic scales. 2

A star’s magnitude The magnitude of a star is the value of the star’s brightness. The first scale of magnitudes went from 6 to 0, with 0 being the brightest. Future astronomers chose to use this convention, but discovered magnitudes beyond 0 and 6. 3

Absolute Magnitude Absolute magnitude is the apparent magnitude a star would have if it were located 10 parsecs away. The inverse law of radiation is used to find the luminosity if the flux is measured. 4

Apparent Magnitude Apparent magnitude is how bright a star appears to the naked eye. Astronomers can measure this by flux. 5

The Equations 6

The Distance Modulus If the apparent and absolute magnitude of a star is known, the distance modulus can be employed. 7

Errors with the Distance Modulus One very big problem with the distance modulus is that it does not take into account the dust between Earth and the star! 8

Optical depth and the Extinction Coefficient An extra coefficient,, must be added to account for a change in magnitude. 9

Interstellar Reddening 10 As light passes through dust, high frequency and low frequency waves get filtered since longer wavelengths pass through the dust easier.

Radial Distance and Radial Velocity As an object moves through the Milky Way, it has it’s own “peculiar” velocity and a radial velocity around the galactic center. Based on observations, a “rotation curve” has been fitted for the galactic curve. Where a1 = , a2 = , and a3 =

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Kinematic Distance Now there is a function for α! 14

Kinematic Distance The star is either behind the tangent point, or in front of the tangent point. To solve for this, spectral lines of a cloud at the tangent point are used. Absorption lines = close Emission lines = far 15

Drawbacks to Kinematic Distances There must be a cloud around the tangent point! No cloud means you have two distances with no way of knowing which one is the real value. If not careful, it is easy to choose the wrong distance when looking at the “Radio Recombination Line”. 16

Early Concepts of Expansion Using Doppler shifted spectral lines to uncover the radial velocities of objects in our Milky Way. V.M. Slipher recorded many Doppler shifted spectral lines, and found that most were red shifted. 17

A Universe Bigger than the Milky Way During the time V. M. Slipher was working, Edwin Hubble was able to prove that M31 was “extragalactic”. By using Cepheid variable stars, he showed that the distance to M31, as well as 18 other galaxies, was beyond the reach of the Milky Way 18

A Happy Coincidence After Hubble was able to determine the distance to several galaxies, he found that the distance away from a star is proportional to it’s recessional velocity. This became known as Hubble’s Law 19

Hubble Flow and Peculiar Velocities A galaxy can move through space at it’s own peculiar velocity, but an extra “recessional velocity” is added because space is expanding. 20

Cosmological Redshift As space expands, light leaving a galaxy is stretched out because space is expanding. Although the Doppler shift equations cannot account for curved space, they still prove useful. 21

Ambiguity of the Hubble Constant Ambiguity of the Hubble constant arose since remote galaxies were used to calibrate Hubble’s Law. After the Wilkinson Microwave Anisotropy Probe (WMAP) was launched to explore the CMB, the Hubble constant so that 22

In Summary Knowing distances to stars can give us a 3D map of the Milky Way. Having more than one tool to measure the distance will lead to more accurate results. By using these methods on a cosmological scale, astronomers can determine the in workings of the Universe. 23