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Various Techniques for Measuring Astronomical Distances

Alex Blanton

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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.

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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.

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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.

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Apparent Magnitude

• Apparent magnitude is how bright a star appears to the naked eye.

• Astronomers can measure this by flux.

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The Equations

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The Distance Modulus

• If the apparent and absolute magnitude of a star is known, the distance modulus can be employed.

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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!

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Optical depth and the Extinction Coefficient

• An extra coefficient, , must be added to account for a change in magnitude.

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

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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 = 1.00767 , a2 = 0.0394, and a3 = 0.00712

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Kinematic Distance

Now there is a function for α!

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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 = closeEmission lines = far

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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”.

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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.

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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

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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

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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.

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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.

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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

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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.