Measuring Galactic Distances from Earth Alex Blanton 1

Introduction The most accurate way to measure the distance of a star is through the parallax method. When the parallax method is not applicable, the distance modulus can be used. For other extreme cases, Kinematic distances are much more reliable. 2

The Parallax Method The parallax method uses Earth’s perigee and apogee as a “depth perception”. Astronomers take pictures of a celestial body at the apogee and one at the perigee. The star will appear to “move” in the sky. 3

The Parallax Method As Earth goes around in it’s orbit, it sees the body at different points. However, the line of sight from the perigee and apogee will converge on a center point with respect to a certain angle. The half angle of this is the parallax angle. The distance to a star is given by Where p’’ is measured in arcseconds, and pc is Parsecs. 4

Drawbacks of the Parallax Method The parallax method is one of the most accurate methods to gain the distance of a body, but it only works for relatively close objects. The distance to the Orion nebula can be measured with a high degree of confidence, but other methods must be used is the angle is too small 5

A star’s magnitude The magnitude of a star how bright it shines. In other words, it’s the Luminosity The first scale of magnitudes went from 6 to 0, with 0 being the brightest. The modern scale still uses this system, but astronomers have found stars brighter than zero and dimmer than 6. 6

Apparent Magnitude Apparent magnitude is how bright a star appears to the naked eye Astronomers can measure this by flux. Simply point a detector at a star, and start recording how many photons you get per second. 7

Absolute Magnitude Absolute magnitude is the apparent magnitude a star would have if it were located 10 parsecs away. This value depends on luminosity The inverse law of radiation is used to find the luminosity if the flux is measured. 8

The Equations 9

The Distance Modulus If the apparent magnitude of a star is know, the absolute magnitude can be known. Using the inverse law of radiation and the definition of apparent magnitude, the distance modulus can be solved as 10

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! If the dust is not taken into account, the distance will be much farther away than it really is. 11

Radial Distance and Radial Velocity As an object moves through the Milky Way, it has it’s own “peculiar” velocity, and a radial velocity in reference to the galactic center. Based on observations, a function has been constructed that depends on an objects radial velocity and distance from the galactic center. Where a1 = , a2 = , and a3 =

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Kinematic Distance Now there is a function for α! 15

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 16

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”. 17

In Summary Although there are a myriad of ways to measure the distance to a celestial body, some methods work better for different objects Using all of the methods, Astronomers can check if distances are reasonable or not. With distances to stars, the Milky Way Galaxy can be mapped out. 18