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### 3. Blast from the Past

Dr. Shri Kulkarni of the California Institute of Technology and his colleagues found that a certain gamma-ray burst came from a faint galaxy with a redshift of 3.4. "That means that the burst originated over 12 billion light-years away," Dr. Kulkarni said. How did he know that?

Redshift is a term astronomers often use for the Doppler Shift observed in the spectra of celestial objects. Two things can create the shift - the motion of the object toward or away from the observer, or motion near a strong gravitational field. The Doppler effect is named for Christian Doppler (1803-1853), who pointed out that if a light source is approaching or receding from an observer, the light waves will be (respectively) crowded together or spread out. Consider this: if the light source is stationary with respect to the observer, it will emit wave crests of light at regular intervals 1,2,3,4, and spread out in all directions evenly. However, if the source is moving toward the observer, successive wave crests are emitted from different, shorter distances from the observer. To the observer, this has the effect of making the waves appear shortened...and shorter wavelengths appear toward the blue end of the spectrum. The opposite effect occurs if the emitter is moving away from the observer, the distance between crests appears to be lengthened - or shifted toward the red end of the spectrum.

If the motion is entirely either directly toward or away from the observer, the equation which relates the velocity of the motion to the apparent shift in wavelength is:

Dl/l = (sqrt(1+v/c) / sqrt(1-v/c)) — 1

Dl is the difference between l the emitted wavelength and the wavelength measured by the observer, c is the speed of light, and v is the relative line of sight velocity of the observer and source (it is counted as positive if the velocity is away from the observer and negative if the velocity is toward the observer). If the relative velocity is small compared to the speed of light, this equation reduces to the more common and simpler form

Dl/l = v/c

In astronomy, the Doppler shift is a very powerful tool from which can lead us to know not only how fast something is moving, but also how far away from us it is. Between 1912 and 1925, Astronomer V.M. Slipher at the Lowell Observatory first measured the radial velocities of galaxies using the Doppler shift. He discovered that they all seemed to be moving away from us...the Universe was expanding! By 1929, Edwin Hubble at the Mt. Wilson Observatory determined the distances to galaxies for which velocities had been measured and found that these two parameters were proportional to each other. This relation is now known as the Hubble law. It can be written as v = Hr, where r is the distance, H is the constant of proportionality called the Hubble constant, and v is the velocity. The Hubble constant is currently believed to be between 60 and 75 km/s per million parsecs.

What do the redshifts (which astronomers define as Dl/l) have to do with GRBs? Try this:

In a few cases, shortly after the detection of a GRB, high-powered ground- and space-based observatories were able to detect the afterglow of the event. These observations provided scientists with the data to determine the host galaxy of the event and obtain a redshift measurement of that galaxy. Redshift measurements allowed a determination of the distance to the source of the GRB!

• Examine the table below. Use what you have learned about redshift to determine the velocities and distances of the galaxies which appear to host the GRB events. Perform these calculations with both the minimum and maximum Hubble constant values. HINT: The material associated with GRBs is moving very, very fast — so the simplified version of the Doppler shift equation cannot be used.

 Burst Redshift 970508 0.835 971214 3.418 980703 0.966 990123 1.6

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• Given your knowledge of how fast gamma-rays travel, how long has it taken them to reach us from such a distance?

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• What does this tell us about the age of the Universe?

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• What must have happened in the Universe already in order for a GRB to occur?

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