The Crab Nebula
N.A.Sharp/NOAO/AURA/NSF
The Crab Nebula in the constellation Taurus, the bull, is one of the most fascinating objects in the sky. It vividly demonstrates the violent death of a high-mass star and the subsequent collapse of its core. This cataclysmic event attests to the incomprehensible energy released when a supergiant star reaches the end of its thermonuclear life and forms a neutron star or (possibly) a black hole. It is commonly believed that supernovae such as the Crab Nebula progenitor are at least partially responsible for spewing heavy elements into the interstellar medium and that most of the atoms in us and our world were once forged in the dying cores of stars that long ago exploded and and faded from brilliance. In the photograph above, the resulting rapidly-rotating neutron star (called a pulsar) is shown in a series of freeze-frame images—ordered from upper left to lower right—taken at intervals of about 1 millisecond.
The violence of the explosion that creates a supernova can be imagined by comparing that energy to the output of a fairly typical main sequence star like our sun: when a dying massive star explodes as a supernova, the total energy released at all wavelengths of the electromagnetic spectrum is roughly equivalent to the combined energy output of 1,000 sun-like stars during their entire 10 billion year main sequence lifetimes! Another way of looking at this colossal energy release is to consider that the explosive energy of this one star's death throes is roughly the same as all of the energy given off by everything in the observable universe during one second!
The supernova that created the Crab Nebula was first observed by Chinese astronomers on July 4, 1054. According to their accounts, a "guest" star suddenly appeared where none was known to exist before and was so bright as to be visible in broad daylight. By night it rivaled the quarter Moon, but over several months' time the star slowly faded and disappeared from view. Also viewed by Native American Anastazi and drawn in petroglyphs, it is one of the strange twists of history that there is not a single written account of this supernova being observed in Europe! It wasn't until 1758 that the French amateur astronomer and comet hunter, Charles Messier, discovered a nebulous patch vaguely resembling the claw of a crab near the star Zeta Taurui on the border of Taurus and Auriga. To avoid confusion with other comet-like objects, Messier compiled a list of objects, starting with the Crab Nebula, which he designated as M1. His list of faux-comets eventually numbered 110, but it wasn't until the 1940s that astronomers looking through ancient Chinese records realized that Messier's first object was actually the tangled remnants of that long dead guest star.
Procedure
In this exercise, we will make measurements of two photos of the Crab Nebula to arrive at an approximate date of the supernova's apparation in Earth's sky.
Figure 2.
In order to find the age of the nebula, and hence the year that it was first visible, we will analyze two photographs of the nebula taken 34 years apart, one in 1942 and the latter in 1976 (see page 379 of the laboratory handout). By carefully measuring the positions of filaments of the nebula with respect to the pulsar—the exposed degenerate neutron core of the supergiant star, we can ascertain the expansion rate of the nebula and finally, the year the expansion began.
The collapsed core of the progenitor star, a rapidly rotating neutron star called a pulsar, must first be identified amidst the dangled remnant. It is easier to find the pulsar in the bottom photograph first and it can be identified as the lower right star of a line-of-site pairing at the center of the nebula (see Figure 2).
The first step required to establish the expansion rate is to determine the plate scales (technically called the dispersion) of each photographic plate. Determining the plate scales is relatively easy given that the two marked stars on the photographs are known to be 576 arcseconds apart (see Figure 3 below).
Figure 3.
By measuring the distance between the stars to the nearest one tenth of a millimeter (0.1 mm) and dividing the separation in arcseconds by that number, the dispersion in arcsec/mm can be found. Since we cannot assume these photographs are reproduced to the same scale, we must find the dispersion for both photos.
For example, the dispersion of the 1942 (top) photographic plate can be found as
D1942 = 576" ÷ 181.7mm = 3.17 arcsec/mm
Figure 4.
After determining the dispersion for both photographs, locate 15
easily identifable filaments of gas near the edge of the nebula.
It is important that each of the 15 filaments can be seen in both photos.
Be careful not to accidentally confuse a star with a knot
of gas.
Round objects should be avoided and it is best to stick to locating
wispy structures. Now, carefully measure (again, to the nearest tenth
of a millimeter) the distance from the pulsar to a point on each filament.
If possible, measure to the same point on a filament in both photographs.
An example of a filament and the measurement is shown in Figure 4.
Assuming that the particular filament is measured to be 51.5 mm from the pulsar, the filament's angular distance from the pulsar is
X1942 = 51.5 mm × 3.17 arcsec/mm = 163 arcsec
Age Determination
Using the dispersion of the 1976 photo and the measurement to the same point on the filament in that photograph, we find that the angular distance is X1976 = 171 arcsec. From this, the expansion of the nebula over the intervening 34 yearsis found to be
D = X1976 – X1942 = (171 – 163) arcsec = 8 arcsec.
Dividing the expansion by the elapsed time between the two photographs, we can ascertain the nebula's expansion rate per year. Based on this one comparison, the proper motion of this filament is
µ = 8 arcsec ÷ 34 years = 0.235 arcsec/yr.
Given that the most recent photo was taken in 1976, we can then use the proper motion of the filament to determine how many years ago the filament began moving outward from the pulsar to reach its location in the latest photo. This number—analogous to the age of the nebula—is called the expansion age and is found to be
T = 171 arcsec ÷ 0.235 arcsec/yr = 728 yrs.
Based on the expansion age, the estimated year the supernova was observed is simply
Year = A.D. 1976 – 728 yrs = A.D. 1248.
The calculations must then be repeated for the remaining 14 filaments.
Since there will undoubtably be some variation in the results of each
filament's age
, the 15 values should be averaged to arrive at the
best estimate for the year of observation.
