Astr384 Galaxy Projects, Spring 2010

Light Polarization of the Crab Nebula (M1), Rachel Boerner

The Nebula:

The Crab Nebula is one of the most well known supernova remnants. A supernova remnant (or nebula) is created from the gases of a star explosion. The supernova which created the Crab Nebula could be seen with the naked eye for 23 days during the daytime, and 653 days during the night. It was first recorded as appearing on July 4, 1054 AD by Chinese astronomers. Apparently, archeologists even believe that the appearance of the supernova was recorded in the art of the Native Americans here in the United States. In the modern era, the Crab Nebula was discovered by John Bevis in 1731 and independently by Charles Messier in 1758. It was with the discovery of the Crab Nebula that Messier begin to compile his catalog.

The Crab Nebula is expanding at an average of 0.2 arcsecs per year. As of right now, the Crab Nebula is approximately 10 light years in diameter. The Crab Nebula seems to have two distinct parts to the structure: gaseous filaments and continuum background. The gaseous filaments that surround the nebula seem to be from the former outer layers of the star before it exploded and the continuous background emission consists of highly polarized, synchrotron radiation. Particles that are accelerated in curved paths give off synchrotron radiation. A magnetic field is one of the mechanisms that can cause the particles to accelerated in curved paths. When particles enter the magnetic field, they accelerate in “spirals” around the field lines and emit synchrotron radiation. The magnetic fields of the Crab Nebula are created by one of the most interesting features of the Crab Nebula: the Crab Pulsar.

The Pulsar:

The Crab Pulsar is the neutron star that is all that remains of the exploded star. It is the star's core that is now held up by neutron degeneracy pressure. Neutron stars are second only to black holes as the densest objects in the universe. The Crab Pulsar concentrates more than one solar mass (2x10^30 kg) in a volume just 30 kilometers in diameter. Neutron stars rotate extremely fast since, by conservation of angular momentum, if mass is lost or the radius of the star decreases, then angular speed must increase. It is the collapse of the star to a smaller radius (just prior to the supernova explosion) that increases the angular momentum. The Crab Pulsar rotates near 30 times per second. The fast rotation of the Crab Pulsar creates a "pulsar wind" around the object, which moves charged particles around to create a change in the electric field and in turn is another source for the magnetic field.  

The Light:

The magnetic field of the Crab Nebula does not just create the synchrotron light, it also causes that light to be oriented at a certain angle, which is called polarized light. The stronger the magnetic field, the greater the polarization will be. Polarized light is easy to detect with filters that only allow light with a certain polarization through. Since polarized light is often caused by magnetic fields, learning about the angle of light polarization can teach astronomers about the strength and direction of magnetic fields.

The picture above was taken by the SCUBA (Submillimetre Common User Bolometer Array) Polarimeter instrument on the James Clark Maxwell telescope (JCMT) in Hawaii. The SCUBA Polarimeter has a rotating quartz half-waveplate and a fixed analyzer in order to detect the percentage and direction of linear polarization in objects. The colors indict the brightness of the total light received from the nebula (red/white = bright; blue/black = dark). The arrows on the image indicate the direction of the polarized light and amount of polarized light (longer arrows signify more polarized light). As one can see the light tends to be polarized in a diagonal direction. It starts in the center of the nebula, heads out in a positive slope (bottom left to top right), and then curls outward towards the edges of the nebula.

The image below that was taken with the polarization filters at Calvin. Calvin’s telescope is an optical telescope versus the submillimeter one that the SCUBA is. In the Calvin image, the brightness is shown in a grayscale (white = bright; black = dark). The arrows here also indicate the direction and intensity of the polarized light. The up-side down 50% label shows the length of a line that represents light that is 50% polarized. We are not completely sure at which angle that each of the polarized images were taken. We made sure to keep the angles 45 degrees apart so that we would be able to get logical images that were just offset by a certain amount. We see the right slanting direction of some of the arrows that are consistent with the SCUBA image; however, a lot of our vectors point straight up and down as well. We were unable to determine for certain the amount by which our polarization calibration was offset.

The Reduction of Data:

After determining which of Calvin's polarizer I would use, I used circular graphing paper to mark off 4 consecutive lines 45 degrees apart. I then got images in the Clear filter at each orientation and without the polarizer. After taking the images, I calibrated using the bias and darks taken the night of my data, and the flat taken in each specific filter. Once the calibrated data had been saved, Prof. Haarsma and I sky flattened the images using the Auto-Flatten function in MaxIM. We made sure the images were aligned before performing Pixel Math inside MaxIM to subtracted off the sky background level.

We then switched over to IRAF to complete the rest of the project. We were having difficulties using the hstpolima function because the program complained about the header key words. So, we adjusted those and added some new headers to fit the requirements of the program. We decided to use the imarith function in IRAF to combine the images into Stokes Parameter images. Stokes Parameters are the convenient mathematical method used for categorizing polarized light. G. G. Stokes created four quantities that are observable in electromagnetic wave. Each of these quantities are a combination of filters that are 90 degrees apart so that half of the light is transmitted and half is not. The I quantity passes all orientations of light equally. The Q quantity is linearly polarized light with the transmission axes on the horizontal and vertical axes. The U quantity has transmission axes of 45 degrees and 135 degrees. The V quantity is of left- and right-circular polarized light. They are combined in the following way:

where E is the intensity of the images. For this experiment, we were not interested in the V image or circularly polarized light. So, we measured four orientations: P1 = 0 degrees (Ex), P2 = 45 degrees (E45), P3 = 90 degrees (Ey), and P4 = 135 degrees (E135). Even if the orientations are not exactly these angles, the worst that would occur would be that vectors that show that polarized light are at a fixed offset from the true polarization angle.

After creating the Stokes Parameter images, we switched over to the polimplot function in IRAF in order to create a vector map of the polarization. After fixing a few more bugs, we were finally able to create a percent of polarization intensity image and an image of the degree angle of the polarized light (see below). We could visually see which areas of the nebula were significantly polarized (green circles below); so, we specified only those sections to create our final vector plot (shown in above section).

The above image shows the angle of polarized light. Black represents light that is -180 degrees and white represents light that is polarized +180 degrees, with an arbitrary offset to the true polarization angle. The green circles are the mask that we put on the image in order to specify the nebula only.

References:

Hecht, Eugene. Optics. 4th ed. N.p.: Pearson Education, Inc, 2002.

"Messier 1: Crab Nebula." Students for the Exploration and Development of Space. SEDS, 22 Aug. 2007. Web. 23 May 2010. <http://seds.org/messier/m/m001.html>.

Shklovskii, Iosif S. Stars: Their Birth, Life, and Death. Trans. Richard B. Rodman. San Franciso: W.H. Freeman and Company, 1978. 262-85.

"Planck sees the Crab." Planck. N.p., 29 Sept. 2009. Web. 24 May 2010. <http://planck.cf.ac.uk/node/141>.

"Polarimetry with SCUBA." Joint Astronomy Centre. JCMT, 7 Nov. 2004. Web. 24 May 2010. <http://www.jach.hawaii.edu/JCMT/continuum/background/polarimeter.html>.