Written by Karsen Kitchen, Ishaan Balakrishnan, Jacob Blizzard, James Bowling, and Rianne Eccleston.
Pulsars, pulsating stars. Forming from supernova remnants, these are stars that emit energy from their magnetic fields that are on a different axis than the polar axis, causing these stars to spin when “hot”. The speed at which these pulsars spin is simply determined by how powerful their magnetic fields are and their size. Their size isn’t big, small rather, as they typically would be able to comfortably remain on the surface of a city, that is before its magnetic fields rips the city out of existence. Observing these pulsars can only really be done through radio waves, as optical light wouldn’t be able to reach the pulsars’ distance and small size from earth.
Using radio waves, we’re able to determine the period of the pulsar; how fast it spins. But first the observations need to go in. We were given a table of pulsars we had to split amongst ourselves. This table included the pulsars 0329+54, 2021+51, 1133+16, 1919+21, 0950+08, and 0929+10. Finding the period in these ranged in difficulty from 0329 being the easiest and 0929 being the hardened, but all of these pulsars were bright and slow.
Observing these pulsars was like observing the radio side of the Moon, a simple map of the area in H1 (frequencies 1355 to 1435) in low resolution, with a 3 minute duration. These observations were cheap to do, so it was easily spread between the five of us, with one person observing the 0329 pulsar, and one of us doing the calibration.
The calibration used for these pulsar observations are used to check for polarization in the light that the pulsar emits, but it has to be observed in a different method. The one closest to 0329 was the Crab Nebula, since it isn’t a pulsar we have to observe the nebula like one. This is called a daisy map, where the map looks similar to a daisy, crossing over the source several times, making the signal rise and fall like a pulsar. We used four petals for this observation with a 60 second duration, also with a radius of 135 arcmins. Since these radio observations can be taken during the day, they come back pretty quick making it easy to start trying to find the period of the pulsar. Out of the pulsars that we studied, namely PSR 0329, PSR 0929, and PSR 2021, we were able to successfully analyze their data and identify their periods. However, for the other pulsars that we examined, we were unable to determine their periods.
PSR 0329+54 is a pulsar located in the constellation Camelopardalis, with a rotational period of 0.714 seconds and a dispersion measure of 28.83 pc/cm³. This pulsar is considered easy to observe because it has a high flux density which makes it emit a large amount of radiation per unit area. Its relatively short rotational period of 0.714 also makes it easier to recognize and capture its periodic signals. To analyze the pulsar’s properties, we first obtain its light curve using data from the greenbank observatory’s radio telescope. The initial light curve shows the pulsar’s periodic emission, which appears as a series of peaks separated by its rotation period.
After that we generate a light curve with the data from our observation. This identifies the pulsar’s dominant frequency and any potential harmonics. The periodogram does not show any significant harmonics but does show two main peaks.
From this periodogram, we then create a period folding graph by folding our light curve by using the rotation period to create it. We can see two main peaks here and a broad inter-pulse region. To check for polarization, we analyze two polarization channels using an unpolarized or nearly unpolarized source for calibration. We used Tau A which is the crab nebula. After calibration, we find that PSR 0329+54 is indeed polarized. This suggests that its emission mechanism is likely to involve synchrotron radiation, where charged particles in the pulsar’s magnetosphere emit radiation as they accelerate in magnetic fields.
We also generated a sonogram for this pulsar which was generated to analyze the frequency evolution of the pulsar’s emission. This analysis reveals any potential drifting of sub-pulses or other patterns in the pulsar’s emission.
PSR 0929+10 was classified as the “Very Difficult” pulsar, due to its very odd and irregular periods of emitting radio waves. Since pulsars have different periods, sometimes their beams of electromagnetic radiation isnt always pointed towards us, making them difficult to detect. Pulsar 0929+10 was categorized as particularly challenging to observe and analyze, primarily because of its inconsistent emission pattern, which makes it difficult to accurately determine the periods during which it is active. I gathered by data on the GreenBank Observatory’s preliminary data page, and loaded it into Skynet Graphs. Starting with the periodogram, I noticed a blip in my data around the 0.2 and 0.3 mark, with further observation, I set my start period to 0.21 and my end period to 0.23, and ended up detecting the pulsar’s period, which is 0.2265 seconds. I then set my calibration to 0.8, which we gathered from our Crab Nebula data, and checked for polarization. You can normally tell if a pulsar is polirized by a discrepancy between the Channel 1 and Channel 2 data, which indicates that different amounts of radio light is being emitted from both ends, making it polarized. The discrepancy between my Channel 1 and Channel 2 data was extreme, so I checked with my TA. My TA told me that Channel 1 must’ve been dead when it was observing my data, becuase the difference between the channels was not normal. Although one of my channels was dead, I could tell that the pulsar was polarizied based on the data.
A wealth of information can be garnered from knowing if the light received is polarized light. The first major conclusion to be drawn is that this emission is not thermal emission. Light travels as waves, and waves oscillate in a plane. For polarized light in particular, the geometric planes that the light oscillates in are molded to a certain orientation dictated by the neutron star’s magnetic field. Thermal emission, however, has no set orientation. Each plane is oriented in a random direction, leaving no uniformity in its detection. Thus, the simple fact that the light we receive is polarized allows us to conclude that the emission mechanism is not thermally related. The detection of polarization changes as the telescope moves from one side of the neutron star to the other. Each of the two channels used for this radio detection are oriented perpendicular to each other. Thus, light enters in such a way that one channel experiences a detection greater than the other. This is because the light wave oscillates more in the plane that has a greater detection signal. The presence of strong magnetic fields surrounding and caused by the neutron star collimate the light emitted into distinct directions exiting the star. Particles, ionized by the neutron star’s “hot spots” follow a curved path set by the star’s magnetic fields. As the particles follow this path, they themselves spiral, releasing “curvature” radiation. This radiation is what is collimated as it exits the star’s field, and is what produces the polarized detection in our instrument.
Found in supernova remnant HB21 and classified as moderate difficulty due to the timing of the pulsar being “hot” and not, with a little run of trial and error a period was found. Using the same methods as above, loading 2021’s data into the graphing system surprisingly worked, making it easy to get into work faster. First is to find a proposed period, but it’s difficult given the amount of noise in the radio observation, so instead, it’s onto trying to find a period in the periodogram, ending up with a period of around 0.5 (the first attempt was around 3). Then it’s time to test its viability with period folding, to see if we can further the period number and hear the sonification. This would allow us to be able to hear the pulses of the pulsar and see if it can be refined to sound clearer. This is where polarization is checked too, with the calibration of 0.8 determined by the crab nebula, if the line that appears is similar to the graph then it is polarized. Another way (and sometimes, a better way) to check for polarization is to go back to the periodogram and see if the channels line up better to each other through the points given. Ultimately, pulsar 2021 has polarized light and spins at a rate of 0.592099
When high-mass star death occurs in the universe, a supernova is created along with (usually) a neutron star. Pulsars are a type of neutron star that follows a conventional life path, where they are born hot and cool down as they get older. However, even if you observed the youngest, hottest supernova, you still would not see the neutron star since it has roughly the same surface area as Rhode Island. It doesn’t get any easier as the star cools down either, as it produces even less light for us to detect. However, the unique thing about pulsars is the strength of their magnetic fields. For reference, the magnetic field produced by the sun is only twice as strong as the Earth’s. Pulsars have roughly the same mass as the sun, but condensed into about 20 km, creating a magnetic field 5 billion times stronger than the sun. Along the two magnetic poles of the star are hot spots where particles jet out, creating light beams that are visible from Earth. This is called “curvature” radiation, since the paths of the particles are dictated by the curvature of the field lines surrounding them. If everything is aligned, we see the radiation sweep across our solar system every time the pulsar rotates, which can be as fast as every .1 seconds. We can observe these pulses in the radio, allowing us to study the period, size, and possible polarization of the light being emitted. Based on how quickly the pulsar is rotating, we can put constraints on the size, since nothing can travel faster than the speed of light. For any point on the equator of the star, it can be calculated that the diameter must be less than the speed of light multiplied by the period and divided by pi. This ensures that no point on the star is breaking any laws of physics.
After analyzing the properties and characteristics of six different pulsars, which were 0329+54, 2021+51, 1133+16, 1919+21, 0950+08, and 0929+10, it is really interesting as to how the behavior of each pulsar changes and the reasons for it. Pulsars are rapidly moving neutron stars that rotate and emit beams of electromagnetic radiation, which is how we are able to capture data from it through a radio telescope. All six of the pulsars that we analyzed have different pulse periods, pulse widths, dispersion measures, and scattering times. From pulsar 0329+54 which was bright and highly polarized to pulsar 1919+21 which is fainter and less polarized, all of the pulsars have their own unique characteristics. Pulsars like 0950+08 is a pulsar that exhibits periodic nulling behavior, where the pulse emission turns on and off at regular intervals which makes it very interesting to understand the reasoning behind it. While some pulsars are harder to capture because we may not be able to capture their electromagnetic beam, others are more easier to capture. Overall, studying these pulsars have helped us gain an understanding of rotating neutron stars and their differing behaviors depending on their unique conditions and distances.