Neutron stars… Pulsars… What’s it to you? Well, if you’re anything like us, you’re pretty interested in detecting them and their polarization. But wait, what is all of this? Well, first off, a neutron star is a remnant of a supergiant star and is very dense. This is normally the stage that follows the collapse of a supergiant as it has run out of fuel—causing its core to collapse and become a neutron star. Then, pulsars are basically neutron stars that continuously rotate (sometimes at very rapid speeds) and emit radiation in intervals. Also, as neutron stars are relatively, pretty small (some the size of U.S. states) we are unable to detect at optical wavelengths due to the thermal source being proportional to the size of the star. This is why we are dove into utilizing the pulsar’s magnetic fields to detect them, along with their periods. So, in summary, we are talking about a neutron star’s magnetic fields, measuring their pulse periods, and seeing if the detected pulse is polarized or not!
(Written by Delanie Mitchell)
Pulsar 0329+54
So first up (the team’s favorite) is pulsar 0329+54. For this observation, we used the 20m telescope at the Green Bank Observatory located in West Virginia which has the purpose of capturing the radio observations from our universe. Our radio skynet observation was captured almost instantaneously after submission (done so by Nathan Flinchum) on March 21. The pulsar observation has a frequency of 1395 MHz, a duration of 180.0 seconds, and an integration time of 0.021 seconds. We used the “track” path type to keep the radio telescope pointed at the target while the Earth rotates. For use later, we also observed a calibration source, namely the Crab nebula. We did so using the “daisy” path type with 4 petals to mimic a “pulse” as the telescope points to the target in passing. The radius we used was 3 beams (45 arcmin / beam), the duration was 60 seconds, and the integration time was 0.3 seconds.
Something worth noting is that this particular pulsar (PSR 0329+54) is one of the easiest to detect (since it’s emitting at full strength most of the time / is bright)! Unfortunately, our data was corrupted in some way, so we couldn’t even load it into the Skynet plotting tool. Thankfully, we have access to past observations as well. We made use of another observation made by the user unda_49259, which was also taken on March 21, 2023. Our goal was to measure the period (how quickly the star rotates) and plot it!
A light curve is a plot of our brightness vs. time data that has been background subtracted. After loading the data into the Skynet plotting tool and taking out some potential RFI, the light curve was looking pretty nice! Although not perfect, we can tell that there is some type of sequence in there above the noise. When sonified, you can kind of hear it… but not super well.
We improved our attempt by making use of a “Lomb-Scargle” periodogram. This mathematical algorithm looks for periodicities in the previous light curve. After computing, the plot should have a few spikes (that aren’t noise / misleading values). There should be a spike at the period, ½ the period, ⅓ the period, ¼ the period, and so on. The value we care about is the rightmost spike, which should be our period — 0.7146 seconds.
Period folding chops up the light curve into pieces that are the size of whatever period we give it (we use the one we found in the periodogram), stacks them together, and then averages them. Ultimately, if the period is accurate, then this should reduce noise significantly and give us a plot that reveals the period very nicely.
Polarization
Before we could determine if this light is polarized or not, we had to calibrate our period-folded light curve. This is why we submitted an observation for a calibration source (the Crab nebula) that should only emit unpolarized light. After putting the calibration source data into the plotting tool and setting it up properly, we found the calibration factor to be 0.8, which we would use for calibrating the rest of the pulsars.
After adding the calibration factor (0.8) to PSR 0329+54’s period folded plot, we can see that the difference between the two channels changes from negative to positive during each spike. This means that we successfully detected the change in polarization as the “hot spot” on the neutron star passed by our view (every 0.7146 seconds).
We are looking at polarized light! But how??? We know that it’s not thermal radiation already (since thermal light is never polarized)… so it must be something else. As we mentioned in the introduction, we are actually looking at radiation produced by the neutron star’s magnetic fields! Because neutron stars are so small, their magnetic fields are VERY strong. If the magnetic pole is not aligned with the rotation axis of the star (just like on Earth), then the star will pulse with radiation from a hot spot. This spot is where the magnetic pole intersects with the neutron star’s surface. The pulse we see is that hot spot passing in and out of our observational view very quickly and the polarization is because of the special kind of radiation happening due to the magnetic field.
How does this connect to our period-folded light curve? Well, the change in which channel (from 1 to 2) picks up the strongest signal represents the polarization changing from one side to another (as the hot spot sweeps by; as the star rotates). As we can see this in our plot, we know that the star must be emitting polarized, magnetic-field-generated light that made its way to our telescope.
Sonogram
(Written by Nathan Flinchum)
Pulsar 2021+51
Something crucial to note for this observation is that my team was unable to use our own observation for pulsar 2021+51—so we grab someone else’s data! But hey, no worries! We were still able to have some fun with this despite the obstacle. So, this pulsar observation (which was captured by Brendon Weir) was submitted on March 19, was also captured by the 20m telescope at the Green Bank Observatory, has a frequency of 1395 MHz, a duration of 180.0 seconds, and an integration time of 0.02 seconds.
Above, you can see the chart titled “2021+51—Period Folding” which, just like 0329+54, depicts the ‘Flux Density’ in arbitrary units and the ‘Period Folding Time’ in seconds. Essentially, this chart takes the light curve of pulsar 2021+51, groups them together, and then attempts to find the median. In other words, this chart aims to cut-down on the noise of the pulsar with the intent of making it easier to detect. With the help of this chart, the sonogram for this period-folded data is now way more discernible with the use of a 0.53 measured period value. So, I can’t help but to recommend to you to check on the sonogram for yourself below! What’s your thoughts on this pulsar?
(Written by Delanie Mitchell)
Pulsar 0950+08
Our group had to once again use someone else’s data set to work with, and we’d like to give credit to the observer: tanco_49535 for their observation of the pulsar. This observation was submitted on March 21st using the Greenbank Observatory with the same inputs as the pulsars already mentioned, with a frequency of 1395 MHz, a duration of 180 seconds, and an integration time of .021 seconds. The graph displays the time in seconds on the x axis and the flux density measured in arbitrary units on the y axis. We can see the two very distinct points given by the pulsar, so let’s pull some data out from it shall we!
Thankfully, the analysis of this data was not too difficult. There was one very clear spike in the data that allowed us to find the period without too much trouble. Once we narrowed in on the big spike, we experimented with different start and end periods on the periodogram tab to try and find the precise period. Once we gathered that value, we moved over to the period folding tab and entered in our measured period as well as our .8 calibration value in order to get the graph above. We also made sure to test the decimals of the period, trying to ensure that the flux density was as high as we could get it, however our measured period value at .253066 seconds proved to be the best fit for the data.
This is one of our fastest pulsars, so if you play the sonogram below you can hear just how fast it ticks along.
(Written by Mia Mese)
Pulsar 0929+10
For pulsar 0929+10, our group used observer vdvoyan_49260’s data. This observation was submitted on Wednesday, March 22nd at 10:07 AM using the Greenbank Observatory. We uploaded this data into Skynet’s ASTR 101 L’s graphing tool and selected pulsar for the category of graph. For 0929+10’s graph, there were various peaks, however only a few, especially the ones in the middle, having a closely aligned blue curve with the red curve. This means a lower difference value between them both. We set the difference lines to show in the period folding tab. We zoomed in towards the middle area, testing two areas to see if they both worked. We started testing and plugging in different values for the star and end periods to see which works best and discern the time at which a peak spiked at its topmost value in the periodogram tab. We set the calibration to 0.8 in the period folding tab. We obtained two values: a measured period value of .226505 seconds and .202701 seconds.
We sonified this pulsar, which was distinguished by a very very fast paced, distorted heartbeat like sound.
(Written by Saki Male)
Calculation for our fastest Pulsar
After examining all of our pulsars, which one was the fastest? Well, that would belong to our very last one, pulsar 0929+10 with a period of .226505 seconds. Using the formula D < cP/𝜋, we get that D< (3.0×10^5)(.226505)/𝜋= D< 21,629.634km/12742km= 1.70 Earth diameters.
Faster Pulsars
For pulsar PSR J1748-2446ad, Dr. Reichart provided us with the text data file for this very fast pulsar to give us an idea about how they sound and differ from other pulsars. This pulsar was already dispersion corrected so we could only access the period folding tab and change the number of cycles. The period was .001395 seconds. Once we sonified the pulsar, we found it to be reminiscent of a heartbeat flatline. This pulsar was very different from the other ones, as it didn’t have any beat but was rather just one continuous high-pitched note throughout.
Using the same formula, D < cP/𝜋, we get that D< (3.0×10^5)(.001395)/𝜋= D<133.213 km
Authors of the blog
Delanie Mitchell, Saki Male, Nathan Flinchum, and Mia Mese