1. Pulsar Data I 1

2. Topics How pulsar data is created Data Plots Integrated Pulse Profile
Time Domain plot
Sub-band plot
DM plot
Header

3. GBT raw data. Is there a pulsar in there? This data looks like noise!
If we knew the spin period, we could fold the data to make the pulse signal rise above the noise.
Like this! Unfortunately we are looking for new pulsars, and we don’t know their spin period ahead of time!
Since noise is random, IE filled with ups and downs, and the pulse signal is always positive, it will add up, if we stack the signals up just right, where as the noise will average to zero.

4. You get to see the 24 BEST guesses for each data point in the sky
Presto is a program written by pulsar astronomers, that takes raw data and searches for periodic signals.
It does so by conducting thousands of “guesses”. When a promising signal shows up, the software folds the data at that period. Resulting in a “prepfold plot”
You get to see the 24 BEST guesses for each data point in the sky
Pointing
Spin Period
Signal to Noise, Pnoise
Phase
This is an example of the PRESTO software's output. We call each chunk of data a pointing, which corresponds to a sky location. Each location was observed for 2.5 minutes as the sky drifted over. For each pointing the software attempts to find periodic signals by trying a thousands of different hypothetical pulsar periods. For each period, the software “folds” the data. For example, if the hypothetical period is 1 second, the software would split the data into 1-second chunks (150 of them, for the 2.5 minutes of data) and then add all those chunks together.
Definitions
Pointing- location in the sky. A pointing is one dataset comprised of the bext prpfold plots from one spot in the sky. The GBT pointed at one spot in the sky for about 150 seconds.
Spin Period: how long it take the pulsar to spin around one time.
Signal to noise: is the signal mush stronger than the background noise? How like is it that we have a real periodic signal. This is Pnoise
Phase: one complete spin = phase from 0 to 1

5. Average pulse profile
A single pulse from a pulsar is weak and does not rise far above the noise. But when we add a lot of the pulses together, the noise starts to cancel itself out, while the pulses add constructively and pop out more noticeably.
The top left subplot is an example of what a pulsar's pulses can look like when added together. These added pulses are called the “average pulse profile.” While individual pulses may vary in shape, their average shape is very stable.
The average pulse profile is plotted twice, and the next slide demonstrates why. 5

6. Time domain plot
If we only plotted the pulse profile one time, we would run into problems with plots such as this one. We would only see it at the edges of the subplot, and we and the software might not recognize it as a pulsar. So PRESTO plots the same exact pulse profile two times, so that we will always be able to see the full pulse.
The other subplots also have information plotted twice. The subplot below the pulse profile is called the time domain plot. On the x-axis is a property called “phase,” and on the y-axis is time.
Phase is a way to quantify an object's rotation. Having changed phase by one means that the object has made one full rotation. Imagine (yourself) facing forward—this is 0. Spin ninety degrees to the right—this is 0.25, because you have undergone a quarter rotation. Spin so that you're facing backward—this is 0.5. Keep turning clockwise ninety more degrees, till you're at When you turn so that you're facing front again, that is phase=1. If you then spun 90 more degrees, your phase would be And so on.
The time domain plot shows how signal strength corresponds to the pulsar's spinning. If we see signal at the same point in the pulsar's rotation (at the same phase value), that's a good thing. Thus, we're looking for dark vertical lines.
(This is a pulsar.) 6

7. Reduced Chi-squared
Now, look at the right side of the time domain plot. This plot has axes of “reduced chi-squared” and “fraction of observation.” Reduced chi-squared is a measure of how well data fit a model. If the data and the model look exactly the same, reduced chi-squared is 1. The more different the data and the model are, the higher reduced chi-squared is.
In the case of our plots, the model we're using is noise. Pulsar signals DO NOT look like noise! So a reduced chi-squared that is close to one means “noise”. The farther it is from one, the better.
In this graph, as we get more and more data, our data (if it contains a pulsar) should resemble noise less and less, as our pulses start to add up and pop above the noise. So a reduced chi-squared that increases as the fraction of observation increases is a good sign! 7

8. Signal to noise
Finally, the last thing to notice is the little bar next to the pulse profile. This is essentially an error bar. Compare it to the size of the pulsar signal. If you subtracted half of that error bar from the pulse, how much would the pulse rise above the noise? If it's still large in comparison, it's a good signal. If it would look like noise if you subtracted the “error bar,” it's not so good.
Something useful to think about now is called the “signal-to-noise ratio.” This is another measurement of how much an astronomical signal rises above background noise. Imagine that you have some data on graph paper. Your pulse is ten graph-paper boxes high. The noise is 2 boxes high. The signal-to-noise ratio is 10/2, or 5, meaning that the signal is five times stronger than the noise.
Think about whether these three subplots look like they contain a pulsar. Why or why not? 8

9. 9 Why are there so many pulses in this pulse profile?
Sometimes, the software guesses a period that is close, but not quite right. If it guesses a period that is twice the pulsar's actual period, the average signal will still pop above the noise, but there will be two pulses in the pulse profile, and then those pulses will be plotted twice. If it guesses a period that is three times the actual period, there will be six pulses in the profile.
See the nice vertical bands in the time domain subplot? 9

10. Based on what you know about these plots, why does this one look strange?
The pulses in the profile are not very defined, but are more sinusoidal.
The vertical lines in the time domain do not extend all the way down. This can happen if a pulse drifts into the telescope's view (or out of it) during the observation, but when that happens, the signal will fade in (or out) and not appear (or disappear) sharply.
This is radio-frequency interference (RFI)! It looks like it was turned on part way through the observation (about 110 seconds in). 10

11. The software guessed that this pulsar's period was three times what it actually is, so there are six pulses in the profile and six corresponding vertical lines in the time domain subplot.
You can see the pulsar drifting into the telescope's beam (view) about a minute into the observation. 11

12. This is bad!
The bar in the pulse profile is as big as the pulse itself, there are no vertical lines in the time domain plot, and the reduced chi-squared graph shows no improvement over the course of the observation— it stays close to 1, meaning that this plot looks like noise. 12

13. The Sub-band Subplot
Although we observe with the 350 MHz receiver, that is not the only frequency we detect. The receiver observes many frequencies at once, and 350 MHz is just the center frequency. The range of frequencies is called the receiver’s “bandwidth.”
The bandwidth is divided into 32 sub-bands. The sub-band subplot shows how signal strength relates to frequency. As you learned from your homework, pulsars are stronger at lower frequencies, so intensity does vary depending on what frequency you observe. However, the frequency differences within a single receiver are not large enough for this effect to make a large difference, and we know that pulsars are always supposed to emit some signal across a broad range of frequencies.
Thus, in this plot, we are looking to see if our candidate emits radio waves at all frequencies, or only at a few. If there is only signal in one sub-band (which would appear as a horizontal line), that means the signal is RFI. This kind of signal is called “narrow-band.” Pulsars are “broad-band” and will show vertical lines in this plot.

14. The DM Subplot
As you know, DM can provide information about where a signal is coming from by telling you how much it interacted with the interstellar medium on its way to us.
Like the PRESTO software guesses a bunch of periods, it also guesses a bunch of DMs. It determines how well they fit the data—how well they un-smear the pulse.
If radio waves are coming from the same object, we expect them to have gone through the same chunk of space. For this reason, if a signal comes from a pulsar, we expect it to have a distinct DM.
The DM plot takes all the DMs that the PRESTO software guessed and tells you which is the most likely. The better a DM unsmears the data, the higher the reduced chi-squared.
In the DM plot, we’re looking for a Gaussian-type (bell curve-like) peak. The top of the peak represents the DM that best un-smears the data, and as you go farther (on each side) from the peak, the DM un-smears less well and less well and less well.
A DM that peaks at 0 means the signal didn’t go through any electrons to get to the telescope, which means that the signal must not have gone through space, which means it must have come from Earth.
A DM subplot that does not have a peak means that the signal isn’t coming from a distinct point in space, which means it cannot be a pulsar.

15. Header
What can we learn from the header information? 15

16. We don’t want to go into the weeds too far just yet, but you might recognize some of the information you see:
Telescope that took the data
RA and Dec (position)
Periods are given by P. There is Ptopo and Pbary DM
P(Noise)The Probability that we are just seeing noise