### Astropulse basics

#### Basics

Astropulse is a new type of SETI. It expands on the original SETI@home, but does not replace it. The original SETI@home is narrowband, meaning that it is listening for a particular radio frequency. That's like listening to an orchestra playing, and trying to hear when anyone plays the note "A sharp". Astropulse listens for short-time pulses. In the orchestra analogy, it's like listening for a quick drum beat, or a series of drumbeats. Since no one knows what extraterrestrial communications will "sound like," it seems like a good idea to search for several types of signals. In scientific terms, Astropulse is a sky survey that searches for microsecond transient radio pulses. These pulses could come from ET, or from some other source. I'll define each of those terms:
• Sky survey: The telescope we use (Arecibo Observatory) scans across the sky, searching for signals everywhere. This differs from a directed SETI search, in which the telescope examines a few stars carefully.
• Microsecond: A millionth of a second. Astropulse is better than previous searches at detecting signals that last for a very short length of time. The shorter the signal, the better Astropulse is at detecting it, to a lower limit of 0.4 microseconds. Astropulse can detect signals shorter than 0.4 microseconds, it just stops getting better and better in comparison to other searches.
• Transient: A signal is transient if it is short, like a drumbeat. A transient signal can be repeating (it beats over and over again) or single pulse (it beats only once.)

Here's a picture of a transient radio pulse:

In this plot, the x-axis is time, and the y-axis is frequency. This plot shows that the frequency of the pulse decreased over time, which is exactly what we would expect from a dispersed pulse. See the dispersed pulses section for more.

#### Sources of pulses

Where would a microsecond transient radio pulse come from? There are several possibilities, including:
• ET: Previous searches have looked for extraterrestrial communications in the form of narrow-band signals, analogous to our own radio stations. Since we know nothing about how ET might communicate, this might be a bit closed-minded.
• Pulsars and RRATs: Pulsars are rotating neutron stars that can produce signals as short as 100 microseconds, although typically much longer. 0.4 microseconds seems like a stretch. Astropulse is capable of detecting pulsars, but is unlikely to find any new ones. RRATs are a recently discovered pulsar variant. Perhaps Astropulse will discover a new type of rotating neutron star with a very short duty cycle.
• Exploding primordial black holes: Martin Rees has theorized that a black hole, exploding via Hawking radiation, might produce a signal that's detectable in the radio. Click here to learn about black holes.
• Extragalactic pulses: Some scientists recently saw a single transient radio pulse from far outside the Milky Way galaxy. No one knows what caused it, but perhaps there are more of them for Astropulse to find.
• New phenomena: Perhaps the most likely result is that we will discover some unknown astrophysical phenomenon. Any time an astronomer looks at the sky in a new way, he or she may see a new phenomenon, whether it be a type of star, explosion, galaxy, or something else.

### Dispersed pulses

As a microsecond transient radio pulse comes to us from a distant source in space, it passes through the interstellar medium (ISM). The ISM is a gas of hydrogen atoms that pervades the whole galaxy. There is one big difference between the ISM and ordinary hydrogen gas. Some of the hydrogen atoms in the ISM are ionized, meaning they have no electron attached to them. For each ionized hydrogen atom in the ISM, a free electron is floating off somewhere nearby. A substance composed of free floating, ionized particles is called a plasma.

The microsecond radio pulse is composed of many different frequencies. As the pulse passes through the ISM plasma, the high frequency radiation goes slightly faster than the lower frequency radiation.When the pulse reaches Earth, we look at the parts of the signal ranging from 1418.75 MHz to 1421.25 MHz. This is a range of 2.5 MHz. The highest frequency radiation arrives about 0.4 milliseconds to 4 milliseconds earlier than the lowest frequency radiation, depending on the distance from which the signal originates. This effect is called dispersion. Click here to see how dispersed and undispersed pulses can be composed of many different frequencies

In order to see the signal's true shape, we have to undo this dispersion. That is, we must dedisperse the signal. Dedispersion is the primary purpose of the Astropulse algorithm.

Not only does dedispersion allow us to see the true shape of the signal, it also reduces the amount of noise that interferes with the signal's visibility. Noise consists of fluctuations that produce a false signal. There could be electrical noise in the telescope, for instance, creating the illusion of a signal where there is none. Because dispersion spreads a signal out to be up to 10,000 times as long, this can cause 10,000 times as much noise to appear with the signal. (There's a square root factor due to the math, so there's really only 100 times as much noise power, but that's still a lot.)

The amount of dispersion depends on the amount of ISM plasma between the Earth and the source of the pulse. The dispersion measure (DM) tells us how much plasma there is. DM is measured in "parsecs per centimeter cubed", which is written pc cm-3. To get the DM, multiply the distance to the source of the signal (in parsecs) by the electron density in electrons per cubic centimeter. A parsec is about 3 light years. So if a source is 2 parsecs away, and the space between the Earth and that source is filled with plasma, with 3 free electrons per cubic centimeter, then that's 6 pc cm-3. The actual density of free electrons in the ISM is about 0.03 per cubic centimeter.

### Astropulse algorithm

#### Single Pulse Loops

Astropulse has to analyze the whole workunit at nearly 15,000 different DMs (14,208, to be precise.) At each DM, the whole dedispersion algorithm has to be run again for the entire workunit. The lowest DM is 55 pc cm-3, and the highest is 800 pc cm-3. Astropulse examines DMs at regular intervals between those two. Without going into detail about how to examine a piece of a workunit at a given DM, here is the organization with which Astropulse handles the data: it divides the DMs to be covered into large DM chunks of 128 DMs each, and then small DM chunks of 16 DMs each. It divides the data into chunks of 4096 bytes, and processes them one at a time. Once it has dedispersed the data, Astropulse co-adds the dedispersed data at 10 different levels, meaning that it looks for signals of size 0.4 microseconds, then twice that, 4 times, 8 times, and so on. (0.4 microseconds, 0.8, 1.6, 3.2, 6.4, ...) On the lowest level of organization, astropulse looks at individual bins of data. A bin corresponds to 2 bits of the original data, but after dedispersion, it requires a floating point number to represent it. Here's the breakdown of Astropulse's loops:

1 workunit => 111 large DM chunks
1 large DM chunk => 8 small DM chunks
1 small DM chunk => 2048 data chunks
1 data chunk => 16 DMs
1 DM => 10 fold levels
1 fold level => 16384 bins (or less)
1 bin = smallest unit

So each workunit is composed of 111 large DM chunks, each of which is 0.901% of the whole. Each large DM chunk is composed of 8 small DM chunks, each of which is 0.113% of the whole. And so on.

The number of large DM chunks will probably change before the final version of Astropulse is released.

#### Fast Folding Algorithm

At the end of each small and large DM chunk, Astropulse performs the Fast Folding Algorithm. This algorithm checks for repeating pulses over a certain range of periods. (The period is the length of time after which the pulse repeats.) When the fast folding algorithm is performed after each large DM chunk, it searches over an entire 13 second workunit, and looks for repeating signals with a period of 256 times the sample rate (256 * 0.4 microseconds) or more. When the FFA is performed after each small DM chunk, it searches over a small fraction of the workunit, and looks for repeating signals with a period of 16 times the sample rate or more.