The How of the Wow

In 1977, the Big Ear radio telescope at Ohio State University [alma mater-mandated "Boo!"] picked up a burst of energy that was dubbed the "Wow! signal" thanks to researcher Jerry Ehman's note on the printout:

Big Ear

There's been a lot of speculation on possible sources – It was an exceptionally strong signal in a narrow bandwidth. On top of that, the frequency of the signal is associated with hydrogen's emission line, which had been identified by the first SETI paper in 1959 as a likely choice for extraterrestrial species to send messages. If you look closely at the image above, the circled bit reads "6EQUJ5". As this story got around, some people misunderstood this as a message in the signal, but it's actually the measurement of the signal-to-noise ratio in time: Each character is the SNR for a 10-second span, with letters A-Z representing SNRs of 10-35 – Quite high values!

A lot of the mystery surrounding this signal has been its transient nature. Followup searches found no recurrence of the signal, which ruled out a pulsar as the source, but also calls the ET explanation into doubt – Wouldn't a message like that be repeated? However, one of the arguments for the signal being artificial is its narrow bandwidth. Coincidentally, I've been listening to old episodes of the Futility Closet Podcast, and I came across an episode from almost 10 years ago about this signal. They liken the Big Ear telescope to a row of radios in a line, each tuned to a slightly different station – These correspond to the different columns in the printout above. One of the surprising things about the Wow! is that it only appears in one column. Most astrophysical signals would have more variation.

The signal is back in the news thanks to a new paper identifying its source. The authors were using the Arecibo Telescope (RIP) to search for similar signals to the Wow!, and were able to find several with the same spectral qualities, though never with the high intensity of the original signal. The hypothesis they arrived at was that an object like a magnetar or a soft gamma repeater released a burst of photons, which passed through a cloud of hydrogen, causing stimulated emission (the se in "laser") of photons at the detected frequency:

Figure 4

It might seem disappointing to have the possibility of a signal from aliens ruled out, but it's also an opportunity to understand the universe better, which in turn gives us better chances of finding a real signal in the future. Alternatively, we could end up making our own version of the Wow! for another species out there.

Stirring Coffee with My Thumb

Recently I was listening to the song The Frozen Logger, which my father Steve often sang when I was growing up. When I got to the line "at a million degrees below zero" though, the physicist part of my brain butted in to point out that the lowest the temperature can get is absolute zero, or -459.67 °F. Could he have been talking about wind chill? We can rearrange the equation for wind chill to give the velocity required to get from a given true temperature to -1 million °F:

Even at absolute zero, the wind speed would need to be 100 trillion times light speed, which is just not how anything works. A temperature this low is far outside the realm of possibility, but I'm not one to make a fuss over poetic license.

As I was thinking about this though, I started wondering about the other direction: Is there a maximum temperature allowed by physics? One way to think about temperature is the average speed of the molecules in a substance. Using the Maxwell distribution, we can find the temperature associated with an average speed:

Plugging in c for the velocity and the mass of hydrogen, we get a maximum temperature of 7.7 x 10^12 °F. Like the above, this has it's own set of problems: The v in the equation above is the average speed, but the particles all need to stay in (roughly) one place. That means rapidly changing direction, which would require enormous forces. In any case the speed distribution above was derived without considering relativity, so we can't actually apply it to speeds this fast.

I decided to see what possibilities the larger physics community had come up with for maximum temperatures, and I found this article polling some experts. Most of those arguments go back to the early universe, since the Big Bang model of the universe posits that all energy started at a point and has been expanding and cooling since. That concept leads to Planck units, which are combinations of the constants that go into the four fundamental forces in our universe. In the earliest stages of the universe, these forces are believed to have been unified into a single force, but we don't have a model for that yet (the elusive "Unified Field Theory"). The Planck units represent the scale for different quantities at which our understanding begins to break down. For temperature, this is 1.4 x 10^32 K – Converting this to °F doesn't make much difference, since it's still 20 orders of magnitude larger than our previous estimate.

One thing I find really interesting about physics is how well a model can work in one regime, but the same model gives bonkers predictions on a different scale. It's strange to have islands of complete understanding surrounded by seas of uncertainty.

Scents and Scents-Ability

[Yes, it's a homophonous headline!]

We adopted Eros from the Humane Society, which had picked him up as a stray, so we know nothing about his breed and history. He reminds Marika of the beagle she grew up with though, and he has many hound-like traits, including an intense interest in smells. Often during walks he'll plant his feet for several minutes, and swing his head back and forth sniffing.

I was curious what kind of directionality he could get just by moving his head – I imagined that after a good distance, the scents would be too blended to pick out individual sources.

Smells are created by bits of a substance that are picked up by the air. Those bits then spread out according to Fick's Laws of Diffusion. The form of this equation, where the change in time depends on the Laplacian of the current state, is exactly the same as that of the heat equation, which I've discussed before. What's interesting about this case though is that heat has only one type spreading out, while we can have different smells that diffuse and mix.

I decided to adapt my cake-heating simulation to look at how much directional information Eros can get from his head movements. The setup is two sources of scents that emit particles according to Fick's laws. Eros then senses the concentration of each in a cone in front of his nose. I struggled to find a good way to display the concentrations, which drop off rapidly from the sources, but I suppose that's just a testament to the sensitivity of dogs' noses. The first case has the two sources equidistant:

Like I said, you can't see much past the central dots, but if we add up everything in the white cone,

Now we do get directionality. I was curious to see what happens when we put one source closer:

For this case the concentrations are

Because the blue scent is closer, it has a higher concentration in all directions, but comparing the left and right ends of each curve, we see we can still find a direction that gives more scent.