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It’s been miserably cold in Boise, and we’ve had record snowfall during the last few weeks.

Sunday, however, it was relatively warm — warm enough, in fact, that the snow that was slated to fall fell as sleet instead.

So I took my daughter over to a friend’s house for a playdate, and as we walked over, we heard the beautiful sound of the tiny icy pebbles clattering to the ground. The sound was so distinctive and regular that I whipped out my phone to record it.

When I got home later, it seemed like there must be something interesting I could do with the recording, and the first thing that struck me was to analyze the frequency of the clattering sound. In other words, how often did I hear a sleet pellet strike the ground?

To begin, I imported the m4a file from my iphone and then convert it via command-line into a wav file (since I planned to use python and it was easier to find ways to manipulate wav than m4a files):
ffmpeg -i Sleet_Falling.m4a Sleet_Falling.wav

Then I fired up ipython notebook and imported and plotted the wav file:

%matplotlib inline
 
import numpy as np
import wave
import matplotlib.pyplot as plt
 
from scipy.io import wavfile
# Load the data and calculate the time of each sample
samplerate, data = wavfile.read('Sleet_Falling.wav')
times = np.arange(len(data))/float(samplerate)
 
# Make the plot
# You can tweak the figsize (width, height) in inches
fig = plt.figure(figsize=(6, 4))
ax = fig.add_subplot(111)
ax.plot(times, data, lw=0.5) 
ax.set_xlim([0,10])
ax.set_ylim([-2000,2000])
ax.set_xlabel('time (s)')
 
fig.savefig('Sleet_Falling.png', dpi=500

The distinctive rapid crackling is apparent in the waveform.

Next, I calculated a Fourier transform of the signal:

from numpy.fft import rfft
 
ft = np.fft.rfft(data)
n = data.size
timestep = 1./samplerate
freq = np.fft.rfftfreq(n, d=timestep)
period = 1./freq
 
fig = plt.figure(figsize=(6, 6))
ax = fig.add_subplot(111)
ax.semilogx(period, abs(ft), lw=0.5)
 
mx_arg = abs(ft).argmax()
print(period[mx_arg])
 
fig.savefig('Sleet_Falling_fft.png', dpi=500)

which shows a distinct peak at about 1 millisecond.

Assuming the sleet I saw is about 5 mm in radius, I estimate a terminal velocity of about 5 m/s. If I imagine (unrealistically) that the sleet particles are falling in a single column, with one directly above another and traveling at 5 m/s, then one striking the ground every millisecond means the sleet balls are basically packed end to end, as tightly as they can be [1 ms = (5 mm)/(5 m/s)]. Of course, if the pellets were spread out and striking the ground at random places, they could be way more spread out and not as many would have to fall at a time in order to make the sound I heard.

Turns out I’m not the first person to try estimating the precipitation rate using sound. NASA deploys microphones in the ocean to record the distinctive sound of raindrops.

From http://earthobservatory.nasa.gov/Features/Rain/rain_2.php.

In fact, different size raindrops make different sounds because some sizes of drops generate bubbles and others do not, and so scientists can actually estimate the sizes of raindrops by just looking at the distribution of frequencies.

Unfortunately, I can’t make the same kinds of measurements using my iPhone because I haven’t calibrated the microphone using a sound of known amplitude. Maybe something for the future.

A very active and engaging morning session on detecting exoplanets via the transit method on AAS 229 Day 1. Lots of good talks (although all of the talks were by male astronomers) and probing but polite questions (again, mostly by male astronomers – interesting study on these trends here). A few talks stuck out in my mind.

Aaron Rizzuto from UT Austin looked for transiting planets in stellar clusters spanning a range of ages using data from the K2 Mission and found there seem to be fewer hot Jupiters in clusters 10 million years old than there are in older (hundreds of millions of years old) clusters. He suggested that this may mean it takes 100s of millions of years for the migration that makes hot Jupiters to take place. That would probably rule out one standard model for making hot Jupiters, namely gas disk migration, since that probably takes place within a few 10s of millions of years.

Dave Kipping of Columbia University discussed his search for transits of Proxima b, the recently discovered, Earth-sized planet just four light years from Earth. Unfortunately, the host star, Proxima, is a highly variable star due to almost constant flaring. As a result, it would be very difficult to see the planet’s transit – as Kipping said, it requires wading through “a sea of variability”. However, Kipping and his group struggled valiantly to recover the transit using data from the Canadian MOST satellite, and it looks like the planet just does not transit. So we probably won’t know the planet’s radius (at least not for a long time). Bummer.

The last talk of the session was from George Ricker, the PI of the TESS mission, the follow-up mission to Kepler, about TESS’s status and prospects. Apparently, the mission will observe more than 2 million stars! Orbiting many of those stars will be nearby habitable planets, and Ricker showed an amazing simulation of where those stars might be found (courtesy of Zach Berta-Thompson of UC Boulder), a still from which is shown below.

I’m prepping for my classical mechanics course, scheduled to start next week. One of the first things we discuss is uniform circular motion and how it looks projected along the x- and y-axes, so I thought it would be useful to have an animation showing that. I found a few animations online, but none really showed the x and y projections I was looking for.

So I decided to create my own using my go-to language of choice Python. Fortunately, python guru Jake Vanderplas has created a very nice animation module usable in iPython Notebooks.

Based on his example here, I put together the following code to generate the desired animation:

Friends,
As of this morning, we are halfway to our goal of $8,000. And in only the first week. Thanks very much to all those who have given, including Barbara Hatcher and Jim Ogle.

Please talk to your friends and family and share your enthusiasm for our project and for astronomy. Your support means a lot to me personally and will help us usher in an amazing resource for astronomy education here in Boise.

At journal club, we discussed the discovery of two new hot Jupiters using data from ESA‘s CoRoT mission, with the names CoRoT-28 b and -29 b. Both systems seem a little off.

The host star CoRoT-28 has an inflated radius, suggesting it is ancient and on its way off the main sequence. But it has a lot more lithium than we’d expect for an old star, and its rotation rate is similar to the Sun’s, much faster than we would expect.

Equally puzzling is the transit light curve for CoRoT-29 b (shown below at left). Most transit curves are u-shaped, but CoRoT-29 b’s is strangely asymmetric. The asymmetry resembles what has been seen for a planet transiting a rapidly rotating star — rapid rotation reduces the gravity at the stellar equator, resulting in a cooler, darker region. Barnes et al. (2013) looked at the transit light curves for such a Kepler system and actually used the light curve to study the planet’s orbital inclination.

(left) CoRoT-29 b transit light curve. (right) Planet transiting star spot.

(left) CoRoT-29 b transit light curve. (right) Planet transiting star spot.

But CoRoT-29 doesn’t appear to be a rapid rotator. So instead Cabrera et al. suggest that perhaps the star has a large, nearly stationary star spot and that the planet transits the spot over and over again. However, this scenario would require a nearly stationary spot with a very long lifetime (~90 days), neither of which is expected.

So a few more astrophysical conundra to add to the growing list of puzzling exoplanet discoveries.

Journal club attendees included Jennifer Briggs, Emily Jensen, and Hari Gopalakrishnan.