Oh what a great day! Not a lot of research got done; NSF proposals, letters of recommendation, and all that. But in the afternoon, undergraduate researcher Abby Shaum (NYU) and I looked at her project to do frequency demodulation on asteroseismic modes to find orbital companions and we got one. Our target is a hot star that has a few very strong asteroseismic modes (around 14 cycles per day in frequency), and our demodulator is actually a phase demodulator (not frequency) but it's so beautiful:
The idea of the demodulator is that you mix (product) the signal (which, in this case, is bandpass-filtered NASA Kepler photometric data) with a complex sinusoid at (as precisely as you can set it) the asteroseismic carrier frequency. Then you Gaussian smooth the real and imaginary parts of that product over some window timescale (the inverse bandwidth, if you will). The resulting extremely tiny phase variations (yes these stars are coherent over years) have some periodogram or power spectrum, which shows periodicity at around 9 days, which is exactly the binary period we expected to find (from prior work).
I'm stoked! the advantages of our method over previous work are: Our method can easily combine information from many modes. Our method can be tuned to any modes that are in any data. We did not have to bin the lightcurve into bins; we only had to choose an effective bandwidth. The disadvantages are: We don't have a probabilistic model! We just have a procedure. But it's so simple and beautiful. I'm feeling like the engineer I was born to be.
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