Note: all linked words lead to their definitions in the glossary at the bottom of this page.

    Our research concerns pulsar scintillation.  Ultimately, our goal is to better understand the interstellar medium (ISM) and the workings of neutron stars.  Currently, our data is taken from Dan Stinebring's sixteen pulsar study during 1991 and 1992.  The ISM is made up of ninety percent hydrogen, nearly ten percent helium, and less than one percent heavier elements. Electron density fluctuations (in both time and position) in the ISM scatter radio waves from the pulsar; sometimes these are scattered back to the telescope, placing them out of phase.  The density fluctuations in the ISM produce fluctuations in the index of refraction, which cause phase shifts, which cause fluctuations in the pulsar signal.  The modulation in pulsar dynamic spectra was the first observational clue to the existence of random variations in the plasma density of the ISM.  To learn more about pulsars, see our What is a Pulsar page.
    We began the summer studying Mark Walker and Mark Wardle's model of interstellar hydrogen "bubbles," which attempts to explain the so-called missing matter in the universe.  They hypothesize that there are numerous spheres of cool hydrogen gas in the ISM; their low temperature would make them difficult to detect (hence the "missing" part), but they might be numerous enough to account for the matter which astronomers have determined must be present to explain the current rate of expansion of the universe.
    Dan Stinebring hypothesized that the existence of these clouds could be demonstrated by the amount of refraction that neutron star pulses undergo in passing through the clouds.  Using Snell's law and a lot of geometry, we were able to predict how large the scattering angle would be for such an event; it was very, very small, to be unscientific about it.  While this might have led to proving or disproving the Walker/Wardler model, we discovered upon further calculation that, statistically speaking, we did not have enough data to detect such an effect.  We currently have on hand 357 dynamic spectra taken during 1991 and 1992 (the focus of the rest of this summer's work) and this sort of scattering, because of the narrow path which neutron star pulses traverse and the relatively small radius of these clouds, would occur only once in approximately every five thousand observations.
    After this disappointment, we tackled IDL, a data analysis and visualization software (we have an introduction to IDL here).  Dan had a conference to speak at in San Diego, so we spent some time preparing the data for that.  We ended up spending quite a while figuring out how to save and print images of dynamic and secondary spectra as postscript files.  One of the difficulties we encountered here was that the postscript saving appeared to gum up the data: our hard copy was much less precise and informative than what we had on the screen.
    We also created an IDL procedure which called up the dynamic and secondary spectra of a specified pulsar observation and allowed these data to be manipulated.  At first, the manipulation was limited to the high and low cutoffs of the pixel values and to how much or whether we wanted the data smoothed; now it has become much more complicated.  The secondary spectrum can be toggled between a linear and logarithmic display.  We can take intensity profiles along any path in either spectrum, and do Gaussian fits of these profiles.  The color table is also manipulable.
    For a while we got bogged down in the secondary spectra: taking horizontal and vertical profile cuts along the axes yielded very spiky data, and we couldn't figure out what was going wrong.  We thought we should have something that looked at least vaguely Gaussian, but eventually realized that this was merely the result of much larger scintils than the sample data we had been using.
    Finally, we tabulated the width and height of the secondary spectra and the dbw and tauiss of the autocorrelation functions of the most interesting data sets.  For those who are working in the lab, we have created a separate page that lists where you can find everything you should need.
 

Gaussian fits:    A Gaussian function is one of the form A₀*e^-(z²/2), where z=(x - A₁)/A₂.  Essentially, this is a bell curve.  Creating a Gaussian fit for a data curve means coming up with the best approximation to the data in the form of a Gaussian. A₂ is a width parameter, A₁ determines distance of the peak from the origin, and A₀ indicates the height of the curve's peak.

intensity profiles:    The dynamic and secondary spectra are multi-colored: the different colors (or shades of gray, depending on the color table you use) indicate varying intensities of signal.  While they are technically two-dimensional, I find the easiest way to think of them is that the colors represent heights, rather like a contour map of a mountain range.  Then, you can think of a profile cut as a cross-section of these mountains, showing their height at every point along the line of your cut.

interstellar medium:    Although we think of the vast distances between stars and other such large objects as a vacuum, or "empty" space, they are actually filled with dust and gas.  This particulate matter is nowhere near as dense as any definable objects are, but is such that it interferes measurably in any signals broadcast through significant distances, causing intensity variations.

missing matter:    The rate of expansion of the universe is dependent on how much matter the universe contains.  Since matter warps time and space (by Einstein's general theory of relativity) and since it has a gravitational pull for all other matter, a more massive universe would expand more slowly.  The rate of expansion as currently measured suggests that there is more mass in the universe than has been detected and inferred.  This is referred to as the missing matter problem.

pulsar scintillation:  A pulsar's signal is often uneven and slightly smeared over a range of wavelengths.  When you see a star "twinkling" in the night sky, this is also scintillation: if you could see a pulsar, the visual effect would be similar, except it would come in pulses instead of steadily.  Current theory holds that scintillation is an effect of the uneven distribution of gas and dust in the ISM.

rate of expansion:    The current rate of expansion of the universe is measured by examining the redshift of certain distant objects.  When an object is moving away from you, the wavelengths of the light it gives off appear to be longer.  This applies to all waves and is referred to as the Doppler effect: think of how, when an ambulance is far away, the pitch of its sirens seem to rise as it nears you and then deepen as it moves away again.  Lengthened lightwaves are shifted to the lower frequency, or redder, end of the spectrum: hence the name redshift.  Since the universe is expanding, everything in it (more or less) is moving away from us.  This might sound like we are necessarily in the center of the universe, but this is not so.  Astronomers' favorite analogy is that of a loaf of raisin bread: as the bread rises, there is more dough inbetween each raisin (galaxy): no matter which raisin you sit on, you will always see all the other raisins moving away from you.

secondary spectra:    The Fourier transform of the dynamic spectra.  Indicative of refraction and diffraction in the dynamic spectrum.

Snell's law:    For a lightray leaving a medium of index of refraction n1 and entering a medium of index of refraction n2, the following formula always holds: n₁sin theta₁=n₂ sin theta₂, where theta₁ is the angle of incidence (angle relative to the normal) while the lightray is in the first medium, and theta₂ is the angle of refraction within the second medium.  Given any three of these parameters, it is possible to find the fourth.

 
 
 
 
 
 

         I want to go home!
 
 
 

Last Updated June 1998