Life of an Electron

Fingerprinting Light

• The discrete energy levels result in line spectra
• These spectra are unique for each atom and molecule, so they work as fingerprints!

Seems Sus

• Stars (especially the surface) are made almost entirely of hydrogen
• So why do we get a (mostly) blackbody curve when looking at stars, and not sharp hydrogen emission peaks?

Stars \(\neq\) Gas Lamps

• Atoms in close proximity to one another influence each other’s energy levels

Evolution of Spectra

Absorption Spectra and Goldilocks

• What if we have a cooler, diffuse gas, but with blackbody radiation shining on it?
• Some of the radiation will be absorbed
• Only the “just right” wavelengths corresponding to certain energy steps

Sample Case: Hydrogen

That Spectra is Stellar!

Viewing Absorption Differently

But wait, there’s more!

The Doppler Effect

• The Doppler effect affects all types of waves, including light!
• Approach waves get compressed (smaller wavelengths)
• Receding waves get stretched (larger wavelengths)

Putting Numbers to It

For our purposes: \[ \frac{\lambda_{obs} - \lambda_{rest}}{\lambda_{rest}} = \frac{V}{c} \] where:

• \(\lambda_{obs}\) is the wavelength you, the observer, see
• \(\lambda_{rest}\) is the normal wavelength you’d see if the object was not moving
• \(V\) is the speed of the light source relative to you
  • Negative if coming towards you
  • Positive if moving away from you
• \(c\) is the speed of light

Astronomy Implications

• We can measure radial speeds of objects!
• Approaching objects are blueshifted
• Receding objects are redshifted

Maximum Redshift

• Stars are considered “hypervelocity stars” if they have radial speeds of around 500 km/s or higher
• Take a moment to compute how much of a shift this would cause in the \(H_\alpha\) line usually at 656.464 nm.

Gaussians

• Measure peak placement precisely involves fitting a model to the peak
• One of the most common is that of a Gaussian: \[ g(x) = H + A\exp\left(\frac{-(x-x_0)^2}{2\sigma^2}\right) \] where
  • \(H\) is the offset or shift of the baseline
  • \(A\) is the peak height above the baseline (can be negative)
  • \(x_0\) is the \(x\) at which the peak is centered
  • \(\sigma\) is the spread of the peak

The Continuum

• Peaks often show up on areas of the blackbody spectrum that are heavily sloped
• Fitting them well requires “flattening”, or normalizing out this background continuum
• Most common approach is to fit a line or polynomial to just the background (not the peak!) and then divide the entire background by this signal
• If done well, you should get a clean peak sitting on a level surface, ready for fitting
• For velocities or identifying chemical composition, determining \(x_0\) is the most important, as that is the wavelength the peak is centered at

Example Using Solar Spectra

• To illustrate this approach, let’s investigate the \(H_\alpha\) line in the solar spectra given here
• Want to:
  • Establish there is a peak approximately where we expect it
  • Normalize the background
  • Fit a gaussian to determine peak location

Velocity Computing