One star covers several pixels
Photograph a distant lamp at night and it often becomes a small patch with a bright center and fading edges. A star makes a similar image. Its own angular size may be far too small to resolve, but the optics, atmosphere and detector spread its light. Astronomers call the shape of that patch the point-spread function, or PSF. It describes where light from a point source lands.
Draw a circle around the patch and add the pixels inside. That is the simplest way to measure its brightness. The circle is a photometric aperture: a selection on the image, distinct from the opening of the telescope. Increasing its radius collects more of the target light. Eventually there is little target light left outside.
Reading: Photutils 3.1.1, Aperture photometry
A circle can collect somebody else’s light
Place another star nearby. The edges of the two patches overlap first; then their centers become hard to distinguish. The target can remain perfectly steady while its aperture collects more light as the neighbor approaches. A subtler problem arises if the neighbor itself brightens. The circle around the target then brightens too, and a sum of pixels can assign the change to the wrong star.
A smaller circle rejects some neighboring light, but it also loses more of the target. To compensate, we need the fraction of target light inside. If the circle captures nine tenths, divide its background-subtracted count by nine tenths. This aperture correction compensates for the target’s missing light. Any neighbor light already inside is enlarged by the same division.
Two carefully corrected measurements can therefore disagree. Their hidden assumption was that all the remaining light belonged to the target.
Reading: Photutils 3.1.1, PSF photometry
A dark sky still sends photons
The space between stars has a background. Airglow, scattered light and the instrument can add a floor to the image. Summing a large circle counts that floor many times. A tiny error in the estimated background per pixel becomes a larger error when many pixels are included.
Subtracting the average background leaves its fluctuations behind. Photons arrive individually, and equal exposures do not receive exactly equal counts. This counting scatter is photon noise. A longer exposure usually makes the stellar signal clearer. Separating two overlapping stars also needs information about where their light lands.
Use the shape of both patches
Suppose we know the star positions and their image shapes. Guess a brightness for each, predict the light in every pixel, and adjust the two guesses until the whole image agrees. Pixels near one star tend to favor that star; pixels near the other favor its neighbor. The fit uses those clues together.
PSF fitting allows one pixel to contain light from both stars. When the patches are well separated, assigning the light is straightforward. When they nearly coincide, moving brightness from one star to the other can leave almost the same image. The resulting uncertainty should appear in the quoted error.
Real stellar images vary across a detector and are rarely perfect circles. Once random noise becomes small, an inaccurate profile or a misplaced center can dominate. Inspecting the pattern left after a fit is part of a careful measurement.
Reading: Photutils 3.1.1, PSF photometry
Turn individual images into a history
The TESS satellite repeatedly images the same sky to find small brightness changes. Its data include little pixel stamps around selected targets as well as ready-made light curves. Keeping the pixels lets a reader change the aperture and investigate a background or neighboring source.
The companion exercise freezes measured pixels of TIC 25155310, also called WASP-126. It retains uncertainties and quality flags. Following those images into a light curve makes the measurement choices tangible: the selected pixels and the background convention both matter.