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The term wide binaries refers to binary stars that are orbiting each other, yet are thousands of AU distant from each other: one criteria is "on the order of 7000 AU". By this criteria, Alpha Centauri (including Proxima Centauri) comprises a wide binary. Wide binaries have gained interest as offering tests of gravitational models, including Newtonian gravity and general relativity (GR), along with the theory of dark matter.
The visible portion of galaxies and galaxy clusters do not follow these gravitational models without assuming there is matter that has not been otherwise detected (for which the term dark matter has been coined). Galaxies and galaxy clusters are the largest scale gravitationally-bound objects available for analysis to explore this. If gravity has some still-unknown characteristic affecting gravity over large scales (i.e., that makes it act differently than Newtonian gravity and GR), then there is interest in the analysis at scales large enough that such effects might be discerned, such as might be provided by of wide binaries. Stellar clusters promise to be of similar use.
Studies have claimed that observed wide binaries do not fit the concept of dark matter, based upon orbital speeds that are faster than can be explained by GR or Newtonian gravity, yet should not be affected by dark matter. Such a high relative velocity could merely indicate the pair are not actually bound, but changes in their relative velocity over time could prove that they are indeed bound. Also, given a set of apparent wide binaries, statistics might indicate a certain percentage are likely to be gravitationally bound.
Wide binaries also have the potential for other possible information: for example, they have been of interest regarding star formation and planet formation; a presumption is that the percentage of wide binaries formed together may differ from that of close binaries, and the demographics of extra-solar planets hosted by each might throw light on the relation between star formation and planet formation. The abbreviation PHWB has been used for planet-hosting wide binaries.