A variable star is a star whose brightness as seen from Earth (its apparent magnitude) fluctuates.

This variation may be caused by a change in emitted light or by something partly blocking the light, so variable stars are classified as either:

* Intrinsic variables, whose luminosity actually changes; for example, because the star periodically swells and shrinks.
* Extrinsic variables, whose apparent changes in brightness are not due to changes in the star itself; for example, because the star has an orbiting companion that periodically eclipses it, or when an (invisible) companion dumps material on the star that ignites and causes an abrupt change in brightness.

Many, probably most, stars have at least some variation in luminosity when studied in sufficient detail: the energy output of our Sun, for example, varies by about 0.1% over an 11-year solar cycle. On the other hand the Sun also oscillates on a timescale of 5 minutes.
Even for intrinsic variables the cause of the variations can be manyfold, for example due to changes on the surface (spots, convection) or in the interior of the star.

The website of the General Catalog of Variable Stars gives a nice overview of the many types of variability.

At the Observatory we mainly study variables whose cause of variability lies in the interior of the star and where the variations are periodic, i.e. a main characteristic of such stars is the pulsation period, and that it is linked to the intrinsic or true brightness of the star. Such, so-called, period-luminosity (PL-) relations are a very important way to determine distances to these stars, also in other galaxies.
 

Variables of interest

• Classical Cepheids :  (or  δ Cephei variables) are population I (young, massive, and luminous) yellow supergiants which undergo pulsations with very regular periods on the order of days to  months.
  One important topic of investigation is the exact form of the PL-relation in different wavelength bands, and in particular if it depends on metallicity, which could be important if the PL-relation is applied to Cepheids in different galaxies.
   

  Lemasle B., Groenewegen M.A.T., Grebel E.K., et al. 2017, A&A 608, A85
  "Detailed chemical composition of classical Cepheids in the LMC cluster NGC 1866 and in the field of the SMC"

  Groenewegen M.A.T.  2013, A&A 550, A70
  "Baade-Wesselink distances to Galactic and Magellanic Cloud Cepheids and the effect of metallicity"

•  Type-II Cepheids : they pulsate with periods typically between 1 and 100 days. These are population II stars: old, typically metal-poor, low mass objects.

  However, this classical picture is challenged. The Type-II Cepheids (T2C) are a mixed bag of objects typically subdivided into the BL Her, W Vir and RV Tau subclasses depending on period, which likely follow very different evolutionary paths.

  Recent work has shown that in the Magellanic Clouds there exist T2C (of the W Vir kind) with a clear dust excess at luminosities lower than expected from the evolution of a single star. Possibly they already evolved from cool to hotter temperatures, crossing the instability strip, when being on the First Red Giant Branch. The link with the more luminous RV Tau class is obvious, where many also show an excess in the mid infrared, which is linked to binarity.

  This interesting link between (binary) stellar evolution and T2C is further studied by PhD student Joonas Saario for Galactic T2C (in collaboration with Prof. Hans van Winckel from  KU Leuven University), making use of Gaia data and the HERMES spectrograph.

  Kamath D., Wood P.R., Van Winckel H., Nie J.D.    2016, A&A 586, L5
  "A newly discovered stellar type: dusty post-red giant branch stars in the Magellanic Clouds"

  Groenewegen M.A.T., Jurkovic M.I.  2017, A&A 603, A70
  "Luminosities and infrared excess in Type II and anomalous Cepheids in the Large and Small Magellanic Clouds"

  Groenewegen M.A.T., Jurkovic M.I.  2017, A&A 604, A29
  "The period-luminosity and period-radius relations of Type II and anomalous Cepheids in the Large and Small Magellanic Clouds"