The 21 cm Signature of the First Stars

We predict the 21-cm signature of the first metal-free stars. The soft X-raysemitted by these stars penetrate the atomic medium around their host halos,generating Lyman alpha photons that couple the spin and kinetic temperatures.These creates a region we call the Lyman alpha sphere, visible in 21-cm againstthe CMB, which is much larger than the HII region produced by the same star.The spin and kinetic temperatures are strongly coupled before the X-rays cansubstantially heat the medium, implying that a strong 21-cm absorption signalfrom the adiabatically cooled gas in Hubble expansion around the star isexpected when the medium has not been heated previously. A central region ofemission from the gas heated by the soft X-rays is also present although with aweaker signal than the absorption. The Lyman alpha sphere is a universalsignature that should be observed around any first star illuminating itsvicinity for the first time. The 21-cm radial profile of the Lyman alpha spherecan be calculated as a function of the luminosity, spectrum and age of thestar. For a star of a few hundred solar masses and zero metallicity (asexpected for the first stars), the physical radius of the Lyman alpha spherecan reach tens of kiloparsecs. The first metal-free stars should be stronglyclustered because of high cosmic biasing; this implies that the regionsproducing a 21-cm absorption signal may contain more than one star and willgenerally be irregular and not spherical, because of the complex distributionof the gas. We discuss the feasiblity of detecting these Lyman alpha spheres,which would be present at redshifts $z\sim 30$ in the Cold Dark Matter model.Their observation would represent a direct proof of the detection of a firststar.Comment: replaced with ApJ accepted version. Many minor revisions and additional references, major results unchange