Cosmic compass - First tomography of an outer 3D sub-Gauss field via atomic alignment

Sub-Gauss magnetic fields are crucial for many physical processes from Galactic $kpc$ scale to stellar $Au$ scale, but are nontrivial to detect. All present magnetic diagnoses trace only one component of a magnetic field at best. Here we report the first observational results that unveil 3D topology as well as the strength of a sub-milliGauss magnetic field beyond our solar system. We found that two weak neutral iron absorption lines from the ground state in the atmosphere of $89~Her$ produced counterintuitive high-amplitude polarizations and consistent polarization angles, exactly in line with the theoretical prediction from ground state alignment (GSA). Our analysis reveals the first sub-AU scale magnetic field on $89~Her$, that is $1.3kpc$ away, has a 3D orientation aligned to the stellar outflow axis and a strength of $70\mu{G} \lesssim B \lesssim150\mu{G}$, thus substantially improving the accuracy by five orders of magnitude compared to the previous $10G$ upper limit set by non-detection of Zeeman effect. This long-awaited discovery is anticipated to usher in a new era of precise measurement of sub-gauss magnetic field in the Universe.