Limits on the Dependence of the Fine-Structure Constant on Gravitational Potential from White-Dwarf Spectra

Abstract

We propose a new probe of the dependence of the fine-structure constant on a strong gravitational field using metal lines in the spectra of white-dwarf stars. Comparison of laboratory spectra with far-UV astronomical spectra from the white-dwarf star G191-B2B recorded by the Hubble Space Telescope Imaging Spectrograph gives limits of Á = ¼ ð4:2 AE 1:6Þ Â 10 À5 and ðÀ6:1 AE 5:8Þ Â 10 À5 from FeV and NiV spectra, respectively, at a dimensionless gravitational potential relative to Earth of Á % 5  10 À5 . With better determinations of the laboratory wavelengths of the lines employed these results could be improved by up to 2 orders of magnitude. DOI: 10.1103/PhysRevLett.111.010801 PACS numbers: 06.20.Jr, 31.15.am, 32.30.Jc, 97.20.Rp Light scalar fields can appear very naturally in modern cosmological models and theories of high-energy physics, changing parameters of the standard model such as fundamental coupling constants and mass ratios. Like the gravitational charge, the scalar charge is purely additive, so near massive objects such as white dwarfs the effect of the scalar field can change. For objects that are not too relativistic, such as stars and planets, both the total mass and the total scalar charge are simply proportional to the number of nucleons in the object. However, different types of coupling between the scalar field and other fields can lead to an increase or decrease in scalar coupling strengths near gravitating massive bodies [1]. For small variations, the scalar field variation at distance r from such an object of mass M is proportional to the change in dimensionless gravitational potential ¼ GM=rc 2 , and we express this proportionality by introducing the sensitivity parameter k [2]. Specifically, for changes in the fine-structure ''constant'' , we writeThis dependence can be seen explicitly in particular theories of varying , such as those of Bekenstein [3] and Barrow-Sandvik-Magueijo [4], and their generalizations [5], where can increase (Á = > 0) or decrease (Á = < 0) on approach to a massive object depending on the balance between electrostatic and magnetic energy in the ambient matter fields [1]. The most sensitive current limits on k come from measurements of two Earth-bound clocks over the course of a year [2,[6][7][8][9][10][11][12]. The sensitivity is entirely due to ellipticity in Earth's orbit, which gives a 3% seasonal variation in the gravitational potential at Earth due to the Sun. The peak-to-trough sinusoidal change in the potential has magnitude Á ¼ 3  10 À10 . Each clock has a different sensitivity to variation, and so Á = can be measured and hence k extracted.Because of the high precision of atomic clocks, k is determined very precisely despite the relatively small seasonal change in the gravitational potential. By contrast, we examine a ''medium strength'' field, where Á is 5 orders of magnitude larger than in the Earth-bound experiments, and the distance between the probe and the source is $10 4 times smaller than 1 AU. This allows us to probe nonlinear coupling of Á...

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