Probing the Gravitational Dependence of the Fine-Structure Constant from Observations of White Dwarf Stars
Matthew B. Bainbridge, Martin A. Barstow, Nicole Reindl, W.-? Lydia Tchang-Brillet, Thomas R. Ayres, John K. Webb, John D. Barrow, Jiting Hu, Jay B. Holberg, Simon P. Preval, Wim Ubachs, Vladimir A. Dzuba, Victor V. Flambaum, Vincent Dumont, Julian C. Berengut
uuniverse
Conference Report
Probing the Gravitational Dependence of theFine-Structure Constant from Observations ofWhite Dwarf Stars
Matthew B. Bainbridge *, Martin A. Barstow , Nicole Reindl , W.-Ü Lydia Tchang-Brillet ,Thomas R. Ayres , John K. Webb , John D. Barrow , Jiting Hu , Jay B. Holberg ,Simon P. Preval , Wim Ubachs , Vladimir A. Dzuba , Victor V. Flambaum ,Vincent Dumont and Julian C. Berengut Department of Physics and Astronomy, University of Leicester, University Road, Leicester LE1 7RH, UK;[email protected] (M.A.B.); [email protected] (N.R.) LERMA, Observatoire de Paris-Meudon, PSL Research University, CNRS, UMR8112, F-92195 Meudon,France; [email protected] Sorbonne Universités, UPMC University Paris 6, UMR8112, LERMA, F-75005 Paris, France Center for Astrophysics and Space Astronomy, University of Colorado, Boulder, CO 80309-0389, USA;[email protected] School of Physics, University of New South Wales, Sydney, NSW 2052, Australia;[email protected] (J.K.W.); [email protected] (J.H.); [email protected] (V.A.D.);v.fl[email protected] (V.V.F.); [email protected] (J.C.B.) DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road,Cambridge CB3 0WA, UK; [email protected] Lunar and Planetary Laboratory, Sonett Space Sciences Building, University of Arizona, Tucson, AZ 85721,USA; [email protected] Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK; [email protected] Department of Physics and Astronomy, LaserLab, VU University, De Boelelaan 1081,NL-1081 HV Amsterdam, The Netherlands; [email protected] Department of Physics, University of California, Berkeley, CA 94720-7300, USA;[email protected] * Correspondence: [email protected] Editors: Mariusz P. D ˛abrowski, Manuel Krämer and Vincenzo SalzanoReceived: 31 January 2017; Accepted: 17 March 2017; Published: 30 March 2017
Abstract:
Hot white dwarf stars are the ideal probe for a relationship between the fine-structureconstant and strong gravitational fields, providing us with an opportunity for a direct observationaltest. We study a sample of hot white dwarf stars, combining far-UV spectroscopic observations,atomic physics, atmospheric modelling, and fundamental physics in the search for variation in thefine structure constant. This variation manifests as shifts in the observed wavelengths of absorptionlines, such as quadruply ionized iron (FeV) and quadruply ionized nickel (NiV), when comparedto laboratory wavelengths. Berengut et al. (
Phys. Rev. Lett. , , 010801) demonstrated thevalidity of such an analysis using high-resolution Hubble Space Telescope (HST)/Space TelescopeImaging Spectrograph (STIS) spectra of G191-B2B. We have made three important improvements by:(a) using three new independent sets of laboratory wavelengths; (b) analysing a sample of objects; and(c) improving the methodology by incorporating robust techniques from previous studies towardsquasars (the Many Multiplet method). A successful detection would be the first direct measurementof a gravitational field effect on a bare constant of nature. Here we describe our approach and presentpreliminary results from nine objects using both FeV and NiV. Keywords: varying constants; varying alpha; hot white dwarf stars; absorption spectra analysis
Universe , a r X i v : . [ a s t r o - ph . C O ] A p r niverse , , 32 2 of 6 A common feature of many schemes to unify the strong, electro-weak, and gravitational forces ofnature is the prediction of violation of local Lorentz invariance and the Einstein equivalence principleat high energy [1]. This can manifest itself as variations in the fundamental constants of physics(Newton’s constant, G ; proton-to-electron mass ratio, µ ; fine structure constant, α ; etc.) due to lightscalar fields, the presence of extra space dimensions, or the non-uniqueness of the quantum vacuumstate for the universe. Probing the variation of fundamental constants in the distant universe isan important test of the equivalence principle and prospective theories of Grand Unification.In a light scalar field the total mass and the total scalar charge are both proportional to thenumber of nucleons, for objects that are not too relativistic, so observing fundamental constants neargravitating massive bodies is one way to probe the form of a potential variation and the existence ofscalar fields. However, the effect of a light scalar field on fundamental constants near massive bodiesdepends heavily on the theory being considered, particularly the type of coupling between the scalarfields and other fields [2]. Flambaum and Shuryak (2008) [3] considered a linear coupling betweenalpha and gravitational potential through the introduction of a massless scalar field, leading to thesimple relationship ∆ α / α ≡ α ( r ) − α α ≡ k α ∆ φ = k α ∆ (cid:18) GMrc (cid:19) where φ is the dimensionless gravitational potential ( φ = GMrc ), k α is a dimensionless dependencyparameter, M is the mass of the object, r is the radial distance from the object’s center, and α is thelaboratory value of the fine structure constant. If the relationship is indeed linear (or close to), then k α is a constant and can be very accurately determined by high-precision atomic clocks [3–11]. However, k α may not be constant [12], and the assumption that this relationship is linear needs testing. To probea non-linear relationship, we need to observe k α under conditions different than those on Earth.Hot white dwarf stars are the ideal probe for a relationship between α and strong gravitationalfields. Hot white dwarfs—with masses comparable to the sun and radii comparable to Earth—generatestrong gravitational fields and are typically bright (enough for precision spectroscopic analysis)with numerous absorption lines. Within the absorption spectra of white dwarfs, variation in α ismanifested as shifts in the observed wavelengths of absorption lines when compared to laboratorywavelengths [13], providing us with an opportunity for a direct observational test.Berengut et al. (2013) [14] recently used Hubble Space Telescope (HST)/Space Telescope ImagingSpectrograph (STIS) spectra of the hot white dwarf star G191-B2B to constrain ∆ α / α , by observingthe wavelength shifts in 96 quadruply ionized iron (FeV) and 32 quadruply ionized nickel (NiV)absorption features and deriving a separate limit for each metal: ∆ α / α = ( ± ) × − for FeVand ∆ α / α = ( − ± ) × − for NiV. Berengut et al. (2013) [14] suggest that this inconsistencyis due to a systematic effect in the laboratory wavelengths used. We have extended this work by:(a) using new laboratory wavelengths; (b) analysing a sample of objects rather than a single object;and (c) refining the analysis methodology by incorporating robust techniques from previous studiestowards quasars (the Many Multiplet method [15–17]).We are using three new independent lists of laboratory wavelengths to investigate the suspectedsystematic gain calibration error suspected by Berengut et al. (2013) [14]. This apparent systematiceffect is an important problem, because the effect is dependent on transition wavelength—just likea wavelength shift due to ∆ α / α . In 2013, there were two lists of laboratory wavelengths available forFeV and NiV with reasonable precision and within the wavelength range of interest: Ekberg (1975) [18]for FeV and Raassen & van Kleff [19] for NiV. Since then, three new lists have become available:the (a) Kramida; (b) Tchang-Brillet; and (c) Nave wavelength lists. Kramida (2014) [20] publishedan updated list of laboratory wavelengths for FeV, based on more recent observations by Azarov et al.(2001) [21] (outside of our wavelength range of interest) in addition to the Ekberg (1975) [18] laboratoryresults. Between 2014–2015 Tchang-Brillet (LERMA, Meudon, France) and a group led by Gillian Nave(NIST, Gaithersburg, MD, USA) independently re-observed the FeV laboratory wavelengths [22–24].The team at NIST also re-observed the NiV laboratory wavelengths. The apparent systematic effect in niverse , , 32 3 of 6 the Raassen NiV laboratory wavelengths noted by Berengut et al. (2013) [14] does not appear to bepresent in the new Nave NiV wavelengths from NIST.In order to study a broader compactness range and to enlarge the size of our sample, we conducteda search of both the literature and the Mikulski Archive for Space Telescopes (MAST). We usedthe following selection criteria: (a) photospheric absorption lines of FeV or NiV (atomic transitions forwhich we have new accurate laboratory wavelengths); (b) observed in the far-UV (the wavelength rangeof the FeV and NiV absorption lines) using HST/STIS Echelle spectroscopy; and (c) signal-to-noiseratio greater than 30 (a threshold for reasonable statistical uncertainties we determined using numericalsimulations). We found that only the HST/STIS Echelle spectra provide the necessary wavelengthaccuracy (1 km · s − [25]) needed for this project. In addition to G191-B2B (the object studied in [14]),we identified nine hot, bright white dwarfs and sub-dwarfs. We were also awarded 12 orbits withHST/STIS (scheduled for autumn 2017) to obtain new far-UV observations of three bright whitedwarfs known to have photospheric Fe and Ni absorption lines. Table 1 provides an overview ofthe 13 objects that will be studied in the course of this project. Our sample includes objects withgravitational potentials spanning four orders of magnitude. Table 1.
Characteristics of the white dwarf and sub dwarf sample. Uncertainties are 1 σ . g = GM / r ,the surface gravity in cm · s − . Object Type RA (J2000) Dec. (J2000) T e f f log g Ref.(Degrees) (Degrees) (K) vz 1128 O(H) 205.569792 28.433639 36, 600 ±
400 3.9 ± − ± ± ◦ ± ± ± ± − ±
10, 000 7.2 ± ± ± ±
530 7.47 ± ± ± ±
900 7.53 ± − ± ± − ± ± − ± ± − ± ± * To be observed with Hubble Space Telescope (HST)/Space Telescope Imaging Spectrograph (STIS) during cycle 24. We examine the spectral data of each object before fitting the absorption lines to identify the FeVand NiV transitions relevant for estimation of ∆ α / α . All transitions were visually checked for obviouscases of blends, and where found, those transitions were discarded. In addition, for the purposes ofthe preliminary results in this paper, we confine ourselves to using the FeV and NiV transitions listedin Berengut et al. (2013) [14]. However, we use the three new laboratory wavelengths (the Kramida,Tchang-Brillet, and Nave wavelength lists) available for these transitions as discussed above.We fit the absorption spectra in the normal way, using the Many Multiplet method and thesoftware VPFIT For each object, we initially construct a Voigt profile model (by visual inspection)with a single velocity component (absorption line), including all suitable transitions. We then applyVPFIT to optimise the Voigt profile parameters, including ∆ α / α as a free parameter in the fit.Statistical uncertainties are determined from the diagonal terms of the covariance matrix at thebest-fitting solution.Our analysis is on-going, but shows the preliminary results. These preliminary results serve tohighlight the importance of this kind of analysis. However, at this early stage, it would be premature niverse , , 32 4 of 6 to draw any conclusions about the relationship between ∆ α / α and gravitational potential. We do notinclude a table of ∆ α / α estimates or a weighted mean for this reason.A detailed consideration of possible systematic effects is required. The results shown in Figure 1neglect several possible sources of systematic effects, which may explain this apparent detectionof variation in α : imprecise wavelength calibration, long and short range wavelength distortions,and systematic effects in the laboratory wavelengths (despite the new measurements). It is importantthat these possible sources of bias are investigated. Additionally, these preliminary results include only9 of the 13 objects in our sample. The remaining four objects (BD + 28 ◦ HS050+0112 Ton21vz 1128ROB 162 Feige 24G191−B2B REJ0558−373Sh2−313Sh 2−174 −50−2502550 0e+00 2e+07 4e+07 6e+07
Surface Gravity
Daa غ − øß name aaaaaaaaa Feige 24G191−B2BHS050+0112REJ0558−373ROB 162Sh 2−174Sh2−313Ton21vz 1128 g [cm s − ] Figure 1.
Preliminary ∆ α / α results. Variation in the fine structure constant vs estimated surfacegravity, g = GM / r . For each object in the sample we fitted Voigt profiles simultaneously to therelevant quadruply ionized iron (FeV) and quadruply ionized nickel (NiV) absorption lines of eachobject and estimated ∆ α / α using VPFIT. Here we show an example of our preliminary results, usingthe Ward and Nave (2015) [22] laboratory wavelengths. We see a similar trend using the Kramida andTchang-Brillet wavelength lists. Error bars are 1 σ . The error bars on surface gravity for ROB 162 andvZ 1128 (both sub-dwarf objects) are too small to be seen in this plot. Studies such as the one summarised here provide a unique way of constraining new ideas infundamental physics. The equivalence principle is at the heart of general relativity, and it fixes thefundamental constants of nature into an absolute unvarying structure—a structure independent ofthe material content of the universe. Probing the variation of fundamental constants tests the deepestdepths of our current knowledge of physics, with the possibility of illuminating the next frontierof physics. This study is the first statistical sample of constraints on alpha from high-resolutionwhite dwarf spectra. Forthcoming HST observations will enhance that sample and improve theconstraints further.
Acknowledgments:
We thank Gillian Nave (NIST) and Jacob Ward (NIST) for providing preliminary FeV andNiV wavelengths prior to publication. This research used the ALICE High Performance Computing Facilityat the University of Leicester. This project is funded by a Leverhulme Trust Research Grant. WULTB wishesto acknowledge support from the LABEX Plas@par managed by the French ANR (ANR-11-IDEX-0004-02).J.D. Barrow is supported by the STFC of the UK.
Author Contributions:
JDB, MAB and JKW conceived the project. MAB leads and supervises the project. JBcontributed to the concept and design of the project. MBB and NR performed the data analysis and interpretation.TRA contributed the co-added spectral data. WULTB contributed new FeV laboratory wavelengths. JB, V. Dzubaand VF contributed to the theoretical background and alpha sensitivity parameters for the atomic transitions. niverse , , 32 5 of 6 V. Dzuba, VF and JKW invented the Many Multiplet method used in this work and first demonstrated theadvantages of this method. JKW, JH, JBH, SPP, JB and V. Dumont provided discussion of methodology andpotential systematic effects. MBB wrote the paper. WU provided critical revision of the paper. All authorscommented on the manuscript at all stages and approved the final version to be published.
Conflicts of Interest:
The authors declare no conflict of interest.
Abbreviations
The following abbreviations are used in this manuscript:HST, Hubble Space Telescope,STIS, Space Telescope Imaging Spectrograph,LERMA, Laboratoire d’Etudes du Rayonnement et de la Matière en Astrophysique et Atmosphères,NIST, National Institute of Standards and Technology, andVPFIT, Voigt Profile FITting software.
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