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UMD PHYS 402 - Search for Time Variation of the Fine Structure Constant

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VOLUME 82 NUMBER 5 PHYSICAL REVIEW LETTERS 1 FEBRUARY 1999 Search for Time Variation of the Fine Structure Constant John K Webb 1 Victor V Flambaum 1 Christopher W Churchill 2 Michael J Drinkwater 1 and John D Barrow3 1 2 School of Physics University of New South Wales Sydney New South Wales 2052 Australia Department of Astronomy Astrophysics Pennsylvania State University University Park Pennsylvania 16802 3 Astronomy Centre University of Sussex Brighton BN1 9QJ United Kingdom Received 13 February 1998 revised manuscript received 9 July 1998 An order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant a Applied to a sample of 30 absorption systems spanning redshifts 0 5 z 1 6 we derive limits on variations in a over a wide range of epochs For the whole sample Daya s21 1 6 0 4d 3 1025 This deviation is dominated by measurements at z 1 where Daya s21 9 6 0 5d 3 1025 For z 1 Daya s20 2 6 0 4d 3 1025 While this is consistent with a time varying a further work is required to explore possible systematic errors in the data although careful searches have so far revealed none S0031 9007 98 08267 2 PACS numbers 06 20 Jr 95 30 Dr 95 30 Sf 98 80 Es There are several theoretical motivations to search for space time variations in the fine structure constant a Theories which attempt to unify gravity and other fundamental forces may require the existence of additional compact space dimensions Any cosmological evolution in the mean scale factor of these additional dimensions will manifest itself as a time variation of our bare three dimensional coupling constants 1 Alternatively theories have been considered which introduce new scalar fields whose couplings with the Maxwell scalar Fab F ab allow a time varying a 2 The measurement of any variation in a would clearly have profound implications for our understanding of fundamental physics Spectroscopic observations of gas clouds seen in absorption against background quasars can be used to search for time variation of a Analyses involving optical spectroscopy of quasar absorbers have concentrated on the relativistic fine structure splitting of alkali type doublets the separation between lines in one multiplet is proportional to a 2 so small variations in the separation are directly proportional to a to a good approximation While the simplicity of that method is appealing the relativistic effect causing the fine splitting is small restricting the potential accuracy We demonstrate below how a substantial sensitivity gain is achieved by comparing the wavelengths of lines from different species and develop a new procedure simultaneously analyzing the Mg II 2796y2803 doublet and up to five Fe II transitions Fe II 2344 2374 2383 2587 2600 from three different multiplets These particular transitions are chosen for the following reasons i They are commonly seen in quasar absorption systems ii they fall into and span a suitable rest wavelength range iii an excellent database was available 3 iv extremely precise laboratory wavelengths have been measured and v the large Fe and Mg nuclear charge difference yields a considerable sensitivity gain 884 0031 9007y99y82 5 y884 4 15 00 We describe the details of the theoretical developments in a separate paper 4 here summarizing the main points The energy equation for a transition from the ground state within a particular multiplet observed at some redshift z is given by a a Ez Ec 1 Q1 Z 2 fs az0 d2 2 1g 1 K1 sLSdZ 2 s a0z d2 a 1 K2 sLSd2 Z 4 s a0z d4 1 where Z is the nuclear charge L and S are the electron total orbital angular momentum and total spin respectively and Ec is the energy of the configuration center The term in the coefficient Q1 describes a relativistic correction to Ec for a given change in a a0 is the zero redshift value and az is the value at some redshift z Rearranged this gives a Ez Ez 0 1 fQ1 1 K1 sLSdgZ 2 fs az0 d2 2 1g a 1 K2 sLSd2 Z 4 fs a0z d4 2 1g 2 Equation 2 is an extremely convenient formulation the second and third terms contributing only if a deviates from the laboratory value Accurate values for the relativistic coefficients Q1 K1 and K2 have been computed using relativistic many body calculations and experimental data The coefficients and laboratory rest wavelengths are given in Eq 3 For Fe II the relativistic coefficients Q1 are at least 1 order of magnitude larger than the spinorbit coefficients K1 The variation of the Fe II transition frequencies with a is thus completely dominated by the Q1 term In Mg II the relativistic corrections are small due to the smaller nuclear charge Z see Eq 2 so while a change in a induces a relatively large change in the observed wavelengths of the Fe II transitions the change is small for Mg II The relative shifts are substantially greater than those for a single alkali doublet alone such as Mg II so Mg II acts as an anchor against which the larger Fe II shifts are measured A comparison of the observed wavelengths of light and heavy atoms thus provides a dramatic increase in sensitivity compared to analyses of alkali doublets alone 1999 The American Physical Society VOLUME 82 NUMBER 5 PHYSICAL REVIEW LETTERS Since it is already clear from previous observational constraints that any change in a will be very small 5 7 it is vital that Ez 0 is known accurately enough Indeed the change in the frequency interval between Mg II 2796 and Fe II 2383 induced by a fractional change Daya 1025 is using Eq 3 0 03 cm21 Thus independent of the quality of the observations the limiting accuracy in a determination of Daya is 1025 for an uncertainty in the laboratory frequency of 0 03 cm21 This highlights the advantage of comparing light and heavy atoms Previous analyses of alkali doublets 5 6 have used frequencies of about the accuracy above but have been restricted to placing limits of Daya 1024 Very precise laboratory spectra of the Mg II 2796 and Mg II 2803 lines have recently been obtained 8 in excellent agreement with previous accurate measurements of Mg II 2796 alone 9 10 Similarly precise Fe II hollow cathode spectra exist 11 Inserting these laboratory wavelengths and our Q and K coefficients into Eq 2 we obtain the dependence of frequency on a for Mg II top two equations in Eq 3 below and Fe II 2 P J 1y2 v 35 669 286s2d 1 119 6x J 3y2 6 D J 9y2 6 6 v 35 760 835s2d 1 211 2x v 38 458 9871s20d 1 1394x 1 38y J 7y2 v 38 660 0494s20d 1 1632x 1 0y F J 11y2 v 41 968 0642s20d 1


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