- Email: [email protected]
On cosmic time variability of the fine-structure constant
0083-6656/93 $24.00 @ 1993 PergmnonPress Ltd
V/.t.tas/nA~romwny, VoL 37, pp. 535--538, 1993
Printed in GreetBritain. All rightsm~'ved.
ON COSMIC TIME VARIABILITY OF THE FINE-STRUCTURE CONSTANT Sergei A. Levshakov Department of Theoretical Astrophysics, A.F. Ioffe Physico-Technical Institute, St Petersburg 194021, Russia
Abstract
It is shown that the 2p2P fine-structure intervals of LiI-like ions and 3p2p intervals of NaI-]Jke ions measured in absorption-line spectra of quasars at high redshifts (z > 1) are systematically larger than those in laboratory. If this difference is caused by time variation of the fine-structure constant, a = e2/hc, then a fractional deviation of az at the epoch z - 2 from the present time a equals A a / a = (0.3 ~ 0.1)% (la). Cosmic time variation of fundamental physical constants was proposed in a number of theories (see Dyson 1972, Maeda 1988, Sisterna and Vucetich 1990, and Wesson 1992, for review). Consider a possible variability of the Sommerfeld fine-structure constant, a ~ 1/137.036. Since is concerned with radiative processes, the problem of its variability is of great importance for cosmology. However the variability of a at high redshlfts has not been thoroughly investigated so far. Here we discuss the preliminary results on this problem. In our analysis we have used absorption lines of resonance doublets of LiI- and NaI-like ions observed in quasar spectra at z > 1. The ratio of a relativistic fine-structure splitting to wavelength is proportional to a i in atomic spectra. Therefore the relation (,~:/,~):'
=
(A,t:IX:)ICA.Ui),
(1)
can be used as a measure of the variability of a. Here A~.. and ~, are, respectively, the finestructure separation and the weighted mean wavelengths for a given ion at certain z, while AA, are corresponding quantities from laboratory data. Let ~z(~l), ~rz(~2) be the inner errors of measuring the wavelengths hi, A2 of a redshifted doublet, and let a($1), a(~2) be the accuracy of corresponding laboratory wavelengths (typically, a..()~) .-. 0.1 + 0.01/~ and a(A) ~ 0.001/~). Then the error ~ ( A a / a ) can be estimated as ~r(Aa/c0 ~ ~ ' a [
AA2(1 + z)2
+
.
(2)
536
$. A. Levshakov
We have selected those doublets from the published quasar spectra which yield or(As/a) < 1%. This means that relatively weak absorption lines are excluded from our sample. Furthermore, to avoid large systematical errors of A s / s we have chosen those doublets which do not lie (i) in the Lyman-alpha forest, (ii) on steep emission line profiles or near strong absorption troughs, (iii) at the edges of observed spectral regions, and (iv) near strong night sky lines. Besides, to reduce the effect of possible correlation between az(A1) and a~(A2) we have included in our sample only isolated pairs which have no overlapping wings with other absorption lines. A sample of 36 such doublets is listed in Table 2. All wavelengths are vacuum and heliocentric, and A s / s have been calculated using laboratory wavelengths compiled by Morton et a/.(1988). The ordinary mean of this set is ( A n / s ) = (0.3 ± 0.1)% (la), and residuals are normally distributed. More robust location estimators such as, for example, the median, the 10%-trimmed mean or the Huber-rejection rule X84 (see Hampel et al.,1986) yield, respectively, A s / s = (0.4 ± 0.2)%, (0.36 4- 0.08)%, and (0.3 ± 0.1)%. We have used also five UV-doublets listed in Table 1 to control the bias of {As~s) caused by possible uncertainties in laboratory wavelengths. These lines have more accurate wavelengths (az(A) ~ 0.005A) than the quasar data, and we have not found a significant positive bias at zero redshift where (As~s) = -(0.17 4-0.09)% (la). Nevertheless. it is still difficult to assess the significance of the obtained result on the variability of s at z > 1 because quasar spectra available do not possess a required quality. Perhaps new technique of quasar spectroscopy, with improvements in resolution and sensitivity, will yield valuable information on the variability of the fundamental constants. I would like to thank D. Yakovlev, V. Nikulin, and D. Vaxshalovich for useful discussions. I also thank I. Agafonova for her valuable advicesconcerning robust statistics.
Table 1. The Sample of Resonance Doublets at zaba ~- 0 No. 1 2 3 4 5
Objec~ SN1987A SN1987A SN1987A 3C273 3C273
Ion CIV AIIII SiIV CIV MgII
A1, A 1552.20 1864.52 1404.06 1550.72 2803.49
A2, A 1549.65 1856.44 1395.06 1548.16 2796.31
z~bo 0.0009 0.0009 0.0009 -3e--5 -le--5
As/a% -0.48 -0.004 -0.13 -0.23 0.007
Refs BWPGPW BWPGPW BWPGPW MWSG MWSG
Cosmic Time Variability
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Table 2. The Sample of Resonance Doublets with z~b, > Object Ion )~1, h ;~2, h z~b, Aa/a% Q2206-199 MgII 5654.51 5640.01 1.0169 0.07 Q0256-000 MgII 6163.00 6147.11 1.1983 0.34 Q0256-000 MgII 6162.90 6147.46 1.1983 -1.09 Q0957+561B MgII 6701.46 6684.12 1.3903 0.52 Q0957+561A MgII 6701.89 6684,06 1.3904 1.93 Q0352-275 MgII 6742.44 6725.08 1.4050 0.27 Q1756+237 CIV 3816.32 3809.93 1.4609 0.48 Q0058+019 CIV 3820.53 3814.16 1.4636 0.26 Ql148-001 CIV 3825.78 3819.24 1.4670 1.53 Q0347-383 MgII 7082.63 7064.31 1.5263 0.51 Q1017+280 CIV 4024.42 4017.68 1.5951 0.49 Q1017+280 CIV 4044.46 4037.87 1.6081 -0.88 Q1556+335 SiIV 3662.17 3638.72 1.6107 -0.18 Q0237-233 CIV 4048.86 4042.14 1.6109 O.04 Q1756+237 S i I V 3665.46 3642.89 1.6134 -2.12 Q1715+535 CIV 4083.32 4076.43 1.6330 0.87 Q1756+237 S i I V 3751.00 3727.16 1.6741 -0.56 Q1245+345 CIV 4152.48 4145.73 1.6777 -1.00 Q0424--131 CIV 4212.10 4205.06 1.7161 0.39 Q1017÷280 CIV 4339.80 4332.56 1.7985 0.29 QO229q-131 CIV 4501.04 4493.27 1.9023 2.02 Q2206-199 AlIII 5440.27 5416.41 1.9204 0.60 Q1435+638 CIV 4533.82 4526.13 1.9235 1.13 Q1222+228 CIV 4555.08 4547.43 1.9373 0.63 Ql157+014 MgII 8251.57 8230.56 1.9433 -0.28 Q0042-264 AlIII 5644.03 5619.23 2.0298 0.69 Q0450-132 CIV 4755.98 4748.18 2.0669 -0.56 Q0450-132 SiIV 4302.23 4274.40 2.0669 0.33 Q0450-132 CIV 4817.24 4809.23 2.1063 0.13 Q0528-250 CIV 4870.26 4862.04 2.1405 0.88 Q0528-250 c I v 4870.75 4862.41 2.1408 1.61 Q0002-422 c I v 4913.2 4905.0 2.1682 0.31 Q2239-386 AIIII 6290.99 6263.66 2.3772 0.12 Q0153+045 CIV 5271.99 5263.04 2.3995 1.17 Q0207-003 SiIV 5013.42 4980.93 2.5738 0.42 Q0347-383 SiIV 5345.23 5310.48 2.8103 0.58
537
1 Refs SBS Sa Sb C C SSB FWPSMC SBS SBS Sa SBS SBS FWPSMC SBS FWPSMC SBS FWPSMC SBS SBS SBS SBS SBS SBS SBS C Sa SBS SBS SBS CM SBS SYBCW Sa KYG SBS Sa
538
$. A. Levs/mkov REFERENCES
Blades, J.C., Wheatley, J.M., Panagia, N., Grewing, M., Pettini, M. and Wamsteker, W. (1988) An ultraviolet spectral atlas of interstellar lines towards SN1987A. Astvophys. J. 334, 308 - 335 (BWPGPW). Caulet, A.(1989) The evolution of low-ionization QSOs absorption systems. Astrophys. J. 340, 9 0 - 116 (c). Chen, J.-s. and Morton, D.C. (1984) Further spectroscopic observations of the QSO PKS 0528250. Mort. Not. R. astr. Soc. 208, 167- 178 (CM). Dyson, F.J. (1972) The fundamental constants and their time variation. In Aspects of Quantum Theory, Eds. Salam, A. ~z Wigner, E.P. pp.213 - 236. Cambridge University Press, Cambridge. Foltz, C.B., Weymann, R.J., Peterson, B.M., Sun, L., Malkan, M.A. and Chaffee, F.H.,Jr. (1986) CIV absorption systems in QSO spectra: is the character of systems with Z,bs ~-- z ~ different from those with Z~b, << z,~ ? Astrophys. J. 307, 504 - 534 (FWPSMC). Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986) Robust Statistics. Wiley & Sons, New York, 1986. Khare, P., York, D.G. and Green, R. (1989) Absorption lines at z > 2.3 in spectra of quasi-stellar objects. Astrophys. J. 347, 627 - 639 (KYG). Maeda, K. (1988) On time variation of fundamental constants in superstring theories. Mod. Phys. Left. A 3, 243 - 249. Morris, S.L., Weymann, R.J., Savage, B.D. and Gilliland, R.L. (1991) First results from the Goddard high-resolution spectrograph: the Galactic halo and the Lyct forest at low redshift in 3C273. Astrophys. J. Left. 377, L21 - L24 (MWSG). Morton, D.C., York, D.G. and Jenkins, E.B. (1988) A search list of lines for quasi-stellar objects absorption systems. Astrophys. J. Suppl. Set. 68, 449 - 461. Sargent, W.L.W., Young, P.J., Boksenberg, A., Carswell, R.F. and Whelan, J.A.J. (1979) A highresolution study of the absorption spectra of the QSOs Q0002-422 and Q0453-423. Astrophys. J. 230, 49 - 67 (SYBCW). Sargent, W.L.W., Boksenberg, A. and Steidel, C.C. (1988) CIV absorption in a new sample of 55 QSOs: evolution and clustering of the heavy element absorption redshifts. Astrophys. J. Suppl. Set. 68, 539 - 641 (SBS). Sargent, W.L.W., Steidel, C.C. and Boksenberg, A. (1989) A survey of Lyman limit absorption in the spectra of 59 high redshift QSOs. Astrophys. J. Suppl. Ser. 69, 703 - 761 (SSB). Sisterna, P. and Vucetich, H. (1990) Time variation of fundamental constants: bounds from geophysical and astronomical data. Phys. Ray. D 41, 1034 - 1046. Steidel, C.C. (1990) A high-redshift extension of the survey for CIV absorption in the spectra of QSOs: the redshift evolution of the heavy-element absorbers. Astrophys. J. Suppl. Set. 72, 1 39 (Sa). Steidel, C.C. (1990) The properties of Lyman limit absorbing clouds at z = 3: physical conditions in the extended gaseous halos of high-redshift galaxies. Astrophys. J. Suppl. Set. 74, 37 - 91 (Sb). Wesson, P.S. (1992) Constants and cosmology: the nature and origin of fundamental constants in astrophysics and particle physics. Space Sci. Rev. 59, 365 - 406.
V/.t.tas/nA~romwny, VoL 37, pp. 535--538, 1993
Printed in GreetBritain. All rightsm~'ved.
ON COSMIC TIME VARIABILITY OF THE FINE-STRUCTURE CONSTANT Sergei A. Levshakov Department of Theoretical Astrophysics, A.F. Ioffe Physico-Technical Institute, St Petersburg 194021, Russia
Abstract
It is shown that the 2p2P fine-structure intervals of LiI-like ions and 3p2p intervals of NaI-]Jke ions measured in absorption-line spectra of quasars at high redshifts (z > 1) are systematically larger than those in laboratory. If this difference is caused by time variation of the fine-structure constant, a = e2/hc, then a fractional deviation of az at the epoch z - 2 from the present time a equals A a / a = (0.3 ~ 0.1)% (la). Cosmic time variation of fundamental physical constants was proposed in a number of theories (see Dyson 1972, Maeda 1988, Sisterna and Vucetich 1990, and Wesson 1992, for review). Consider a possible variability of the Sommerfeld fine-structure constant, a ~ 1/137.036. Since is concerned with radiative processes, the problem of its variability is of great importance for cosmology. However the variability of a at high redshlfts has not been thoroughly investigated so far. Here we discuss the preliminary results on this problem. In our analysis we have used absorption lines of resonance doublets of LiI- and NaI-like ions observed in quasar spectra at z > 1. The ratio of a relativistic fine-structure splitting to wavelength is proportional to a i in atomic spectra. Therefore the relation (,~:/,~):'
=
(A,t:IX:)ICA.Ui),
(1)
can be used as a measure of the variability of a. Here A~.. and ~, are, respectively, the finestructure separation and the weighted mean wavelengths for a given ion at certain z, while AA, are corresponding quantities from laboratory data. Let ~z(~l), ~rz(~2) be the inner errors of measuring the wavelengths hi, A2 of a redshifted doublet, and let a($1), a(~2) be the accuracy of corresponding laboratory wavelengths (typically, a..()~) .-. 0.1 + 0.01/~ and a(A) ~ 0.001/~). Then the error ~ ( A a / a ) can be estimated as ~r(Aa/c0 ~ ~ ' a [
AA2(1 + z)2
+
.
(2)
536
$. A. Levshakov
We have selected those doublets from the published quasar spectra which yield or(As/a) < 1%. This means that relatively weak absorption lines are excluded from our sample. Furthermore, to avoid large systematical errors of A s / s we have chosen those doublets which do not lie (i) in the Lyman-alpha forest, (ii) on steep emission line profiles or near strong absorption troughs, (iii) at the edges of observed spectral regions, and (iv) near strong night sky lines. Besides, to reduce the effect of possible correlation between az(A1) and a~(A2) we have included in our sample only isolated pairs which have no overlapping wings with other absorption lines. A sample of 36 such doublets is listed in Table 2. All wavelengths are vacuum and heliocentric, and A s / s have been calculated using laboratory wavelengths compiled by Morton et a/.(1988). The ordinary mean of this set is ( A n / s ) = (0.3 ± 0.1)% (la), and residuals are normally distributed. More robust location estimators such as, for example, the median, the 10%-trimmed mean or the Huber-rejection rule X84 (see Hampel et al.,1986) yield, respectively, A s / s = (0.4 ± 0.2)%, (0.36 4- 0.08)%, and (0.3 ± 0.1)%. We have used also five UV-doublets listed in Table 1 to control the bias of {As~s) caused by possible uncertainties in laboratory wavelengths. These lines have more accurate wavelengths (az(A) ~ 0.005A) than the quasar data, and we have not found a significant positive bias at zero redshift where (As~s) = -(0.17 4-0.09)% (la). Nevertheless. it is still difficult to assess the significance of the obtained result on the variability of s at z > 1 because quasar spectra available do not possess a required quality. Perhaps new technique of quasar spectroscopy, with improvements in resolution and sensitivity, will yield valuable information on the variability of the fundamental constants. I would like to thank D. Yakovlev, V. Nikulin, and D. Vaxshalovich for useful discussions. I also thank I. Agafonova for her valuable advicesconcerning robust statistics.
Table 1. The Sample of Resonance Doublets at zaba ~- 0 No. 1 2 3 4 5
Objec~ SN1987A SN1987A SN1987A 3C273 3C273
Ion CIV AIIII SiIV CIV MgII
A1, A 1552.20 1864.52 1404.06 1550.72 2803.49
A2, A 1549.65 1856.44 1395.06 1548.16 2796.31
z~bo 0.0009 0.0009 0.0009 -3e--5 -le--5
As/a% -0.48 -0.004 -0.13 -0.23 0.007
Refs BWPGPW BWPGPW BWPGPW MWSG MWSG
Cosmic Time Variability
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36
Table 2. The Sample of Resonance Doublets with z~b, > Object Ion )~1, h ;~2, h z~b, Aa/a% Q2206-199 MgII 5654.51 5640.01 1.0169 0.07 Q0256-000 MgII 6163.00 6147.11 1.1983 0.34 Q0256-000 MgII 6162.90 6147.46 1.1983 -1.09 Q0957+561B MgII 6701.46 6684.12 1.3903 0.52 Q0957+561A MgII 6701.89 6684,06 1.3904 1.93 Q0352-275 MgII 6742.44 6725.08 1.4050 0.27 Q1756+237 CIV 3816.32 3809.93 1.4609 0.48 Q0058+019 CIV 3820.53 3814.16 1.4636 0.26 Ql148-001 CIV 3825.78 3819.24 1.4670 1.53 Q0347-383 MgII 7082.63 7064.31 1.5263 0.51 Q1017+280 CIV 4024.42 4017.68 1.5951 0.49 Q1017+280 CIV 4044.46 4037.87 1.6081 -0.88 Q1556+335 SiIV 3662.17 3638.72 1.6107 -0.18 Q0237-233 CIV 4048.86 4042.14 1.6109 O.04 Q1756+237 S i I V 3665.46 3642.89 1.6134 -2.12 Q1715+535 CIV 4083.32 4076.43 1.6330 0.87 Q1756+237 S i I V 3751.00 3727.16 1.6741 -0.56 Q1245+345 CIV 4152.48 4145.73 1.6777 -1.00 Q0424--131 CIV 4212.10 4205.06 1.7161 0.39 Q1017÷280 CIV 4339.80 4332.56 1.7985 0.29 QO229q-131 CIV 4501.04 4493.27 1.9023 2.02 Q2206-199 AlIII 5440.27 5416.41 1.9204 0.60 Q1435+638 CIV 4533.82 4526.13 1.9235 1.13 Q1222+228 CIV 4555.08 4547.43 1.9373 0.63 Ql157+014 MgII 8251.57 8230.56 1.9433 -0.28 Q0042-264 AlIII 5644.03 5619.23 2.0298 0.69 Q0450-132 CIV 4755.98 4748.18 2.0669 -0.56 Q0450-132 SiIV 4302.23 4274.40 2.0669 0.33 Q0450-132 CIV 4817.24 4809.23 2.1063 0.13 Q0528-250 CIV 4870.26 4862.04 2.1405 0.88 Q0528-250 c I v 4870.75 4862.41 2.1408 1.61 Q0002-422 c I v 4913.2 4905.0 2.1682 0.31 Q2239-386 AIIII 6290.99 6263.66 2.3772 0.12 Q0153+045 CIV 5271.99 5263.04 2.3995 1.17 Q0207-003 SiIV 5013.42 4980.93 2.5738 0.42 Q0347-383 SiIV 5345.23 5310.48 2.8103 0.58
537
1 Refs SBS Sa Sb C C SSB FWPSMC SBS SBS Sa SBS SBS FWPSMC SBS FWPSMC SBS FWPSMC SBS SBS SBS SBS SBS SBS SBS C Sa SBS SBS SBS CM SBS SYBCW Sa KYG SBS Sa
538
$. A. Levs/mkov REFERENCES
Blades, J.C., Wheatley, J.M., Panagia, N., Grewing, M., Pettini, M. and Wamsteker, W. (1988) An ultraviolet spectral atlas of interstellar lines towards SN1987A. Astvophys. J. 334, 308 - 335 (BWPGPW). Caulet, A.(1989) The evolution of low-ionization QSOs absorption systems. Astrophys. J. 340, 9 0 - 116 (c). Chen, J.-s. and Morton, D.C. (1984) Further spectroscopic observations of the QSO PKS 0528250. Mort. Not. R. astr. Soc. 208, 167- 178 (CM). Dyson, F.J. (1972) The fundamental constants and their time variation. In Aspects of Quantum Theory, Eds. Salam, A. ~z Wigner, E.P. pp.213 - 236. Cambridge University Press, Cambridge. Foltz, C.B., Weymann, R.J., Peterson, B.M., Sun, L., Malkan, M.A. and Chaffee, F.H.,Jr. (1986) CIV absorption systems in QSO spectra: is the character of systems with Z,bs ~-- z ~ different from those with Z~b, << z,~ ? Astrophys. J. 307, 504 - 534 (FWPSMC). Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, W.A. (1986) Robust Statistics. Wiley & Sons, New York, 1986. Khare, P., York, D.G. and Green, R. (1989) Absorption lines at z > 2.3 in spectra of quasi-stellar objects. Astrophys. J. 347, 627 - 639 (KYG). Maeda, K. (1988) On time variation of fundamental constants in superstring theories. Mod. Phys. Left. A 3, 243 - 249. Morris, S.L., Weymann, R.J., Savage, B.D. and Gilliland, R.L. (1991) First results from the Goddard high-resolution spectrograph: the Galactic halo and the Lyct forest at low redshift in 3C273. Astrophys. J. Left. 377, L21 - L24 (MWSG). Morton, D.C., York, D.G. and Jenkins, E.B. (1988) A search list of lines for quasi-stellar objects absorption systems. Astrophys. J. Suppl. Set. 68, 449 - 461. Sargent, W.L.W., Young, P.J., Boksenberg, A., Carswell, R.F. and Whelan, J.A.J. (1979) A highresolution study of the absorption spectra of the QSOs Q0002-422 and Q0453-423. Astrophys. J. 230, 49 - 67 (SYBCW). Sargent, W.L.W., Boksenberg, A. and Steidel, C.C. (1988) CIV absorption in a new sample of 55 QSOs: evolution and clustering of the heavy element absorption redshifts. Astrophys. J. Suppl. Set. 68, 539 - 641 (SBS). Sargent, W.L.W., Steidel, C.C. and Boksenberg, A. (1989) A survey of Lyman limit absorption in the spectra of 59 high redshift QSOs. Astrophys. J. Suppl. Ser. 69, 703 - 761 (SSB). Sisterna, P. and Vucetich, H. (1990) Time variation of fundamental constants: bounds from geophysical and astronomical data. Phys. Ray. D 41, 1034 - 1046. Steidel, C.C. (1990) A high-redshift extension of the survey for CIV absorption in the spectra of QSOs: the redshift evolution of the heavy-element absorbers. Astrophys. J. Suppl. Set. 72, 1 39 (Sa). Steidel, C.C. (1990) The properties of Lyman limit absorbing clouds at z = 3: physical conditions in the extended gaseous halos of high-redshift galaxies. Astrophys. J. Suppl. Set. 74, 37 - 91 (Sb). Wesson, P.S. (1992) Constants and cosmology: the nature and origin of fundamental constants in astrophysics and particle physics. Space Sci. Rev. 59, 365 - 406.