A New Limit on the Total Neutrino Mass from the 2Df Galaxy Redshift Survey

Home , Redshift survey

View metadata, citationA new and similar limit papers on at thecore.ac.uk total neutrino mass from the 2dF Galaxy Redshift Surveybrought to you by CORE provided by CERN Document Server Ø. Elgarøy1,O.Lahav1,W.J.Percival2,J.A.Peacock2,D.S.Madgwick1, S. L. Bridle1,C.M.Baugh3,I.K. Baldry4, J. Bland-Hawthorn5, T. Bridges5,R.Cannon5,S.Cole3, M. Colless6, C. Collins7,W.Couch8,G.Dalton9, R. De Propris8,S.P.Driver10,G.P.Efstathiou1, R. S. Ellis11,C.S.Frenk3, K. Glazebrook5,C.Jackson6, I. Lewis9, S. Lumsden12, S. Maddox13, P. Norberg3,B.A.Peterson6, W. Sutherland2,K.Taylor11 1 Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK 2 Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edingburgh EH9 3HJ, UK 3 Department of Physics, University of Durham, South Road, Durham DH1 3LE, UK 4 Department of Physics & Astronomy, John Hopkins University, Baltimore, MD 21218-2686, USA 5 Anglo-Australian Observatory, P. O. Box 296, Epping, NSW 2121, Australia 6 Research School of Astronomy & Astrophysics, The Australian National University, Weston Creek, ACT 2611, Australia 7 Astrophysics Research Institute, Liverpool John Moores University, Twelve Quays House, Birkenhead, L14 1LD, UK 8 Department of Astrophysics, University of New South Wales, Sydney, NSW 2052, Australia 9 Department of Physics, University of Oxford, Keble Road, Oxford OX1 3RH, UK 10 School of Physics and Astronomy, University of St. Andrews, North Haugh, St. Andrews, Fife, KY6 9SS, UK 11 Department of Astronomy, California Institute of Technology, Pasadena, CA 91125, USA 12 Department of Physics, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, UK 13 School of Physics & Astronomy, University of Nottingham, Nottingham NG7 2RD, UK

We constrain fν Ων /Ωm, the fractional contribution of neutrinos to the total mass density in the Universe, by comparing≡ the power spectrum of fluctuations derived from the 2dF Galaxy Redshift Survey with model matter power spectra. The model considered is a spatially flat universe with four components: baryons, cold dark matter, massive neutrinos (hot dark matter) and a cosmological constant. By adding constraints from other independent cosmological probes we find fν < 0.13 and mν,tot < 1.8 eV (at 95% confidence), for a prior of 0.1 < Ωm < 0.5, and assuming the scalar spectral index n = 1. The corresponding results for n =1.1arefν < 0.16, mν,tot < 2.2 eV. Very similar results are obtained using instead a prior on Ωm from Type Ia supernovae surveys.

Whether neutrinos are massive or not has been an open redshift survey [19,20], to obtain an upper bound on the question for a long time, but the recent data from atmo- sum of the neutrino masses. spheric and solar neutrino experiments [1–7] are most naturally interpreted in terms of neutrino oscillations, Massive neutrinos make up part of the dark matter which implies that not all neutrinos are massless [8–10]. in the Universe. In the cosmological model favoured However, since the oscillation probability depends on by data on large-scale structure and the observed fluc- the mass-squared differences, and not on the absolute tuations in the Cosmic Microwave Background (CMB) masses, the oscillation experiments cannot provide abso- [21,22], the Universe is flat, and the contributions to lute masses for neutrinos. The mass scale can in principle the mass-energy density in units of the critical density be obtained from e.g. the energy spectrum in the beta- are ΩΛ 0.7 from vacuum energy or a ‘quintessence’ ≈ decay of 3H [11], or from neutrinoless double beta decay field, and Ωm 0.3 from matter. Baryons make up ≈ [12]. Recently, a detection was claimed of the neutrino- only fb Ωb/Ωm 0.15 of the matter contribution 76 76 ≡ ≈ less double beta decay process Ge Se+ 2e−, which [21,22], most of the remaining being in the form of cold if confirmed also would prove that→ neutrinos are their dark matter (CDM), the exact nature of which is still own antiparticles [13]. However, the status of this result unknown. ‘Cold’ in this context means that the par- is still under some debate [14,15]. At the present, cosmo- ticles were moving at non-relativistic speeds when they logical data [16–18] provide stronger constraints on the dropped out of thermal equilibrium. Particles drop out total neutrino mass than particle physics experiments. of equilibrium roughly when their interaction rate falls Since neutrinos with masses of the order of a few tenths below the expansion rate of the Universe. For neutrinos of an electron volt (eV) can have a significant effect on with masses in the eV range this happened when they the formation of large-scale structures in the Universe, were still relativistic, and so they will be a ‘hot’ compo- observations of the distribution of galaxies can provide nent of the dark matter (HDM). This has implications for us with an upper bound on the density of massive neutri- large-scale structure, since the neutrinos can free-stream nos. We will in this paper use data from the 2dF Galaxy over large distances and erase small-scale structures (see Redshift Survey (2dFGRS), which is the largest existing e.g. [23] for an overview). As a result, mass fluctuations are suppressed at comoving wavenumbers greater than

1 1/2 1/2 1 2 2 knr =0.026(mν/1eV) Ωm h Mpc− [24], where mν is had χ =32.9, Ων =0.01 gives χ =33.4, whereas the the neutrino mass of one flavour. The neutrino contribu- model with Ων =0.05 provides a poor fit to the data 2 tion to the total mass-energy density, Ων , in units of the with χ =92.2. critical density needed to close the Universe, is given by Clearly, the inference of the neutrino mass depends on m our assumptions (‘priors’) on the other parameters. We Ω h2 = ν,tot , (1) ν 94 eV therefore add constraints from other independent cosmological probes. The Hubble parameter has been de- where m is the sum of the neutrino mass matrix ν,tot termined by the HST Hubble key project to be h = eigenvalues, and the Hubble parameter H0 at the present 1 1 0.70 0.07 [29], and Big Bang Nucleosynthesis gives a epoch is given in terms of h as H = 100 h km s Mpc− . 0 − constraint± Ω h2 =0.020 0.002 on the baryon density Eq. (1) assumes that all three neutrino flavours drop out b [30]. For these parameters,± we adopt Gaussian priors of equilibrium at the same temperature, which is a rea- with the standard deviations given above. The position sonable approximation. The suppression of the matter of the first peak in the CMB power spectrum gives a power spectrum P (k) on small scales is given approxi- m strong indication that the Universe is spatially flat, i.e. mately by (see e.g. [25]) Ωm +ΩΛ = 1 [21,22]. The CMB peak positions are ∆Pm not sensitive to neutrino masses, because the neutrinos 8fν , (2) Pm ≈− were non-relativistic at recombination, and hence indis- tinguishable from cold dark matter. Here we consider where fν Ων /Ω . Therefore even a neutrino mass as ≡ m flat models only. The latest CMB data are consistent small as 0.1 eV gives a reduction in power of 5-15 %. with the scalar spectral index of the primordial power The 2dFGRS has now measured over 220 000 galaxy spectrum being n = 1 [22], but we also quote results for redshifts, with a median redshift of zm 0.11, and is the n =0.9andn =1.1. largest existing galaxy redshift survey≈ [19]. A sample of this size allows large-scale structure statistics to be mea- Perhaps the least known prior is the total matter den- sured with very small random errors. An initial estimate sity Ωm. When the constraint of a flat universe is com- of the convolved, redshift-space power spectrum of the bined with surveys of high redshift Type Ia supernovae [31,32], one finds Ω =0.28 0.14. However, studies 2dFGRS has been determined [20] for a sample of 160 000 m ± 1 of the mass-to-light ratio of galaxy clusters find values redshifts. On scales 0.02

2 virtually no eﬀect on the results. We evaluated the like- results are consistent with this range. If the largest neu- lihood on a grid with 0.1 < Ω h<0.5, 0 fν < 0.3, trino mass is in fact of order a tenth of an eV, it should be m ≤ 0

3 [36] T. H. Reiprich and H. Boehringer, Ap. J. 567 716. [40] S. D. M. White, J. F. Navarro, A. E. Evrard, and C. S. [37] P. T. P. Viana, R. C. Nichol, and A. R. Liddle, astro- Frenk, Nature 366 (1993) 429. ph/0111394. [41] P. Erdogdu, S. Ettori, and O. Lahav, astro-ph/0202357. [38] A. Blanchard, R. Sadat, J.G. Bartlett, and M. LeDour, [42] L. M. Krauss and B. Chaboyer, astro-ph/0111597. A&A 362 (2000) 809. [43] N. A. Arhipova, T. Kahniashvili, and V. N. Lukash, A&A [39] V. R. Eke, S. Cole, C. S. Frenk, and J. P. Henry, MNRAS in press. 298 (1998) 1145. [44] Z. Xing, hep-ph/0202034.

105 ) 3

4 Mpc 10 −3 (k) (h g P

103 0.01 0.10 k (h Mpc−1)

FIG. 1. Power spectra for Ων = 0 (solid line), Ων =0.01 (dashed line), and Ων =0.05 (dot-dashed line) with amplitudes fitted to the 2dFGRS power spectrum data (vertical bars) in redshift space. We have fixed Ωm =0.3, ΩΛ =0.7, h =0.7, 2 Ωbh =0.02. The vertical dashed lines limit the range in k used in the fits.

FIG. 2. 68 (solid line), 95 (dashed line) and 99% (dotted line) conﬁdence contours in the plane of fν Ων /Ωm and Γ Ωmh, 2 ≡ ≡ with marginalization over h and Ωbh using Gaussian priors, and over A using a uniform prior in 0.5

4 FIG. 3. Probability distributions, normalized so that the area under each curve is equal to one, for fν with marginalization over the other parameters, as explained in the text, for Nν = 3 massive neutrinos and n =0.9 (dotted line), 1.0 (solid line), and 1.1 (dashed line).

Ωm =0.28 0.14 (SNIa) 0.1 < Ωm < 0.5 ± nfν mν,tot (eV) fν mν,tot (eV) 0.9 0.12 1.5 0.11 1.5 1.0 0.14 1.8 0.13 1.8 1.1 0.16 2.1 0.16 2.2

TABLE I. Summary of 95% conﬁdence upper bounds on fν and mν,tot with our chosen priors on Ωm. The central values are used for Ωm in the conversion of fν to mν,tot.