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Neutrinos and the Lyman-α forest: myth or reality?
Nuclear Physics B (Proc. Suppl.) 168 (2007) 54–56 www.elsevierphysics.com
Neutrinos and the Lyman-α forest: myth or reality? Matteo Vielab
∗
a
INAF Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131, Trieste (Italy)
b
Institute of Astronomy, Madingley Road, CB30HA, Cambdridge (UK) I will review constraints on sterile and active neutrino masses that can be obtained using the Lyman-α forest.
1. Framework The Lyman-α forest, the ubiquitous absorptions produced by neutral hydrogen along the lines-of-sight to distant quasars, is a powerful cosmological tool. It allows to measure the underlying matter power spectrum (amplitude, slope, curvature) and its evolution at scales (few up to 80 comoving Mpc) and redshifts (z = 2 − 4) that are not probed by any other observables. In recent years, after the seminal works of [1], two groups have measured the dark matter power spectrum with different techniques and data sets. On one side we have the unprecedented capability of the SDSS quasar spectra [2] and on the other the high resolution spectra obtained with the VLT [3]. These two groups have also relied on two different theoretical analysis: approximated hydro-dynamical simulations based on the Hydro-Particle Mesh approximation and full hydro-dynamical simulations performed with the GADGET-II code (on a smaller portion of the parameter space) for the SDSS and the highresolution spectra, respectively (see [4] for a more extensive discussion). Despite the very different frameworks the results are in reasonable agreement between each other and in slight “tension” with the latest WMAP3 data release. More precisely, while the high resolution spectra are not constraining any more for the cosmological parameters when combined to WMAP3, the SDSS ones, since they have smaller error bars, are com∗ Computations were done at the COSMOS supercomputer center, funded by PPARC, HEFCE and Silicon Graphics/Cray Research.
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.02.058
patible only at the ∼ 2σ level [5]. Here, I will concentrate more on the perspective of using both these data sets to constrain the properties of active and (putative) sterile neutrino particles, than on the cosmological parameters that can be recovered [6,7]. 2. Results on active neutrinos Massive (active) neutrinos act as hot dark matter and smooth the matter power spectrum below their free streaming length, which, at the redshifts of interest here is well approximated by kF S ∼ 0.4 (1 + z)−0.5 (m/1eV) h/Mpc, with m the total mass in neutrinos. The power spectrum feature introduced by neutrinos depend on their masses and number but can be considered as an overall reduction in the amplitude for scales below the number above. For a 1eV total mass the feature is in the portion of power spectrum probed by the Lyman-α forest, while for smaller masses it shifts to larger scales that are probed by galaxy redshift surveys. Both these two observables are thereby important in getting constraints on the neutrino masses and numbers in addition to the (much poorer) constraints that can be achieved from the CMB. In Figure 1 I show the 1 and 2σ contours obtained from WMAP year one, the 2dFGRS and the high resolution Lyman-α data (the LUQAS sample). At the 2 − σ level we have Σmν < 0.9 eV [8]. These limits have been updated recently by [5] in which a combined analysis of WMAP year three, the SDSS galaxy power spectrum, bias, baryonic acoustic oscillations, supernovae and the SDSS Lyman-α power has been
M. Viel / Nuclear Physics B (Proc. Suppl.) 168 (2007) 54–56
Figure 1. Lyman-α forest data combined with the 2dF galaxy power spectrum and with the WMAP one year data.
performed. The impressive upper limit is now Σmν < 0.17 (95% C.L.) and the number of effective neutrinos is Nef f = 5.3 (with the canonical Nef f = 3 allowed only at 2.4 − σ). In this analysis, allowing a fourth thermalized sterile neutrino gives ms < 0.26 eV at 95% C.L. (still at odds with the LSND results), and much lighter than the sterile neutrino candidate of the next section. 3. Results on sterile neutrinos A sterile neutrino with a mass in the keV range is a promising dark matter candidate [9]. Depending on its mass it will act as warm dark matter smoothing out the perturbation below a scale which is roughly given by ks ∼ 5 (ms /4.43)3/4(Tν /Ts ) Mpc−1 , with Ts the temperature at which the sterile neutrinos decouple and Tν the neutrino temperature [11]. The more massive the sterile neutrino the less smoothed will be the matter power spectrum relative to the ΛCDM (cold dark matter with a cosmological constant) case. The Lyman-α forest at high redshift is particularly suitable for giving tight constraints on warm dark matter candidates: at high redshifts the intergalactic structures are more lin-
55
ear and should better resemble the underlying matter power spectrum. In a recent analysis it has been found a 2 − σ lower limit on the sterile neutrino mass of 13 keV, by analysing the SDSS Lyman-α forest [12]. In an independent analysis of the same data performed with full hydrodynamical simulations [10] found ms > 9 − 10 keV (both these last two limits are 95% C.L.). In Figure 2 I show the constraining power of the SDSS data set in the σ8 − 1/ms plane: the contour significantly shrink when including the high redshift bins. Note that for this analysis only the Lyman-α data have been used (since all the other data sets are very little constraining). These limits have the strong advantage of being independent of the mixing angle with active neutrinos and are in strong contradiction with upper limits obtained with X-ray observations. These latter results are based on observations of astronomical objects such as cluster of galaxies, dwarf galaxies or Andromeda to find the distinctive feature of a radiative decay line (the line flux is related both to the sterile neutrino mass and the mixing angle) and give ms < 3 − 6 keV in the standard production scenario that assumes conservation of the leptonic number. The main result is that dark matter particles cannot be sterile neutrinos, unless they are produced by a nonstandard mechanism (resonant oscillations, coupling with the inflaton) or get diluted by a large entropy release. The corresponding lower limit for thermal relic is 2 keV [10]. 4. Systematics Could the Lyman-α data or their interpretation be wrong? The Lyman-α flux is measured to an unprecedented statistical precision and (known) major sources of systematics in the data could be the metal lines or the continuum fluctuations of the distant QSO. All these two effects have been modelled and extensively considered [2,3]. The main uncertainty is probably related to the simulations involved when interpreting the observed flux. Resolution effects and all the physics that give rise to Lyman-α absorptions have been accurately investigated but not yet at the percent or sub-percent level. Note that the exquisite tight
56
M. Viel / Nuclear Physics B (Proc. Suppl.) 168 (2007) 54–56
Sterile neutrinos Both the SDSS data sets and the reanalysis of the SDSS data set performed in [4] agree in setting the following lower limit on the sterile neutrino ms > 9 − 10 keV. A limit that is independent of the mixing angle with the active neutrinos and in strong disagreement with other observational probes (X-ray fluxes from clusters, clusters’ periphery, Milky Way, Large Magellanic Cloud etc.). Thus, the sterile neutrino model is probably ruled out in the standard production scenario which assumes a conservation of the lepton number. We stress that these Lyman-α forest limits are particularly robust: there is power at high redshift and at scales that would be strongly suppressed with a warm dark matter particle less massive than above values. Figure 2. Constraints obtained from the SDSS data set analysed independently with full hydrodynamical simulations. The constraining power of the highest redshift bins is particularly evident: the contours represent the 1, 2−σ confidence level in the σ8 − keV/msterile plane for all the bins with z < 3.2 (dark blue), z < 3.6 (cyan) and z < 4.2 (green).
limit on active neutrinos will be much more sensitive to these effects than the sterile neutrino limits. More work is needed in order to explore the parameter space with full hydro-dynamical simulations and not with approximated technique which, although calibrated on full hydro physics, might be prone to poor understood systematic effects [13,14]. 5. Summary The Lyman-α forest is a fundamental tool to constrain the properties of neutrinos. Active neutrinos The incredibly strong limit Σmν < 0.17 eV obtained recently by [5] might be true or might be a product of a still unknown systematic effect that bias the estimate of the SDSS Lyman-α power at these scales. This has to be checked by using hydro-dynamical simulations that treat self-consistently the neutrino component. For the time being, a more conservative Σmν < 0.9 eV is probably more reliable.
REFERENCES 1. Croft et al., ApJ 581 (2002) 20 2. McDonald P., et al., ApJ, 635 (2005) 761 3. Kim T.-S., Viel M., Haehnelt M.G., Cristiani S., Carswell R.F., MNRAS 347(2004) 355 4. Viel M., Haehnelt M.G., MNRAS 365 (2006) 231 5. Seljak U., Slosar A., McDonald P., JCAP 0610 (2006) 014 6. Viel M., Haehnelt M.G., Lewis A., MNRAS 370 (2006) 51L 7. Viel M., Haehnelt M.G., Weller J., MNRAS 355 (2004) 23L 8. Viel M., Probing Galaxies through Quasar Absorption Lines, IAU Colloquium Proceedings of the International Astronomical Union 199, (2005) arXiv: astro-ph/0504645 9. Abazajian K., Koushiappas S.M., Phys.Rev. D74 (2006) 023527 10. Viel M., Lesgourgues J., Haehnelt M.G., Matarrese S., Riotto A., PhRvL 97 (2006) 071301 11. Viel M., Lesgourgues J., Haehnelt M.G., Matarrese S., Riotto A., Phys Rev D 71 (2006) 063534 12. Seljak U., Makarov A.; McDonald P., Trac H., PhRvL 97 (2006) 1303 13. McDonald P., et al., ApJS 163 (2006) 80 14. Viel M., Haehnelt M.G., Springel V., MNRAS 354 (2004) 684
Neutrinos and the Lyman-α forest: myth or reality? Matteo Vielab
∗
a
INAF Osservatorio Astronomico di Trieste, via Tiepolo 11, I-34131, Trieste (Italy)
b
Institute of Astronomy, Madingley Road, CB30HA, Cambdridge (UK) I will review constraints on sterile and active neutrino masses that can be obtained using the Lyman-α forest.
1. Framework The Lyman-α forest, the ubiquitous absorptions produced by neutral hydrogen along the lines-of-sight to distant quasars, is a powerful cosmological tool. It allows to measure the underlying matter power spectrum (amplitude, slope, curvature) and its evolution at scales (few up to 80 comoving Mpc) and redshifts (z = 2 − 4) that are not probed by any other observables. In recent years, after the seminal works of [1], two groups have measured the dark matter power spectrum with different techniques and data sets. On one side we have the unprecedented capability of the SDSS quasar spectra [2] and on the other the high resolution spectra obtained with the VLT [3]. These two groups have also relied on two different theoretical analysis: approximated hydro-dynamical simulations based on the Hydro-Particle Mesh approximation and full hydro-dynamical simulations performed with the GADGET-II code (on a smaller portion of the parameter space) for the SDSS and the highresolution spectra, respectively (see [4] for a more extensive discussion). Despite the very different frameworks the results are in reasonable agreement between each other and in slight “tension” with the latest WMAP3 data release. More precisely, while the high resolution spectra are not constraining any more for the cosmological parameters when combined to WMAP3, the SDSS ones, since they have smaller error bars, are com∗ Computations were done at the COSMOS supercomputer center, funded by PPARC, HEFCE and Silicon Graphics/Cray Research.
0920-5632/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nuclphysbps.2007.02.058
patible only at the ∼ 2σ level [5]. Here, I will concentrate more on the perspective of using both these data sets to constrain the properties of active and (putative) sterile neutrino particles, than on the cosmological parameters that can be recovered [6,7]. 2. Results on active neutrinos Massive (active) neutrinos act as hot dark matter and smooth the matter power spectrum below their free streaming length, which, at the redshifts of interest here is well approximated by kF S ∼ 0.4 (1 + z)−0.5 (m/1eV) h/Mpc, with m the total mass in neutrinos. The power spectrum feature introduced by neutrinos depend on their masses and number but can be considered as an overall reduction in the amplitude for scales below the number above. For a 1eV total mass the feature is in the portion of power spectrum probed by the Lyman-α forest, while for smaller masses it shifts to larger scales that are probed by galaxy redshift surveys. Both these two observables are thereby important in getting constraints on the neutrino masses and numbers in addition to the (much poorer) constraints that can be achieved from the CMB. In Figure 1 I show the 1 and 2σ contours obtained from WMAP year one, the 2dFGRS and the high resolution Lyman-α data (the LUQAS sample). At the 2 − σ level we have Σmν < 0.9 eV [8]. These limits have been updated recently by [5] in which a combined analysis of WMAP year three, the SDSS galaxy power spectrum, bias, baryonic acoustic oscillations, supernovae and the SDSS Lyman-α power has been
M. Viel / Nuclear Physics B (Proc. Suppl.) 168 (2007) 54–56
Figure 1. Lyman-α forest data combined with the 2dF galaxy power spectrum and with the WMAP one year data.
performed. The impressive upper limit is now Σmν < 0.17 (95% C.L.) and the number of effective neutrinos is Nef f = 5.3 (with the canonical Nef f = 3 allowed only at 2.4 − σ). In this analysis, allowing a fourth thermalized sterile neutrino gives ms < 0.26 eV at 95% C.L. (still at odds with the LSND results), and much lighter than the sterile neutrino candidate of the next section. 3. Results on sterile neutrinos A sterile neutrino with a mass in the keV range is a promising dark matter candidate [9]. Depending on its mass it will act as warm dark matter smoothing out the perturbation below a scale which is roughly given by ks ∼ 5 (ms /4.43)3/4(Tν /Ts ) Mpc−1 , with Ts the temperature at which the sterile neutrinos decouple and Tν the neutrino temperature [11]. The more massive the sterile neutrino the less smoothed will be the matter power spectrum relative to the ΛCDM (cold dark matter with a cosmological constant) case. The Lyman-α forest at high redshift is particularly suitable for giving tight constraints on warm dark matter candidates: at high redshifts the intergalactic structures are more lin-
55
ear and should better resemble the underlying matter power spectrum. In a recent analysis it has been found a 2 − σ lower limit on the sterile neutrino mass of 13 keV, by analysing the SDSS Lyman-α forest [12]. In an independent analysis of the same data performed with full hydrodynamical simulations [10] found ms > 9 − 10 keV (both these last two limits are 95% C.L.). In Figure 2 I show the constraining power of the SDSS data set in the σ8 − 1/ms plane: the contour significantly shrink when including the high redshift bins. Note that for this analysis only the Lyman-α data have been used (since all the other data sets are very little constraining). These limits have the strong advantage of being independent of the mixing angle with active neutrinos and are in strong contradiction with upper limits obtained with X-ray observations. These latter results are based on observations of astronomical objects such as cluster of galaxies, dwarf galaxies or Andromeda to find the distinctive feature of a radiative decay line (the line flux is related both to the sterile neutrino mass and the mixing angle) and give ms < 3 − 6 keV in the standard production scenario that assumes conservation of the leptonic number. The main result is that dark matter particles cannot be sterile neutrinos, unless they are produced by a nonstandard mechanism (resonant oscillations, coupling with the inflaton) or get diluted by a large entropy release. The corresponding lower limit for thermal relic is 2 keV [10]. 4. Systematics Could the Lyman-α data or their interpretation be wrong? The Lyman-α flux is measured to an unprecedented statistical precision and (known) major sources of systematics in the data could be the metal lines or the continuum fluctuations of the distant QSO. All these two effects have been modelled and extensively considered [2,3]. The main uncertainty is probably related to the simulations involved when interpreting the observed flux. Resolution effects and all the physics that give rise to Lyman-α absorptions have been accurately investigated but not yet at the percent or sub-percent level. Note that the exquisite tight
56
M. Viel / Nuclear Physics B (Proc. Suppl.) 168 (2007) 54–56
Sterile neutrinos Both the SDSS data sets and the reanalysis of the SDSS data set performed in [4] agree in setting the following lower limit on the sterile neutrino ms > 9 − 10 keV. A limit that is independent of the mixing angle with the active neutrinos and in strong disagreement with other observational probes (X-ray fluxes from clusters, clusters’ periphery, Milky Way, Large Magellanic Cloud etc.). Thus, the sterile neutrino model is probably ruled out in the standard production scenario which assumes a conservation of the lepton number. We stress that these Lyman-α forest limits are particularly robust: there is power at high redshift and at scales that would be strongly suppressed with a warm dark matter particle less massive than above values. Figure 2. Constraints obtained from the SDSS data set analysed independently with full hydrodynamical simulations. The constraining power of the highest redshift bins is particularly evident: the contours represent the 1, 2−σ confidence level in the σ8 − keV/msterile plane for all the bins with z < 3.2 (dark blue), z < 3.6 (cyan) and z < 4.2 (green).
limit on active neutrinos will be much more sensitive to these effects than the sterile neutrino limits. More work is needed in order to explore the parameter space with full hydro-dynamical simulations and not with approximated technique which, although calibrated on full hydro physics, might be prone to poor understood systematic effects [13,14]. 5. Summary The Lyman-α forest is a fundamental tool to constrain the properties of neutrinos. Active neutrinos The incredibly strong limit Σmν < 0.17 eV obtained recently by [5] might be true or might be a product of a still unknown systematic effect that bias the estimate of the SDSS Lyman-α power at these scales. This has to be checked by using hydro-dynamical simulations that treat self-consistently the neutrino component. For the time being, a more conservative Σmν < 0.9 eV is probably more reliable.
REFERENCES 1. Croft et al., ApJ 581 (2002) 20 2. McDonald P., et al., ApJ, 635 (2005) 761 3. Kim T.-S., Viel M., Haehnelt M.G., Cristiani S., Carswell R.F., MNRAS 347(2004) 355 4. Viel M., Haehnelt M.G., MNRAS 365 (2006) 231 5. Seljak U., Slosar A., McDonald P., JCAP 0610 (2006) 014 6. Viel M., Haehnelt M.G., Lewis A., MNRAS 370 (2006) 51L 7. Viel M., Haehnelt M.G., Weller J., MNRAS 355 (2004) 23L 8. Viel M., Probing Galaxies through Quasar Absorption Lines, IAU Colloquium Proceedings of the International Astronomical Union 199, (2005) arXiv: astro-ph/0504645 9. Abazajian K., Koushiappas S.M., Phys.Rev. D74 (2006) 023527 10. Viel M., Lesgourgues J., Haehnelt M.G., Matarrese S., Riotto A., PhRvL 97 (2006) 071301 11. Viel M., Lesgourgues J., Haehnelt M.G., Matarrese S., Riotto A., Phys Rev D 71 (2006) 063534 12. Seljak U., Makarov A.; McDonald P., Trac H., PhRvL 97 (2006) 1303 13. McDonald P., et al., ApJS 163 (2006) 80 14. Viel M., Haehnelt M.G., Springel V., MNRAS 354 (2004) 684