Neutrinos in Large-scale structure

Transcription

1 Neutrinos in Large-scale structure Marilena LoVerde University of Chicago ( Fall 2015 > Yang Institute for Theoretical Physics, Stony Brook University)

2 Neutrinos in Large-scale structure Marilena LoVerde University of Chicago ( Fall 2015 > Yang Institute for Theoretical Physics, Stony Brook University) ML and Zaldarriaga ML ML 1404:4858 ML in prep.

3 Outline Neutrinos in Cosmology Scale-dependent structure growth from massive neutrinos Scale-dependent halo bias from massive neutrinos Observational Consequences

4 Neutrinos

5 flavor eigenstates ν electron ν tau ν muon Neutrinos! ν 1 ν 3 ν 2 mass eigenstates Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962

6 flavor eigenstates ν electron ν tau ν muon Neutrinos! ν 1 ν 3 ν 2 mass eigenstates oscillation data gives mass splittings m m 1 2 = (7.5 ± 0.2) 10-5 ev 2 m m 22 = ( ) 10-3 ev 2 (solar neutrino oscillations) (atmospheric neutrino oscillations) Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962

7 flavor eigenstates ν electron ν tau ν muon Neutrinos! ν 1 ν 3 ν 2 mass eigenstates but the absolute masses are unknown! ``Normal ``Inverted ``Degenerate mass ν eV ν eV ν 1 0eV ν eV ν eV ν 3 0eV? ν 1 ν 2 ν 3 Pontecorvo 1957, 1958, 1967; Maki, Nakagawa, Sakata 1962

8 Neutrinos in Cosmology

9 Neutrinos in cosmology neutrinos in equilibrium with photons e +, e- Tγ = Tν 1/a neutrinos decoupled Tν 1/a Tν 1/a

10 Neutrinos in cosmology neutrinos in equilibrium with photons e +, e- Tγ = Tν 1/a neutrinos decoupled Tν 1/a Tν 1/a relativistic, in thermal equilibrium at early times n 1 ν ~ Tν 3 Tγ /3 Tν

11 Neutrinos in cosmology neutrinos in equilibrium with photons e +, e- Tγ = Tν 1/a neutrinos decoupled Tν 1/a Tν 1/a relativistic, in thermal equilibrium at early times n 1 ν ~ Tν 3 Tγ /3 Tν energy density dominated by mass at late times ρν ~ mνi n 1 ν i

12 Neutrinos in cosmology neutrinos in equilibrium with photons e +, e- Tγ = Tν 1/a neutrinos decoupled Tν 1/a Tν 1/a relativistic, in thermal equilibrium at early times n 1 ν ~ Tν 3 Tγ /3 Tν energy density dominated by mass at late times ρν ~ mνi n 1 ν i n 1 ν is known, so a measurement of ρν gives mν

13 Neutrinos in Large-scale structure time (Kravtsov)

14 Massive neutrinos and linear structure growth The gravitational evolution of large-scale structure is different for fast and slow moving particles

15 Massive neutrinos and linear structure growth The gravitational evolution of large-scale structure is different for fast and slow moving particles (clump easily) (don t clump easily)

16 Massive neutrinos and linear structure growth The gravitational evolution of large-scale structure is different for fast and slow moving particles (clump easily) baryons and cold dark matter (don t clump easily) neutrinos (or other exotic light dark matter)

17 Massive neutrinos and linear structure growth small-scale density perturbations don t retain neutrinos cold dark matter and baryons density perturbation growing neutrino density perturbation decaying time δρ c ρ c δρν ρν

18 Massive neutrinos and linear structure growth small-scale density perturbations don t retain neutrinos large-scale density perturbations do retain neutrinos cold dark matter, baryons and neutrinos growing together time δρν ρν δρ c ρ c

19 Massive neutrinos and linear structure growth small-scale density perturbations don t retain neutrinos Growth of matter large-scale density perturbations do retain neutrinos perturbations is scaledependent time

20 Massive neutrinos and linear structure growth small-scale density perturbations don t retain neutrinos Growth of matter large-scale density perturbations do retain neutrinos perturbations is scaledependent time Relevant scale:! Typical distance a neutrino can travel in a Hubble time fs ~ uν/h

21 Massive neutrinos and linear structure growth small-scale density perturbations don t retain neutrinos Growth of matter large-scale density perturbations do retain neutrinos perturbations is scaledependent time Relevant scale:! Typical distance a neutrino can travel in a Hubble time fs ~ uν/h free-streaming scale

22 Scale-dependent growth change in typical amplitude of δ m (k) from mν= 0 Pmm(k)/Pmm(k) large compared to free streaming larger scales wave number k (1/Mpc) Probability cosmological constraints! Planck Data Ade et al 2013 Bond, Efstathiou, Silk 1980 Hu, Eisenstein, Tegmark i mνi (ev)

23 The scale-dependent growth of density perturbations causes halo bias to be scale dependent

24 Scale-dependent bias: halos are biased tracers of the matter density field

25 Scale-dependent bias: halos are biased tracers of the matter density field the number density of halos is modulated by long-wavelength fluctuations in the matter density field

26 Scale-dependent bias: halos are biased tracers of the matter density field the number density of halos is modulated by long-wavelength fluctuations in the matter density field δn n b δρ ρ b is the halo bias long-wavelength

27 Scale-dependent bias: In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength increasing time δρ ρ _ (k, z final ) D(z final ) δρ _ ρ (k, z initial )

28 Scale-dependent bias: In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength increasing time δρ ρ _ (k, z final ) D(z final ) δρ _ ρ (k, z initial ) halos can t tell the wavelength of the background matter density perturbation

29 Scale-dependent bias: In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength increasing time halos can t tell the wavelength of the background matter density perturbation the effect of δρ ρ _ on the halo field (the linear bias) is independent of k

30 Scale-dependent bias: In a universe with CDM only, the linear evolution of matter fluctuations is independent of their wavelength increasing time halos can t tell the wavelength of the background matter density perturbation δρ ρ _ massive neutrinos break this the effect of on the halo field (the linear bias) is independent of k halo bias can depend on k

31 Scale-dependent bias: increasing time neutrinos cold dark matter

32 Scale-dependent bias: WANT: estimate of k-dependence of the halo bias caused by massive neutrinos increasing time neutrinos cold dark matter

33 Scale-dependent bias: WANT: estimate of k-dependence of the halo bias caused by massive neutrinos increasing time neutrinos cold dark matter ( see also Hui & Parfrey 2008; Parfrey, Hui, Sheth 2011;)

34 Prescription for calculating the halo bias in a universe with massive neutrinos

35 Prescription for calculating the halo bias initial density field initial proto-halo distribution late time halo distribution δn n b δρ ρ long-wavelength (ML 2014) Gunn & Gott 1972 Press & Schechter 1974

36 Prescription for calculating the halo bias initial density field initial proto-halo distribution late time halo distribution δn n b δρ ρ long-wavelength want this! (ML 2014) Gunn & Gott 1972 Press & Schechter 1974

37 Numerical estimates for scaledependent halo bias

38 Numerical results for halo bias scale-dependent change to final bias δn(k)/n = b(k) δ matter (k) (Use Bhattacharya et al 2011 for n(m δ crit ) b(k) = Phh(k)/Pmm(k) fractional change in Eulerian halo bias wavenumber k (Mpc -1 ) (ML 2014)

39 Numerical results for halo bias scale-dependent change to final bias δn(k)/n = b(k) δ matter (k) amplitude of feature in the halo bias (Use Bhattacharya et al 2011 for n(m δ crit ) (ML 2014)

40 Observational consequences of scaledependent bias?

41 Observational consequences of scale dependent bias? (incorrectly) assuming constant bias suppression in galaxy power spectrum less than in matter power spectrum k (wave number ) (ML 2014)

42 But the scale-dependent halo bias is itself an observable! fractional change in Eulerian halo bias

43 The scale-dependent halo bias is an observable! ratio of bias factors for two galaxy populations b2(k)/b1(k) 1 b1/b2 n1 P g2g2 k (wave number) (ML in prep.)

44 The scale-dependent halo bias is an observable! ratio of bias factors for two galaxy populations (multipole moment) b1/b2 1 N n 1 C g2g2 (ML in prep.)

45 Accuracy of these predictions? N-body simulations are the community standard for cold dark matter structure. Simulations with massive neutrinos? (i) Tricky. very few exist, very new (ii) Want a model that provides insight into the physical processes responsible for new effects (iii) Don t want to rerun for every possible neutrino mass hierarchy scenario (iv) It will be great to make comparisons in the future! Viel, Haehnelt, Springel 2010; Marulli, Carbone, Viel, Moscardini, Cimatti 2011; Agarwal & Feldman 2011; Brandbyge, Hannestad, Haugboelle, Wong 2012; Upadhye, Biswas, Pope, Heitmann, Habib 2013: Villaescusa-Navarro, Bird, Pena-Garay, Viel 2013;

46 Scale-dependent 2.0 bias 2.0 from massive bhkl 1.8 bhkl neutrinos1.8 my calculations comparison with sims looks reasonable! Mpc -1 D Mpc -1 D simulations from Castorina et al M > 2â10 13 M ü z = 0.5 three 0.2eV ν M > 2â10 13 M ü z = 0.5 three 0.2eV ν halo bias b(k) three 0.1eV ν bhkl massless ν halo bias b(k) bhkl three 0.1eV ν 2.2 wavenumber k (h/mpc) 2.2 massless ν Mpc -1 D Mpc -1 D wavenumber k (h/mpc) Figure 6. Halo bias as a function of scale determined from the simulation Set A for halos with M > h 1 M. Left panels show the measurements of linear bias b (hh) c (continuous curves) andb (hh) m (dashed curves) from the halo power spectrum P hh (k). Right panels show b (hc) c (continuous curves) andb (hm) m (dashed curves) respectively from the P hc and P hm cross-power spectra. Top left panels correspond to z =0,bottom (ML panels 2014) to z = 0.5. The continuous and dotted horizontal lines show the constant bias values determined from 1

47 Conclusions Cosmology provides interesting information about neutrino physics! Scale-dependent halo bias is a new signal of massive neutrinos in large-scale structure Scale-dependent halo bias is a new systematic for massive neutrinos in large-scale structure