March 26, Large Scale Simulations: properties of the 21cm signal Garrelt Mellema Stockholm Observatory Collaborators: Martina Friedrich, Ilian Iliev, Paul Shapiro, Ue-Li Pen, Yi Mao & the LOFAR EoR Key Project team.

March 26, Contents The 21cm signal The 21cm signal Simulation methodology Simulation methodology Image cubes Image cubes Statistical properties: global signal, power spectra, redshift space distortions, skewness. Statistical properties: global signal, power spectra, redshift space distortions, skewness. Helium photo-ionization Helium photo-ionization Conclusions Conclusions

March 26, The Redshifted 21cm Signal The measured signal is the differential brightness temperature The measured signal is the differential brightness temperature Depends on: Depends on: –x HI : neutral fraction –δ: overdensity –T s : spin temperature The image cube: images stacked in frequency space θyθy z θxθx time For T s »T CMB, the dependence on T s drops out. For T s »T CMB, the dependence on T s drops out. The signal is line emission: carries spatial, temporal, and velocity information. The signal is line emission: carries spatial, temporal, and velocity information.

March 26, Simulation Methodology To better learn the properties of the 21cm signal we are studying it with detailed large scale cosmological simulations. To better learn the properties of the 21cm signal we are studying it with detailed large scale cosmological simulations. Three steps: Three steps: –Evolution of IGM density (δ) & (proto-)galaxies from a cosmological simulation. –Assign EUV luminosity to (proto-)galaxies. –Transfer EUV radiation through the IGM (x HI ). For large scale simulations galaxy formation is unresolved and baryons and dark matter have the same distribution: For large scale simulations galaxy formation is unresolved and baryons and dark matter have the same distribution: –Cosmological N-body simulation (for DM). –Transfer of EUV radiation can be done in postprocessing mode. See talk by Ilian Iliev this afternoon. See talk by Ilian Iliev this afternoon.

March 26, 21cm LOS Reionization History From the calculated evolution of the ionized densities we can construct reionization histories along the line of sight. From the calculated evolution of the ionized densities we can construct reionization histories along the line of sight. Frequency/redshift direction contains evolutionary, geometrical and velocity information. Frequency/redshift direction contains evolutionary, geometrical and velocity information. redshift Simulation: Box size: 114/h=163 Mpc Box size: 114/h=163 Mpc M halo > 10 8 M  M halo > 10 8 M  Radiative feedback on halos 10 8 < M halo < 10 9 M  (‘self-regulation’) Radiative feedback on halos 10 8 < M halo < 10 9 M  (‘self-regulation’) ’Slice of Sight’

March 26, The sensitivity of the upcoming EoR experiments will be too low to image 21cm from reionization pixel by pixel: Statistical measurements needed. The sensitivity of the upcoming EoR experiments will be too low to image 21cm from reionization pixel by pixel: Statistical measurements needed. –First goal: to reliably detect signatures from reionization (and separate them from foreground and instrumental effects). –Second goal: to interpret them in terms of astrophysics (source population and properties). Luckily, the 21cm line signal is rich in properties: Luckily, the 21cm line signal is rich in properties: –Global signals: rms fluctuations. –Angular properties: power spectra –Frequency properties: Kaiser effect –Non-Gaussianity: skewness Statistical Measurements

March 26, Global Signals An interferometer measures the change of the 21cm (rms) fluctuations. An interferometer measures the change of the 21cm (rms) fluctuations. Peak of these falls around 60-70% ionized (depends on spatial/frequency resolution). Peak of these falls around 60-70% ionized (depends on spatial/frequency resolution). Simulations shown: Simulations shown: –114/h Mpc –114/h Mpc & clumping –37/h Mpc –37/h Mpc & clumping No fluctuations Fluctuations

March 26, Power Spectra Information about the length scales can be obtained from the power spectra. Information about the length scales can be obtained from the power spectra. Simulations show clear trends of shifting power to larger scales as reionization progresses, and a flattening of the power spectra. Simulations show clear trends of shifting power to larger scales as reionization progresses, and a flattening of the power spectra. Note that the angular power spectrum is measured directly by an interferometer, the multipole l is equivalent to √(u 2 +v 2 ) in a visibility map. Note that the angular power spectrum is measured directly by an interferometer, the multipole l is equivalent to √(u 2 +v 2 ) in a visibility map. 114/h Mpc volume Angular Power Spectra

March 26, Redshift Space Distortions Due to the peculiar velocity field, the signal can be displaced from its cosmological redshift. Due to the peculiar velocity field, the signal can be displaced from its cosmological redshift. `Kaiser effect´ or `velocity compression´: due to infall, signal concentrates at the high density peaks. `Kaiser effect´ or `velocity compression´: due to infall, signal concentrates at the high density peaks. It is clearly seen in the simulation results and gives ~30% increase in fluctuations (and up to a factor of 2). It is clearly seen in the simulation results and gives ~30% increase in fluctuations (and up to a factor of 2).

March 26, RSD Effects on the Image Cube Adding the redshift space distortions visibly increases the fluctuations in the neutral medium. Adding the redshift space distortions visibly increases the fluctuations in the neutral medium. The effect remains noticeable even at LOFAR-like resolution (3’, 440 kHz). The effect remains noticeable even at LOFAR-like resolution (3’, 440 kHz). Simulation shown: 114/h Mpc volume. Simulation shown: 114/h Mpc volume. No velocity With velocity

March 26, RSD Effects on the Image Cube Adding the redshift space distortions visibly increases the fluctuations in the neutral medium. Adding the redshift space distortions visibly increases the fluctuations in the neutral medium. The effect remains noticeable even at LOFAR-like resolution (3’, 440 kHz). The effect remains noticeable even at LOFAR-like resolution (3’, 440 kHz). Simulation shown: 114/h Mpc volume. Simulation shown: 114/h Mpc volume. No velocity With velocity

March 26, Power spectrum Since the velocity gradients responsible for the distortions are related to the density field, one can write the total (3D) power P(k) in terms of a polynomial in μ=cos(θ k ), the angle between the LOS and the k vectors (see e.g., Barkana & Loeb 2005). Since the velocity gradients responsible for the distortions are related to the density field, one can write the total (3D) power P(k) in terms of a polynomial in μ=cos(θ k ), the angle between the LOS and the k vectors (see e.g., Barkana & Loeb 2005). P(k)= (P δδ - 2P xδ + P xx ) +2(P δδ - P xδ )μ 2 + P δδ μ 4 P(k)= (P δδ - 2P xδ + P xx ) +2(P δδ - P xδ )μ 2 + P δδ μ 4 Since P δδ goes with μ 4, it should be possible to separate it from the dependence on the ionized fraction x, and thus directly find the density power spectrum. Since P δδ goes with μ 4, it should be possible to separate it from the dependence on the ionized fraction x, and thus directly find the density power spectrum.

March 26, And in Fourier Space... 3D Fourier transform of (part) of the image cube shows the effect of redshift distortions. 3D Fourier transform of (part) of the image cube shows the effect of redshift distortions. Without distortions the contours are spherical in the spatial-spatial plane and in the frequency- spatial plane. Without distortions the contours are spherical in the spatial-spatial plane and in the frequency- spatial plane. With distortions the power in the spatial-spatial plane is still isotropic, but the frequency-spatial plane shows elliptical contours. With distortions the power in the spatial-spatial plane is still isotropic, but the frequency-spatial plane shows elliptical contours. k x,k y, no distortions k x,k y, with distortions k x,k z, no distortions k x,k z, with distortions k (h/Mpc)‏ k z (Hz -1 )‏ Spatial-spatial plane Frequency-spatial plane

March 26, Reionization and Redshift Space Distortions Since reionization affects the high density regions first, the redshift space distortions become much less noticeable as reionization progresses. Since reionization affects the high density regions first, the redshift space distortions become much less noticeable as reionization progresses. This can be seen in the angular power spectra, as well as in the image cube power spectra. This can be seen in the angular power spectra, as well as in the image cube power spectra. k (h/Mpc)‏ k z (Hz -1 )‏ =0.2 =0.7 Angular Power Spectra Solid lines: without redshift distortions Dashed lines: with redshift distortions

March 26, Skewness The probability distribution function for 21cm is non- Gaussian. The signal shows a clear evolution of skewness with increasing ionization. The probability distribution function for 21cm is non- Gaussian. The signal shows a clear evolution of skewness with increasing ionization. Finite resolution modifies skewness, but does not remove it. Finite resolution modifies skewness, but does not remove it. Skewness may offer an alternative way to detect the signal, if remnants of foreground subtractions and other effects are dominantly Gaussian (Harker et al. 2009). Skewness may offer an alternative way to detect the signal, if remnants of foreground subtractions and other effects are dominantly Gaussian (Harker et al. 2009). Mean signal Skewness Mean signal and its skewness for three different reionization simulations, Harker et al. (2009)

March 26, Helium Photo-Ionization We are working on adding helium to our code C2-Ray (Martina Friedrich). We are working on adding helium to our code C2-Ray (Martina Friedrich). Comparing results to Cloudy and other codes (SPHRAY, Gabriel Altay; CRASH) on Test Problem 1 of the Cosmological Comparison Project. Comparing results to Cloudy and other codes (SPHRAY, Gabriel Altay; CRASH) on Test Problem 1 of the Cosmological Comparison Project.

March 26, Time = 500 Myrs

March 26, Time = 4 Gyrs

March 26, Fractions For a mix of H and He, the photons need to be distributed over the species. For a mix of H and He, the photons need to be distributed over the species. There are several recipes given in the literature for which fraction of photons gets absorbed by species 1 given a mix of species 1 and 2 (and by analogy for more than 2 species): There are several recipes given in the literature for which fraction of photons gets absorbed by species 1 given a mix of species 1 and 2 (and by analogy for more than 2 species): 1. Lidz (Altay?): 1. Lidz (Altay?): 2. CRASH: 2. CRASH: 3. Bolton: 3. Bolton:

March 26, Fractions Which one is correct? Which one is correct? For τ 1,τ 2 → 0, all recipes are equivalent. For τ 1,τ 2 → 0, all recipes are equivalent. Consider τ 1,τ 2 → ∞ and τ 2 /τ 1 = 2 : Consider τ 1,τ 2 → ∞ and τ 2 /τ 1 = 2 : –Recipe 1: f 1 =0.333 –Recipe 2: f 1 =0.5 (for all τ 2 /τ 1 )‏ –Recipe 3: f 1 =0.0 (for all τ 2 /τ 1 )‏ This suggests that recipe 1 is the correct one. This suggests that recipe 1 is the correct one. Monte Carlo experiments also show that recipe 1 is the correct one. Monte Carlo experiments also show that recipe 1 is the correct one. Note: for the test problem results the actual choice does not make a large difference. Note: for the test problem results the actual choice does not make a large difference.

March 26, Conclusions The 21cm signal has a rich set of properties which should help in recognizing it in the data of upcoming EoR experiments. The 21cm signal has a rich set of properties which should help in recognizing it in the data of upcoming EoR experiments. The later stages of the EoR are characterized by an increase followed by a decline of the rms fluctuations, and the reverse behaviour for the skewness. The later stages of the EoR are characterized by an increase followed by a decline of the rms fluctuations, and the reverse behaviour for the skewness. The angular power spectra show a characteristic evolution to flatter structures. The angular power spectra show a characteristic evolution to flatter structures. Redshift space distortions important, but less easily measured once reionization gets going. Redshift space distortions important, but less easily measured once reionization gets going. He-photoionization: In a mix of absorbing species, photons should be distributed according to the ratios of their optical depths. He-photoionization: In a mix of absorbing species, photons should be distributed according to the ratios of their optical depths.

March 26, Reionization with Multifrequency Datasets, Stockholm, August 17-21, 2009 Meeting on combining information of different datasets for studying reionization: 21cm, Ly-a, QSOs, CMB, backgrounds. Invited speakers: Ger de Bruijn, Gil Holder, Ilian Iliev, Nobunari Kashikawa, Antony Lewis, Adam Lidz, Miguel Morales, Jochen Weller Organizers: Garrelt Mellema, Göran Östlin, Saleem Zaroubi, Axel Brandenburg Venue: AlbaNova Centre, Stockholm, Sweden