21cm Cosmology Tomo Takahashi (Saga University) YITP , Kyoto University September 14, 2015
Plan of this talk What is 21 cm? Basics of 21cm cosmology 21cm global signal Power spectrum Some examples: Dark matter, primordial fluctuations,…
ページ ページ What is 21cm? [http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/h21.html] ν 0 = 1420 . 4057517 MHz λ 0 = 21 . 106114 cm ν 0 Frequency observed: ν = 1 + z
21cm comes from neutral hydrogen neutral hydrogen (HI) gas (Intergalactic medium: IGM) backlight observer absorption emission
21cm comes from neutral hydrogen neutral hydrogen (HI) gas (Intergalactic medium: IGM) observer absorption emission CMB photon as backlight z=0 z~1000 today
21cm comes from neutral hydrogen neutral hydrogen (HI) gas (Intergalactic medium: IGM) observer absorption emission CMB photon as backlight galaxies, ..... dark age z~6 z~30 z=0 z~1000 today reionization First star completed
21cm cosmology … 21cm line can probe dark ages (which cannot be probed with other observations.) 21cm can probe 3D directions (can do tomography). SKA will operate in 2020s and is expected to give us a lot of information. (e.g., 21cm can probe fNL better than CMB, …) [For review, see Furlanetto, Oh, Briggs astro-ph/0608032; Pritchard, Loeb 1109.6012 ]
Intensity of absorption/emission (Frequency at the source) (Observed frequency) ν 0 = 1420 MHz at z = z ∗ absorption I ν (0) emission CMB photon as backlight ds z=0 z~1000 today
Radiative transfer equation (describes the evolution of the intensity) s (L ine of sight distance) I ν (0) ds dI ν Radiative transfer equation: ds = − α ν I ν + j ν Emission coefficient Absorption coefficient Rewriting this equation with the optical depth Source function optical depth: d τ ν = α ν ds
Radiative transfer equation When Emission = Absorption When is constant over the line of sight, assuming Compared to w/ backlight: :Absorption :Emission
Brightness temperature Intensity is often represented by an “effective” temperature called “brightness temperature” Definition: Black body distribution In Rayleigh-Jeans (low frequency) region,
Brightness temperature With Tb, the radiative transfer equation can be written as: Temperature of the medium (from ) Emission Absorption No signal The evolution of T is very important.
Spin temperature Number densities of the states (intergalactic medium: IGM) can be described by Boltzmann distribution. 1 1 S 1 / 2 3 = 1 0 S 1 / 2 n 1 ≡ g 1 e − E 10 /k B T s = 3 e − T ∗ /T s n 0 g 0 =1 Spin temperature ( T ∗ = E 10 /k B = 68 mK)
A little wrap up… Intensity is often represented by an “effective” temperature called “brightness temperature” (brightness temperature ~ intensity) The temperature of IGM (gas of neutral hydrogen) is called “the spin temperature.” 21cm signal (absorption, emission) depends on the spin temperature (relative to the CMB).
Optical depth dI ν Definition: d τ ν = α ν ds ds = − α ν I ν + j ν Absorption coefficient To evaluate the intensity (brightness temperature), we need to know the explicit forms of absorption and emission coefficients. The absorption and emission coefficients are determined by microscopic processes.
ページ Einstein coefficients Description of the 2 level system Spontaneous emission (Einstein A coefficient) (energy ) 1 Probability: 0 Absorption (Einstein B coefficient) 1 Probability: 0 (Radiation intensity) Induced emission 1 Probability: 0
Microscopic description of radiative transfer equation Absorption emission Line profile function (Unit: /time/area/sr) (induced emission included here since it depends on ) The absorption coefficient is determined as
Optical depth After some calculations… [Einstein’s relation] [Number density ratio] [Line profile]
Differential brightness temperature (observed quantity) = T s − T γ ( z ) (1 − e − τ ν ) � T s � T γ ( z ) τ ν 1 + z 1 + z : emission T s > T γ T s < T γ : absorption Δ T b depends on baryon density, neutral fraction and the spin temperature
What determines the spin temperature? Absorption (and spontaneous emission) of CMB photon + B 10 I + A 10 + B 01 Collisions ( HH, He and Hp ) (C 01 (excitation rate by collision) (de-excitation rate by collision) (C 10 � � C 01 = g 1 1 − T � T K : Gas temperature e − T � /T K ≈ 3 . C 10 g 0 T K Scattering of Ly α photons (After first astrophysical sources are switched on.) (excitation rate by Ly α photon) P 01 � � : Color temperature P 01 1 − T � T c (de-excitation rate by Ly α photon) ≡ 3 + P 10 P 10 T c
Three processes determine the spin temperature n 1 (C 10 + P 10 + A 10 + B 10 I CMB ) = n 0 (C 01 + P 01 + B 01 I CMB ) , + x c T − 1 T − 1 + x � T − 1 � c K T − 1 , = S 1 + x c + x � Scattering of Ly α photons Collision x α ≡ P 10 T ∗ x c ≡ C 10 T ∗ Coupling coefficients: A 10 T γ A 10 T γ (In most cases of interest, Tk = T α )
Evolution of Δ T b (assuming no astrophysical sources) B C A (a) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A A (a) After recombination, there remains residual free electrons to keep T γ and T K via Compton scattering. Collisional couplings are strong: T K = T s (no 21cm signal) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A (a) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A B (a) Coupling between CMB photon and the gas becomes ineffective (collisional couplings are effective). T K CMB cools down adiabatically: (absorption signal) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A (a) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A C (a) As the gas density decreases, the collisional coupling between T s and T K becomes ineffective. Relatively, coupling between T s and T α becomes bigger to give Ts = T γ . (no 21cm signal) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (assuming no astrophysical sources) B C A (a) (b) [Furlanetto, Oh, Briggs astro-ph/0608032 ]
Evolution of Δ T b (after first astrophysical sources switched on) E D [From Pritchard, Loeb 0802.2102]
Evolution of Δ T b (after first astrophysical sources switched on) E D D After astrophysical sources are switched on, T s ~ T K. Heating is not enough to reach T K > T γ (absorption signal) [From Pritchard, Loeb 0802.2102]
Evolution of Δ T b (after first astrophysical sources switched on) E D [From Pritchard, Loeb 0802.2102]
Evolution of Δ T b (after first astrophysical sources switched on) E D E Heating becomes significant, the gas temperature exceed T γ . Spin temperature follow T K. (emission signal) [From Pritchard, Loeb 0802.2102]
Evolution of Δ T b (after first astrophysical sources switched on) E D [From Pritchard, Loeb 0802.2102]
Dark Matter annihilation effect on 21cm signal [Valdes et al 2013] Dark matter annihilation deposits energy into IGM. ⟨ σ v ⟩ (cm 3 s − 1 ) ϵ 0 (eV s − 1 ) DM model Mass (GeV) Line style δτ e W + W − ⟨ σ v ⟩ th = 3.0 × 10 − 26 5.35 × 10 − 25 1.53 × 10 − 3 200 Blue solid W + W − ⟨ σ v ⟩ max = 1.2 × 10 − 24 2.14 × 10 − 23 6.09 × 10 − 2 200 Blue dashed b ¯ ⟨ σ v ⟩ th = 3.0 × 10 − 26 1.07 × 10 − 23 1.80 × 10 − 2 b 10 Red solid b ¯ ⟨ σ v ⟩ max = 1.0 × 10 − 25 3.57 × 10 − 23 5.76 × 10 − 2 b 10 Red dashed µ + µ − ⟨ σ v ⟩ th = 3.0 × 10 − 26 1.07 × 10 − 25 1.42 × 10 − 4 1000 Green solid µ + µ − ⟨ σ v ⟩ max = 1.4 × 10 − 23 4.99 × 10 − 23 6.18 × 10 − 2 1000 Green dashed
Effects of warm DM [Sitwell et al 2014] Non-negligible velocity by WDM suppresses the formation of low- mass halos. WDM (mX=3keV) The star formation is delayed. f*/f*(fid) =0.1 (CDM) CDM The change in the early sources affects the 21 cm signal. (f*: fraction of baryon incorporated into star)
Fluctuations of 21 cm
Fluctuations in Δ T b (Differential) brightness temperature can also fluctuate in space: These parts can fluctuate Define fluctuation in Δ T b:
Power spectrum cosmology 21cm fluctuations cosmology baryon Ly α hydrogen gas velocity density neutral coupling temperature gradient fraction (Ts) (Ts) (ionization fraction) Power spectrum 21cm power spectrum can probe in 3D. [For review, see Furlanetto, Oh, Briggs astro-ph/0608032; Pritchard, Loeb 1109.6012 ]
Power spectrum Power spectrum as a function of multipole for a fixed z � � [Loeb, Zaldarriaga 2004]
Power spectrum Power spectrum as a function of z for a fixed k [Mesinger et al 2014]
Power spectrum [Kleban et al., 2007] 21cm can probe smaller scales than CMB.
Power spectrum: current data (2 σ upper bound) GMRT at z=8.6 MWA at z=9.5 PAPER-32 at z=7.7 PAPER-64 at z=8.4 theoretical prediction (xi=0.5) [Parsons et al 1502.06016]
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