large scale simulations: properties of the 21cm signal

March 26, 2008March 26, 2008 Reionization@RingbergReionization@Ringberg 11

Large Scale Simulations: Large Scale Simulations: properties of the 21cm properties of the 21cm signalsignal

Garrelt MellemaGarrelt Mellema

Stockholm Observatory Stockholm Observatory

Collaborators: Martina Friedrich, Ilian Iliev, Paul Shapiro, Ue-Li Pen, Yi Mao & the LOFAR EoR Key Project team.


ContentsContents

The 21cm signalThe 21cm signal Simulation methodologySimulation methodology Image cubesImage cubes Statistical properties: global signal, power Statistical properties: global signal, power

spectra, redshift space distortions, skewness.spectra, redshift space distortions, skewness. Helium photo-ionizationHelium photo-ionization ConclusionsConclusions


The Redshifted 21cm SignalThe Redshifted 21cm Signal

The measured signal is the The measured signal is the differential brightness differential brightness temperaturetemperature

Depends on: Depends on: – xxHIHI: neutral fraction : neutral fraction

– δ: overdensityδ: overdensity– TTss: spin temperature: spin temperature

The image cube: images stacked in frequency space

θy

z

θx

time

For TFor Tss»»TTCMBCMB, the dependence , the dependence on Ton Ts s drops out.drops out.

The signal is The signal is lineline emission: emission: carries carries spatial, temporal, spatial, temporal, and and velocityvelocity information. information.


Simulation MethodologySimulation Methodology

To better learn the properties of the 21cm signal we are To better learn the properties of the 21cm signal we are studying it with studying it with detailed large scale cosmological detailed large scale cosmological simulationssimulations..

Three steps:Three steps:– Evolution of IGM density (Evolution of IGM density (δ) δ) & (proto-)galaxies from a & (proto-)galaxies from a

cosmological simulationcosmological simulation..– Assign EUV luminosityAssign EUV luminosity to (proto-)galaxies. to (proto-)galaxies.

– Transfer EUV radiationTransfer EUV radiation through the IGM (x through the IGM (xHIHI).).

For large scale simulations galaxy formation is For large scale simulations galaxy formation is unresolved and baryons and dark matter have the same unresolved and baryons and dark matter have the same distribution:distribution:– Cosmological N-body simulation (for DM).Cosmological N-body simulation (for DM).– Transfer of EUV radiation can be done in postprocessing Transfer of EUV radiation can be done in postprocessing

mode.mode. See talk by Ilian Iliev this afternoon.See talk by Ilian Iliev this afternoon.


21cm LOS Reionization 21cm LOS Reionization HistoryHistory

From the From the calculated calculated evolution of the evolution of the ionized densities ionized densities we can construct we can construct reionization reionization historieshistories along the along the line of sightline of sight..

Frequency/redshift Frequency/redshift direction contains direction contains evolutionaryevolutionary, , geometricalgeometrical and and velocityvelocity informationinformation..

redshift

Simulation: Simulation: Box size: 114/h=163 Mpc Box size: 114/h=163 Mpc MMhalohalo > 10 > 108 8 MM

Radiative feedback on halos 10Radiative feedback on halos 1088 < < MMhalohalo < 10 < 1099 M M (‘self-regulation’)(‘self-regulation’)

’Slice of Sight’


The The sensitivitysensitivity of the upcoming EoR experiments will of the upcoming EoR experiments will be be too lowtoo low to to imageimage 21cm from reionization pixel by 21cm from reionization pixel by pixel: Statistical measurements needed.pixel: Statistical measurements needed.– First goalFirst goal: to reliably : to reliably detectdetect signatures from signatures from

reionization (and separate them from foreground and reionization (and separate them from foreground and instrumental effects).instrumental effects).

– Second goalSecond goal: to : to interpretinterpret them in terms of them in terms of astrophysics (source population and properties).astrophysics (source population and properties).

Luckily, the 21cm line signal is rich in Luckily, the 21cm line signal is rich in propertiesproperties::– Global signalsGlobal signals: rms fluctuations.: rms fluctuations.– AngularAngular properties: power spectra properties: power spectra – FrequencyFrequency properties: Kaiser effect properties: Kaiser effect– Non-GaussianityNon-Gaussianity: skewness: skewness

Statistical MeasurementsStatistical Measurements


Global SignalsGlobal Signals

An An interferometerinterferometer measures the change measures the change of the 21cm (rms) of the 21cm (rms) fluctuationsfluctuations. .

Peak of these falls Peak of these falls around 60-70% ionized around 60-70% ionized (depends on (depends on spatial/frequency spatial/frequency resolution).resolution).

Simulations shown: Simulations shown: – 114/h Mpc114/h Mpc – 114/h Mpc & clumping114/h Mpc & clumping– 37/h Mpc37/h Mpc – 37/h Mpc & clumping37/h Mpc & clumping

No fluctuations

Fluctuations


Power SpectraPower Spectra

Information about the Information about the length scaleslength scales can be can be obtained from the power obtained from the power spectra.spectra.

Simulations show clear Simulations show clear trends of shifting power trends of shifting power to larger scales as to larger scales as reionization progresses, reionization progresses, and a and a flatteningflattening of the of the power spectra.power spectra.

Note that the angular power Note that the angular power spectrum is measured spectrum is measured directly by an directly by an interferometer, the interferometer, the multipole l is equivalent to multipole l is equivalent to √(u√(u22+v+v22) in a vi) in a visibility map.sibility map.

114/h Mpc volume114/h Mpc volume

Angular Power Spectra


Redshift Space DistortionsRedshift Space Distortions

Due to the peculiar velocity field, the signal can be Due to the peculiar velocity field, the signal can be displaced from its cosmological redshift. displaced from its cosmological redshift.

`̀Kaiser effectKaiser effect´ or `´ or `velocity compressionvelocity compression´: due to ´: due to infallinfall, , signal concentrates at the high density peaks.signal concentrates at the high density peaks.

It is clearly seen in the simulation results and gives It is clearly seen in the simulation results and gives ~30% ~30% increase in fluctuationsincrease in fluctuations (and up to a factor of (and up to a factor of 2).2).


RSD Effects on the Image RSD Effects on the Image CubeCube

Adding the redshift Adding the redshift space distortions space distortions visibly visibly increases the increases the fluctuationsfluctuations in the in the neutral medium.neutral medium.

The effect remains The effect remains noticeable even at noticeable even at LOFAR-like LOFAR-like resolution (3’, 440 resolution (3’, 440 kHz).kHz).

Simulation shown: Simulation shown: 114/h Mpc volume.114/h Mpc volume.

No velocity

With velocity


Power spectrumPower spectrum

Since the velocity gradients responsible for the Since the velocity gradients responsible for the distortions are related to the density field, one can distortions are related to the density field, one can write the total (3D) power P(write the total (3D) power P(kk) in terms of a polynomial ) in terms of a polynomial in in μ=cos(θμ=cos(θkk)), the angle between the LOS and the , the angle between the LOS and the k k vectors (see e.g., Barkana & Loeb 2005).vectors (see e.g., Barkana & Loeb 2005).

P(P(kk)= (P)= (Pδδδδ - 2P - 2Pxδxδ + P + Pxxxx) +2(P) +2(Pδδδδ - P - Pxδxδ)μ)μ22 + P + Pδδδδμμ44

Since PSince Pδδδδ goes with μ goes with μ44, it should be possible to separate , it should be possible to separate it from the dependence on the ionized fraction x, and it from the dependence on the ionized fraction x, and thus directly find the thus directly find the density power spectrumdensity power spectrum..


And in Fourier Space...And in Fourier Space...

3D Fourier transform3D Fourier transform of of (part) of the (part) of the image cubeimage cube shows the effect of shows the effect of redshift distortions.redshift distortions.

Without distortions the Without distortions the contours are spherical in contours are spherical in the the spatial-spatial planespatial-spatial plane and in the and in the frequency-frequency-spatial plane.spatial plane.

With distortions the With distortions the power in the spatial-power in the spatial-spatial plane is still spatial plane is still isotropic, but the isotropic, but the frequency-spatial plane frequency-spatial plane shows shows elliptical contours.elliptical contours.

kx,ky, no distortions

kx,ky, with distortions

kx,kz, no distortions

kx,kz, with distortions

k (h/Mpc)

k (h/Mpc)

k (

h/M

pc)

k (

h/M

pc)

k (

h/M

pc)

k (

h/M

pc)

kz (Hz-1)

kz (Hz-1)

Spatial-spatial plane Frequency-spatial plane


Reionization and Redshift Reionization and Redshift Space DistortionsSpace Distortions

Since reionization affects the Since reionization affects the high density regions first, high density regions first, the redshift space distortions the redshift space distortions become much become much less less noticeablenoticeable as reionization as reionization progresses.progresses.

This can be seen in the This can be seen in the angular power spectra, as angular power spectra, as well as in the image cube well as in the image cube power spectra.power spectra.

k (

h/M

pc)

k (

h/M

pc)

kz (Hz-1) kz (Hz-1)

<x>=0.2 <x>=0.7

Angular Power Spectra

Solid lines: without redshift distortionsDashed lines: with redshift distortions


SkewnessSkewness

The probability distribution The probability distribution function for 21cm is function for 21cm is non-non-GaussianGaussian. The signal shows a . The signal shows a clear evolution of skewness clear evolution of skewness with increasing ionization.with increasing ionization.

Finite resolution modifies Finite resolution modifies skewness, but does not skewness, but does not remove it.remove it.

Skewness may offer an Skewness may offer an alternative wayalternative way to detect the to detect the signalsignal, if remnants of , if remnants of foreground subtractions and foreground subtractions and other effects are dominantly other effects are dominantly Gaussian (Harker et al. 2009).Gaussian (Harker et al. 2009).

Mean signal

Skewness

Mean signal and its skewness for three different reionization

simulations, Harker et al. (2009)


Helium Photo-IonizationHelium Photo-Ionization

We are working on adding helium to our code C2-Ray We are working on adding helium to our code C2-Ray (Martina Friedrich).(Martina Friedrich).

Comparing results to Cloudy and other codes (SPHRAY, Comparing results to Cloudy and other codes (SPHRAY, Gabriel Altay; CRASH) on Test Problem 1 of the Gabriel Altay; CRASH) on Test Problem 1 of the Cosmological Comparison Project.Cosmological Comparison Project.


Time = 500 MyrsTime = 500 Myrs


Time = 4 GyrsTime = 4 Gyrs


FractionsFractions

For a mix of H and He, the photons need to be For a mix of H and He, the photons need to be distributeddistributed over the species. over the species.

There are several recipes given in the literature for There are several recipes given in the literature for which fraction of photons gets absorbed by species 1 which fraction of photons gets absorbed by species 1 given a mix of species 1 and 2 (and by analogy for given a mix of species 1 and 2 (and by analogy for more than 2 species):more than 2 species):

1. Lidz (Altay?): 1. Lidz (Altay?):

2. CRASH: 2. CRASH:

3. Bolton:3. Bolton:


FractionsFractions

Which one is correct?Which one is correct? For For ττ11,,ττ22 → → 0, all recipes are equivalent.0, all recipes are equivalent. Consider Consider ττ11,,ττ22 → ∞ → ∞ andand ττ22//ττ11= 2 := 2 :

– Recipe 1: fRecipe 1: f11=0.333=0.333– Recipe 2: fRecipe 2: f11=0.5 (for all =0.5 (for all ττ22//ττ11))– Recipe 3: fRecipe 3: f11=0.0 (for all =0.0 (for all ττ22//ττ11))

This suggests that This suggests that recipe 1recipe 1 is the correct one. is the correct one. Monte Carlo experiments also show that recipe 1 is the Monte Carlo experiments also show that recipe 1 is the

correct one.correct one.

Note: for the test problem results the actual choice Note: for the test problem results the actual choice does not make a large difference.does not make a large difference.


ConclusionsConclusions

The The 21cm signal21cm signal has a rich set of properties which has a rich set of properties which should help in recognizing it in the data of upcoming should help in recognizing it in the data of upcoming EoR experiments.EoR experiments.

The later stages of the EoR are characterized by an The later stages of the EoR are characterized by an increase followed by a decline of the increase followed by a decline of the rms fluctuationsrms fluctuations, , and the reverse behaviour for theand the reverse behaviour for the skewness skewness. .

The angular The angular power spectrapower spectra show a characteristic show a characteristic evolution to flatter structures.evolution to flatter structures.

Redshift space distortionsRedshift space distortions important, but less easily important, but less easily measured once reionization gets going.measured once reionization gets going.

He-photoionizationHe-photoionization: In a mix of absorbing species, : In a mix of absorbing species, photons should be distributed according to the ratios of photons should be distributed according to the ratios of their optical depths.their optical depths.


Reionization with Multifrequency Reionization with Multifrequency Datasets, Stockholm, Datasets, Stockholm, August 17-21, 2009August 17-21, 2009

Meeting on combining information of different datasets for Meeting on combining information of different datasets for studying reionization: 21cm, Ly-a, QSOs, CMB, studying reionization: 21cm, Ly-a, QSOs, CMB, backgrounds.backgrounds.

Invited speakersInvited speakers: Ger de Bruijn, Gil Holder, Ilian Iliev, : Ger de Bruijn, Gil Holder, Ilian Iliev, Nobunari Kashikawa, Antony Lewis, Adam Lidz, Miguel Nobunari Kashikawa, Antony Lewis, Adam Lidz, Miguel Morales, Jochen WellerMorales, Jochen Weller

OrganizersOrganizers: Garrelt Mellema, Göran Östlin, Saleem Zaroubi, : Garrelt Mellema, Göran Östlin, Saleem Zaroubi, Axel BrandenburgAxel Brandenburg

VenueVenue: AlbaNova Centre, Stockholm, Sweden: AlbaNova Centre, Stockholm, Sweden

http://agenda.albanova.se/conferenceDisplay.py?http://agenda.albanova.se/conferenceDisplay.py?confId=1186confId=1186

large scale simulations: properties of the 21cm signal

Documents

reionization pixel

line signal

h mpc clumping37h mpc

angular properties

reionization histories

reionization progresses

mpc mhalo

signal conce