21-cm signature of the first sources in the Universe : prospects of detection with SKA

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21-cm signature of the first sources in the Universe : prospects of detection with SKA

Raghunath Ghara

NCRA-TIFR [email protected]

February 12, 2016

Raghunath Ghara (NCRA-TIFR) Detecting early sources February 12, 2016 1 / 23

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Plan of the talk

Efforts to detect and understand the early sources : 21-cm signal, JWST, TMT..

21-cm observation of the reionization :

Evolution of the global 21-cm signal, power spectrum, rms etc.. Detection of ionized bubble,isolated sourcein visibilityand image base techniques.

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Plan of the talk

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Plan of the talk

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Plan of the talk

Evolution of the global 21-cm signal, power spectrum, rms etc..

Detection of ionized bubble,isolated sourcein visibilityand image base techniques.

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Motivation

Can we detect the first sources with radio interferometers like the SKA1-low? What informations can be obtained from that?

IGM properties: Neutral fraction Kinetic temperature Source properties:

Mass of the source Age

Escape fraction of UV photonsfesc

UV and X-ray luminosity etc..

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Motivation

Can we detect the first sources with radio interferometers like the SKA1-low? What informations can be obtained from that?

IGM properties:

Neutral fraction Kinetic temperature Source properties:

Mass of the source Age

Escape fraction of UV photonsfesc

UV and X-ray luminosity etc..

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Possible sources: popIII stars, Galaxies, mini-QSO, HMXBs..

10²² 10²⁴ 10²⁶ 10²⁸

10¹ 10² 10³

Lν (erg/s/Hz)

λ (Å) PopIII

Galaxy Mini−QSO HMXBs

HI Lyα

HeI

HeII100 eV

M_? = 10³ M for popIII

= 10⁷ M for others.

Spectral indexα= 1.5 Ratio of X-ray and UV luminosity fX = 0.05 fesc = 0.1

t_age = 20Myr

The stellar part of the source is generated using PEGASE code : Salpeter IMF with 1-100M population II stars, metallicity 0.001Z. Mini-QSO : I_q ∝E^−α , PopIII : black-body spectrum, HMXBs : absorption of soft-X-rays in ISM (Fragos et al 2013)

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Possible sources: popIII stars, Galaxies, mini-QSO, HMXBs..

10²² 10²⁴ 10²⁶ 10²⁸

10¹ 10² 10³

Lν (erg/s/Hz)

λ (Å) PopIII

HI Lyα

HeI

HeII100 eV

Spectral indexα= 1.5 Ratio of X-ray and UV luminosity fX = 0.05 fesc = 0.1

t_age = 20Myr The stellar part of the source is generated using PEGASE code : Salpeter IMF with 1-100M population II stars, metallicity 0.001Z. Mini-QSO : Iq ∝E^−α , PopIII : black-body spectrum, HMXBs : absorption of soft-X-rays in ISM (Fragos et al 2013)

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Simple Model

Rectangular simulation box.

Length of the box along the frequency direction is determined by the

observational band width.

We assume that the source is at the center of the simulation Box.

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Simple Model

Solve 1-D radiative transfer equations, generate x_HI andT_K profiles.

Assume Lyα photon flux reduces as 1/R² with radial distanceR.

Calculate the coupling coefficients and spin temperature (TS) profile.

1-D δT_b profile used to generate δT_b map in the simulation box.

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Signal

Differential brightness temperature :

δT_b(~θ, ν)∼27×x_HI(x,z) [1+δ_B(x,z)]

1 +z 10

1/2

1− T_γ(z) TS(x,z)

mK, (1)

Neutral fraction of hydrogen

Spin temperature (depend on CMBR, Collisional, Lyα coupling and TK )

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δT

_b

profiles

10²² 10²⁴ 10²⁶ 10²⁸

10¹ 10² 10³

Lν (erg/s/Hz)

λ (Å) PopIII

HI Lyα

HeI

HeII100 eV

−300

−250

−200

−150

−100

−50 0 50

10⁻¹ 10⁰ 10¹ 10²

δTb (mK)

R (cMpc) PopIII Galaxy Mini−QSO HMXBs

Signals are different around different type of sources. Redshift = 15

δT_b pattern around a source :

Hii region at the center (δT_b= 0), Emission region (δTb>0),

Absorption region (δTb<0), Signal vanishes at far away region.

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δT

_b

profiles

10²² 10²⁴ 10²⁶ 10²⁸

10¹ 10² 10³

Lν (erg/s/Hz)

λ (Å) PopIII

HI Lyα

HeI

HeII100 eV

−200

−150

−100

−50 0 50

10⁻¹ 10⁰ 10¹ 10²

δTb (mK)

R (cMpc) Mini−QSO

Signals are different around different type of sources. Redshift = 15 δT_b pattern around a source :

Hii region at the center (δT_b= 0), Emission region (δT_b>0),

Absorption region (δTb<0),

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Visibility

Differential brightness temperature :

δT_b(~θ, ν)∼27x_HI(x,z) [1+δ_B(x,z)]

1 +z 10

1/2

1− Tγ(z) T_S(x,z)

mK,

Direct measurable quantity is visibility.

V(U~, ν) = Z

d²θ I_ν(~θ) A(~θ) e^i2π~^θ·^U^~, (2)

Sky specific intensity : Iν(~θ) = ^2k_c^B2^ν²δTb(~θ, ν)

Primary beam pattern

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Signal Visibility

−300

−250

−200

−150

−100

−50 0 50

10⁻¹ 10⁰ 10¹ 10²

δTb (mK)

10⁻⁶ 10⁻⁴ 10⁻² 10⁰

10 100 1000

|S(U, νc)| mJy

U PopIII

Redshift = 15.

α= 1.5,f_X = 0.05 ,f_esc= 0.1,t_age = 20Myr, density contrastδ= 0

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Noise

Signal with system noise and foregrounds.

V(U~, ν) =S(U~, ν) +N(U, ν~ ) +F(U~, ν), (3) S(U~, ν) is the 21-cm signal visibility

N(U~, ν) is the system noise F(U~, ν) foreground contributions

The system noise at different baselines and frequency channels are expected to be Gaussian random variables with zero mean.

rms noise :

q

hN²i=

√

2k_BTsys

A_eff√

∆ν_c ∆t_c, (4)

rms noise can be reduced over long observation time tobs (by a factor of p

∆t_c/t_obs).

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Noise

Signal with system noise and foregrounds.

V(U~, ν) =S(U~, ν) +N(U, ν~ ) +F(U~, ν), (3) S(U~, ν) is the 21-cm signal visibility

N(U~, ν) is the system noise F(U~, ν) foreground contributions

The system noise at different baselines and frequency channels are expected to be Gaussian random variables with zero mean.

rms noise :

q

hN²i=

√

2k_BTsys

A_eff√

∆ν_c ∆t_c, (4)

rms noise can be reduced over long observation time tobs (by a factor of p

∆t_c/t_obs).

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Baseline distribution

10⁻⁷ 10⁻⁵ 10⁻³ 10⁻¹ 10¹

10² 10³

nB(U, ν)

U ν = 90 MHz

SKA1−low MWA GMRT LOFAR

10⁻¹ 10⁰ 10¹ 10²

10² 10³

σ(U, ν) mJy

U

BaselineU =dant/λ. dant is the distance between the antenna pair andλobservational wavelength.

n_B(U, ν) is the number of antenna pairs having same baselineU at frequency ν.

rms noise can be further reduced by a factor of 1/p

2πn_B(U, ν)U∆U

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Visibilities

−300

−250

−200

−150

−100

−50 0 50

10⁻¹ 10⁰ 10¹ 10²

δTb (mK)

10⁻⁴ 10⁻² 10⁰

10 100 1000

|S(U, νc)| mJy

U

SKA1−low

PopIII Galaxy Mini−QSO HMXBs

Redshift = 15, ν_c = 90 MHz,B_ν = 16 MHz, ∆ν_c = 50 kHz, tobs = 1000 h.

Signal is detectable at the low baselines for the fiducial galaxy, mini-QSO and HMXBs.

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Visibilities : mini-QSO

10⁻⁵ 10⁻² 10¹

10 100 1000

|S(U, νc)| mJy

U

SKA1−low

10⁶ M_O_· 10⁷ M_O_· 10⁸ M_O_· 10⁹ M_O_·

10⁻⁵ 10⁻² 10¹

10 100 1000

|S(U, νc)| mJy

U

SKA1−low

f_X=0.05, α=1.5 f_X=0.10, α=1.5 f_X=0.05, α=0.5

Redshift = 15, νc = 90 MHz,Bν = 16 MHz, ∆νc = 50 kHz, t_obs = 1000 h.

Position of the first zero crossing shift towards lower baselines as mass increases.

Visibilities at low baselines are insensitive to f_X andα.

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Visibilities : mini-QSO

0 0.1 0.2 0.3 0.4 0.5

−8 −6 −4 −2 0 2 4 6 8 |S(U, νc)| mJy

∆ν (MHz)

U = 10 U = 50 U = 100 NS

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

−8 −6 −4 −2 0 2 4 6 8 |S(U, νc)| mJy

∆ν (MHz) U = 10 20 Myr^{1 Myr}

100 Myr NS

Redshift = 15, νc = 90 MHz,Bν = 16 MHz, ∆νc = 50 kHz, t_obs = 1000 h.

Visibility peaks at the central frequency channel at the position of the centre of the source.

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Signal to noise ratio

SNR :

SNR= 1 σ_N

R d²UR

dν nB(U, ν) S(U, ν~ ) R d²UR

dν n_B(U, ν) , (5) where

σ_N =

√

2k_BTsys

Aeff

ptobs Bν Nant(Nant−1)/2. (6)

10⁻⁵ 10⁻³ 10⁻¹ 10¹

10 100 1000

|S(U, νc)| mJy

U

SKA1−low

Mini−QSO

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SNR

20 40 60 80 100 120 140 160 180 200

6 7 8 9

SNR

log (M_★/M_O_· ) 2 3 4 5 6 7 8 9 10

0 0.2 0.4 0.6 0.8 1 f_esc

8.6 8.8 9 9.2 9.4

0 0.05 0.1

f_X

8 8.5 9 9.5 10 10.5 11 11.5 12

0.5 1 1.5 2

SNR

2 4 6 8 10 12

20 40 60 80 100 5 10 15 20 25 30 35 40 45 50

10 15 20

Fiducial mini-QSO : SNR ∼9 for t_abs = 1000 h, ∆ν = 50 kHz.

SNR depend on the source properties, in particular on the mass and age of the source and the escape fraction of ionizing photons.

SNR weakly depend on the X-ray properties.

SNR decrease with increasing redshift.

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Overlap between sources

10⁻³ 10⁻² 10⁻¹ 10⁰

100 1000

|S(U, νc)| mJy

U Overlapped Massive−halo Isolated Analytical

Noise 10⁻¹

10⁰ 10¹

−10 −5 0 5 10

|S(U=20, ν)| mJy

∆ν (MHz)

Overlapped: Minimum halo mass∼4×10⁹ M. Massive-halo: Minimum halo mass∼2×10¹⁰ M. Isolated: Single source at the center of FOV.

We ensure that the maximum source mass in the box is 10⁷ M and the source is at the center of the FOV.

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Foregrounds

10⁻⁴ 10⁻² 10⁰ 10² 10⁴ 10⁶

10 100 1000

|V(U, νc)| mJy

U Signal

NS FG

10⁻⁴ 10⁻² 10⁰ 10² 10⁴ 10⁶

−8 −6 −4 −2 0 2 4 6 8

|V(U=10, ν)| mJy

ν (MHz)

Foregrounds contribution is very large compared to the signal and the system noise.

Foregrounds : Galactic synchrotron radiation.

One can try to remove the foregrounds from the total signal by

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Using a filter

Signal estimator:

DEˆ E

= Z

d²U Z

dν S(U, ν~ )S_f^?(~U, ν) nB(U, ν~ ) (7) Noise :

D

(∆ ˆE)²E

NS=A_NS Z

d²U Z

dν |S_f(U~, ν)|² n_B(U~, ν) (8) where,

ANS= DNˆ²

E 2 Nant(Nant−1)

∆νc

Bν

(9) Foregrounds : (Datta et al 2007)

D

(∆ ˆE)²E

FG= Z

d²U Z

dν₁ Z

dν₂ 2K_B

c² 2

(ν₁ν₂)²

×nB(U, ν~ 1) nB(U~, ν2) C2πU(ν1, ν2)

×S_f^?(U~, ν₁)S_f(~U, ν₂) (10)

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Using a filter

−15

−10

−5 0 5

−8 −6 −4 −2 0 2 4 6 8 sT (µJy)

ν(MHz) B_f

10⁻⁵ 10⁻⁴ 10⁻³ 10⁻²

0 0.5 1 1.5 2

<E>

B_f (MHz) Signal

NS

FG 34

5 6 7 8 9 10 11

0 0.5 1 1.5 2

2 11 22 33 44

SNRE

B_f (MHz) r (cMpc)

Filter :

Sf(U, ν~ ) = ν

νc

2

[ST(U~, ν,Bf)−Θ(1− |ν−νc|/B⁰) B⁰

×

Z νc+B⁰/2

ν −B⁰/2

ST(U~, ν⁰,Bf) dν⁰] (11)

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Conclusions

We investigate the detectability of early sources like popIII stars, mini- QSO, galaxy and HMXBs, by comparing the 21-cm visibility signal with the system noise appropriate for a telescope like the SKA1-low.

Upon integrating the visibility around a typical source over all

baselines and over a frequency interval of 16 MHz, we find that it will be possible make a ∼9σ detection of the isolated sources like PopII galaxies, mini-QSOs and HMXBs at z ∼15 with the SKA1-low in 1000 hours.

The exact value of the signal to noise ratio (SNR) will depend on the source properties, in particular on the mass and age of the source and the escape fraction of ionizing photons.

The predicted SNR decreases with increasing redshift.

We can use filters to detect the sources while the signal is much weaker than the system noise and foregrounds.

Thank you

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Conclusions

We investigate the detectability of early sources like popIII stars, mini- QSO, galaxy and HMXBs, by comparing the 21-cm visibility signal with the system noise appropriate for a telescope like the SKA1-low.

Upon integrating the visibility around a typical source over all

baselines and over a frequency interval of 16 MHz, we find that it will be possible make a ∼9σ detection of the isolated sources like PopII galaxies, mini-QSOs and HMXBs at z ∼15 with the SKA1-low in 1000 hours.

The exact value of the signal to noise ratio (SNR) will depend on the source properties, in particular on the mass and age of the source and the escape fraction of ionizing photons.

The predicted SNR decreases with increasing redshift.

We can use filters to detect the sources while the signal is much weaker than the system noise and foregrounds.

Thank you

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Including the light-cone effect

10⁻³ 10⁻² 10⁻¹ 10⁰

100 1000

|S(U, νc)| mJy

U Overlapped Massive−halo Isolated Analytical

Noise 10⁻¹

10⁰ 10¹

−10 −5 0 5 10

|S(U, νc)| mJy

∆ν (MHz)