Constraints on photoionization rate and
escape fraction at z < 0.5
Prakash Gaikwad
Tirthankar Roy Choudhury (NCRA), R. Srianand (IUCAA), Vikram Khaire (IUCAA)
June 21, 2016
National Centre for Radio Astrophysics
Tata Institute of Fundamental Research
Plan of talk
• Introduction
• Observation: hst-cos
• Simulation: cite
• Method:
• Flux PDF
• Flux Power Spectrum
• Results:
• ΓHI constraint
• ΓHI Evolution
• fesc constraint
• Summary
2
Introduction
Introduction
• QSO absorption spectra: Ly-α forest
•
•
•
•
•
IGM (Overdensity ∆ ≤ 10)
Large redshift coverage
Thermal history
Ionization state
UV background (UVB)
• UVB sources:
• Radiation from accretion of matter on
to blackhole
• Stellar contribution from galaxies
• Escape fraction (fesc ):
• Types of stars
• Galaxy ISM: Gas distribution
• H i photoionization rate, ΓHI
4
H i Photoionization rate
[Khaire & Srianand, 2015a], [Khaire et.al, 2015b]
• [Kollmeier et.al 2014] and [Shull et.al 2015]: hst-cos, same statistics, No
errorbars
• [Kollmeier et.al 2014] ⇒ fesc ∼ 4%,
[Shull et.al 2015]
⇒ fesc ∼ 0%
• 3σ upper limit from sample of galaxies at z < 2 : fesc ≤ 2% [Cowie et al. 2009] 5
H i Photoionization rate
[Khaire & Srianand, 2015a], [Khaire et.al, 2015b]
• ΓHI with appropriate error bars at z < 0.5?
• Evolution of ΓHI and Escape fraction fesc ?
• hst-cos data, but different statistics
5
Observation
Data
[Danforth et.al, 2015]
• Instrument: HST-COS
• Number of spectra: 82
I
sbs1122
sbs1108
pks0552
3c57
s080908
pks0637
3c263
he0238
pmn2345
pg1424
pks0405
hs1102
he0226
pg1259
he0153
pg0003
ton236
pg1222
he0435
1es1553
s094952
1es1028
pg1049
b0117
rxj2154
3c66a
pg1216
pg0832
pg1001
s09255b
h1821
ton580
pks1302
f1010
rxj0439
s092909
pg0953
s50716
pg1121
rbs1892
phl2525
phl1811
p1103
pg1309
pg1116
pg2349
1sj1032
pg1048
h2356
he0056
pg0157
3c273
pg1307
rxj0956
pg1115
s135712
pg0026
pks0558
q0045
pg1626
pg0838
i06229
mrk876
pg1435
mrk106
q1230
pks2155
tons210
rbs542
uks0242
pg0804
i22456
mrk478
ton1187
pks2005
pg0844
rxj0503
mr2251
pg1229
mrk1513
rbs144
pg1011
0.0
II
III
IV
ª
• SNR : 4 to 16
• Resolution ∆v ∼ 17km/s
• Instrumental Broadening: Not
Gaussian
• Continuum Fitting
• Metal Lines and higher transition
lines are removed
0.1
0.2
0.3
Redshift z
0.4
0.5
• QSO proximity zone : High
ionization due to radiation from
QSO itself (∼ 25h−1 Mpc)
7
Simulation
SPH Simulation
Density
50
Velocity
50
40
30
30
30
10
0
y (h−1 Mpc)
40
20
20
10
0
10
1.881
20
30
x (h−1 Mpc)
0.014
40
1.854
log(∆)
τGP ∝
50
3.722
0
Temperature
50
40
y (h−1 Mpc)
y (h−1 Mpc)
[Springel, 2005]
20
10
0
10
681
20
30
x (h−1 Mpc)
211
(Ωb h2 )2 Ω−0.5
m
ΓHI
v
259
40
50
730
0
0
0.419
10
20
30
x (h−1 Mpc)
2.683
40
4.947
log(Tg )
• Advantages : Parameter space
• ΛCDM cosmology
• Disadvantage: No ionization evolution
• 2 × 512 DM + Baryons
7.211
T0−0.7 ∆2−0.7γ (1 + z)6
• gadget-2 sph
3
50
• Equation of state at high z: T = T0 ∆γ−1
• Box size: 50h−1 Mpc
9
gadget-2: T − ∆ Relation
8
2.8
7
2.4
log(T)
6
2.0
5
1.6
4
1.2
3
0.8
2
1
T0 = 15000.0, γ = 1.30
T0 = 5000.0, γ = 1.57
1
0
1
2
log(∆)
3
4
5
0.4
0.0
10
Temperature Evolution Equation
dT
dt
|{z}
Temperature
evolution
[Hui & Gnedin, 1997]
2T d∆
= −
| 2HT
{z } + 3∆ dt +
| {z }
Hubble
expansion
Adiabatic
Term
dQ
2
3kB nb dt
| {z }
Other Heating /
Cooling Processes
+
dTshock
| dt
{z }
Shock
heating
• Other heating / cooling processes term is not included in Gadget-2
except shock heating
• Other heating processes: Photo-heating
• Cooling processes: Recombination Cooling, Collisional ionization,
Collisional excitation, Bremsstrahlung, Inverse Compton Cooling
11
Code for Ionization and Temperature Evolution (CITE)
1. GADGET-2 snapshots stored at z = 2.1, 2.0, 1.9, · · · , 0.1, 0.0
2. Assuming initial equation of state for z = 2.1 e.g.
T0 = 15000 K and γ = 1.3.
3. Solve ionization evolution equation
4. Calculate photoheating and radiative cooling rates (dQ/dt).
5. Solve the temperature evolution equation for zprev and get
temperature for next step znext ,
dT
2T d∆
2
dQ
dT
= − 2HT +
+
+
dt
3∆ dt
3kB nb dt
dt shock
6. Repeat Step 3 to Step 5 for next redshift
12
Comparison with other simulation
T − ∆ relation (z = 0.3)
8
4.8
6
5
4.2
7
3.6
6
3.0
5
2.4
1.8
4
1.2
T0 = 15000, γ = 1.30
T0 = 4902, γ = 1.53
3
2
1
0
1
log(∆)
2
3
4
log(T)
7
log(T)
T0 -γ Effect
2.8
2.4
2.0
1.6
4
1.2
3
0.8
0.6
2
0.0
1
T0 = 15000.0, γ = 1.30
T0 = 5000.0, γ = 1.57
1
0
1
2
log(∆)
3
4
5
0.4
0.0
• Color represents density of points in log
Red ⇒ high density of points,
Blue ⇒ low density of points
• T0 and γ are in agreement with those from simulations in literature
14
Phase Distribution of Baryons (z = 0)
Feedback
9
WHIM: 28.77%
Missing Baryons
8
Hot Halo: 18.32%
Cluster gas: X-rays
log(T)
7
6
5
4
3
2
1
Diffuse: 34.09% Condensed: 18.82%
Ly-α Forest
Galaxies
0
1
2
3
4
5
log(∆)
Fractions consistent with those from simulations in the literature
15
Method
Normalised Flux
Simulated Spectrum
1.5
1.0
0.5
0.0
1.5
1.0
0.5
0.0
1.5
1.0
0.5
0.0
SiII
Ly α
Ly γ
Ly α
Ly α
CIV
CIV
Ly α
3C57 With Metal
SiIII
3C57 Metal Removed
Simulated Spectrum
1520
1530
1540
Wavelength (λ) in Å
1550
1560
• Metal lines are replaced by continuum added with noise
• Convolved with instrumental broadening profile. (Not a Gaussian)
• Added SNR similar to observed spectra
17
3 Statistics
• Flux Probability Distribution Function (Flux PDF):
101
1.4
1.2
1.0
100
PDF
F
0.8
0.6
10-1
0.4
0.2
0.0
1520
1540
1560
1580
λ
1600
1620
10-2
0.0
1640
0.2
0.4
F
0.6
10-3
• Flux Power Spectrum:
0.8
1.0
Observation z = 0.2
•
σF2
=
R∞
PF (k) dk /2π
P F ( k)
• PF (k) = |F [(F (x)]|2
10-4
−∞
• Column Density Distribution:
10-5
100
k h Mpc−1
101
18
Matching Simulation with Observation
Covariance
• Simulation: ΓHI as free parameter.
χ2 = [Pobs − Psim ] C−1 [Pobs − Psim ]T
• How to estimate Covariance Matrix C ?
• Observation: Jackknife Estimation? ⇒ Underestimated
• Simulation ⇒ Converge
[Rollinde et.al. 2013]
• Recovery using 2 statistics is well.
19
Result
ΓHI Constraint: Flux PDF and Flux Power Spectrum
10 1
10 -4
Observation
Model: Γ12 = 0.100
5
Observation
Model: Γ12 = 0.100
Flux PDF
Power Spectrum
Combine
4
z = 0.2
10 0
2
χdof
P F ( k)
dP/dF
3
10 -5
10 -1
2
1
0.0
0.2
0.4
F
0.6
0.8
1.0
10 -1
10 0
k h Mpc −1
10 1
0
10 -2
10 -1
Γ 12
• Flux PDF: Range: 0 ≤ F ≤ 0.8
• Covariance Matrix from mock samples
• Flux Power spectrum
• Γ12 ⇒ ΓHI in units of 10−12 s−1
• Smooth χ2 parabola ⇒ No instability in statistics
• Statistical uncertainty: χ21σ = χ2min + ∆χ21σ
21
Total ΓHI Error Budget: Systematic and Statistical Uncertainty
Redshift ⇒
Type of simulated spectra ⇒
Best Fit Γ12
Statistical Uncertainty
Cosmological parameters (∼ 10%)
Cosmic Variance (∼ 3%)
Total statistical errors
Continuum uncertainty (systematic)
Total error
0.1125
Ly-α forest
0.2
Ly-α forest
0.3
Ly-α forest
0.4
Ly-α forest
0.066
± 0.007
± 0.007
± 0.002
± 0.010
± 0.005
± 0.015
0.100
± 0.013
± 0.010
± 0.003
± 0.016
± 0.005
± 0.021
0.145
± 0.022
± 0.015
± 0.004
± 0.027
± 0.010
± 0.037
0.155
± 0.030
± 0.021
± 0.006
± 0.037
± 0.015
± 0.052
• Statistical Uncertainty: Includes uncertainty in initial T0 and γ
• Cosmic Variance: Identical cosmological parameters but different
initial conditions.
• Cosmological Parameters: Ωm , Ωb h2 , ns ,σ8
τGP ∝
(Ωb h2 )2 Ω−0.5
m
ΓHI
T0−0.7 ∆2−0.7γ (1 + z)6
22
ΓHI Evolution:
Ly-β Forest
Γ HI (in 10 −12 s −1 )
This Work; Γ12 = 0. 040 ± 0. 001(1 + z)4. 99 ± 0. 12
Kollmeier+2014
This Work (Ly-α forest)
This Work (Ly-α + Ly-β forest)
10 -1
0.0
0.1
0.2
0.3
z
0.4
0.5
0.6
23
Column Density Distribution: ΓHI consistency
Simulation
Observation
d2 NHI
dlogNHI dz
102
101
12.5
13.0
13.5
14.0
logNHI
χ2dof = 1.15
14.5
15.0
24
UV background model:
[Khaire & Srianand, 2015a], [Khaire et.al, 2015b]
Γ HI (in 10 −12 s −1 )
10 0
HM12 f(NHI ,z); α = − 1. 4
HM12 f(NHI ,z); α = − 1. 7
Inoue f(NHI ,z); α = − 1. 4
Inoue f(NHI ,z); α = − 1. 7
Kollmeier+2014
Shull+2015
Becker+2013
Bolton+2007
This Work
10 -1
0.0
0.5
1.0
z
1.5
2.0
2.5
UVB at z ≤ 2.5 is dominated by QSO i.e. fesc = 0%
25
UV background model:
[Khaire & Srianand, 2015a], [Khaire et.al, 2015b]
Γ HI (in 10 −12 s −1 )
10 0
HM12 f(NHI ,z); α = − 1. 4
HM12 f(NHI ,z); α = − 1. 7
Inoue f(NHI ,z); α = − 1. 4
Inoue f(NHI ,z); α = − 1. 7
Kollmeier+2014
Shull+2015
Becker+2013
Bolton+2007
This Work
10 -1
0.0
0.5
1.0
z
1.5
2.0
2.5
3σ upper limit on fesc is 0.8% ⇒ Low mass galaxy contribution to
25
UVB is negligible
Summary
Summary
• Observation : Analysis of 82 HST-COS quasar absorption spectra
• cite:
• T0 ∼ 4000 − 5000K, γ ∼ 1.6
• Phase diagram: Diffuse phase ∼ 30 − 40%, WHIM ∼ 40 − 25%
• Computationally less expensive
• Method
• 2 Statistics: Flux PDF and Flux power spectrum
• Covariance Matrix is calculated from Simulation
• Result
•
•
•
•
•
ΓHI constraints in 4 redshift bins.
Uncertainty: Systematic and Statistical
ΓHI constraints consistent with CDDF
Evolution of Γ12 is consistent with fesc = 0%
3σ upper limit on fesc = 0.8% ⇒ Low mass galaxy contribution
negligible
27
Acknowledgement
• Aseem Paranjape
(IUCAA)
• Sowgat Muzahid
(Department of Astronomy, Penn state University)
• Charles Danforth
(Department of Astrophysical & Planetary Science, University of Colorado)
Computing Facility
• HPC Cluster (NCRA)
• Perseus Cluster (IUCAA)
• Ganga (NCRA)
28
F
F
F
HI Interlopers:
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1.2
1.0
0.8
0.6
0.4
0.2
0.0
1675
Go back
Summary
Line
λ in Å
Strength
Ly-α
Ly-β
Ly-γ
Ly-δ
Ly-ω
1215.6701
1025.7223
972.5368
949.7431
937.8035
1
6.17−1
17.78−1
38.02−1
69.18−1
Ly-α Forest: From Simulation @ z = 0. 4
Ly-β Forest: From Simulation @ z = 0. 6
Ly-α + Ly-β Forest: Simulation
1680
1685
λ
1690
1695
1700
29
ΓHI Evolution:
Go back
Summary
Γ HI (in 10 −12 s −1 )
This Work; Γ12 = 0. 040 ± 0. 001(1 + z)4. 99 ± 0. 12
Kollmeier+2014
This Work (Ly-α forest)
This Work (Ly-α + Ly-β forest)
10 -1
0.0
0.1
0.2
0.3
z
0.4
0.5
0.6
30
Covariance Matrix
Go back
Summary
Simulation
NSpectra = 16
Mock Sample 1
NSpectra = 16
Observation
Flux PDF / PS: 1
Simulation
NSpectra = 16
Mock Sample 2
Flux PDF / PS: 2
Mean PDF / PS
Mean PDF / PS
Covariance Matrix
NSpectra = 16
Mock Sample 500
Flux PDF / PS: 500
31
Effect of Feedback:
[Smith et. al. 2011]
Go back
Summary
32
Go back
7
7
6
6
log(T)
log(T)
Effect of initial T0 and γ
5
5
4
4
T0 = 10000.0, γ = 1.10
T0 = 4589.0, γ = 1.51
3
2
1
0
1
log(∆)
2
3
4
2
7
7
6
6
5
T0 = 10000.0, γ = 1.80
T0 = 4568.0, γ = 1.60
3
log(T)
log(T)
Summary
1
0
1
log(∆)
2
3
4
5
4
4
T0 = 20000.0, γ = 1.10
T0 = 5383.0, γ = 1.44
3
2
1
0
1
log(∆)
2
3
4
T0 = 20000.0, γ = 1.80
T0 = 5279.0, γ = 1.61
3
2
1
0
1
log(∆)
2
3
4
33
UV background model:
[Khaire & Srianand, 2015a], [Khaire et.al, 2015b]
• Source Term 1: Galaxy Contribution (Stellar Light)
• Free parameter: Escape fraction fesc
• Source Term 2: QSO contribution (Blackhole accretion)
• Uncertainty in Spectral Energy Distribution index: α
• α = −1.4
• α = −1.7
[Stevans et al. 2014]
[Lusso et al. 2014]
• Sink Term: IGM attenuation (τeff )
• Cloud distribution f (NHI , z)
• HM12: f (NHI , z)
• Inoue: f (NHI , z)
[Haardt & Madau 2012]
[Inoue et.al 2014]
34