Talk given at the symposium "Escape of Lyman radiation from cosmic labyrinths" in Kolympari, Crete (2018). Results presented have been published in Astronomy and Astrophysics: https://doi.org/10.1051/0004-6361/201834164

1. The Lyman α Emitter Luminosity Function at
3 < z < 6 from MUSE-Wide
(Paper submitted to A&A)
Edmund Christian Herenz & MUSE Collaboration
Stockholm University
September 13, 2018

2. Why do we care about the Lyα Luminosity Function?
dNLAE = φ(LLyα)dLLyαdV
Luminosity functions provide the gold standard for
summarising the changing demographics of galaxies with
cosmic look back time.
Essential physical mechanisms of galaxy formation and
evolution are “frozen-in” into the LF.
Substantial high-redshift galaxy samples:
Continuum Selection (≈LBGs)
Emission Line Selection (LAEs)
LFs connected via EWLyα distribution: P(MUV|EWLyα)

3. The MUSE-Wide (MW) survey
Herenz et al. (2017) - 24 MUSE pointings - 237 LAEs
DR1: Urrutia et al. (in prep.) - 44 MUSE pointings - 479 LAEs

4. MW LAEs not listed in 3D/HST or CANDELS
catalogues
20 22 24 26 28
JHmag
17.5
17.0
16.5
16.0
15.5
15.0
logFline(3RKron)[ergs−1cm−2]
Lyα

5. Selection function fc(FLyα, λobs
Lyα) from source insertion
and recovery experiments
Artificial point sources:
3D Gaussian, FWHM(λ) as PSF, vFWHM = 250 km s−1
⇒ PSSF (point source selection function)
Flux rescaled MUSE-HDFS LAEs (degraded to
MUSE-Wide PSF)
⇒ RSSF (real source selection function)
4990 5000 5010
0.0
2.5
5.0
7.5
10.0
12.5
15.0
σλ[10−20ergs−1cm−2Å]
5000Å
6860 6870
0.0
2.5
5.0
7.5
10.0
12.5
15.0
σλ[10−20ergs−1cm−2Å]
6861.25Å
7090 7100 7110
0.0
2.5
5.0
7.5
10.0
12.5
15.0
σλ[10−20ergs−1cm−2Å]
7100Å
7240 7250
0.0
2.5
5.0
7.5
10.0
12.5
15.0
σλ[10−20ergs−1cm−2Å]
7242.5Å
8290 8300
0
5
10
15
20
σλ[10−20ergs−1cm−2Å]
8295Å
5000 6000 7000 8000 9000
λ[Å]
0
10
20
30
σλ[10−20ergs−1cm−2Å]

6. Individual selection functions
15.516.016.517.017.518.0
−log10Fin [erg s−1cm−2]
0.0
0.2
0.4
0.6
0.8
1.0
Ndet/Ntot
Point Source - Field ID 1
8292.5
5000
7242.5
6861.25
7100
PSSF
15.516.016.517.017.518.0
−log10Fin [erg s−1cm−2]
0.0
0.2
0.4
0.6
0.8
1.0
Ndet/Ntot
Stacked HDFS Sources - Field 01
8292.5
5000
7242.5
6861.25
7100
RSSF

7. Final selection functions
5000 6000 7000 8000 9000
λ[Å]
17.6
17.4
17.2
17.0
16.8
16.6
16.4
16.2
16.0
log(F[ergs−1cm−2])
Realistic LAEs
5000 6000 7000 8000 9000
λ[Å]
17.6
17.4
17.2
17.0
16.8
16.6
16.4
16.2
16.0
Point Source LAEs
0.0
0.2
0.4
0.6
0.8
1.0
fc
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
zLyα
41.5
42.0
42.5
43.0
43.5
44.0
log(LLyα[ergs−1])
Realistic LAEs
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
zLyα
41.5
42.0
42.5
43.0
43.5
44.0
Point Source LAEs
0.0
0.2
0.4
0.6
0.8
1.0
fc

8. LAE Sample for LF: fc > 15 %
3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5
zLyα
41.50
41.75
42.00
42.25
42.50
42.75
43.00
43.25
43.50
logLLyα[ergs−1]
fc =15%
fc =85%
Conf. 2&3,fc >15%
Conf. 1,fc >15%
Conf. 1,fc <15%
Conf. 2&3,fc <15
AGN
179 of 237 remain (75.6 %)

9. Non-parametric Test for LF evolution.
Using a test developed by Efron & Petrosian (1992) we can test
for seperability of the LAE LF (H0):
Ψ(L, z) = φ(L)ρ(z) .
Redshift range |τPSSF| |τRSSF| pPSSF pRSSF
2.9 < z ≤ 4 0.47 0.24 0.32 0.40
4.0 < z ≤ 5.0 0.79 0.98 0.21 0.16
5.0 < z ≤ 6.9 0.05 0.29 0.48 0.39
2.9 < z ≤ 6.9 0.46 0.31 0.32 0.38
⇒ H0 can not be rejected. We can determine global φ(L).

10. 3 different methods to calculate LAE LF
1/Vmax (Schmidt 1968):
Vmax,i = ω
zmax
zmin
fc(LLyα,i, z)
dV
dz
dz
φ1/Vmax
( LLyα ) =
1
∆LLyα
k
1
Vmax,k
Φ(LLyα,k ) =
i≤k
1
Vmax,i
C− (Lynden-Bell 1971):
Φ(LLyα,k) = Φ(LLyα,1)
k
i=2
1 +
1
Ti
withTi =
Ni
j=1
fc(LLyα,i, zj)
fc(LLyα,j, zj)
Page & Carrera (2000):
φPC( LLyα ) =
N LLyα
ω
Lmax
Lmin
zmax
zmin
fc(LLyα, z) dV
dz dz dL

12. Bias in LAE LF when not accounting for Lyα haloes!
ΦRSSF(log LLyα = 42.2) = 2.5 × ΦPSSF(log LLyα = 42.2)
10-6
10-5
10-4
10-3
10-2
Φ(LLyα)[Mpc−3]
ΦC− (RSSF)
ΦC− (PSSF)
ΦC− (RSSF)
ΦC− (PSSF)
42.2 42.4 42.6 42.8 43.0 43.2
log10(LLyα[ergs−1])
0
50
100
ΦRSSF−ΦPSSF
ΦPSSF
[%]
relative difference: ΦRSSF − ΦPSSF
ΦPSSF

13. C−
LAE LF ≈ 1/Vmax LAE LF
Φ1/Vmax
(log LLyα = 42.2) = 1.2 × ΦC− (log LLyα = 42.2)
10-6
10-5
10-4
10-3
10-2
Φ(LLyα)[Mpc−3]
C−
− 1/Vmax comparison Φ1/Vmax
ΦC−
Φ1/Vmax
ΦC−
42.2 42.4 42.6 42.8 43.0 43.2
log10(LLyα[ergs−1])
0
10
20
Φ1/Vmax−ΦC−
Φ1/Vmax
[%]
relative difference

14. Maximum-Likelihood Analysis (Sandage 1976):
φ(L) dL = φ∗ L
L∗
α
exp −
L
L∗
dL
L∗
(Schechter 1976)
L =
NLAE
i=1
p(Li, zi) ⇐ p(Li, zi) =
φ(Li)fc(Li, zi)
Lmax
Lmin
zmax
zmin
φ(L)fc(L, z)dV
dz dL dz
42.2 42.4 42.6 42.8 43.0 43.2 43.4
logL ∗
[ergs−1]
2.5
2.0
1.5
1.0
α
∆S=2.3 (68.3% CI)
∆S=6.17 (95.4% CI)
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
logφ∗
[Mpc−3]
42.2 42.4 42.6 42.8 43.0 43.2
log10(LLyα[ergs−1])
10-6
10-5
10-4
10-3
10-2
Φ(LLyα)[Mpc−3]
Φ1/Vmax SF fit 2σ CI SF fit 1σ CI
log L∗
[erg s−1
] = 42.66+0.22
−0.16 and α = −1.84+0.42
−0.41

15. Differential (binned) LAE LFs
41.5 42.0 42.5 43.0 43.5
10-6
10-5
10-4
10-3
10-2
10-1
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
3<z 4
D17az∼ 3− 4
MW3<z 4 (RSSF)
MW3<z 4 (PSSF)
MW (AGN)
41.5 42.0 42.5 43.0 43.5
10-6
10-5
10-4
10-3
10-2
10-1
4<z 5
D17az∼ 4− 5
MW4<z 5 (RSSF)
MW4<z 5 (PSSF)
41.5 42.0 42.5 43.0 43.5
log10(LLyα[ergs−1])
10-6
10-5
10-4
10-3
10-2
10-1
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
z>5
D17az∼ 5− 7
MWz>5 (RSSF)
MWz>5 (PSSF)
41.5 42.0 42.5 43.0 43.5
log10(LLyα[ergs−1])
10-6
10-5
10-4
10-3
10-2
10-1
Global: 3<z<6.7
B16z∼ 3− 7
D17bz∼ 3− 7
D17az∼ 3− 7
MW (RSSF)
MW (PSSF)

16. 42.5 43.0
logL ∗
[ergs−1]
2.5
2.0
1.5
1.0
α
∆logLLyα[ergs−1]=0.075
42.5 43.0
logL ∗
[ergs−1]
∆logLLyα[ergs−1]=0.1
42.5 43.0
logL ∗
[ergs−1]
∆logLLyα[ergs−1]=0.15
42.5 43.0
logL ∗
[ergs−1]
∆logLLyα[ergs−1]=0.2
42.5 43.0
logL ∗
[ergs−1]
∆logLLyα[ergs−1]=0.25
42.00
42.05
42.10
42.15
42.20
logLLyα[ergs−1]StartingBin
Resulting L∗ and α depend sensitively on size of the bins and
bin placement.
⇒ Don’t fit to binned data!

17. Comparison to literature
41.5 42.0 42.5 43.0 43.5
log10(LLyα[ergs−1])
10-5
10-4
10-3
10-2
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
3<z 4
M17z=3.1
C11z∼ 3− 4
O08z∼ 3
G09z∼ 3
S18z∼ 3.1
MW3<z 4 (PSSF)
MW (AGN)
41.5 42.0 42.5 43.0 43.5
log10(LLyα[ergs−1])
10-5
10-4
10-3
10-2
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
4<z 5
O08z∼ 4
D07z∼ 4
S09z∼ 4
P18z=4.8
S18z∼ 4.7
S18z∼ 3.9
MW4<z 5 (PSSF)
41.5 42.0 42.5 43.0 43.5
log10(LLyα[ergs−1])
10-5
10-4
10-3
10-2
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
z>5
S18z∼ 5.4
C11z∼ 4.5− 6.5
K18z∼ 6
O08z∼ 6
S16z∼ 6
S06z∼ 6
MWz>5 (PSSF)
42.0 42.5 43.0 43.5 44.0
log10(LLyα[ergs−1])
10-5
10-4
10-3
10-2
φ(LLyα)[Mpc−3(∆log10LLyα[ergs−1])−1]
Global: 3<z<6.7
S18SC4K/noAGN
MW (RSSF)
MW (PSSF)

18. Summary
(LLyα, z)-space probed by MUSE-Wide:
42.2 ≤ log LLyα[erg s−1
] ≤ 43.5 2.9 ≤ z ≤ 6.7
(Herenz+2017 sample: ω = 22.2 ˆ= V = 2.3 × 105 Mpc3)
Within this sampled region (LLyα, z)-space LAE LF.
appears non-evolving.
Schechter parameterisation provides good fit - Power law
not (see Paper).
log L∗
[erg s−1
] = 42.66+0.22
−0.16 α = −1.84+0.42
−0.42
log φ∗
[Mpc−3
] = −2.71
Literature LFs not accounting for extended low-SB Lyα
halos (basically all, except Drake et al. 2017) are
significantly biased at L < L∗.