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Table 1: The Schechter function parameters of the Sobral
et al
(2012) HαLF (model
i
= 3),
and the corrections applied.
z
= 0.40
z
= 0.84
z
= 1.47
z
= 2.23
Faint end slope α
−1.60
−1.60
−1.60
−1.60
Original log
10
ϕ
*
[Mpc
−3
]
−3.12
−2.47
−2.61
−2.74
Original log
10
L
*
[erg s
−1
]
42.09
42.25
42.56
42.86
Cosmological volume correction to
ϕ
*
[dex]
+0.01
−0.01
−0.02
−0.03
Cosmological distance correction to
L
*
[dex]
−0.01
0.00
+0.01
+0.01
Undoing extinction correction to
L
*
[dex]
−0.40
−0.40
−0.40
−0.40
Aperture correction to
L
*
[dex]
+0.02
+0.07
+0.07
+0.06
Final log
10
ϕ
*
[Mpc
−3
]
−3.11
−2.48
−2.63
−2.76
Final log
10
L
*
[erg s
−1
]
41.71
41.92
42.23
42.54
The code prints a description of the chosen HαLF to the screen so that the user can verify
the correct selection.
Conditional size distributions:
The
recommended
j
= 2 size distribution is based on the CMC, updated as of August
15, 2011.
16
The objects with redshifted Hα wavelength between 1.1—2.0 μm were selected,
and split into bins based on the Hα flux
F
Hα
[W m
−2
]. For five bins in log
10
(F
Hα
[W m
−2
])
centered at −19.0(0.2)−18.2, and in two wavelength ranges (1.1—1.5 and 1.5—2.0 μm) the
effective radii are well fit by
€
log
10
r
eff
arcsec
=
−
0.66
+
0.06
ξ
+
(0.27
+
0.01
ξ
) 19
+
log
10
F
H
α
W m
-2
⎛
⎝
⎜
⎞
⎠
⎟
±
0.2
,
where
€
ξ
=
1.75
−
λ
H
α
,obs
[
µ
m]
0.45
,
and where 0.2 dex denotes the 1σ dispersion. Note that the effective radii were measured
in the F814W band (rest frame ~
u
band continuum), whereas for WFIRST or Euclid it is
actually the effective radius in the Hα line (also a tracer of star formation) that is relevant.
Since we do not have sufficient data on the latter, the CMC radii are probably the most
accurate we have at this time, and we adopt the above lognormal
P
(
r
eff
|
F
Hα
).
The
j
= 0 size distribution is based on the original version of the CMC and had a
wavelength range of 1.5—2.0 μm, but the construction procedure was otherwise
equivalent. This distribution is
16
S. Jouvel
et al.
, “Designing future dark energy space missions: I. Building realistic galaxy
spectro-‐photometric catalogs and their first applications.”
Astron. Astrophys.
504
:359—371
(2009)