The Star Formation Rate of the Universe
at z=0.24 and z=0.40 from Hα
Sergio Pascual
Jesús Gallego
Jaime Zamorano
Universidad Complutense de Madrid
October, 2004
Abstract
We present the results of a survey searching for galaxies with emission in Hα
at z=0.24 and z=0.4 using narrow-band filters. The Hα luminosity, related to the
number of massive stars, is a direct measurement of the current star formation rate.
The study of the colors of different objects (stars and galaxies) in the system of
narrow- and broad band filters shows strong increase of color as different emission
lines enter the narrow band filter. It is thus possible to make a feasible selection of
emission line galaxies using narrow band filters. The relations between the broadband magnitude and narrow-broad color with the line flux and the equivalent width
of the emission line are developed. These relations are used to obtain the luminosity of the emission line. The SFR of the two samples is calculated assuming that
every candidate selected in both filters (after stars removal) is a Hα emitter. With
this conditions, the SFRs are 3 times the SFR of the local Universe at z ∼0.24 and
5 times at z ∼0.40.
1 Introduction
This contribution is a short summary of the Ph.D. thesis presented in the Universidad
Complutense de Madrid on July 2004 titled: La tasa formación estelar del Universo a
z=0.24 y z=0.40 a partir de Hα.
One of the leading objectives of observational cosmology is the discovery of how
the Universe became the place we see today. The Star Formation Rate (SFR) is one of
the key observables needed for our understanding of the galaxy evlution.
The union of the high redshift measurements of the SFR with those of star-forming
samples at lower redshift (Gallego et al., 1995; Gronwall et al., 1997; Tresse & Maddox, 1998; Treyer et al., 1998; Steidel et al., 1999; Glazebrook et al., 1999; Sullivan
et al., 2000; Tresse et al., 2002; Pettini et al., 2001; Wilson et al., 2002) has focused attention towards the determination of the cosmic star formation history of the Universe.
The increase by an order of magnitude of the global comoving star formation rate from
z=0 to z ≈1 has been well established
Knowledge of both the global star formation history of the Universe and the nature
of individual star-forming galaxies at different look-back times are essential to our
understanding of galaxy formation and evolution. Deep redshift surveys suggest starformation activity substantially increases with redshift until z '1 (see Ellis, 1997, for
a review). Theoretical works can provide a reasonable match to both the present-day
characteristics of galaxies, as well as the properties of galaxies at high redshift.
One of the major problems that arises when analyzing galaxy evolution is how to
make a meaningful comparison between high-z data and local samples. To test directly
whether substantial evolution in the star-formation activity has occurred we need to
measure the SFR density and the properties of the corresponding star-forming galaxy
populations at different redshifts using similar techniques.
1
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The Hα luminosity, related to the number of massive stars, is a direct measurement of the current star formation rate. Metallic nebular lines such as [OII ]λ3727 and
[OIII ]λ5007 (affected by excitation and metallicity) are rather star-formation indicators than quantitative measurements (Gallagher et al., 1989; Kennicutt, 1992a, see,
e.g.). Using optical telescopes, the best way to quantify current star formation is by using an Hα-selected sample of galaxies (Charlot, 1998). Quoting Charlot & Longhetti
(2001): “while insufficient by itself, the Hα line is essential for estimating the star formation rate from the optical emission of a galaxy.” Although star formation in heavily
obscured regions could not be revealed by Hα (Serjeant et al., 2002, see discussion by),
if we select the galaxies with the same criteria at all redshifts, the samples —and the
derived SFRs— will be directly comparable.
A few pioneering works have estimated average SFR densities measuring in the nIR
Hα luminosities for small samples at z=1 (Glazebrook et al., 1999; Yan et al., 1999;
Tresse et al., 2002; Doherty et al., 2004; Glazebrook et al., 2004), z ∼2 (Iwamuro et
al., 2000; van der Werf et al., 2000; Moorwood et al., 2000) and z ∼3 (Pettini et al.,
1998, 2001; Erb et al., 2003).
Despite all the progress made in the last years, the physical nature of intermediate
and high-redshift galaxies remains unclear, and this hinders our understanding of how
they connect with present-day massive galaxies. In particular we still do not know
to what extent the detectable high-z galaxies are representative of the entire galaxy
population of the distant universe. The large number of starbursts-like objects questions
the standard evolution scenarios for the Hubble galaxies. Characterizing the physical
nature, metallicity and recurrence of starbursts in galaxies is a way of addressing the
above issues.
Work on the nature of distant and young galaxies greatly benefits from studies of
their analogues in the more nearby universe. The analysis of the nature of this sample of
intermediate starburst galaxies will provide new light into the galaxy evolution studies.
Our purpose is to extend the UCM survey to higher redshifts. To do this we employ
the narrow-band filter technique. The objects are selected in this way by their line
flux. The filters are centered at 8200Å and 9200 Å, where there is a substantial gap on
the night sky spectrum. When detecting the line Hα, this wavelenght corresponds to
z=0.24 and z=0.4.
The outline of the contribution is as follows. In Section 2 we depict the observations
made with the narrow band filters. A fraction of the candidates have been confirmed
spectroscopichally, so the spectroscopic observations are included. Section 3 illustrates
the process of selection, using the contrast between the magnitude in the broad and
narrow-band filters. We finish with Section 4, with the luminosity function of the
objects selected is obtained and the star formation rates calculated.
All along the paper we assume the concordance cosmology with the paramaters
given in Tegmark et al. (2003): H0 = 100 h km s−1 , with h=0.7, ΩΛ =0.7 and ΩM =0.3.
2 Observations
The satisfactory results of the UCM survey (Gallego et al., 1996) sugested us, as a
natural extension, the search for emission-line galaxies at higher redshifts. The nightsky spectrum shows zones of low emission around 8200Å and 9200Å, corresponding to
Hα at redshift z=0.24 and z=0.4 respectively. Using two narrow-band filters centered
at those redshifts, several photometric campaigns were carried out. To confirm the
presence of the emission line, follow-up spectroscopy of the candidates was made.
2.1 Photometry
For the photometric survey, it was projected to use the Wide Field Camera (WFC, Ives
et al., 1996) in the 2.5m INT telescope at Observatorio del Roque de los Muchachos
(ORM). Two filters of 50Å FWHM were designed for this instrument, with maximum
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transmission in the optimal regions of the night-sky spectrum. The filters are denoted
#208 (centered at 9200Å) and #209 (centered at 8200Å) in the filter database1 ).
Another filter was used in the subsequent development of the survey, during the
observations in Calar Alto observatory with the focal reducer CAFOS 2 in the 2.2m
telescope. This filter of 150Å width was not designed for this task, but it fits in the
region of 8200Å.
The fields observed are: Selected Areas 95 and 114 and the field ELAIS-N1 (European Large-Area ISO Survey) (Rowan-Robinson et al., 1999; Oliver et al., 2000). This
three regions are observed with the INT Wide Field Survey. With this survey, U griz
photometry and catalogs of objects are available for the field ELAIS-N1.
A total of six observing campaigns were carried out in the telescopes INT at La
Palma and 2.2m in Calar Alto. One of them was completely lost due to bad weather.
The remaining campaigns are a combination of photometric and non-photometric nights.
The exposure times were about 5000s for the narrow-band filter and 500s in the broad
band. The mean seeing was 100 in La Palma and 1.00 2 in Calar Alto.
The images were processed using IRAF3 (Image Reduction and Analysis Facility). The individual frames were bias-subtracted, corrected for pixel-to-pixel sensitivity
variations and corrected for the large-scale illumination pattern. The fringing patterns
are specially severe in the I region and in the narrow-band filters. A fringing pattern is constructed using the science exposures (in fact, deep dark-sky exposures) and
subtracted using the task rmfringe of the package mscred. Fringing removal is
specially important in our case, as the fringes harden the detection of objects.
The individual frames were combined to obtain a better signal to noise ratio. The
task combine was used, with the iterative rejection algorithm CRREJECT. Precise
astrometry is calculated for the combined frames using OPERA (Garcı́a-Dabó, 2002;
Garcı́a-Dabó & Gallego, 1998). The astrometric solution has a mean precision better
than 1.00 0.
Finally, catalogs of objects were constructed for the images using SExtractor (Bertin
& Arnouts, 1996) version 2.3.2. The images were scanned in double-image mode,
when the narrow band image is used for object detection and the flux is measured in
the same position in the broad- and narrow-band images.
2.2 Spectroscopy
It was necessary to spectroscopically confirm the candidates selected by their excess
in the narrow-band filter. A sample of the objects selected with the filter at 8200Å
were observed with two different double-arm spectrographs: TWIN 4 at the 3.5m telescope in Calar Alto observatory and ISIS5 at the WHT in ORM. The two instruments
were configured in a very similar mode. The red arm is centered on 8200Å to recover the Hα line with the maximum resolution available. This allows to resolve the
emission line from the OH lines of the background and to separate it from the neighbor [NII ]λλ6548,6584 lines. the blue arm is tuned to recover, with lower resolution,
[OII ]λ3727, [OIII ]λλ4959,5007 and Hβ.
3 Selection of candidates using narrow-band filters
The selection of candidates to be emission-line galaxies is made comparing the flux in
a narrow band centered in the emission line and a broad band filter used to probe the
continuum.
The notation used in the formulae of this sewction is sumarized in Table 1.
1 http://www.ing.iac.es
2 http://www.caha.es/CAHA/Instruments/index.html
3 http://iraf.noao.edu/
4 http://www.caha.es/pedraz/Twin/index.html
5 http://www.ing.iac.es/Astronomy/instruments/isis/index.html
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Table 1: Notation used
Symbol
Magnitude
Units
dimensions
N
n
g
t
AT
fλ
fL
T (λ)
Q(λ)
Counts
Counts per second
Gain
Exposure time
Colector area
Flux per λ interval
Flux of the emission line
Transmission
Quatum efficiency
ADU
ADU/s
e− /ADU
s
cm2
erg cm−2 s−1 Å−1
erg cm−2 s−1
-
[T−1 ]
[T]
[L2 ]
[ML−1 T−3 ]
[M T−3 ]
-
3.1 Flux and equivalent width of the emission line
The flux of the object is proportional to the number of counts N :
Z
λ
1
fλ dλ
N = AT t TT (λ) TF (λ) Q(λ)
g
hc
(1)
To lighten the notation, we introduce the effective transmission of the filter Tb(λ),
defined as the product of the transmissions of the telescope TT (λ), of the filter TF (λ)
and the quantum efficiency Q(λ)
Tb(λ) ≡ TT (λ) TF (λ) Q(λ)
(2)
The next definitions will be of use:
∆ ≡
λ ≡
λ2
≡
λn
≡
R
T (λ) dλ
T
R max
λ T (λ) dλ
R
T (λ) dλ
R 2
λ T (λ) dλ
R
T (λ) dλ
R n
λ T (λ) dλ
R
T (λ) dλ
The mean value of the flux through the filter will be:
R
Z
fλ Tb(λ) λ dλ
1
fλ = R
fλ Tb(λ) λ dλ
=
Tbmax λ ∆
Tb(λ) λ dλ
(3)
(4)
(5)
(6)
(7)
where the definition of λ (equation 4) has been used and Tbmax is the maximum value
of the effective transmission.
Using the equation 1, the number of counts is:
N=
1 1
AT t Tbmax λ ∆ f λ
g hc
(8)
We will recover the equivalent width (EW) and the flux line from the magnitudes
in the two filters. We will suppose that the flux per unit wavelength of a galaxy at
a redshift z with a emission line, with rest wavelength λ0 , can be expressed in first
approximation as:
fλ = fλc + fL δ(λ − λz )
(9)
The wavelength λz of the emission line is λz = λ0 (1 + z).
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The mean flux inside a filter of a object with flux given by equation 9 is calculated
using equation 7. As the result does not depend on the normalization of the transmission Tb, we introduce the normalized effective transmission Tb :
Tb (λ) ≡ Tb(λ)/Tbmax
(10)
The mean flux inside a filter is:
R
R
fλ Tb(λ) λ dλ
fλ Tb (λ) λ dλ
Tb (λz )λz
fL
fλ = R
= R
= fλc +
∆λ
Tb(λ) λ dλ
Tb (λ) λ dλ
(11)
The object is observed with two filters, denoted as A (broad) and E (narrow). The
flux inside each filter is:
A
f λ = fλc +
TbA (λz )λz
fL
∆A λ A
E
f λ = fλc +
TbE (λz )λz
fL
∆E λ E
(12)
1
fL
∆0E
(14)
As it is shown, the mean flux depends on the transmission of the filter on the redshifted
wavelength of the emission line λz . To take into account this, we introduce a new
quantity, the corrected width of the filter:
! ∆
λ
0
(13)
∆ ≡
b
λ
z
T (λz )
so equation 12 can be rewritten as:
A
f λ = fλc +
1
fL
∆0A
E
f λ = fλc +
From equation 14, we can work out the value of the line flux and the continuum flux:
fL
=
∆0A ∆0E E
A
fλ − fλ
0
0
∆A − ∆ E
A
fλc
=
(15)
E
f λ ∆0A − f λ ∆0E
∆0A − ∆0E
(16)
We define now , the quotient of the widths of the filters (usually 1):
≡
∆0N
∆0B
(17)
Rewriting equation 14, we have:
fL
fλc
EW
1
E
A
= ∆0E f λ − f λ
1−
1 − Q
A
= fλ
1−
1
fL
0
=
∆
(Q
−
1)
≡
E
fλc
1 − Q
(18)
(19)
(20)
where Q is the quotient of the fluxes of the filters and is defined as:
E
Q≡
fλ
A
(21)
fλ
Therefore, the measured flux line depends on the difference between the fluxes on
the two bands and, in first approximation, is proportional to the corrected width of the
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narrow filter. The EW depends only on the quotient of fluxes in the two bands and it is
proportional (in first order of ) to the corrected width of the filter.
There exists an upper limit to the color mA − mE that a object with a emission line
can have due to the presence of the emission line:
Qmax =
lim Q(EW) =
EW→∞
1
(mA − mE )max = 2.5 log Qmax = 2.5 log
(22)
∆0A
∆0E
(23)
3.2 Luminosity of the objects
The luminosity of the object is obtained from the line flux, calculated with equation 18.
We expect that the majority of the candidates will be Hα emitters and postpone the discussion on contaminants to Section 4.1. The lines of the [NII ]λλ6548,6584 doublet are
separated from Hα less than 20 Å. As the width of the filters is lesser than ∼ 50Å it is
necessary to correct their contribution to the flux assigned to the line. We have assumed
Hα/[NII ]=2.3. This values has been obtained by Kennicutt (1992a) and Gallego et al.
(1997). It is also the mean value for the galaxies of the UCM survey (Gallego et al.,
1996).
The mean value is generally used in studies with Hα where the doublet cannot be
resolved, for example: Tresse & Maddox (1998); Yan et al. (1999); Iwamuro et al.
(2000); Pascual et al. (2001); Fujita et al. (2003); Umeda et al. (2004).
Another issue is obscuration. Obscuration is well known to affect measurements
of galaxy luminosity at optical wavelengths. AHα = 1m is assumed for emission line
measurements, often found as the average extinction to Hα emission in samples of
local galaxies (e.g., Kennicutt, 1983, 1992a; Hopkins et al., 2003). We correct also for
the small amount of the galactic obscuration in the broad band with the COBE/DIRBE
& IRAS/ISSA dust maps of Schlegel et al. (1998).
The equivalent width calculated with equation 20 is measured in the observer’s rest
frame. The equivalent width in the object’s rest frame (REW) is augmented by a factor
1 + z. Combining these effects:
REW(Hα) ≡
EW(Hα) =
1
EW(Hα)
1+z
1
EW(Hα + [NII ])
II ]
1 + [N
Hα
(24)
(25)
The luminosity of the emission line it is obtained after correcting from obscuration
and the contribution of the [NII ]λλ6548,6584 doublet. The corrected flux is:
f0 (Hα) = f (Hα + [NII ])
1
100.4(AHα+AG )
[N
II ]
1 + Hα
(26)
and the luminosity is:
L(Hα) = 4πd2l (z)f0 (Hα)
(27)
where d2l (z) is the luminosity distance.
3.3 Mean colors
The key parameter to selection is the color excess. We have studied the color of stars
and galaxies to determine which of them and under what conditions could be misidentified with emission line galaxies. The color normalization is mA − mE =0 for the Vega
spectrum given by Colina et al. (1996); Castelli & Kurucz (1994).
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3.3.1 Colors of stars
First, we will deal with the colors of stars. We have used the library of stellar spectra of
Pickles (1998) 6 that includes stars of low and high metal content. In Figure 1 appears
the color mA − mE as function of spectral type, as well as the color of the blackbody
of effective temperature related with the spectral type by Aller et al. (1982).
We can see in Figure 1 that the stars follow in general the behavior of the black
body. It is in the latest spectral types, where the appearance of molecular bands varies
the trend. In the CAHA filters, the color drops for the late spectral types. For the
ORM filters, the color rises for the late spectral types. The difference in the behavior
is defined by the different shapes of the narrow and broad band filters.
The same analysis can be done with the filter around 9200Å. In Figure 2 we have
again the color of the stars, flat spectrum and black body as a function of temperature.
The tendency is very similar to the filter of 9200Å.
As a conclusion, we can see that the shape of the filters has a great influence on the
colors of the stars. The molecular bands cause the increase or decrease of the color of
the object.
Stars with emission lines Some types of stellar objects show emission lines in the
wavelength interval where the filters are defined. Novae, symbiotic stars, cataclysmic
variables (generally speaking: low mass stars, with either coronal activity or binaries)
can show emission in the line Pa9 (9229 Å). Close in time to a nova explosion there is
emission in the multiplet OI near 9261-9266 Å and the line HeII in 8236 Å.
There can be found also lines of NI and NaII between 8185 and 8242 Å (Rudy
et al., 2003). Massive stars, such as some Wolf-Rayet, can exhibit emission lines of
Pa9 (9229 Å) and in HeII+CIV (8236 Å) (Crowther et al., 2002).
The intensity of these lines is small and the types of stars are rare, so we will
suppose that they do not mold in the type of objects detected.
3.3.2 Colors of galaxies
The search of emission-line galaxies using narrow band filters is open to different lines
at different redshifts. The lines we expect to detect are Hα, Hβ, [OIII ]λλ4959,5007
y [OII ]λ3727 (Tresse et al., 1999; Kennicutt, 1992b). Figure 3 shows how the combination of redshift and rest wavelength makes the lines enter in the filters. Due to the
differences in the narrow band filters, in effective width as well as in central wavelength, the covered volume and the redshift of the detected galaxy are different.
We use templates of galaxies of Kinney et al. (1996) to calculate the mean color
as a function of the redshift in the tree filters used. In Figure 4 the color mA − mE is
represented as a function of redshift.
The behavior is slightly different in the two cases. In Figure 4(a) we can see that
the peaks of color are wider then the peaks visible in Figure 4(b). On the other side, the
color excess is larger in the WFC filter (about 1.5m ) than in the CAFOS filter (0.7m ).
The narrower filter (#209) is more sensitive to the EW (Equation 20). For a given
equivalent width, the filter #209 produces more contrast than the filter 816/16.
To end the discussion, in the Figure 5 we can see the behavior with the filter centered around 9200 Å. It has complex peaks, as the different spectral features enter inside
the filters. The narrow-band filters used, at 8200Å as well as 9200 Å are sensitive to
the emission lines and they are cable of detecting them efficiently.
3.3.3 Simulates images
We have computed simulated images, using a program developed by the authors for this
purpose. Figure 6 is a simulation where the sources of noise (read-out noise, photonic
noise) are not included. The uncertainty in the magnitudes in both filters is very small
6 http://www.ifa.hawaii.edu/˜pickles/AJP/hilib.html
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Spectral type
B5
A5
O5
8
F5
G5 K5
M9
5000
3000
G5 K5
M9
5000
3000
0.2
0
mA−mE
−0.2
−0.4
−0.6
I
II
III
IV
V
−0.8
−1
40000
20000
O5
0.6
0.5
mA−mE
0.4
12000
B5
8000
A5
F5
I
II
III
IV
V
0.3
0.2
0.1
0
−0.1
40000
20000
12000
8000
Effective temperature [K]
Figure 1: Mean color of spectra of stars and a black body for the filters centered
around 8200 Å. On top, the filters of CAFOS; on bottom, the filters of the WFC. The
black body is indicated with a line and the different luminosity classes (from dwarfs
to supergiants) is denoted with the symbols in the box. The dotted line represents the
color of a flat spectrum
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Spectral type
B5
A5
O5
1.6
F5
G5 K5
M9
5000
3000
I
II
III
IV
V
1.4
1.2
1
mA−mE
9
0.8
0.6
0.4
0.2
0
−0.2
40000
20000
12000
8000
Effective temperature [K]
Figure 2: Mean color of spectra of stars and a black body for the filters centered around
9200 Å. The black body is indicated with a line and the different luminosity classes
(from dwarfs to supergiants) is denoted with the symbols in the box. The dotted line
represents the color of a flat spectrum
1.8
1.6
1.4
Hα
[OIII]
Hβ
[OII]
1.2
z
1
0.8
0.6
0.4
0.2
0
7000
7500
8000
8500
9000
9500
10000
Wavelength [Å]
Figure 3: Wavelength of the emission line depending on the redshift of emitter galaxy.
Each emission line is represented by lines rising with wavelength. Hα in red, in green
[OIII ]λ5007, in light blue Hβ and finally [OII ]λ3727 in dark blue. The filters are
symbolized by the vertical lines. the CAHA filter in red color and the two WFc filters
in black.
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0.8
0.6
0.4
mA−mE
0.2
0
−0.2
−0.4
−0.6
−0.8
−1
−1.2
0
0.5
1
1.5
2
z
(a) Mean colors of the galaxies using the filters CAHA 850/150b and 816/16
2
1.5
mA−mE
1
0.5
0
−0.5
−1
0
0.5
1
1.5
2
z
(b) ean colors of the galaxies using the filters ORM #194 and #209
Figure 4: Mean color of the spectra of galaxies for the filters centered around 8200Å
as a function of redshift.
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2
mA−mE
1.5
1
0.5
0
−0.5
0
0.5
1
1.5
2
z
Figure 5: Mean color of the spectra of galaxies for the filters #194 and #208, centered
around 9200 Å as a function of redshift.
and due to errors on the measurement by sextractor only. Two types of spectra are
included: A0V and K0III.
Without noise, the objects distribute in two thin lines, only affected by the errors
in the measurements. This can be seen on Figure 7. We show 2000 simulated stellar
(A0V) objects, with magnitudes between 15 and 20. With different colors are marked
color-magnitude diagrams with different noise contributions. In blue the measure without noise, in green read-out noise plus photonic noise only for the object and in red
read-out noise plus photonic noise for the object and the sky. We can see how the sky
noise contribution is significant about 17m and dominant about 18m .
The sky background contributes to increase the noise in the measure of the flux
of the objects and, consequently, in the color. In Figure 8 we show the results of
the simulations for three stellar spectra: A0V, M8III y M10III, using the instrument
CAFOS, in the 2.2m telescope at CAHA. The distribution of colors widens with the
fainter objects. The mean color is equal to the color shown in Figure 1.
3.4 Candidate selection
The candidates are selected by their excess in the color. We can obtain the line flux and
the equivalent width from the magnitudes in the broad and narrow band images.
3.4.1 Dispersion on the flux quotient
The measurement of the flux ob the object inside an aperture. the measure has a contribution from the sky and the object: NO+S . The number counts of the object comes
from the sky subtraction:NO = NO+S − NS .
The standard deviation associated to the pixels inside an aperture of size A is:
2 !
R
1 1
2
N +A
σ [N ] =
(28)
kc g
g
with kc the number of frames combined.
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0.02
0
mA−mE
−0.02
−0.04
−0.06
−0.08
−0.1
14
15
16
17
18
19
20
21
mE
Figure 6: Simulated selection diagram, without noise. Two types of stellar spectra are
included: A0V (mean color 0) and K0III (mean color ∼ -0.1). The scattered points are
produced when more than one object is inside the photometric aperture.
0.6
0.5
0.4
mA−mE
0.3
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
15
16
17
18
mE
19
20
21
Figure 7: Dispersion of the color with several noise sources. In blue without noise,
in red read-out plus photonic noise only for the source. In red, read-out noise plus
photonic noise for the source and the sky background.
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2
A0V
M8III
M10III
1.5
1
mA−mE
0.5
0
−0.5
−1
−1.5
−2
15
16
17
18
19
mE
20
21
22
23
Figure 8: Simulation with three different spectra. There is confusion in the classification of the spectral types for the faintest objects.
The σ of the number counts of the object is:
"
2 #
R
1 1
2
2
2
σ [NO ] = σ [NO+S ] + σ [NS ] =
(NO + 2NS ) + 2A
kc g
g
(29)
so the signal-noise ratio for the object is:
SNR =
√
NO
k c N0
=p
σ[NO ]
(NO + 2NS )/g + 2A(R/g)2
(30)
We are going to estimate the σ of the quotient of the fluxes in the broad and narrow
bands. We denote C the quotient of counts in both filters and c the quotient per unit
time. Using equation 8 we have:
R
tE TbE (λ) λ fλ dλ
NE
TbE λE ∆E tE
Q
(31)
C ≡
=
= max
R
A λ ∆ t
NA
tA TbA (λ) λ fλ dλ
Tbmax
A A A
R
TbE (λ) λ fλ dλ
NE /tE
tA
TbE λE ∆E
Q=C
c ≡
= R
(32)
= max
A λ ∆
NA /tA
tE
Tbmax
TbA (λ) λ fλ dλ
A A
As Q, C and c are proportional:
σ[Q]
σ[C]
σ[c]
=
=
Q
C
c
We can obtain σ as:
2 2 2 2
σ[Q]
σ[C]
σ[NOA ]
σ[NOE ]
=
=
+
Q
C
NOA
NOE
From equation 30 we introduce the number counts:
2
(NA + 2NAS )/g + 2AR2 /g 2
(NE + 2NES )/g + 2AR2 /g 2
σ[Q]
=
+
2
Q
k A NA
kE NE2
(33)
(34)
(35)
JENAM meeting 2004
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4
3
∞
2
3
1
102
0
0
−1
EW [Å]
mA−mE
10
2.3σ
2σ
1σ
−2
19
20
21
22
23
24
mE
Figure 9: Simulation of the detection of objects with CAFOS. Exposure times are
tA =500 s and tE =6000 s. The FWHM if the seeing is 1”. It is represented the curves
with Q ± nσ[Q], being n=1, 2 and 2.3.
We use c to put the expression as a function of nE only:
σ[Q]
Q
2
2
c
1 c2 nSE
1
1
1
+
+
+
+
=
gnE kE tE
k A tA
g k E tE
kA tA cS n2E
2 c2
1
1
R
+
(36)
+ 2A
g
kE t2E
kA t2A n2E
Of the three terms, the last one depends on the read-out noise and it is completely
negligible for long exposures.
Once that we know σ[Q], we can calculate the value of:
(mA − mE )∓ = −2.5 log (Q ± nσ σ[Q])
(37)
3.4.2 Discussion on the selection diagram
In Figure 9 we show how changes σ[Q] with the brightness of the objects in a simulated
image of CAFOS, at the 2.2m telescope of CAHA, with a total of 2000 objects, exposure times tA =500 s, tE =6000 s and FWHM of the seeing 100 . Two solid lines mark the
magnitude limits in the narrow (vertical) and broad (crossing) images. The maximum
color given by equation 23 is represented by a horizontal solid line. Finally, we have
the curves representing Q ± nσ σ[Q], with nσ : 1, 2 and 2.3. We have verified (after
2000 simulations with 2000 objects each) that the objects follow the Gauss statistics.
As can be seen from equation 36, σ[Q] depends on the exposure times in the two
bands and the brightness of the sky background. In figure 10 we show how varies the
selection curve (with nσ =2.3) with the exposure time in the two bands.
Analogously, we show the variation of the selection curve with the sky background
in figure 11. Increasing the sky background magnitude increases the magnitude limit
of the images and changes the inclination of the selection curve.
The selection of the candidates is made at a level of separation from the mean that
the presence of a object without emission line is little probable. Experience shows that
JENAM meeting 2004
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4
tA=200
tA=500
tA=800
tA=1100
3.5
3
mA−mE
2.5
2
1.5
1
0.5
0
19
20
21
22
23
24
mE
4
4
3.5
3.5
3
3
2.5
2.5
mA−mE
mA−mE
Figure 10: Selection curves with varying exposure times. The broad band exposure
times are 200, 500, 800 and 1100 s, where as the exposure time in the narrow band
filter is 800 s
2
2
1.5
1.5
1
1
0.5
0.5
0
0
19
20
21
22
23
19
24
20
21
4
4
3.5
3.5
3
3
2.5
2.5
mA−mE
mA−mE
22
23
24
22
23
24
mE
mE
2
1.5
2
1.5
1
1
0.5
0.5
0
0
19
20
21
22
mE
23
24
19
20
21
mE
Figure 11: Selection curves with varying sky background. From left to right and top
to bottom, the magnitude of the sky background is 17, 17.5 18 and 18.5 m arcsec −2 .
JENAM meeting 2004
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nσ =2.3 is a good level of compromise. After the selection, it is necessary to check
that the object is truly a galaxy. This can be done using the stellarity parameter of
SExtractor.
3.4.3 Sensitivity to the emission line
We know how to relate the broad and narrow band magnitudes with the parameters
of the line. We have also developed the relationships needed to select candidates to a
certain signification level. Finally, we address the question of “how is distributed the
flux line on the selection diagram?”.
We start from equations 14. If we suppose the line flux constant, we can put the
magnitudes and the color, as a function of the line flux and the equivalent width only:
1
1
(38)
mA = KA − 2.5 log fL − 2.5 log
+ 0
EW ∆A
1
1
mE = KE − 2.5 log fL − 2.5 log
(39)
+ 0
EW ∆E
!
1 + EW
∆0E
(40)
mA − mE = 2.5 log
1 + EW
∆0
A
where KA and KE are the photometric zero points for the bands.
In the case of fixing the continuum flux and the equivalent width, we have:
EW
mA = KA − 2.5 log fc − 2.5 log 1 + 0
∆A
EW
mE = KE − 2.5 log fc − 2.5 log 1 + 0
∆E
(41)
(42)
With the knowledge of the parametric form of color and magnitude as a function
of EW, we can put limits for, e.g., the luminosity of the objects. In Figures 12 and
13 we show magnitude-color selection diagrams with the filters used in this studies.
The isolines of continuum flux, line flux, luminosity and broad-band magnitude are
represented with lines in red, green, blue and pink.
When, maintaining constant the line flux, the equivalent width increases, the total
flux decreases, with the magnitudes in the two filters decreasing whereas the color
increases. If we maintain constant the continuum flux, when we increase the EW the
line flux increases also. This increases the magnitudes in the bands and the total color.
The two diagrams are different in sensitivity. That is, for given magnitudes m A and
mE , we detect objects with fainter flux line in the case of using the filters of the WFC.
This is due to the lesser width of the narrow-band filter. The disadvantage of using very
narrow filters is the need of more exposure time to achieve the same deepness in the
images.
4 The SFR of the Universe at z=0.24 and z=0.40
The observed fields were selected by being covered by the INT wide Survey (Irwin &
Lewis, 2001). For the fields, there is multicolor photometry available for the bands U ,
g, r, i y z.
For the filters centered on 8200Å, 521 objects on 13 pointings have been selected.
Of them, 26 are objects with stellar profiles (5%) and 127 (25%) are marginal detections. The rest are 359 (70%) objects detected in both bands. The total are covered
is 1.4 square degrees, therefore the density of candidates is 366 candidates per square
degree for a flux limit of (9 ± 2) 10−17 erg s−1 cm−2 .
For the survey with the filter centered on 9200Å, 586 objects have been selected
in 9 pointings. With a total area of 2.16 square degrees, this translates to a density of
JENAM meeting 2004
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CAFOS
3
∞
2
1
3
300
EW [Å]
mA−mE
10
100
30
0
−1
15
16
17
18
19
20
mE
4
∞
3
103
2
300
EW [Å]
mA−mE
WFC
100
1
30
0
−1
15
16
17
18
19
20
21
22
mE
Figure 12: Magnitude-color selection diagram . Isolines of continuum flux (red),
with curves of 10−17 and 10−16 erg s−1 cm−2 Å−1 for CAFOS and 10−18 , 10−17 and
10−16 erg s−1 cm−2 Å−1 for WFC; isolines of flux lines (green) 10−13 and 10−14 erg
s−1 cm−2 for CAFOS and 10−14 y 10−15 erg s−1 cm−2 for WFC; in blue isolines of
luminosity: L∗ y 0.1L∗ for the two instruments; isolines of broad-band magnitude (violet) from 17m to 20m for CAFOS, from 19m to 22m for WFC.
JENAM meeting 2004
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5
∞
3
103
2
300
1
100
EW [Å]
mA−mE
4
30
0
−1
15
16
17
18
19
20
mE
Figure 13: Magnitude-color selection diagram . Isolines of continuum flux (red), with
curves of 10−18 , 10−17 and 10−16 erg s−1 cm−2 Å−1 ; isolines of flux lines (green)
10−14 and 10−15 erg s−1 cm−2 ; in blue isolines of luminosity: L∗ y 0.1L∗ isolines of
broad-band magnitude (violet) from 17m to 20m .
271 candidates per square degree to a flux limit of (1.8 ± 0.2) 10 −16 erg s−1 cm−2 .
The density is lesser that the survey at z=0.24. Of the total of candidates, 164 are
stars (28%), 363 are objects detected on both images (62%) and 59 (%10) are marginal
detections.
4.1 Contaminants
The survey is open to different lines at different redshifts. The limit flux translates into
different luminosities for each line. Furthermore, each line is detected in a different
volume.
We make a first approximation to estimate the number of contaminants following
Jones & Bland-Hawthorn (2001). The luminosity function of Hα has been determined
for several redshifts, for example: Gallego et al. (1995) and Nakamura et al. (2003)
at z=0, Tresse & Maddox (1998); Hippelein et al. (2003) at z=0.24 and Yan et al.
(1999); Hopkins et al. (2000); Tresse et al. (2002) at z ∼1. The luminosity functions of
other important lines are obtained redimension the parameter L∗ of the Hα luminosity
function with mean line ratios of Kennicutt (1992a), weighted with the relative numbers
of galaxies of each kind (see Jones & Bland-Hawthorn (2001) and references therein).
The rest of the parameters are supposed equal to the Hα luminosity function.
The figure 14 shows the prediction of the number of objects for the lines Hα, Hβ,
[OII ]λ3727 and [OIII ]λλ4959,5007. The population of Hα emitters dominates clearly
at bright fluxes.
The fraction of contaminants depends on the limit flux of the survey. Figure 14
includes the limits as vertical lines.
4.2 Luminosity functions
Information about the quantity and distribution of the star formation can be obtained
building the luminosity function. We take into account the number of contaminants
JENAM meeting 2004
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1
Fraction of objects
0.8
0.6
Hα
[OIII]
Hβ
[OII]
0.4
0.2
0
−18
10
−17
10
−16
−15
10
10
−1
−2
Line of the flux [erg s cm ]
10
−14
1
Hα
[OIII]
Hβ
[OII]
Fraction of objects
0.8
0.6
0.4
0.2
0
10−18
10−17
10−16
10−15
Line flux [erg s−1 cm−2]
10−14
Figure 14: Differential fraction of objects with emission line Hα, Hβ, [OII ]λ3727 and
[OIII ]λλ4959,5007. On top the narrow band filter of CAFOS, on bottom the narrow
band filter at 9200Å of the WFC.
JENAM meeting 2004
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20
log SFR(Hα) [M yr-1]
1
2
0
CAHA 00
CAHA 01
-1
log Φ [Mpc-3]
INT 01
-2
-3
-4
PSfrag replacements
-5
41
42
43
-1
log L(Hα) [erg s ]
Figure 15: Luminosity function of the objects with the best fit to a Schechter function
of Gallego et al. (1995) (black), Tresse & Maddox (1998) (red) and Tresse et al. (2002)
(blue). The bars include only Poissonian uncertainties.
found.
The interval in redshift covered is very small, so we can build the luminosity function using the method V/Vmax (Schmidt, 1968) of this simple form:
Φ(log Li ) =
X 1
1
∆ log L j V (z)j
(43)
with | log Lj − log Li | < ∆ log L, where V (z)j is the comoving volume where the
object can be detected. the luminosity function has been calculated for the three campaigns at z=0.24 and the campaign at z=0.4. figures 15 and 16 show the luminosity
functions calculates, compared with Gallego et al. (1995) at z=0 (black) , Tresse &
Maddox (1998) (red) and Tresse et al. (2002) (blue). For figure 15, there is a small
correction for contaminants. The black empty triangle corresponds to the corrected
luminosity function.
With the given coverage of luminosities, we can fit a Schechter function to the LF.
We fix the parameter α to -1.3, the value in the local Universe (Gallego et al., 1995).
The result for z=0.24 is:
φ∗ = 10(−1.6±0.1) h3 Mpc−3
and
L∗ = 10(41.46±0.05) h−2 erg s−1
whether for z=0.4 is:
φ∗ = 10(−1.9±0.2) h3 Mpc−3
and
L∗ = 10(41.9±0.2) h−2 erg s−1
JENAM meeting 2004
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log SFR(Hα) [M yr-1]
0
1
2
-1
log Φ [Mpc-3]
-2
-3
-4
PSfrag replacements
-5
41
42
43
-1
log L(Hα) [erg s ]
Figure 16: Luminosity function of the objects with the best fit to a Schechter function
of Gallego et al. (1995) (black), Tresse & Maddox (1998) (red) and Tresse et al. (2002)
(green). The bars include only Poissonian uncertainties.
4.3 Star formation rate density
The Hα luminosity density is obtained multiplying the number of objects by the luminosity of each object and integrating.
Z ∞
L=
Lφ (L) d L = φ∗ L∗ Γ (α + 2)
(44)
0
The integrated luminosity density is 1039.9±0.2 h erg s−1 Mpc−3 for z=0.24 and (1.3±
0.8) 1040 h erg s−1 for z=0.4.
The active galactic nuclei (AGN) contribute to the Hα luminosity, although this
luminosity does not come from star formation. the contribution of the AGN is 8% in
the number of objects and 15% in the luminosity of the sample. Assuming that the
contribution have not varied to z=0.4, the corrected luminosity will be 10 39.2±0.2 h erg
s−1 Mpc−3 at z=0.24 and (1.1 ± 0.7) 1040 h erg s−1 Mpc−3 at z=0.4.
The star formation rate can be estimated from the Hα luminosity using (Kennicutt,
1998):
SFR(Hα) [M a−1 ] = 7.9 10−42L(Hα) [erg s−1 ]
(45)
Therefor, the star formation rate density is (0.07±0.02) h M a−1 Mpc−3 at z=0.24
and (0.10±0.07) M a−1 Mpc−3 at z=0.40. The AGN contribution is inside the error
bars.
Figure 17 shows the Madau plot with our results. All the points have been calculated using the same cosmology and the same conversion between SFR and luminosity.
The star formation rate calculated is a factor ∼1.3 times greater between z=0.24
and z=0.40 and a factor of 5 when compared with the local value of Gallego et al.
(1995). the evolution between the three redshifts can be expressed as ∝ (1 + z) β , with
β=4.8±0.2. If we take into account the over estimation of the SFR measured from
the photometric redshifts calculated at z=0.24 (25%) and we supose that it is equal at
z=0.40, we find that the evolution is ∝ (1 + z)β with β=4.1 ± 0.1. The evolution is
slightly more intense than the accepted value of ∝ (1 + z)3 and is compatible with a
strong increase in the SFR density of the Universe between z=0 and z=1.
JENAM meeting 2004
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0.1
22
Desplazamiento hacia el rojo
0.2
0.5
1
2
-0.4
40.6
PSfrag replacements
-0.8
40.2
-1
-1.2
39.8
-1.4
-1.6
39.4
-1.8
log L (Hα) [erg s-1 Mpc-3]
log ρ ? [M a-1 Mpc-3]
-0.6
-2
39
-2.2
0
2
4
6
8
10
Tiempo retrospectivo [Ga]
Figure 17: Evolution of the SFR measured with Balmer recombination lines the selection methods of the samples is encoded in the color. In blue when the selection
has been made directly with Hα. In green the SFR has been measured with Hβ. In
red the results of the UCM survey (z=0) and this work (z=0.24 and z=0.4). Finally
in black, the samples where the selection is not Hα-based. Points are: Gallego et al.
(1995) (red full triangle), Nakamura et al. (2003) (empty black circle), Gronwall (1999)
(blue cross), Brinchmann et al. (2003) (empty black square), Tresse & Maddox (1998)
(black empty triangle), Fujita et al. (2003) (empty blue circle), this work (red full triangle), Hippelein et al. (2003) (full blue square), Jones & Bland-Hawthorn (2001) (empty
blue squares), Tresse et al. (2002) (black asterisk), Glazebrook et al. (1999) (full black
circle), Hopkins et al. (2000) (full black triangle), Yan et al. (1999) (blue asterisk),
Iwamuro et al. (2000) (full blue circle), Moorwood et al. (2000) (full blue triangle); the
point measured with Hβ is Pettini et al. (1998) (full green pentagon).
JENAM meeting 2004
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-2
0
2
4
23
6
8
10
exponent β
Figure 18: Values of β for different surveys. From top to bottom (squares) Lilly et al.
(1996), Hammer et al. (1997), Rowan-Robinson et al. (1997), Hogg (1998), Cowie
et al. (1999), Flores et al. (1999), Mobasher et al. (1999), Haarsma et al. (2000), Jones
& Bland-Hawthorn (2001), Lanzetta et al. (2002) y Hα combined. The last point (circle) corresponds to this work.
Figure 18 shows the values of β for several surveys. the mean values is 2.5 and the
mean value for the surveys in Hα only is 3.6.
Acknowledgment
Based on observations collected at the Centro Astronómico Hispano Alemán (CAHA)
at Calar Alto, operated jointly by the Max-Planck Institut für Astronomie and the Instituto de Astrofı́sica de Andalucı́a (CSIC).
The Isaac Newton Telescope and the William Herschel Telescope are operated on
the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del
Roque de los Muchachos of the Instituto de Astrofı́sica de Canarias.
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