A&A 460, 681-694 (2006)
DOI: 10.1051/0004-6361:20065493
M. Hayes - G. Östlin
Stockholm Observatory, AlbaNova University Centre, 106 91 Stockholm, Sweden
Received 25 April 2006 / Accepted 5 September 2006
Abstract
Context. Numerous surveys are currently underway or planned that aim to exploit the strengths of the Lyman-alpha emission line for cosmological purposes. Today, narrowband imaging surveys are frequently used as a probe of the distant universe.
Aims. To investigate the reliability of the results of such high-z Ly
studies, and the validity of the conclusions that are based upon them. To determine whether reliable Ly
fluxes (
)
and equivalent widths (
)
can be estimated from narrowband imaging surveys and whether any observational biases may be present.
Methods. We have developed software to simulate the observed line and continuum properties of synthetic Ly
galaxies in the distant universe by adopting various typical observational survey techniques. This was used to investigate how detected
and
vary with properties of the host galaxy or intergalactic medium: internal dust reddening; intervening Ly
absorption systems; the presence of underlying stellar populations.
Results. None of the techniques studied are greatly susceptible to underlying stellar populations or the relative contribution of nebular gas. We find that techniques that use one off-line filter on the red side of Ly
result in highly inaccurate measurements of
under all tests. Adopting two off-line filters to estimate continuum at Ly
is an improvement but is still unreliable when dust extinction is considered. Techniques that employ single narrow- and broad-band filters with the same central wavelength are not susceptible to internal dust, but Ly
absorption in the IGM can cause
to be overestimated by factors of up to 2: at z=6, the median
is overestimated by
25%. The most robust approach is a SED fitting technique that
Key words: methods: observational - cosmology: observations - galaxies: high-redshift - galaxies: starburst
Galaxies hosting young, violent starbursts are expected to accommodate
numerous massive, hot stars that are bright in the far ultraviolet (UV)
regime.
UV photons with wavelengths shortwards of the Lyman break ionise their
local interstellar media (ISM), resulting in recombination
nebulae bright in hydrogen lines.
Two-thirds of the Lyman-continuum photons are reprocessed as Lyman-alpha
(Ly)
under the assumption of case B recombination, and it could be
expected that young starburst regions should be consistently
Ly
-bright.
Early observations of local star-forming galaxies with the International Ultraviolet Explorer (IUE) demonstrated this not to be
the case.
In small samples of relatively un-evolved galaxies (low dust and metal
content) Ly
was frequently shown to be absent or unexpectedly weak
(e.g.
Meier & Terlevich 1982;
Hartmann et al. 1988;
Calzetti & Kinney 1992).
Although dust could be invoked to explain the absence of
this FUV emission line,
Giavalisco et al. (1996)
demonstrated that pure dust
extinction could not explain the weak Ly
fluxes from any of the
galaxies in the IUE samples.
Instead results suggest that Ly
photons have
decoupled from the non-resonant continuum radiation, resulting in
line-photons escaping the host over significantly extended
path-lengths; thereby increasing their sensitivity to dust
(Neufeld 1990).
On the other hand, Neufeld (1991)
also found that resonance scattering can cause less attenuation of
Ly
photons compared to continuum if the ISM is multiphase:
if dusty, neutral clouds are embedded in a dust-free, ionised ISM,
resonance scattering can reflect Ly
photons from the surface of the
clouds, allowing them to diffuse out of the ISM relatively unattenuated.
Radiative transport in such multiphase, clumpy media has more recently
been studied by
Hansen & Oh (2006)
who found Ly
equivalent widths (
)
could be "boosted'' by factors
of 2-3.
In the local universe, the observational situation was
further-complicated by Ly
spectroscopic observations using the
Goddard High-Resolution Spectrograph (GHRS) and Space
Telescope Imaging Spectrograph (STIS) both onboard Hubble Space
Telescope (HST).
In a sample of 8 local starbursts,
Kunth et al.
(1998)
found that when Ly
is seen in emission, blueshifted Ly
absorption
features are also common, leading to P-Cygni-like profiles.
In the same study, O I and Si II UV absorption lines were
also blueshifted with respect to the ionised gas, indicating large-scale
outflows of the ISM with velocities up to 200 km s-1.
Mas-Hesse et al.
(2003)
demonstrated that varying Ly
profiles from starbursts are well
explained by an evolutionary super-shell model; over the lifetime of a
starburst, absorption, pure emission, and P-Cygni emission phases will
all be observed, depending on the properties of the outflow and viewing
angle.
If Ly
escape is associated with winds and photons can diffuse
through H I, low surface brightness Ly
emission may be expected
to span large areas, significantly more extended than the starburst
itself as probed by FUV emission.
Hence imaging becomes an efficient method by which the line can be
isolated.
This was the motivation for our HST survey using the Advanced
Camera for Surveys (ACS;
Kunth et al. 2003).
Such Ly
imaging studies are extremely sensitive to how the continuum
is subtracted and much supporting data is required in order to estimate
the continuum flux at Ly
.
We found in
Hayes et al. (2005)
that at least three off-line imaging observations are necessary in order
to estimate the continuum flux at Ly
.
We determined it necessary to sample the UV continuum slope and 4000 Å break
in order to disentangle the effects of age and reddening, allowing us to
estimate the flux due to continuum processes in the on-line filter from
synthetic models.
In our sample, luminous blue compact galaxy ESO 338-IG04 shows regions
of diffuse Ly
emission spanning several kpc, and patchy structure
consistent with an inhomogeneous and outflowing ISM.
In the diffuse regions
is shown to be very large (>
)
where continuum flux is weak, but integrated over the whole galaxy
is
20 Å, an order of magnitude lower.
Damped absorption with
-40 Å is also observed in some
central regions, demonstrating the sensitivity of Ly
to
small-scale variations in the ISM.
Due to its sensitivity to star-forming activity, high natural
equivalent widths (up to 240 Å;
Charlot & Fall 1993)
sensitivity to dust, and convenient spectral positioning in the FUV,
Ly
has long been considered a competitive tracer of primeval high-zgalaxies as they form their first generation of stars.
Partridge & Peebles
(1967)
suggested that in a collapsing H I halo, as much as 7% of the
gravitational energy could be radiated in the Ly
line.
While surveys that target continuum emission or utilise dropout techniques may
have been highly successful in recent years, they all share one common
weakness: a luminosity bias in favour of galaxies with strong continuum.
Such a bias leads to incompleteness at low luminosity
and these surveys would miss the numerous low-mass, star-forming
objects; the dominant species in the paradigm of hierarchal galaxy
formation.
The early days of high-z Ly
studies were largely unsuccessful (see
Pritchet
1994
for a review) and it was not until the late 1990's that searches for
high-z Ly
-emitters (LAE) became fruitful.
Despite the complications, high-z Ly
-emitting objects are now routinely
being discovered by imaging techniques
(Cowie & Hu 1998;
Rhoads et al. 2000;
Fynbo et al. 2003;
Kodaira et al. 2003;
Yamada et al. 2005),
fields surrounding massive objects
(e.g. Monaco et al. 2005), and
spectroscopic observations
(e.g. Kurk et al. 2004).
After much initial disagreement, the predicted and observed luminosity
functions (LF) of LAEs at high-z may be converging
(Le Delliou et al. 2005).
Interestingly however, a fraction of the LAEs uncovered in the high-zuniverse have very large measured equivalent widths
(Cowie & Hu 1998;
Malhotra & Rhoads 2002).
In the case of Malhotra & Rhoads (2002),
their LAE population at z=4.5 was shown to have a median
of
400 Å, 65% greater than the maximum value of 240 Å
(Charlot & Fall 1993)
that can
be generated by pure star-formation models with normal metallicities
and IMFs.
These authors interpreted this to imply that either these objects were
type II quasars or star-forming galaxies with very top-heavy IMFs or
zero-metallicity stars.
Subsequent X-ray observations with the Chandra satellite ruled out the
possibility that these objects could be AGN
(Wang et al. 2004).
Jimenez & Haiman (2006)
demonstrate how this (and other effects) can be explained if 10-30% of
the stars in these galaxies are primordial.
"Normal'' starburst conditions could still explain such high equivalent
widths but the system would have to be perfectly configured so
as to allow Ly
photons to leak out while dust blocks much of the
stellar UV radiation.
Another possibility is that this is the result of some other
astrophysical effect, external to the host galaxy that may cause certain
observational techniques to overestimate
when such narrowband
imaging techniques are used.
While Ly
may provide a "clean'' probe of the high-zuniverse, the common observational trade-off is evident: spectroscopic
studies may be rich in information regarding the line, while narrowband
imaging studies may be efficient for detections.
Future generations of high-z-optimised integral field units (e.g. the
Multi Unit Spectroscopic Explorer (MUSE) bound for ESO's VLT) have
the potential to provide significant advances in this area.
However, in the cases where narrowband imaging alone is used to derive
information about the line, it is essential to examine exactly how
efficient the technique is in doing so.
To our knowledge, no such comprehensive study has previously been
performed and this article represents the first step in doing so.
We here simulate how various survey techniques may estimate Ly
detection properties - line flux (
)
and equivalent width (
)
-
of galaxies at high-z.
The paper is organised as follows:
in Sect. 2 we describe the software;
in Sect. 3 we present the simulations we have performed;
in Sect. 4 we present and discuss some of the
more important results; and
in Sect. 5 we present our concluding remarks.
We assume a flat cosmology with
,
,
H0=70 km s-1 Mpc-1 throughout.
The Ly
galaxy simulation software follows a simple three-step
prescription:
(i) the restframe spectral energy distribution (SED) of a the
test galaxy is generated and the Ly
line is added;
(ii) the SED is redshifted and the effects of intervening material (IGM
absorption) are applied to the spectrum; and
(iii) the spectrum is convolved with various filter response profiles
and fluxes are computed.
Restframe SEDs of starburst galaxies are generated from the Starburst99 (hereafter SB99; Leitherer et al. 1999; Vázquez & Leitherer 2004) synthetic spectral models. No nebular emission lines are thought to be strong enough to significantly contribute to fluxes in the UV filters considered here (see Sect. 2.3 for a description of the filters) - filters are broad and continuum dominated, and in Hayes et al. (2005) we concluded that optical emission lines had negligible impact upon our study. Hence the SB99 spectra are used unmodified, free of nebular emission lines but including nebular continuum emission. The software was designed for flexibility and to cover as wide parameter space as possible, enabling the user to perform a wide array of parameter dependency tests. Spectra can be selected from the 1999 SB99 data-release, choosing star formation history (instantaneous burst or continuous star formation), composition (stellar-only or stellar+nebular), metallicity, initial mass function, and age. In addition to the standard set of spectra, SED modification code was written to allow the selection of:
![]() |
(1) |
Ly
is the only Lyman series feature added to the SED - the
O VI-Ly
-C II complex between 1032 and 1038 Å does not fall within any of the filter bandpasses considered here (Sect. 2.3).
The C IV
1549 Å absorption feature (although
frequently observed with P-Cygni profiles), common in star-forming
galaxies, does fall centrally in one of the bandpasses we use.
In a sample of 45 local galaxies observed with the IUE,
Heckman et al. (1998)
find a (C IV+Si IV)/2 median equivalent width of
-4.6 Å, with the
absorption features never stronger than -10.1 Å.
Crowther et al. (2006)
re-measured these equivalent widths, finding an offset of
1-2 Å relative to the Heckman et al. result.
The filter bandpass that the C IV feature falls in is broad
(
Å, centred at 1500 Å;
see Sect. 2.3) so the presence of the strongest locally
observed C IV feature would affect the integrated flux by only
3% with no redshift dependence.
Moreover, these authors found that this equivalent width is positively
correlated with metallicity.
Since strong Ly
emission is often interpreted as a sign of low-metallicity stars, we decided not to apply the C IV feature
to our SEDs.
In order to complete the restframe SED, it can be reddened using the Galactic laws of Seaton (1979), or Cardelli et al. (1989), the SMC law fit of Prévot et al. (1985), the LMC law of Fitzpatrick et al. (1985), and the Starburst law of Calzetti et al. (2000).
The restframe SED is first shifted to the desired redshift and the
luminosity distance
computed from the formula
![]() |
(2) |
Given that we want to study all the possible astrophysical effects,
including possible extreme cases, we chose
to treat the effects of intervening H I clouds by generating
random distributions of individual clouds, not by applying some
general average prescription (e.g. Madau 1995).
The effect of intervening H I clouds (Ly
forest (LAF) to
damped Ly
(DLA) systems) is implemented by first assuming the number
density of absorbing clouds
as a function of redshift takes the form of the power-law
in the redshift range 0 to z
where
N0 = 0.07+0.13-0.04 and
(Peroux et al. 2003).
Firstly the total number of clouds in the given redshift range is
generated by biasing a uniform variate pseudo-random number (PRN)
by the distribution function, within the observational constraints.
For each cloud, a position in redshift space is generated in the
same manner: by weighting a PRN by the distribution function.
The column density
of each cloud is generated by
assuming
the distribution obeys the power-law
(Rao et al. 2006)
for
and column densities in the range
.
Once the redshift-column-density distribution is generated, the effect
on the SED of each cloud is determined from its equivalent width
in absorption (
).
We compute restframe
from the effective optical depth
at line-centre (
)
following the curve of growth method
(Spitzer 1978).
After cosmological scaling
,
and the continuum flux-density at
are then used to
remove the requisite amount of flux from the appropriate bins in the
redshifted spectrum.
In cases where the absorption is damped (
is greater
than the bin size), the flux in that bin is set to zero and flux is
symmetrically removed from neighbouring bins until the required
has been met.
Significant attention has been paid to the possibility of
reddening of high-z quasar spectra by DLA systems (e.g.
Pei et al. 1991).
However, recent studies have demonstrated the typical mean cumulative
reddening from DLA systems to be small.
For example
Ellison et al. (2005)
found mean
EB-V < 0.04 at the
level for SMC-type dust in a
sample of 14 high-z quasars with DLAs, while from a sample of 72 DLA
quasars from the Sloan Digital Sky Survey,
Murphy & Liske (2004)
found mean
EB-V < 0.02 at
for SMC dust.
On the other hand,
Wild et al. (2006)
find evidence for significant reddening in Ca II and
Mg II absorbing systems:
EB-V = 0.105 for SMC type dust in
the selected strongest absorbers (
EB-V = 0.066 for their complete
sample).
Such objects are shown to be similar to DLAs with a number density of
20-30% that of DLAs at the same redshift.
While we do not claim that some high-z LAEs would not be heavily dust
reddened, we chose for this part of the study not to implement
dust-reddening by high-H I column-density systems.
At z=0, the redshifted SED can be reddened once more using the laws of Cardelli et al. (1989) or Seaton (1979) to simulate Milky-Way reddening.
For the sake of simplicity (our aim was to study astrophysical
processes, not observational complexities) the filters are perfect.
Defined only by their central wavelength and effective width, they
provide 100% transmission inside the passband and zero otherwise.
That is, the filters are as close to perfect top-hats as possible,
without introducing numerical, resolution-dependent inconsistencies
at the edges.
Narrowband filters targeting the Ly
line are defined to have
a full width of 2% their central wavelength
while
broadband filters have full widths of 20%
.
That is, the width of the broadband filters scales with
in approximately the same way as it does in the
Johnson-Cousins/Bessell and JHKLM systems. The narrowband filters
scale similarly so as not to introduce effects that may result from
sampling different spectral regions at different redshifts.
One issue that arises when using narrow filters to isolate an emission
line is the positioning of the line within the filter profile.
That is, is the line centrally positioned and narrow enough to allow
maximum transmission of the line flux?
Chemistry and manufacturing processes dictate that filters (particularly
narrowband)
cannot be perfectly rectangular and most frequently take the form of
bell-curves.
Whilst photometric redshifts or drop-out techniques may be used to
remove interlopers (most notably [O II]
Å),
photo-z's of individual objects do not reach the required levels of
accuracy to determine the position of Ly
within a narrow bandpass
(typical photo-z accuracies of
cannot determine
whether the line falls within a 2%
narrowband filter
or not).
In addition, photo-z methods tend to be reliant upon sampling the
Balmer/4000 Å break which is lost from optical multiband datasets at
,
something we discuss in another context in Sect. 4.
At high-z and without spectroscopic data, the selection of LAE
candidates by detection in the narrowband filter becomes the most
accurate estimate of redshift.
Hence effects that result from the line falling in the wing of a
filter will always be something that has to be considered.
Starburst galaxies do not exhibit significantly broadened spectral
lines: concerning Ly
,
Matsuda et al.
(2006)
spectroscopically measured the widths of 37 LABs at z=3.1, finding
Ly
full widths (FWHM) in the range
150-1700 km s-1 with a median
value of 550 km s-1.
This corresponds to a maximum Gaussian
of 3 Å at Ly
(median value of
1 Å).
Thus given the 2%
narrowband filters used here,
even the broadest Ly
lines will be completely transmitted (2%
rectangular filters drop to 99% of complete line transmission at
km s-1).
The bin size of our SEDs is 1 Å and, since the median
of the
Matsuda et al. study is 1 Å, we feel safe in depositing all of the Ly
flux in one bin (see Sect. 2.1).
"Observed'' fluxes in all filters are computed by convolution of the
profile and the spectrum, and integration.
In order to estimate true line-fluxes (
), it is essential to have
a robust estimate of the flux due to continuum processes that is present
in the on-line filter.
This estimate of the continuum flux at 1216 Å is central to
Ly
studies and here we use various methods to scale the nearby
continuum flux to Ly
(described below).
With estimates of the line and continuum fluxes, equivalent widths,
defined as
,
are computed, where
is the continuum flux density at
line-centre.
To this end, a number of different commonly implemented and feasible
observational techniques are employed from which
and
are
estimated.
For on-line observations, a narrowband (2%
)
filter is
used, centred at the observed wavelength of redshifted Ly
.
Broadband (20%
)
filters are positioned at various
wavelengths in the
redshifted SED in the UV and optical, sampling the restframe SED at
1216, 1500, 2200, 3300, and 4400 Å.
That is, filter wavelengths and full widths are defined in the
restframe - the same region of the SED is sampled at all redshifts.
Using these broadband filters, continuum flux at Ly
is estimated
using four techniques numbered (#1-#4) in order of the central
wavelength of the reddest filter used. A schematic
representation can be seen in Fig. 1.
![]() |
Figure 1:
Schematic diagram of filter positioning for the four
observational approaches described in Sect. 2.3 the text.
Narrowband filters (on-line, black) have widths of 2% their central
wavelengths and
broadband filters (continuum, grey) have widths of 20%
![]() ![]() |
Open with DEXTER |
The techniques are:
where F and W represent the flux and filter width, and subscripts n and b refer to the narrow and broadband filters, respectively. This is the same observational setup as used by Cowie & Hu (1998) and Fynbo et al. (2002), and dividing the first part of Eq. (3) by the second, one obtains the equivalent width expression used by Malhotra & Rhoads (2002).
Our simulations aim to understand the way in which astrophysical
conditions in the host-galaxy and inter-galactic medium (IGM) manifest
themselves in the determination of
and
.
To this end, we devised a number of different tests, varying
individually the parameters that describe the host galaxies,
in order to examine their impact.
In order to standardise the parameter setup, a "standard'' restframe
template was defined, the key parameters of which can be seen in
Table 1.
Table 1: The parameters of the "standard'' restframe SED.
By default, single stellar populations are treated, with the inclusion of
stellar and nebular emission, the relative contributions of which are
left unchanged.
Unless otherwise stated, the equivalent width of the Ly
line added
to the spectrum is 100 Å for ease of visualisation (i.e.
fractional/percentage deviations are easily interpreted).
No internal or Galactic extinction is applied to the spectra by default.
We determined it necessary to run tests to study the impact of redshift
and H I absorption along the line-of-sight, internal dust
reddening, and mixing of stellar populations.
Burst age is not considered in this paper for the following reason:
our preliminary tests showed that the recovery of
and
by all four techniques were self-consistent to within 2%, (no age
dependence on the recovered observables with age) over the first 200 Myr.
In addition,
Charlot & Fall (1993)
demonstrated Ly
in emission can only be expected from considerably
younger star-forming galaxies of ages
40 Myr; over this time we found
evolution in the observables below the 1% level.
Technique #2 allows for the UV continuum slope ()
to be arbitrarily
chosen.
In a large sample of LBGs re-sampled into quartiles according to
,
Shapley et al. (2003)
find median values of
for the strongest Ly
emitters
(upper quartile) with the continuum flattening to
for the
weakest, lower quartile where the median
is -14.92 Å.
In contrast, the Starburst99 models show
in the range -2.6 to -2.0
over the first
50 Myr.
Excess flux in a narrowband filter (n-b < X) is a typical selection
function although the amount of excess X is arbitrarily chosen.
X=0 would correspond to a flat continuum, whereas X<0 would imply the
continuum level is rising towards Ly
.
While X can be computed by making some simple assumptions, the range
in the power-law index (
)
from which X would be computed
can be very large.
Without any additional data to constrain the continuum slope, any
assumption is ad hoc but, for the sake of simplicity, in the simulations
presented here we assume
(i.e. a flat continuum).
Moreover, only a modest dust content is required to flatten the steep
continuum slopes observed in the FUV.
Additionally, it should be mentioned that the Eq. (3)
(technique #1) only holds exactly if
,
although the total
spectral region sampled by this technique is much smaller.
It would also be interesting to simulate more realistic samples of
galaxies.
The Ly
luminosity function has been compiled at z=5.7 and 6.5
by
Malhotra & Rhoads (2004).
However, while spectroscopic observations were used in the compilation
of these luminosity functions for statistical purposes, the luminosities
of the LAEs themselves have been derived photometrically.
Hence, they may well contain observational biases of the type we attempt
to address here.
Additionally, we would have to assume the characteristics of the
observation itself such as sky-noise and
it was deemed more revealing to study populations of identical objects.
Again without the effects of intervening H I systems, we
investigate how accurately
and
are recovered when the
Ly
emitting object hosts varying components from an underlying
population.
This is mainly relevant to technique #4 which relies upon sampling of
the 4000 Å break, and, while we don't study
or
vs.
age directly, this study addresses the effect an aged stellar population
may have.
As before we adopt the default template spectrum as a "primary''
SED
(i.e. the single stellar population starburst spectrum defined in Table 1 with an age of 4 Myr).
We then add an assortment of older, post-starburst spectra to the
primary, scaling to varying normalisation factors at a
wavelength of 4500 Å (i.e. scaling by the approximate B-band
luminosity).
We thereby artificially create young starburst galaxy spectra with a
population of older stars.
This normalisation factor is designated n4500 and, by this
definition:
n4500=0 is just the default SED defined in Table 1;
n4500=1 means the default and aged populations
contribute equally at 4500 Å; and
n4500=10 means the old
population is a factor of 10 more luminous than the starburst SED at
4500 Å.
The parameters used in the generation of SED of the underlying
population can be seen in Table 2 but briefly, we perform
tests to examine the age of the underlying population, its metallicity,
and its normalisation coefficient, n4500.
Then, after redshifting the SEDs, we investigate what values of
and
our techniques recover.
When the SED-fitting technique is used (technique #4), we always used
the unmodified set of starburst templates for fitting.
Tests are performed at redshifts of 2, 4, and 6.
Table 2 shows the different old stellar populations
and their contributions as applied to the standard setup, along
with the resulting
calculations.
Table 2:
The influence of old stellar populations on detected
- the
effects of age and metallicity.
As described in Sects. 2.3 and 3.1 we
generate populations of galaxies at a given redshift, and
determine the mean, median, and refined mean values of observed
and
for this population using the four observational
techniques.
Figure 2 shows a set of histograms representing the
distribution of these observed quantities for a population of 10 000 galaxies
at z=5.7, selected to correspond to the redshift of number of Ly
surveys (e.g.
Thommes et al. 1998;
Rhoads & Malhotra 2001;
Westra et al. 2005).
Restframe
is 100 Å.
![]() |
Figure 2:
Histograms showing the distribution of detected Ly![]() ![]() ![]() ![]() ![]() |
Open with DEXTER |
A noteworthy feature, present in all these plots is the population of
750
galaxies with
and
around zero (and slightly
negative).
In the line-of-sight to these objects a DLA system has been generated
near to the target LAE, the red damping wing of which has removed the
Ly
line from the spectrum.
The slight negativity of these values comes from the fact that, in order
to estimate the line-only flux, the continuum has been subtracted and,
in all these cases, continuum subtraction has resulted in negative
fluxes in the line.
These objects would not be found by imaging observations that target
emitters and hence
including them in the computation of average quantities would be
misleading.
This effect therefore leads to a redshift-dependent
incompleteness, which at z=6 is about 10% for these filters.
Such effects would need to be treated in the computation of the Ly
luminosity
function.
It is for this reason that we compute refined mean values for the
population of objects with detected
> 20 Å only.
Dashed vertical lines have been added to all these histograms in three
colours.
The red line shows the flux or equivalent width of the Ly
line that was
added to the restframe spectrum, the green line shows the mean of the
recovered quantities, and the blue line shows the refined mean.
The top pair of plots in Fig. 2 represent the
quantities as determined using technique #1 (a narrow and broad filter
centred at
).
The
histogram shows a strong peak in the distribution that
perfectly corresponds to intrinsic line flux.
The mean of the distribution falls 15% short of this value.
The coincidence of the peak in flux distribution and intrinsic flux
demonstrates the power of this method in determining line flux.
The top right panel in this figure shows the distribution of
when
computed by this technique (#1).
While
is accurately recovered and evenly distributed around the
correct value, the
distribution cuts on
sharply at
= 100 Å, peaks, and exhibits a long tail, extending to
220 Å.
While some flux may be removed from the narrowband filter by intervening
H I clouds, the broadband filter samples the continuum
significantly bluewards of Ly
.
Hence H I clouds in the IGM can remove a significant amount of flux
from this broadband observation.
Consequently, the continuum flux at Ly
can be drastically underestimated,
resulting in a doubling of observed
in extreme cases.
The black dotted line in this plot shows the fraction of objects with
recovered
greater than the value on the abscissa.
It crosses the red dashed line (100 Å) at 0.8, implying that
has
been overestimated for 80% of all the objects (including those
with
0 that represent the incompleteness in the observed
population).
After removing the
0 Å objects, this fraction is more like 90%.
![]() |
Figure 3:
The evolution of
![]() ![]() ![]() ![]() |
Open with DEXTER |
The second pair of plots represents the distribution of the same detection
properties, as determined by technique #2.
Here the same on-line filter is used but a single broadband filter
centred at
Å is used to estimate the
continuum at Ly
by assuming
between the spectral regions
sampled by these filters.
Since our standard restframe template is that of a 4Myr starburst with
no dust, the continuum is increasing towards the line
(
)
and the subtraction of an underestimated continuum results in a slight
shift of the distribution towards higher fluxes.
In this case where the line is strong, the measured flux in the
narrowband filter is dominated by the line, and the relative effect of
underestimating the continuum is small.
We have verified that the effect is more significant when smaller rest
equivalent widths are input (i.e. continuum-dominated observations).
In this example, underestimating the continuum
flux has a more pronounced impact upon the estimate of
and
the mode in the
distribution is shifted from 100 Å to
170 Å.
While technique #2 may provide reliable line-fluxes when the line is
strong, any equivalent widths derived in this manner cannot be
considered robust.
Even if there is no line (
= 0), for a young, unreddened burst
with
,
the assumption of
will result in a positive
observed equivalent width and false positive detection of narrowband excess.
Techniques #3 and #4 reliably reproduce both
and
in this study.
Technique #3 assumes the UV continuum slope to be a power-law between
2200 Å and Ly
and uses off-line filters placed at restframe 1500
and 2200 Å to extrapolate to Ly
.
Technique #4 makes no assumptions about the continuum, and uses a
4-filter SED-fitting technique to estimate the continuum level at Ly
.
With the exception of the small peaks around
and
= 0, these
distributions are strongly peaked around their intrinsic values.
The narrow distribution of
demonstrates how successful these techniques are at estimating the
continuum fluxes at line-centre.
The refined mean values of
are in error by only
5%.
In reality, all the accuracy of all these results would be dependent on the recovered flux in the various bands and the sky-noise. While this is not strictly the angle we have chosen for this article, we investigate and discuss the effects of sky noise below. Figure 4 demonstrates how the various techniques fare near the detection limit with the application of a simple sky-noise model.
Figure 3 shows the evolution of the total mean, refined
mean, and median values of
and
as a function of redshift.
The blue curves represent technique #1, green curves technique #2,
red curves technique #3, and black curves technique #4.
The flux values are the average observed fluxes, normalised by the computed
intrinsic line
flux at the observatory (i.e. the intrinsic line-luminosity scaled down
by the luminosity distance).
As previously discussed, technique #1 reliably recovers
in the
line-dominated limit and this is here demonstrated to be independent of
redshift.
However,
as computed using this technique becomes progressively
worse with increasing redshift as can be seen from the right plot
- the refined mean value for
at z=6.5 is overestimated by 20%.
This is a result of the increasing redshift-density of intervening
clouds with redshift (
(1+z)2.45), causing a systematic
decrease of the estimate of the continuum flux.
Technique #2 overestimates
by
10% at z=2.
This results from the assumption of a flat spectrum not accounting for
the blue continuum slope of a young stellar population.
This technique is unreliable in estimating
and at all redshifts
as the right plot shows, never comes close to estimating the correct
.
Again as demonstrated in Fig. 2, techniques #3 and
#4 both reliably determine
and
at low and high redshift
- the refined mean values of
deviate from the expected values by
less than 9, and 5%, respectively, at z=6.
It is, of course, possible to fit a function to any of the
redshift-evolution curves shown in Fig. 3,
thus obtaining a functional prescription for the fractional under- or
over-estimate of
and
as a function of redshift.
Such a formula would be highly desirable as it would be directly
applicable to the results obtained by previous surveys.
However such a corrective formula would not only be a function of
redshift, but also of the filter widths, response profiles, and
positioning in wavelength.
Of course, such information is well-known and we recommend simulations
to be carried out on a survey-by-survey basis, and with appropriate
consideration of the errors and selection criteria.
![]() |
Figure 4:
Histogram showing the detected
![]() |
Open with DEXTER |
Malhotra & Rhoads (2002) used a technique similar to
technique #1 to observe LAEs at a redshift of 4.5, uncovering a
population of galaxies with curiously high equivalent width (median
400 Å).
Since there is no AGN activity associated with these objects (Wang et al. 2004) and
the maximum
available from star-formation (with "normal'' IMFs and
metallicities) is 240 Å
(Charlot & Fall 1993),
such a discovery attracts speculation.
Using our simulations we determine that at z=4.5, the median value of
may be overestimated by a factor of only
12% - clearly
Malhotra & Rhoads'
high-
result is not
an observational effect of the type under consideration in this article.
However, the effect of intervening H I on
as computed
by technique #1 is that a large spread in
is produced (see Fig. 2, top right), leading to
a significant fraction of LAEs with overestimated
- 20% of all the
objects have
overestimated by more than 40%.
Certain selection functions (e.g. narrowband excess) will then be more
inclined to pick up these objects.
![]() |
Figure 5:
Recovered
![]() ![]() |
Open with DEXTER |
In order to further investigate some more realistic observational effects,
we implemented a simple noise model.
Taking the fluxes obtained from the population of objects shown in Fig. 2 (10 000 objects at z=5.7 with
= 100 Å),
we assumed that the criterion for a "detection'' is
.
We then assigned a S/N = 5 to each narrowband flux, and weighted this by
the ratio of detected
to the intrinsic line flux
(
).
S/N was assigned to the broadband observations in an identical manner: 5 weighted by the ratio of the observed flux to the intrinsic flux.
Note this weighting modification of S/N=5 is only applicable to the
broadband filter centred at Ly
- the redder filters are not affected
by H I clouds in the IGM, and all have S/N=5.
With
for all the observations, we used Box-Muller transforms to
generate Gaussian deviates around the fluxes in each passband.
We fed these fluxes back into the expressions used to derive
and replotted the resulting distributions of
which can be seen in
Fig. 4.
In all cases, the main distribution is now significantly broadened;
the mode has shifted towards lower values of
,
and a high
tail has been produced.
This results from the fact that equivalent width is the quotient of two
values
.
Symmetrical redistribution of the denominator results in asymmetric
redistribution of the combined quotient; compressed on the low side of the mean
(lowering the mode) and extended at high values.
This is most striking using technique #1 since signal in the broad
filter is lost to H I absorption in the IGM -
20% of
objects have
overestimated by a factor of 2.
Still the number of objects scattered to very high
is small
overall, we reiterate that some selection criteria will include them:
in a narrowband survey they are likely to exhibit clear narrowband excess.
Redistribution of Ly
has caused the plots for all techniques to
appear similar: modes have been reduced slightly and extended,
high-
tails are present.
One noteworthy feature about the progression from technique #1 through #4 is the movement of the refined mean of the distribution (blue
vertical line) towards the intrinsic value of 100 Å, and for the same
reason, the steepening of the black dotted line.
The addition of more filters is necessary to prevent the extreme spreading
of the distribution and scattering to extreme values of
.
For technique #4 the refined mean value now accurately recovers the intrinsic
values of
,
and
is overestimated by more than 50% for very few
objects.
The tests presented here showed indistinguishable results at redshifts
of 2, 4, and 6, hence the results we present regarding reddening can be
assumed to be independent of redshift.
Figure 5 shows how well
is recovered
for some test cases when dust is added to the system.
The internal reddening for a given extinction law (type of dust) is
represented on the abscissa of the
plots, while the recovered value of
is presented on the ordinate.
Where the SED-fitting technique (#4) is concerned, the assumed
extinction law used by the SED-fitting routine may be different from that
used to redden the restframe
SED and can be seen in the central caption of each figure.
In the tests presented here we only redden the restframe SEDs using the
Calzetti and SMC laws because all other laws show a 2175 Å graphite
feature.
If we believe we are dealing with objects with a very strong UV
radiation field, larger graphite-based molecules will be destroyed,
removing any 2175 Å feature from the reddening vector and producing a
law similar to that of the SMC
(Mas-Hesse & Kunth 1999).
We now only consider the impact upon the determination of
,
having
shown it to be a much more sensitive performance indicator than
.
Intervening H I absorbing systems have been "switched off'' for
this experiment.
The range in
0.0 < EB-V < 0.5 is chosen.
Technique #1 (blue line) is here demonstrated to very accurately recover
in all cases shown.
At
EB-V=0.5 this technique overestimates
by just 3% using the
Calzetti law (central panel) and the technique is largely insensitive to dust.
This minor effect is a result of the steepening extinction curve removing flux
from the broad bandpass, leading to a mild overestimate of the continuum
flux at Ly
.
Conversely, this technique underestimates
by 13% for SMC-type
dust (left panel).
Across the wavelength range of the 1216 Å-centred broad bandpass
(
to
), the
SMC-law provides more extinction than the Calzetti law for a given EB-V,
and has a steeper gradient (more rapidly increasing with decreasing
wavelength).
This results in the stronger suppression of the Ly
line with the SMC law
than that of Calzetti, and turns the mild overestimate of
into a
more significant underestimate.
Technique #2 (green lines) is highly ineffectual at reproducing the
intrinsic
equivalent width when dust is added to the system.
This is also dependent upon the chosen extinction law: SMC-type dust
(left panel)
completely suppresses the unreddened excess of a
= 100 Å line
relative to the 1500 Å flux by
EB-V=0.48.
That is, using technique #2, at
EB-V>0.48 an LAE of
= 100 Å will be seen as a Ly
absorber.
This effect is nowhere near as extreme when the Calzetti law is applied
since the SMC law is significantly steeper in the FUV.
Modeling the UV continuum ()
as a simple power-law (technique #3; red lines) and extrapolating to Ly
only performs marginally better in the
presence of dust.
A clear downward trend is visible with EB-V, although the
dependency is highly sensitive to the extinction law.
At the relatively modest value of
EB-V=0.1, a Ly
emitting object
will have
underestimated by around 10% using the Calzetti law
but by 25% for SMC dust.
By
EB-V=0.5 using the Calzetti law,
is underestimated 30%,
while for SMC dust the line has been almost completely suppressed.
Extrapolating
does not provide a reliable estimate of
when even a modest amount of dust is present since the dust
extinction curve modifies
in such a way that it becomes
inconsistent with a power-law approximation.
The dashed lines in Fig. 5 show how recovery of
is
only very slightly improved when the continuum filter sampling 1500 Å is
moved to 1400 Å.
Of course, it stands to reason that moving the off-line filter nearer to
the line is going to yield a better result and this is something that
must be considered when designing any observation - even when the
filters can be ideally placed (which is also subject to the presence of
sky lines), the gain may not be significant.
Clearly technique #1 is not greatly susceptible to the effects of internal
dust reddening.
In contrast, techniques #2 and #3 are highly susceptible to dust and
these observational configurations do not provide enough information to
handle any reddening in a reliable manner.
Continuum extrapolation techniques are not sufficient and a technique is
required that either handles the reddening explicitly or covers a
sufficiently narrow spectral domain.
Indeed, the technique #4 also becomes increasingly unreliable with
increasing dust content if the extinction law/dust type is not well
known - assuming the wrong dust type renders the SED fitting method
ineffective (Fig. 5, left panel).
However, the 2200 Å continuum filter is well positioned to sample the
2175 Å graphite feature in the reddening vector.
This enables a third dimension to be added to the SED-fitting routine:
the discrete parameter of the dust extinction law.
By fitting age, extinction law, and EB-V, we are able to recover
to within 1% for all values of EB-V for each of the extinction
laws.
See the central panel of Fig. 5 for and example using
Calzetti law.
Due to concerns about fitting three parameters with noisy data,
we adopted a similar noise-model to that described in Sect. 4.1.
Of particular concern was whether we could accurately recover the
extinction law.
All fluxes were assigned S/N=5, randomised within the
corresponding Gaussian ,
and plugged back into the formulae to
compute
.
We now generate 1000 LAEs for each point in EB-V, and compute
the mean values recovered.
Since there are no H I IGM clouds in this simulation, there is no
non-recovered population to that needs to be taken into consideration.
The results can be seen in the right panel of Fig. 5.
Clearly, at the
limit, the concerns about recovery of the
reliability of the fitting routine are not serious - the SED fitting
routing recovers
to within 3% in all cases.
Obtaining such observations of continuum-faint objects at high-z requires a
substantial investment of time; many narrowband Ly
surveys find a significant population of objects with no apparent UV or
optical continuum.
This is one of the areas in which the class of extremely large optical
telescopes has the opportunity to make a significant impact:
with gains in collecting area of a factor of 25, restframe UV detections
of dusty systems may become more of a possibility.
This is one of the reasons why we push this study to
seemingly extreme values of EB-V.
If detections can be made, this will be of importance given that many
Ly
blobs (LABs) have been detected by narrowband imaging observations.
A significant fraction of these LABs are also bright sub-mm sources
(Chapman et al. 2005;
Geach et al. 2005)
implying a very significant dust
content and therefore reddening of the stellar continuum, although it
has not been demonstrated that the Ly
and sub-mm radiation originate
from the same regions of the galaxy.
This is particularly true if the Ly
production in LABs is the result
of accretion of cold gas onto dark matter halos
(e.g. Haiman et al. 2000) in which case the Ly
may be
emitted over significantly extended areas.
There may also be a certain degree of decoupling between
Ly
photons and the nearby UV continuum due to resonance scattering.
In the cases where there is no continuum detection at all in any bands,
(e.g. Nilsson et al. 2006) then equivalent widths are only lower limits.
However,
if there is a detection of (potentially reddened) stellar continuum then
total SED will be the superposition of this with the gas spectrum that
gives rise to Ly
,
whatever the mechanism for its production.
In this case, the SED fitting approach should be applicable and Ly
equivalent widths should be recoverable.
Again intervening H I absorbing systems have been switched off
for these experiments and we only consider the Ly
equivalent
width.
Tests here are carried out using the standard template spectrum (defined
in Sect. 3, Table 1)
combined with various old stellar populations at
redshifts of 2, 4, and 6.
However, within the tests performed here, no redshift dependence at all
was detected and hence, none will be discussed.
The results presented here can be considered to hold at all redshifts.
Table 2 shows the way in which varying the contribution
from an old stellar population affects the computed values of
when the age and metallicity of the underlying population are
varied.
Figure 6 demonstrates the effect of increasing the
relative contribution of a 300 Myr underlying population.
![]() |
Figure 6:
The effect of varying n4500 on the recovered values of
![]() ![]() |
Open with DEXTER |
When considering dependencies upon the normalisation coefficient, no
trends emerge when using technique #1, (for the same reasons this
technique is not sensitive to the age of the underlying population;
Fig. 6).
Technique #3, which extrapolates the measured value of
to Ly
,
tends to overestimate
with increasing n4500.
As n4500 increases, the flatter SED of the old population has the
effect of flattening in the spectrum in the 1500-2200 Å region.
However, the 300Myr burst turns over towards Ly
much more sharply than
the very young SED, and hence doesn't contributed much at 1216 Å.
Hence the continuum flux at Ly
is increasingly underestimated as
n4500 increases.
There is a minor tendency for technique #4 to become less accurate with
increasing n4500, underestimating
by 6% at
n4500 = 10.
The
fitting software selects increasingly older template spectra as the old
population contributes more and more to the 4000 Å break.
However, with increasing n4500, the composite spectrum changes
faster across the 4000 Å break than it does in the FUV.
So as older (redder intrinsically) spectra are selected by the fitting
software, in order to maintain a good fit in the UV,
the best-fit SED will be less reddened than it would otherwise.
This leads to a tendency to slightly overestimate the continuum flux at
Ly
,
and a trend of underestimating
with increasing contribution
from an older population.
In light of these results we made a number of attempts to confuse our
SED-fitting software.
The first was to, as in previous sections, see how the SED fitting
routine fared when the simple noise model was applied.
After applying the aged population at each value of n4500, we
randomised all the computed fluxes by assigning S/N=5 in each filter,
and computed
from these values.
We generated 1000 objects and computed the mean values although these
were never found to be deviant from the values computed without the
noise model at all n4500.
The standard deviation of the recovered
is represented by the
error-bars on the black line (technique #4) of Fig. 6.
Secondly, we randomly selected old populations from any of the templates with
ages greater than 300 Myr,
reddened them with random EB-V in the range 0.0-1.0, and
added them to the template SED with varying n4500 (range: 0.0-3.0).
By applying two old populations to our template spectra in this fashion, we
were not able to make technique #4 reproduce
that was in error by
more than 10%.
The final test devised to confuse the software was to vary the
contribution of the nebular continuum in the template spectra.
The motivation for this test again being that the SED-fitting software is
sensitive to the Balmer jump.
Moreover, our understanding of the ionising
photon production from massive stars is incomplete.
There is a lack of data concerning low-metallicity stars, no single
O type stars can be observed at such FUV wavelengths, and the ionising
contribution from population III objects is largely speculative.
Additionally, Lyman-continuum escape has been observed in very few
cases:
Bergvall et al. (2006)
at low-z in the case of ESO 350-IG38; and
Steidel et al. (2001)
at high-z by stacking composite spectra of Lyman Break Galaxies (LBGs).
It is the reprocessing of these photons that determines the intensity
of the nebular component relative to that of the stars, hence any
Lyman continuum photons that escape are not reprocessed in the
nebular hydrogen emission spectrum (lines or continuum).
We found that, even when scaling the nebular component (see Sect. 2.1) by a factors in the range 0-3, technique #4
recovered
with errors no greater than 5%.
These limits extend between two very extreme cases: one, where all Lyman
continuum photons escape (which would result in no nebular emission
component and therefore no Ly
); and two, the possibility that the estimates
of ionising continuum in stellar atmosphere models are in error
by a factor of 3 and all the ionising photons are reprocessed as
nebular emission.
One of the initial motivating factors for the study of Ly,
dating back to
Partridge & Peebles (1967), was the fact that it could
provide a tracer of early star formation observable from the ground at
redshifts greater than around 2.
At z=2, technique #1 would be equivalent to a narrowband filter at
3600 Å, plus a U filter.
Here the effect of intervening H I systems will be
lower than at higher z and, at the lowest redshifts where Ly
is
observable from the ground, intervening H I affects the
determination of
by technique #1 at the 1% level for our chosen filter
set.
That said, any single measurement by this technique cannot be deemed
reliable without additional observations.
Followup spectroscopy could obviously confirm the presence of
intervening systems and would also yield an accurate measurement of
,
but observational requirements may preclude the possibility of
obtaining such data for every target.
Perhaps cheaper, depending on the design of the survey, would be to use
two off-line filters,say B and V (restframe 1470 Å and 1830 Å,
respectively - where CCDs are typically more sensitive than in U), in
order to estimate the continuum level at Ly
without sampling
bluewards of 1216 Å.
However, the
Shapley et al. (2003)
LBG sample find median EB-V of 0.099 for the strongest Ly
emitters
with EB-V increasing with decreasing
.
At
EB-V=0.1, technique #3 is already underestimating
by 25% for SMC dust.
The dust-sensitivity of technique #3 is independent of redshift and
will not be discussed further.
At z=2, the 4000 Å break can still be sampled by an observation in
the J-band allowing technique #4 to be used in order to properly
handle the effects of dust reddening.
As redshift increases, the effect of intervening H I on technique
#1 becomes more pronounced, reaching the 10% level by z=4.
Systematic uncertainties on numbers derived by this technique only should
probably be addressed using a Monte Carlo-type approach.
At this redshift, the 4000 Å break can still be sampled from the
ground using the
band although the high night-sky background
makes these observations expensive.
In 40 h of integration time on an 8 metre telescope,
a typical
band imaging camera can detect an object of
in the AB magnitude system at S/N = 5
.
At z=4, and assuming the local B-band luminosity function
(Jones et al. 2006)
evolves parallel to the LF at 1500 Å between redshifts of 0,
(Wyder et al. 2005)
and 4
(Yoshida et al. 2006),
this corresponds to a detection limit 0.5 mag fainter than
.
According to James Webb Space Telescope (JWST) Mission Simulator and
NIRCam sensitivity estimates,
such observations to these depths can be obtained at
in just 1 s.
At redshifts greater than 5, L-band observations would be required in
order to sample the 4000 Å break.
While deep observations may be obtainable from the ground at shorter
wavelengths, the sky-background at wavelengths longer than
preclude such observations and current groundbased
facilities do not approach the required sensitivities.
Consequently these observations would need to be carried out by
mid-infrared telescopes in more unfriendly and expensive environments:
for example the Spitzer Space Telescope or JWST, or a proposed MIR telescope
at Dome-C, Antarctica.
This is somewhat contrary to the motivation for using Ly
as a probe
for primeval star-formation.
However, we reiterate that it is only this observation that needs to be
done from space - the other bands may, depending on redshift, more
economically be performed from the ground.
Moreover, in the age of deep multi-band surveys, the amount of
pre-existing data there is for a field is always a consideration.
If observing a deep field at a certain wavelength, it may well be
advantageous to select fields for which much data is already in existence
- observations at new wavelengths are frequently added to existing
datasets (the Chandra Deep Field, for example).
Hence the majority of the observations required for technique #4
(targeting certain redshifts, at least) may already be in place, requiring
only the additional infrared bands and it would be wise for future
Ly
surveys to capitalise on the currently existing data.
It is also likely that early JWST programs will include deep observations of
regions with existing deep optical data.
In addition to the observational, there are also further theoretical uncertainties; mainly concerning the validity of the stellar atmosphere models in the UV. These models have currently not been well tested at these wavelengths. See Sect. 4.3 for a discussion on this.
Acknowledgements
We acknowledge the support of the Swedish National Space Board (SNSB) and the Swedish Research Council (VR). We thank J. M. Mas-Hesse, D. Kunth, J. P. U. Fynbo for their valuable comments on this manuscript and C. Leitherer and A. Petrosian for their work on the Lyman-alpha projects. We would also like to thank the anonymous referee for comments that have sparked numerous improvements to the manuscript.