University of Amsterdam
Master’s Astronomy and Astrophysics
Master Thesis
Dust Obscured Star Formation of
High-Redshift Galaxies
by
Mieke Paalvast
5963435
November 2014
60 ECTS
September 2013 - November 2014
Supervisor:
Dr. Ivo Labb´
e
(Leiden University)
Examiners:
Prof. Dr. Lex Kaper
Dr. Rudy Wijnands
3
Abstract
Using the sensitivity and the long wavelengths of the Herschel Space Observatory at 100 and 160 µm, in combination with the 24 µm obser-vations of the Spitzer Space T elescope, we investigate the dust obscuration of galaxies at high redshift. Our sample consists of 2770 UV-selected galaxies with a photometric redshift of z ∼ 3.8 in the North and GOODS-South fields. After cleaning the background of the infrared images at the positions of these galaxies, we construct mean and median stacks at 24, 100 and 160 µm. To investigate trends with UV luminosity and color, we performed stacking in bins of UV slope (β) and UV luminosity. By compar-ing the stacked fluxes with dust templates, we determined the bolometric infrared luminosity. UV luminous galaxies have an infrared luminosity of LIR ∼ (2.41 ± 0.69) × 1011L based on 160 µm photometry and a mean dust
obscuration LIR/LU V of 10.08 ± 2.89, which is similar to the dust
obscura-tion found for local starburst galaxies. Stacking this UV luminous sample in bins of UV color β demonstrates that galaxies with redder UV slope are dustier than those with a blue slope, and follow the IRX − β relation de-rived for local starbursts. However, this does not hold for the lower UV luminous stacks; these galaxies appear to have a higher dust obscuration than predicted, although these results are of low significance. The compari-son between the results that are obtained using the different infrared bands implies that the 24 µm and 100 µm detections result in higher dust obscu-ration rates compared to the 160 µm stacks. We interpret this difference as a result of contamination due to other galactic processes at the rest-frames of the 24 and 100 µm observations of our galaxies at z ∼ 3.8, because they are at the edge of the dust emission range. In general, the agreement be-tween the dust properties of local starbursts and UV luminous high-redshift galaxies suggests a similarity in the dust production and stellar production rates and geometries between local and distant galaxies.
5
Nederlandse populaire samenvatting
De oorsprong en evolutie van de zichtbare ’baryonische’ materie waaruit sterren en sterrenstelsel bestaan is tot op heden een mysterie. Om antwoorden te vinden op vragen als ’Wanneer in de geschiedenis van het heelal ontstonden de eerste sterren?’ kunnen we verschillende methodes gebruiken. Ten eerste kan de hoeveelheid massa die in sterren is omgezet in elk sterrenstelsels gemeten worden om die vervolgens te analyseren als een functie van tijd of leeftijd van het heelal. Een andere manier is het meten van de stervormingssnelheid, tevens als functie van de leeftijd van het heelal. Dit laatste is het onderwerp van dit onderzoek.
De huidige snelheid waarmee een stelsel sterren vormt, beschrijft hoeveel sterren er geboren zijn in een kort tijdsbestek. Wanneer sterren ontstaan vanuit een molec-ulaire wolk kunnen we theoretisch gezien het aantal sterren van een bepaalde massa tellen, welke ons de distributie van sterren als functie van stermassa geeft (dit wordt ook wel een Initial M ass F unction (IMF) genoemd). In een nieuwe sterpopulatie verbruiken de grootste en heetste sterren hun brandstof het snelst, wat ertoe leidt dat ze het kortst leven. Daarnaast zijn de heetste sterren ook het helderst. Als we dus kunnen meten hoeveel heldere sterren er zich bevinden in een stelsel, kunnen we dit omrekenen naar het totale aantal sterren dat zich heeft gevormd, gebruikmakend van de distributie van sterren per massa.
Jonge, zware sterren stralen voornamelijk hun licht uit in het ultraviolette gedeelte van het spectrum. Hierdoor geeft een meting van dit gebied van het spectrum van een stelsel een eerste inschatting van het aantal zware sterren dat zich binnenin bevindt. Omdat sterren onstaan uit wolken van gas en stof, wordt een deel van het licht dat zij uitstralen geabsorbeerd door het gas en stof om hen heen. Dit zorgt ervoor dat het gemeten UV licht slechts een deel van het totale door de sterren uitgezonden licht bevat.
Er zijn twee mogelijkheden om te corrigeren voor stofabsorptie. Ten eerste kunnen we de hoeveelheid stofabsorptie schatten door de kleur van het galactische spectrum te meten en te vergelijken met wat we verwachten voor een stelsel zonder stof. Het verschil tussen deze waardes is gelijk aan de hoeveelheid waarmee het spectrale licht is verminderd.
In tegenstelling tot het meten van het licht dat we missen in het ultraviolet, kunnen we ook het licht meten dat door het stof door de opwarming zelf wordt
uitgezon-den. Ervan uitgaande dat stof slecht de geabsorbeerde straling van zware sterren opnieuw uitzendt in het infrarood, geeft een meting van de emissie rond deze lan-gere golflengten eenzelfde schatting van de hoeveelheid stof. Helaas is het niet zo gemakkelijk om stelsels te detecteren in infraroodwaarnemingen, omdat de resolutie en sensitiviteit lager is voor langere golflengten. Tot op heden was het alleen mo-gelijk om dichtbijzijnde stelsels die zeer helder zijn in het infrarood waar te nemen, waardoor ’gewone’ stelsels zoals de Melkweg worden uitgesloten.
Het gebrek aan infrarood data zorgt ervoor dat de stervormingssnelheid van stelsels die ver van ons verwijderd zijn alleen kan worden gecorrigeerd op stof door middel van de kleur van het spectrum. Echter, de geldigheid van deze methode is nog niet getest voor stelsels met een hoge roodverschuiving. Gebruikmakend van de hoge sensitiviteit en resolutie van de Herschel Space Observatory en Spitzer Space T elescope wordt de infrarood stofemissie gemeten voor stelsels met een roodverschuiving van gemid-delde 3.8, wat overeenkomt met het bekijken van stelsels die hun licht ongeveer 12 miljard jaar geleden hebben uitgezonden. Daarnaast wordt de stofabsorptie bepaald met behulp van waarnemingen van de Hubble Space T elescope in het UV.
De resultaten laten zien dat de hoeveelheid stofabsorptie, berekend met beide meth-oden, voor de stelsels die helder zijn in het ultraviolet nagenoeg gelijk is. Hoewel voor deze groep de afhankelijkheid van de spectrale kleur exact samenhangt met de gemeten hoeveelheid stof, vinden we een dergelijke correlatie niet direct voor stelsels die minder helder zijn. Dit kan duiden op een andere galactische samenstelling dan verwacht, maar ook op een te lage signaal-ruisverhouding. Dit laatste zal met hogere kwaliteit data op langere golflengten moeten worden gecontroleerd, bijvoorbeeld met waarnemingen van de nieuwe telescoop ALMA.
Wetenschappers die de globale sterformatie van het Universum in kaart proberen te brengen, maken op hoge roodverschuiving vaak gebruik van stofcorrectie op ba-sis van spectrale kleur. De geldigheid van deze methode was tot op heden slechts vastgesteld voor stelsels met een roodverschuiving van ongeveer 2. De resultaten van dit onderzoek impliceren dat deze methode tevens toepasbaar is op ten minste de helderste stelsels met een roodverschuiving van rond de 3.8, iets wat nooit eerder was aangetoond. Hierdoor zijn we weer een stukje verder in het ontrafelen van het mysterie van het onstaan en de evolutie van sterren en sterrenstelsels.
Contents
1 Introduction 9
1.1 Galaxies in an expanding universe . . . 9
1.2 Galaxy evolution and formation . . . 10
1.3 The SED of galaxies . . . 11
1.4 This thesis . . . 13
2 Star formation at high redshift 15 2.1 The star formation history of the Universe . . . 16
2.2 Initial Mass Function (IMF) . . . 16
2.3 LIR determination using IR photometry . . . 18
2.4 LIR determination using UV color . . . 20
2.4.1 Derivation of IRX − β relation . . . 22
2.4.2 IRX − β relation at high redshift . . . 24
3 Data 27 3.1 Observatories . . . 27
3.1.1 Great Observatories Origins Deep Survey . . . 27
3.1.2 Hubble Space Telescope . . . 29
3.1.3 The Spitzer Space Telescope . . . 29
3.1.4 The Herschel Space Observatory . . . 29
3.2 Catalog selection . . . 29
3.3 Photometry . . . 31
3.3.1 Monte Carlo simulation . . . 33
3.4 Modeling the SED . . . 33
3.4.1 Redshift z . . . 34
3.4.2 UV slope β . . . 35
3.4.3 UV luminosity LU V . . . 36
4 Stacking procedure and analysis 37 4.1 Stacking procedure . . . 37 4.2 Background corrections . . . 38 4.3 Other corrections . . . 39 4.4 Error calculations . . . 39 4.5 Construction of subsamples . . . 40 5 Results 43 5.1 Overview dust-corrected LIR . . . 43
5.1.1 Infrared luminosities predicted by the IRX − β relation . . . 43
5.1.2 Infrared luminosities derived by MIPS 24 µm and PACS 100 and 160 µm detections . . . 44
5.2 Comparison between dust attenuations . . . 45
5.3 Comparing the results to other surveys . . . 47
5.4 Dust attenuation of other stacks . . . 49
5.4.1 Trends with luminosity . . . 49
5.4.2 Trends with infrared wavelength . . . 49
5.4.3 Comparison between the results of GOODS-S and GOODS-N 51 6 Summary, discussion and conclusion 53 6.1 Summary . . . 53
6.2 Discussion . . . 54
6.2.1 Comparison with recent studies at z ∼ 2 . . . 54
6.2.2 Differences between 24 µm, 100 µm and 160 µm results . . . . 55
6.2.3 The star formation history of the Universe . . . 57
6.3 Conclusion . . . 57
Appendices 69
Chapter 1
Introduction
For this thesis we studied the dust-obscured star formation rate (SFR) of a sample of high-redshift (z ∼ 3.8) galaxies, where dust obscuration that affects the spectral energy distribution (SED) of galaxies plays an important role. First, we will intro-duce the subject by providing some background information, which will be followed by an overview of the remainder of the thesis.
1.1
Galaxies in an expanding universe
Since the work of Edwin Hubble in 1925, we know that the Milky Way is not the only galaxy in the Universe. Until this discovery, it was believed that the Universe was only consisting of our own Galaxy and observations of external galaxies were interpreted as nebulea within the Galaxy. However, Hubble (1925) measured the distance to these nebulae for the first time, and concluded that they were too distant to exist inside our own galaxy. Furthermore, Hubble was able to measure the sizes of the distant galaxies using their angular size and concluded that the other galaxies were similar to our own Milky Way.
After this great scientific breakthrough, Hubble observed the light that was emitted by distant galaxies and noticed that that it was shifted towards longer wavelengths, e.g. ’redshifted’, and that this shift was proportional to the distance to the galaxies. Finally, he concluded that galaxies are moving away from the Milky Way with an increasing velocity, based on the Doppler effect (Hubble, 1929; Hubble and Humason, 1931). This relation is represented as
cz = H0d (1.1)
which is called the ’Hubble law’. In this equation, c is the speed of light and z the cosmological redshift. Together, these variables represent the recession velocity of the galaxy. Furthermore, H0 is the ’Hubble constant’ and d is the distance to
the galaxy. The observed redshift z can be derived by the difference between the observed and emitted wavelength of a spectral line, given by:
z = λobs− λem λem
(1.2)
The discoveries of Hubble provide us a way to derive the distance to galaxies. Since we can look back in time by observing more distant objects, it indirectly gives us a method to obtain the cosmological evolution of galaxies.
1.2
Galaxy evolution and formation
The question: ’How did galaxies form after around 379.000 years after the Big Bang, out of smoothly distributed non-ionised matter?’ is one of the main topics of modern cosmological research in the field of galaxy formation and evolution. Observations of the cosmic microwave background (CMB) suggest that the Universe is homogeneous and isotropic on large scales. However, if we look in more detail to the CMB, obser-vations show small temperature and density fluctuations (Smoot et al., 1992). The structures we see nowadays, e.g. galaxies and clusters of galaxies, are expected to originate from these primordial fluctuations. In the most commonly accepted theory about structure formation, the Universe expanded and therefore cooled down, which caused the overdense regions to attract more dark and baryonic matter. Eventually, halos and galaxies could form in these regions.
Using cosmological simulations, the evolution of dark matter from density perturba-tions to haloes can be successfully reproduced and explained. However, the formation of galaxies out of the baryonic part of the matter is still unclear. To investigate galaxy formation and evolution, the individual aspects of the evolution of baryonic matter in galaxies, such as stars, gas and dust, need to be understood. This information can be gained from the SED of galaxies, if there are methods available to interpret the galactic spectra properly. Moreover, a study of galaxy evolution requires SEDs of a broad sample of galaxies at different stages of the evolution, so at different redshifts.
1.3. THE SED OF GALAXIES 11
1.3
The SED of galaxies
Galaxies emit radiation at all wavelengths of the electromagnetic spectrum. However, the origin of the light varies for different wavelength ranges. For example, ultraviolet (UV) and optical light originates mainly from direct stellar emission, while mid- to far-infrared emission is caused by indirect star light, where dust has absorbed the stellar emission and has re-radiated the light in the infrared (IR). In Figure 1.1, two pictures of the nearby spiral galaxy M 51 are shown, where the left figure consist of an optical image and the right of an IR image. The left figure consists of light that is directly emitted by the stars (and HII regions), and we see that at some parts the light is absorbed. The dust that is responsible for this re-emits the light in the IR, which is visible in the right image.
Figure 1.1: Image of the nearby spiral galaxy M51 at optical (left) and infrared (right) wave-lengths. There is a difference between the observed light at both wavelengths, which tells us that different processes in the galaxy produce emission at different bands. Image credits: Visible image: Digitized Sky Survey; Infrared image: NASA/JPL-Caltech/R. Kennicutt (University of Arizona)
The above suggests that the relation between the optical and UV light and the IR emission gives an indication of the amount of dust a galaxy contains. Therefore, the
SED of a galaxy includes a lot of information about the content and structure of the galaxy. As an example, in Figure 1.2 an SED of a typical galaxy forming stars at a rate of 1M yr−1 is presented. The shape of this spectrum is dependent on both the
stellar light, as well as on the interaction of this light with dust and gas within the galaxy.
Figure 1.2: Example of a spectral energy distribution of a galaxy with a typical star formation rate of 1 M /yr from the ultraviolet to the infrared wavelength regime. The shape of this spectrum
is dependent on both the stellar light and the interaction of this light with dust and gas within the galaxy. The picture is taken from the PhD thesis of Da Cunha (2008).
Using a model to interpret the multi-wavelength emission of galaxies, physical pa-rameters such as the star formation rate (SFR), stellar mass and dust content can be extracted from the SED. In this thesis, the main focus will be on the first one, the SFR, and the role of dust in absorbing the UV light from newly born massive stars.
1.4. THIS THESIS 13
1.4
This thesis
In order to fully understand and determine the global star formation history of the Universe, the SEDs of galaxy samples of different evolutionary phases need to be compared. For this project, we used a sample of 2770 z ∼ 3.8 galaxies for which we calculated the dust-corrected SFR, using methods including both dust absorption and dust emission. Similar studies have been performed before, but most of these studies are performed up to a redshift of about 2 (for example, Reddy et al. (2012)). We aim to clarify the dust obscuration of galaxies with z ∼ 3.8 in this work.
In the next chapter, we will explain the theoretical background of this project, includ-ing a description of the two different methods to calculate the dust-corrected SFR of the sample, using detections of both dust UV-absorption and dust IR-emission. Chapter 3 will give an overview of the data sample, including the observatories, the observed fields, the sample selection and the photometric data reduction. Fur-thermore, SED modeling to obtain properties such as photometric redshift, dust absorption and bolometric luminosity will be described. Then, in Chapter 4 we ex-plain the stacking procedure, a procedure combining data of multiple galaxies to increase the S/N. The results of this analysis will be presented in Chapter 5. Finally, in Chapter 6 we give a summary of this thesis, that will be followed by a discussion and conclusion.
Chapter 2
Star formation at high redshift
Because the evolution of baryonic matter and more specifically, the evolution of galaxies, is not well understood, investigations of different redshift samples could give more insight into this problem. However, one of the main difficulties in studying galaxy evolution is the lack of observational data of distant galaxies over the whole electromagnetic spectrum. Since IR observatories are less sensitive and provide data of a lower spatial resolution compared to UV data, in the UV detected high-redshift galaxies are difficult to trace in IR observations. This challenge has been the source of many studies related to galaxy evolution, and is the subject of this research. Here, we will investigate the dust properties of a high-redshift galaxy sample to derive the ’galactic activity’, given by the SFR.
In a dust-free model, the light that is emitted by a galaxy does not undergo ob-scuration, which gives a ’clear’ view of the forming stars. In such a case, the star formation rate is related linearly to the integrated UV luminosity, because this part of the SED is expected to originate mainly from the short living O and B stars. How-ever, the derivation of the SFR is not this obvious in reality, because the presence of dust in the inter stellar matter (ISM) is altering the SED in almost all wavelength ranges. Therefore, we need models that include dust attenuation to adjust for this effect. Fundamentally, dust will absorb the UV emitted light from massive stars and will reradiate this light in the IR and far-IR (FIR) bands. Therefore, two methods can be applied to the observed SEDs in order to adjust for dust attenuation. The first one uses the principle of dust extinction by measuring the absorbed UV light and for the second method we measure the reradiated dust emission in the IR and FIR.
In this chapter, we start with discussing the star formation history of the Universe, and how our current view is related to our observations of dust absorption. Then we will explain the principle of an initial mass function (IMF) to relate the SFR to a bolometric luminosity. Afterwards, the two different methods to correct for dust attenuation are explained.
2.1
The star formation history of the Universe
The evolution of the star formation rate of galaxies has been mapped by Madau et al. (1996) for the first time. They derived the redshift evolution until z ∼ 4 of the metal production rate, which is directly proportional to the SFR per volume density, using a dust-free model. In accordance to this work, several surveys have been performed concerning the SFR of samples at different redshifts. Most of these later calculations are dust-corrected based on the UV color. In Figure 2.1, the star formation history of the Universe is presented (from Bouwens et al. (2014)). In this diagram, the SFRs are calculated using UV photometric data only, and the blue and red points and shaded regions are matching the dust-uncorrected and dust cor-rected results, respectively. The corrections are based on UV slope (β) absorption estimations following the IRX − β relationship that will be explained later in this chapter. Until now, this relation between the UV color and dust absorption has been tested using direct IR measurements by multiple surveys, most are concentrated on redshifts up to z ∼ 2. At higher redshift, the star formation history of Figure 2.1 is not verified by direct dust detections. To expand this to higher redshift, we test the relation for a sample of z ∼ 3.8 galaxies.
2.2
Initial Mass Function (IMF)
In order to calculate the total SFR of a galaxy, we need to have information about the bolometric infrared luminosity LIR(bol) that will be derived by the two different
methods. Furthermore, an initial mass function (IMF) gives an conversion factor from LIR to SFR. In this section, the background about IMFs will be discussed.
An IMF is an empirical function that describes the distribution of the initial stel-lar mass (per galaxy). It is assumed that the IMF is relatively invariant from one galaxy to the other, and can also be applied to a smaller group of stars withing the galaxy. The IMF is often stated in terms of a series of power laws, where ξ(m)∆m,
2.2. INITIAL MASS FUNCTION (IMF) 17
Figure 2.1: Determinations of the SFR density (left axis) and the UV luminosity density (right axis) versus redshift (and time) from Bouwens et al. (2014). The SFR densities are inferred from measured luminosity densities, assuming a conversion factor that is relevant for star-forming galaxies with ages of > 108 yr (Kennicutt, 1998; Madau et al., 1998). The UV luminosities on the right
axis are obtained by integrating LFs. The upper and lower set of points and shaded regions (red and blue circles) show the results of corrected and uncorrected for dust effects respectively, using observed UV slopes β and the IRX −β relationships of Meurer et al. (1999), which will be discussed in detail later in this chapter. Furthermore, the SFR densities at z ∼ 2 − 3 from Reddy and Steidel (2009) are shown (green crosses), as well as those at z ∼ 0 − 2 from Schiminovich et al. (2005) (black hexagons) and at z ∼ 9 from Ellis et al. (2013) (black solid circles).
the number of stars with mass in the range m to m + dm within a specified volume of space, is proportional to m−α , where α is a dimensionless exponent. The IMF of stars more massive than our sun was first quantified by Edwin Salpeter (Salpeter, 1955). His work favored an exponent of α = 2.35, where the function is called the Salpeter IMF and is given by
ξ(m)∆m = ξ0( m M )−2.35(∆m M ) (2.1)
The Salpeter IMF provides a tool to calculate the SFR using the infrared luminosity. Assuming that the absorption cross section of the dust in a galaxy is peaked in the
ultraviolet (where the emission is dominated by massive stars), the IR emission is a tracer of young massive stars. Using this principle, Kennicutt (1998) determined a conversion factor between infrared luminosity and SFR that is valid for starburst galaxies, given by:
SF R 1M yr−1 = LIR 2.2 × 1043ergss−1 = LIR 5.8 × 109L (2.2)
where a mean luminosity for 10-100 Myr continuous bursts and solar abundances are adopted. This conversion factor from Kennicutt (1998) is applied to all SFR calculations in this thesis.
2.3
L
IRdetermination using IR photometry
Our main problem is that we have to derive the total infrared luminosity from limited infrared data of three bands. Therefore, we assume the rest of the infrared contin-uum and SED shape by comparing our data to SED models. Several extreme SED shapes are possible, based on different theoretical assumptions. We use the average SED model from Wuyts et al. (2008a), which appears to be a good approximation (see e.g. Wuyts et al. (2011)).
In Figure 2.2 the SED model, νFν versus λ, is displayed which is used in this project
to convert the IR fluxes to total IR luminosities. For every observed wavelength band, the SED gives a conversion factor per observed amount of flux, dependent on redshift, because the observed fluxes will be shifted to longer wavelengths by a factor of 1
1+z with respect to the rest-frame wavelength. As an example, Figure 2.3 gives the
conversion from observed flux (in mJy) to the LIR and SFR (using a Salpeter IMF),
depending on redshift, for 160 µm detections. For our sample of z ∼ 3.8 galaxies, the detection limit for the LIR and the SFR is about 2 × 1012L and 6 × 102M /yr,
2.3. LIR DETERMINATION USING IR PHOTOMETRY 19 log ν Fν + const (ergs ·cm − 2 · s − 1 ) λ(µm)
Figure 2.2: νFν versus λ plot for the mean of extreme SEDs, calculated by Wuyts et al. (2008a).
This SED is used to convert the IR flux to total IR luminosity.
Lbol (IR) (L ) SFR (M /yr) Redshift
Figure 2.3: Total IR luminosity and SFR versus redshift plot, calculated by Wuyts et al. (2008a), at an IR wavelength of 160 µm. The SFR is calculated using the Salpeter IMF (Kennicutt, 1998). The line represents the amount of luminosity and SFR for every amount of observed flux in mJy. Assuming a detection limit of the order of 1 mJy, the detection limit for the LIR and the SFR is
about 2 × 1012L
2.4
L
IRdetermination using UV color
Galaxies with a redshift higher than 2 are difficult to directly detect in IR data. A relation between the UV continuum slope and dustiness found for local starburst (Meurer et al., 1999; Calzetti et al., 2000; Heckman et al., 1998) is helpful in such situations. The technique is based on the principle that dust absorption causes a redder UV slope. Therefore, we can use a measurement of the UV slope to calculate the IR dust emission. This principle is displayed in Figure 2.4, where Adelberger and Steidel (2000) made a sketch of this scenario. In this figure, different ranges of dust obscuration are shown, where A1600 ∼ 0.5 (solid blue line), A1600 ∼ 2.5 (dotted green
line) and A1600 ∼ 4.5 (dashed red line). As we see in this cartoon, a higher dust
absorption correspond to a redder UV slope and a higher IR luminosity compared to a situation with less dust absorption.
Figure 2.4: Schematic spectra of a starburst galaxy with fixed SFR and varying dust opacity, to illustrate the empirical correlation between, UV, far-IR and radio properties of actively star-forming galaxies in the local universe (the latter wavelength range is beyond the scope of this research). As shown in this figure, increasing the dust obscuration makes the UV continuum redder and fainter while boosting the far-IR luminosity. Different ranges of dust obscuration are shown, A1600∼ 0.5
(solid blue line), A1600 ∼ 2.5 (dotted green line) and A1600 ∼ 4.5 (dashed red line). The dotted
and dashed lines nearly overlap, because at A1600∼ 2.5 most of the luminosity of massive stars is
absorbed by dust. Therefore, an increase of the opacity does not significantly increase the absorbed energy. This figure is taken from Adelberger and Steidel (2000).
In 1999, Meurer et al. (1999) developed an empirical relation for local starbursts between the IRX and the UV slope β, where IRX = FIR
F1600, e.g. the ratio of infrared
2.4. LIR DETERMINATION USING UV COLOR 21
will refer to this relation as the IRX − β relation.
The method is based on an observed correlation between the ratio of (far-)infrared to UV fluxes with spectral slope β. The FIR/F1600 versus β relation is calibrated
in terms of the dust absorption at 1600 ˚A(A1600) using International Ultraviolet
Explorer spectra and Infrared Astronomical Satellite fluxes of local starburst galax-ies. Because of the assumed similarities between high redshift Lyman-break galaxies and local starburst galaxies, Meurer et al. (1999) state therefore that the relation is also applicable to high-redshift galaxies. As an example, the UV rest-frame spec-tral energy distributions of local starbursts and distant galaxies detected with the Lyman-dropout technique are similar, even as the dominance of the UV and optical spectra by absorption and emission lines. Therefore, the Lyman-dropout galaxies appear to be scaled-up version of local starbursts, only larger and more luminous.
In Figure 2.5 the measured relation between the ratio of far-infrared to UV flux (cen-tered at 1600 ˚A), FIR/F1600 and the UV spectral slope β for UV-selected starburst
galaxies are shown. Because the far-infrared flux is due to dust radiatively heated by the absorbed UV radiation, the ratio of far-infrared to UV flux is a measure-ment of dust absorption. According to this figure, dust absorption is correlated with UV reddening. Therefore, this figure provides a tool to adjust the measured UV luminosity for dust absorption, using UV data alone, regardless of the nature and geometry of the dust. In order to apply this to other galaxy samples, we need the exact relationship between β and the dust absorption.
Figure 2.5: Ratio of far-infrared to UV flux (centered at 1600 ˚A), FIR/F1600 (left axis) and the
absorption coefficient at 1600 ˚A, A1600 (right axis) versus the UV spectral slope β for UV-selected
starburst galaxies. The figure is taken from Meurer et al. (1999). The data points are derived from observed local starburst galaxies. The solid line matches with the best-fit of the data points, e.g. the IRX − β relation. The dotted line shows the dust-absorption/population model of a previous study from Pettini et al. (1998).
2.4.1
Derivation of IRX − β relation
In this subsection we will discuss briefly the derivation of the IRX − β relation and the β − A1600 calibration, as explained in detail in Meurer et al. (1999).
The UV flux at 1600 ˚A, F1600, is the generalized flux of the form Fλ = λfλ, where
fλ is the flux density per wavelength interval. The UV slope β is determined from
a power-law fit of the form fλ ∝ λβ. Then, assuming that FIR is only due to the
thermal emission of dust heated by the radiation it has absorbed, it will primarily consist of nonionizing photons with the addition of Lyα photons, that are resonantly scattered by hydrogen until they are absorbed by dust grains. Thereby, using the
2.4. LIR DETERMINATION USING UV COLOR 23
assumption that ionizing photons do not significantly contribute to dust heating, the IRX1600 can be written as
IRX1600 = FIR F1600 = FLyα+ ∞ R 912˚A fλ,0(1 − 10−0.4Aλ)dλ F1600,0100.4A1600 (FIR Fbol )Dust (2.3)
In this relation, A1600 is the dust attenuation around 1600 ˚Agiven in magnitudes,
Aλ is the net absorption by dust as a function of wavelengt and is also given in
magnitudes, fλ,0 is the unattenuated flux density of the emitted spectrum and FLyα
is the Lyα flux, derived from the model spectrum for λ<912 ˚A. The first term in equation 2.3 gives the bolometric flux of the absorbed radiation, where, on the other hand, the second term gives the fraction of the bolometric flux that is emitted by the dust in the far-infrared. Formulating this in another way, IRX1600 depends
on the intrinsic spectrum of the galaxy and the absorption curve of the dust, also at all other wavelengths than 1600 ˚A. However, since we can assume that dust heating is dominated by young stellar populations (massive stars), equation 2.3 can be simplified as IRX1600 = (100.4A1600− 1) FLyα+ ∞ R 912˚A fλ,0dλ F1600,0 (FIR Fbol )Dust (2.4)
In this equation, the first term gives the fraction of F1600 that is absorbed by dust.
The second term is the equivalent of a bolometric correction, by giving the maximum amount of dust heating divided by the intrinsic flux at 1600 ˚A. The last term is again the fraction of the bolometric flux that is emitted by the dust in the far-infrared, which is the same as the second term in eq 2.3.
To express the ratio of bolometric to UV flux, we can rewrite equation 2.4 as
Fbol F1600 = Fbol FIR IRX1600 = (100.4A1600− 1) FLyα+ ∞ R 912˚A fλ,0dλ F1600,0 (2.5)
Writing this equation in terms of the bolometric correction, we get Fbol
F1600
= (100.4A1600− 1)BC(1600)
Using population models from Leitherer and Heckman (1995), we see that BC(1600)? = FLyα+ ∞ R 912˚A fλ,0dλ F1600,0 ≈ 1.66 (2.7)
Finally, by inserting equation 2.7 into equation 2.6 we obtain
FIR(bol) = 1.66F1600(100.4A1600− 1) (2.8)
which, obviously, can be rewritten as
LIR(bol) = 1.66L1600(100.4A1600− 1) (2.9)
Equation 2.9 shows that the infrared luminosity, and therefore also the dust-corrected SFR, can be determined by the luminosity and dust absorption coefficient at 1600 ˚
A. The latter parameter is calculated by a linear fit of the IRX − β relation, which is represented in Figure 2.5 as the solid line, and is given by
A1600 = 4.43 + 1.99β (2.10)
The above provides a powerful tool to obtain the dust corrected SFR, using UV data alone, and can be applied to galaxy samples where no IR observations are available.
2.4.2
IRX − β relation at high redshift
Although the correlation between the UV continuum slope with dustiness as found for local starbursts has not been tested sufficiently at high redshifts, it is still ap-plied to distant samples. Since the dust emission from a z > 3 typical galaxy may be several orders of magnitude below the sensitivity of the current existing instru-ments, it is often the only way by which the dust attenuation of these galaxies can be inferred. However, whether this relation is applicable at high redshifts is still not certain. In other words, the assumption that the Lyman-dropout galaxies appear to be scaled-up versions of local starbursts has not been verified yet.
With the first ultra-deep radio and X-ray data (Richards, 2000; Alexander et al., 2003), surveys to dust attenuation at high redshift became possible, although the sensitivity at these wavelengths was insufficient for a direct detection of the objects. Therefore, stacking procedures to increase the signal-to-noise ratio were applied.
2.4. LIR DETERMINATION USING UV COLOR 25
These initial studies suggested an agreement between UV and radio/X-ray mea-surements of dust attenuations at z ∼ 2-3. With the launch of the Spitzer Space Telescope, the first direct detections of dust emission in the IR at 24 µm for galaxies at z ∼ 2 was obtained. Using these data, several studies have demonstrated that the dust attenuation inferred from the direct IR detections are in agreement with that obtained by the UV slope β (Reddy et al., 2006, 2010; Daddi et al., 2007). With the release of the high resolution 100 and 160 µm data from the Herschel Space Observa-tory, the survey of dust emission could be expanded. Reddy et al. (2012) derived the thermal dust emission from a sample of typical star-forming galaxies at z ∼ 2. Their results are shown in the left panel of Figure 2.6, where the mean dust attenuation (LIR/LU V) is plotted against the UV slope β. In this figure, we see that galaxies
with redder β are on average dustier up to luminosities of LIR = 1012L . Besides,
the correlation between dustiness and UV slope is essentially identical to the corre-lation found for local starbursts by Meurer et al. (1999). In addition to this study, Lee et al. (2012) performed a similar survey on a sample of UV luminous z ∼ 3.7 galaxies. Their results are also consistent with the theoretical predictions, except for the highest luminosity bin, that is interpreted as a sample of young galaxies, see Figure 2.6 right. For this thesis, we studied a sample around the same redshift range as Lee et al. (2012), on different fields for a variety of UV luminosity samples.
Figure 2.6: Mean dust attenuation (LIR/LU V vs. UV slope (β). Left: for different subsamples of
z ∼ 2 galaxies, from Reddy et al. (2012). The solid line is the attenuation curve for UV starbursts (Meurer et al., 1999) and the dashed line is the curve for the SMC. The blue and the red point match the results of the stacks with β< − 1.4 and β> − 1.4, respectively. In purple, we see the result of the low luminosity ultra-luminous infrared galaxies (ULIRGs) stacks. Moreover, in cyan the 3 σ upper limit and stacked 24 µm implied value of the dust attenuation for the youngest galaxies in the samples is shown. On average, galaxies with redder β are dustier up to luminosities of LIR= 1012L . Besides, the correlation between dustiness and UV slope is essentially identical
to the correlation found for local starbursts. Right: similar as left, for a sample of z ∼ 3.7 galaxies from Lee et al. (2012). The sample is divided in three UV luminosity dependent bins. We see that for the lowest two bins, the IRX − β relation is satisfied, whereas for the highest luminosity bin it is not: this subsample is interpreted as a group of very young galaxies.
Chapter 3
Data
In this chapter, we will discuss the data sample and data reduction techniques used for this project. This includes an overview of the observatories used to obtain the rest-frame UV and IR images, the selection methods and the software that is used to clean the observed images and to detect the galaxies.
3.1
Observatories
3.1.1
Great Observatories Origins Deep Survey
The data that is used for this project is part of the Great Observatories Origins Deep Survey (GOODS) (Dickinson et al., 2003). The GOODS project covers the two deepest CANDELS fields, of the five fields in total. It combines deep observa-tions from the biggest space telescopes from NASA and ESA, including the Hubble Space Telescope, Spitzer Space Telescope and the Herschel Space Observatory. The obtained data are freely accessible.
Originally, this survey has been launched to make the deepest possible photometric images from the distant Universe. The two GOODS fields, S and GOODS-N, are the successors of the Hubble Deep Field (HDF), a survey done with the Hubble Space Telescope (HST) Wide Field and Planetary Camera 2 (WFPC2), that obtained its fame with its large depth. The project was initiated in 1995 and at the time, it was the deepest optical image of the distant universe ever obtained in four filters from the near UV to far-red optical light. Later on, research had shown that optical and UV data alone was not sufficient to map every action in the field, therefore, other observatories were involved in the project. However, the HDF had limitations
in the sense that it was covering only 5 square arcminutes, which is too small for most statistical surveys. Therefore, the HDF was expanded to around 160 square arcminutes and got the name Hubble Deep Field North. An extra field located at the southern hemisphere became also part of the survey under the name Chandra Deep Field South. The data from both fields, later in this thesis called GOODS-N and GOODS-S, are subject of the project. In the next section, more detailed information about the observatories that are used for this project will be given: the Hubble Space Telescope (HST), Spitzer Space Telescope and the Herschel Space Observatory.
Figure 3.1: Picture of the coverage of the Hubble Space Telescope data of GOODS-S (left) and GOODS-N (right). Both fields cover an area of 10 x 16 arcminutes. Image credits: NASA
3.2. CATALOG SELECTION 29
3.1.2
Hubble Space Telescope
The HST-data used for this project is obtained by the Advanced Camera for Surveys (ACS) (PI: M. Giavalisco, Giavalisco et al. (2004)) and the Wide Field Camera 3 (WFC3) (PI: A. Koekemoer, Koekemoer et al. (2011)). The two instruments together provide photometric data in 8 bands in the range 430-1540 nm, in the rest-frame UV branch for our sample of z ∼ 3.8.
3.1.3
The Spitzer Space Telescope
The Spitzer Space Telescope (SST) is an infrared space observatory that carries three instruments on-board and is part of the GOODS survey (PI: M. Dickinson, Dickinson and GOODS Team (2004)). For this project, data from the Multiband Imaging Photometer for Spitzer (MIPS) was used, which covers three observation bands. However, due to sensitivity and resolution reasons only the 24 µm band is used for this project, which gives deep data of both fields of 5.9 µJy (GOODS-S) and 6.6 µJy (GOODS-N) for a 3σ detection.
3.1.4
The Herschel Space Observatory
The Photodetecting Array Camera and Spectrometer (PACS) instrument on the Herschel Space Observatory provided deep images of the 100 and 160 µm bands of both fields (PI: D. Elbaz, Elbaz et al. (2011)). We found 3σ depths of 0.20 mJy and 0.92 mJy at 100 µm and 160 µm, respectively for GOODS-S, and of 0.38 mJy (100 µm) and 1.8 mJy (160 µm) for GOODS-N. These very large depths provide us to discover the very distant universe. We present a summary of the properties of the data in Table 3.1.
3.2
Catalog selection
The high redshift galaxies are selected using the Lyman-break color selection tech-nique, which has been shown to be a highly effective tool to select galaxies at high redshift (z > 2) (Steidel et al., 1999; Madau et al., 1996). The technique separates galaxies located at high and low redshifts by the intrinsic Lyman edge in the opacity of intergalactic neutral hydrogen. The most notable breaks are the Lyman-break at 912 ˚A and the less strong Balmer-break at around 4000 ˚A. We used the first of these two to photometrically select high-redshift galaxies. Steidel et al. (1999)
Camera Filter λc FWHM Depth Depth Area (arcmin2) Area (arcmin2)
(µm ) (arcsec) GOODS-S GOODS-N GOODS-S GOODS-N
ACS F435W 0.432 0.08 28.95 AB 28.95 AB 16x16 16x16 F606W 0.592 0.08 29.35 AB 29.35 AB 16x16 16x16 F775W 0.769 0.08 28.55 AB 28.55 AB 16x16 16x16 F814W 0.805 0.09 28.84 AB 28.84 AB 16x16 16x16 F850LP 0.906 0.09 28.55 AB 28.55 AB 16x16 16x16 WFC3 F105W 1.06 0.15 27.45 AB 27.45 AB 16x16 16x16 F125W 1.25 0.16 27.66 AB 27.66 AB 16x16 16x16 F160W 1.54 0.17 27.36 AB 27.36 AB 16x16 16x16
MIPS 24 µm 24.9 5.7 5.9 µJy 6.0 µJy 10x16 10x16
PACS 100 µm 100 6.7 0.20 mJy 0.38 mJy 10x10 10x16
160 µm 160 11.0 0.92 mJy 1.8 mJy 10x10 10x16
Table 3.1: Summary of the properties of data of both fields and the observatories. The HST/ACS data originate from Giavalisco et al. (2004), HST/WFC3 from Koekemoer et al. (2011), Spitzer/MIPS from Dickinson and GOODS Team (2004) and Herschel/PACS from Elbaz et al. (2011).The depths of the HST/ACS and HST/WFC3 observations are presented in 5 σ limits and given in AB magnitudes, which is a magnitude system that is based on flux measurements, cali-brated in absolute units. The Spitzer/MIPS and Herschel/PACS depths are given in 3 σ limits, in units of mJy, and is obtained by error calculations of fluxes of individual galaxies.
3.3. PHOTOMETRY 31
showed through spectroscopic work that photometric color criteria are successful in identifying a substantial population of high-redshift galaxies.
Bouwens et al. (2009) selected a sample of Lyman-break galaxies (LBGs) located in the GOODS fields. Using the HST Advanced Camera for Surveys (ACS) and NICMOS, they divided the galaxies in samples of about one redshift bin from z ∼ 2 to z ∼ 6. For this project, we will use the sample with an average redshift of 3.8. Be-cause this group of galaxies is not detected at a wavelength of 450 nm (the B-band) and shorter, these galaxies are called ’B-dropouts’, and follow the relation
[(V606− i775>0.90(i775− z850)) ∨ (V606− i775>2)] ∧ (V606− i775>1.2) ∧ (i775− z850<0.6)
(3.1) where V606, i775 and z850 are the band centered at 606, 775 and 850 nm respectively.
These criteria are shown in a two-color diagram in Figure 3.2. The data sample con-tains 1304 and 1466 z ∼ 3.8 B-dropouts in GOODS-S and GOODS-N, respectively.
3.3
Photometry
To extract the source flux from the MIPS 24 and PACS 100 and 160 images, we used the source-fitting algorithm that was developed by I. Labb´e, as described in Labb´e et al. (2010a,b, 2006); Gonz´alez et al. (2010); Wuyts et al. (2007). This technique makes use of a higher resolution prior, in this case the WFC3 H-band, to localize the B-dropout galaxies in the (F)IR photometry. Obtaining reliable IR fluxes from the MIPS 24 µm and PACS 100 and 160 µm is challenging because of the contamination from the extended point spread function (PSF) wings of nearby foreground stars. By locating the candidates and nearby sources in the H-band image, we can model these objects using their isolated flux profiles. Applying SExtractor (Bertin and Arnouts, 1996) on the H-band image, we created a segmentation map to define the boundaries of each source in the area that needs to be cleaned. To ensure all possible relevant neighbors are fitted, we used a low (2σ) threshold. Furthermore, the light profiles of the sources within the boundaries are assumed to be the empirical light profiles and to be equal for the two different wavelength images. To match the H-band PSF with the PSFs of the IR (MIPS and PACS) images, we convolve the H-band template with a carefully constructed kernel to match the IR PSF. Then we fit the templates simultaneously to the IR images. Afterwards, we subtract the best-fit models of the neighbors by fitting the total flux of each object separately. This yields a clean image of the Lyman-break galaxy in the MIPS and PACS images. This photometric technique is represented in Figure 3.3.
Figure 3.2: Two-color diagram showing the selection criteria to find z ∼ 3.8 B-dropouts from Bouwens et al. (2009). Sources that fall within the shaded regions are included in the selection. The blue lines correspond to the expected colors of starbursts with different UV slopes β. On the other hand, the red tracks correspond to the colors of dusty, low-redshift interlopers, e.g. galaxies that show similar drops in their spectrum as dropout galaxies due to dust obscuration. They have therefore similar (B − V) AB magnitudes compared to ’real’ B-dropouts but can be dissociated by their (V − Z) AB magnitude. The red arrow is the reddening vector from Calzetti et al. (2000). From the plot it is clear that the selection criteria are effective in identifying high-redshift galaxies with β<0.5.
After we have cleaned the IR images in this way, we measured the flux using aperture photometry: for the MIPS 24 µm, PACS 100 µm and PACS 160 µm band we applied
3.4. MODELING THE SED 33
Field Total # objects Band ≥ 3σ detections
GOODS-S 1304 MIPS 24 34 PACS 100 17 PACS 160 27 GOODS-N 1466 MIPS 24 59 PACS 100 29 PACS 160 44
Table 3.2: The obtained ≥3σ detections, given per band for each field separately. The significance is based on Gaussian noise.
an aperture with a radius of a 3.5”, a 4.0” an a 6.0” respectively. Consistent with the point source profiles, the fluxes were corrected by a factor × 2.60 for MIPS 24, 2.45 × for PACS 100 and × 2.60 for PACS 160 to account for light that falls outside the aperture. The number of obtained >3σ detections are presented in Table 3.2. The er-rors include the uncertainty in the best-fit confusion correction, added in quadrature and is based on Gaussian noise. However, to check the reliability of the calculated significance, we performed a Monte Carlo simulation to see if the detections could have arisen randomly.
3.3.1
Monte Carlo simulation
We performed a Monte Carlo (MC) simulation to address the robustness of the IR fluxes, using a catalog of ’fake’ objects that was topologically randomly composed. Running the software over random positions in the fields and comparing the results with the ’real’ results provides a reliable method to verify the calculated errors. Although the results seemed significant by Gaussian noise assumptions, the MC simulation shows similar significance, see Table 3.3. This might indicate that the noise is behaving in a more complicated way than Gaussian and the signal-to-noise (S/N) is not sufficient to work with. Therefore, we increased the S/N by making use of a stacking procedure, which will be discussed in Chapter 4.
3.4
Modeling the SED
We need a more precise determination of the redshift to adjust the sample for ’in-terlopers’, e.g. galaxies that are falsely identified as high-redshift galaxies with the Lyman-break technique, for which we used the photometric redshift code EAZY
Figure 3.3: Example of the photometric data reduction for object GSDB-2526493578 in the 160 µm band (6.5σ detection), illustrating the deblending procedure for MIPS and PACS photometry. (a) shows the confusion by nearby neighbors in the original 160 µm image, which will be reduced using the higher resolution WFC3 H-band image. The objects will first be identified in the SExtrac-tor segmentation map (c). A model of the 160 µm image is created using information on position and extent of the galaxies from the H-band image (d). A model of the nearby neighbors (e) is substracted from the original image to obtain the cleaned image 160 µm (f).
(Brammer et al., 2008). Briefly, the program fits a non-negative superposition of SED templates to the HST ACS and WFC3 measured fluxes. As a side effect, this program also gives us the UV slope β and the LU V. In Wuyts et al. (2008b), a short
description of EAZY is given.
3.4.1
Redshift z
To model the individual UV spectra, we implemented six spectral templates, includ-ing five principal components templates from the library of templates from Grazian et al. (2006). These were followed by the ’nonnegative matrix factorization’ algorithm of Blanton and Roweis (2007) to cover the colors of galaxies in the semianalytic model of De Lucia and Blaizot (2007). In order to take dusty galaxies into account, one dusty template with an age of 50 Myr and AV = 2.75 was added. Using a
tem-plate error function, the program fits a nonnegative superposition of the six SED templates, from which a redshift probability distribution p(z|C, m0) is constructed
3.4. MODELING THE SED 35
Field Sample Total # objects 160 µm detections (≥ 3 σ) Detections/Total
GOODS-S B-dropouts 1304 27 0.021
MC simulation 2592 55 0.021
GOODS-N B-dropouts 1466 44 0.030
MC simulation 3012 70 0.023
Table 3.3: Results of the Monte Carlo simulation for 160 µm. The total amount of ≥ 3σ detections of the Lyman-break galaxies is compared with ≥ 3σ ’fake’ objects of the Monte Carlo simulation. Thereby, the ratio of ≥ 3σ detections to the total amount of objects is given. This ratio is almost similar for both ’real’ and ’fake’ objects.
for each galaxy with observed colors C, using the H-band magnitude m0 as a prior.
Then, the best estimate of the galaxy’s redshift, zmp, is given by
zmp=
R zp(z|C, m0)dz
R p(z|C, m0)dz
(3.2)
where the redshift is marginalized over the total probability distribution. By inte-grating the probability distribution until the integrated probability equals 0.317/2 by changing the limits, the 1σ limits were computed. Figure 3.4 shows an example of an SED model and its redshift probability distribution.
To correct the sample for interlopers, we eliminated all galaxies with a photometric redshift lower than 3 calculated by EAZY. After the selection, we remained with a sample consisting of 1230 and 1338 Lyman-break galaxies for GOODS-S and GOODS-N, respectively, which means that ∼ 7% of the total sample is excluded after the correction.
3.4.2
UV slope β
With the EAZY SED models, the UV slope β can be calculated easily. To derive the rest-frame SED, we simply multiplied the wavelengths by 1/(1 + z). As we saw in the previous chapter, β is defined as
fλ ∝ λβ (3.3)
where Fλ = λfλ. Therefore, β is given by the fit of a log(fλ) vs log(λ) diagram, in a
3.4.3
UV luminosity L
U VWe calculated the integrated flux (Lf ilter) using a filter in the range of 1300-1900 ˚Ain
order to derive LU V. The absolute magnitude of a galaxy is given by
M = −2.5log(Lf ilter) + zeropoint − DM (3.4)
where DM is the distance modulus, which is also calculated with Eazy. The zeropoint depends on the unit of the flux. Finally, the LU V is given by
LU V = 10(M −M )/2.5 (3.5)
Figure 3.4: Example of an Eazy model SED, object GSDB-2526493578, with z = 4.01, β = −1.87 and L1600= 2.14 × 109. In the upper left panel we see the probability distribution of the redshift
Chapter 4
Stacking procedure and analysis
Because the Monte Carlo simulation showed that there are no significant individual detections found in all three bands, we applied a stacking analysis on the data. Stacking is a statistical process by which the signal from multiple undetected sources is combined to increase the overall S/N. Stacking by n images yields an increase of the S/N by √n. In order to obtain a representative flux density of a population, we take the mean and median flux density from the sum of the individual images (see also Reddy et al. (2012); Lee et al. (2012)). In Figure 4.1 an impression of a stacking procedure is shown. Because this analysis provides a higher S/N ratio than compared to individual signals, we are able to look deeper into the IR part of spectra of high-redshift galaxies.
Figure 4.1: Impression of how stacking increases the S/N ratio. Stacking by n images yields an increase of the S/N by√n.
4.1
Stacking procedure
The stacking procedure that is used to stack the MIPS 24 µm and PACS 100 and 160 µm is as follows. A cleaned area of 64”x64” is extracted around each object that needs to be stacked. The area is large enough to obtain a reliable estimate of the local background. After dividing the sample in subsamples, we added the images of each subsample and calculated the average of the sum per pixel. Besides
mean stacks we also performed median stacks to check if the results are biased by bright outliers. We stacked the 24, 100 and 160 µ in the same way irrespective whether the galaxy is detected in the image or not, to ensure a consistent result across wavelengths. Aperture photometry as described in the previous chapter is performed on the images to calculate the mean and median fluxes, from which the radii are given in the first row of Table 4.1.
4.2
Background corrections
Small offsets are probably present in individual stacks and may lead to large dif-ferences in the stacked images. Therefore, adjusting for the background is required to obtain reliable stack outcomes. For every stack, we defined an annulus that is expected to be representative to the total background, with inner radii that are dis-tant enough to the central object, compared to the PSF from the wavelength band, and outer radii not to close to the outer edge, since this is on average negative for unknown reasons. Thereby, the total surface of the annulus is attempted to be ∼ 10 times larger than the surface of the flux measurement aperture. The inner and outer radii of the background annulus for each wavelength band are given in Table 4.1.
The total flux in the annulus is measured and divided through the amount of pixels in the annulus, where subsequently the background flux per pixel is subtracted from all the pixels in the image. Now, the image is corrected from background contamination and a new measure of the flux in the aperture provides the background corrected flux.
To check the effectiveness of the background subtraction, we created random stacks at arbitrary locations in the fields. For each band, we added 300 ’fake’ images into a bootstrap simulation, which is a simulation during which random images (with replacement) of sources from a sample are chosen and stacked. We performed the simulation on the fake images 500 times, which gives 500 different stacks of the 300 images. The results are presented in the histogram in Figure 4.2, which is overplotted by a Gaussian. As we see, the Gaussian is not centered exactly at 0, but has a slight positive offset. This indicates that the background is biased (for unknown reason). Therefore, also the measured flux has to be corrected for this bias, see Table 4.1 for the corrections per band.
4.3. OTHER CORRECTIONS 39
N
flux (mJy)
Figure 4.2: Impression of the background subtraction for random stacks at 160 µm. Lef t : back-ground contaminated image of a random stack with in green the aperture for the flux measurement (r = 6”) and in red the inner and outer radius of the annulus that is used for background subtrac-tion, with rin= 13” and rout = 22”. The radii are chosen to give a reliable representation of the
background, with enough distance between the central aperture and the outer negative band of the image. Center : the background subtracted image, where the total flux in the annulus equals zero. Right : The histogram of the bootstrap simulation of the background subtracted random stack, with a Gaussian function is overplotted. Because the histogram is not exactly centered at zero, the stack results have to be corrected for this bias.
4.3
Other corrections
Besides correcting for background contamination, the measured flux is also biased because part of the flux falls outside the central aperture. Using the normalized PSF that is calculated by cleaning the individual images, adjusting for this effect is pos-sible, by applying the same method for measuring the flux in the central aperture as for normal flux determinations on the PSF image, including background corrections. Thereby, we need to adjust for the fact that the background is biased because it is reduced to a tile size of 64”x64”. This is the last correction factor, and combined with the previous one it gives the total correction factor with which the measured fluxes need to be multiplied, see Table 4.1.
4.4
Error calculations
The width or significance of the Gaussian of the simulated random stacks gives an indication of the error of a stack of 300 images. Since our stacks consist of a variety of number of images, the uncertainties of the stacks are individually determined. By performing a bootstrap simulation on the images of the subsamples, the error for
each individual subsample is determined. This process is repeated 200 times in order to determine the spread in the measured flux of the simulated stacks. The standard deviation of all the fluxes equals the significance of the stacked detection.
24 µm 100 µm 160 µm
r aperture flux measurement 3.5” 4.0” 6.0”
rinannulus background 10” 13” 13”
rout annulus background 20” 22” 22”
tile size 64”x64” 64”x64” 64”x64”
bias background 0.000124 mJy 0.00273 mJy 0.00450 mJy
psf correction factor 1/0.448 1/0.543 1/0.602
tile size correction factor 1.15 1.35 1.35
total correction factor 2.57 2.49 2.24
Table 4.1: Properties that are used for the background correction, psf correction and tile size correction, where the last two are combined in the total correction factor.
4.5
Construction of subsamples
In order to investigate trends in UV slope and luminosity (magnitude), we divided the sample in 6 subsamples, see Table 4.2. Subsamples A, B, C, D are divided based on UV magnitude and together they cover the entire sample, whereas subsamples AI and AII are subgroups of the highest luminosity subsample A, where the devision is based on UV slope β. In this table, also the measured fluxes of the different subsamples are presented. The stacked images are shown in Figure 4.3.
4.5. CONSTRUCTION OF SUBSAMPLES 41 Sample hMHi hβi N f24 f100 f160 GOODS-S A 24.2 -1.45 100 (3.89 ± 0.99) × 10−3 (7.50 ± 2.38) × 10−2 (1.25 ± 0.36) × 10−1 B 24.9 -1.72 350 (1.39 ± 0.42) × 10−3 (<3.28) × 10−2 (6.27 ± 1.79) × 10−2 C 26.3 -1.80 440 (3.62 ± 2.33) × 10−4 (<2.51) × 10−2 (<5.05) × 10−2 D 27.2 -1.85 440 (<8.47) × 10−4 (<2.37) × 10−2 (<4.71) × 10−2 A1 24.1 -1.73 50 (1.77 ± 0.97) × 10−3 (5.87 ± 2.63) × 10−2 (1.23 ± 0.45) × 10−1 A2 4.3 -1.17 50 (6.00 ± 1.80) × 10−3 (9.14 ± 3.78) × 10−2 (1.26 ± 0.63) × 10−1 GOODS-N A 24.2 -1.40 100 (2.32 ± 0.69) × 10−3 (4.81 ± 3.95) × 10−2 (1.12 ± 0.54) × 10−1 B 24.9 -1.61 400 (<1.08) × 10−3 (<4.95) × 10−2 (<9.03) × 10−2 C 26.3 -1.78 469 (<8.27) × 10−4 (<4.31) × 10−2 (3.86 ± 2.95) × 10−2 D 27.2 -1.83 469 (<9.78) × 10−4 (<4.85) × 10−2 (<8.55) × 10−2 A1 24.1 -1.78 50 (<3.69) × 10−3 (<1.10) × 10−1 (<1.76) × 10−1 A2 24.3 -1.13 50 (3.63 ± 0.83) × 10−3 (1.35 ± 0.63) × 10−1 (1.66 ± 0.73) × 10−1
Table 4.2: Subsamples of GOODS-N and GOODS-S. A, B, C and D are classified by H-band AB magnitude. A1 and A2 are β−based subsamples of A. N is the number of galaxies in each subsample. The measured fluxes (in mJy) are presented in the last three columns.
GOODS-S GOODS-N 24µm 100µm 160µm 24µm 100µm 160µm A B C D A1 A2
Figure 4.3: Inverted color map of the average images of the stacks of all subsamples of both fields, centered at 0 mJy. We observe clear detections for the most luminous stacks (A), even as for the stacks that are split by β (A1 and A2).
Chapter 5
Results
In this chapter, we will discuss the results of the stacked images. In what follows, we will start with an overview of the calculated infrared luminosities of the stacks using the IRX − β relation, after which the UV luminosity and UV color β stacks will be reviewed. The section will finish with a comparison between the dust attenuation we calculated and the IRX − β relation.
5.1
Overview dust-corrected LIR
5.1.1
Infrared luminosities predicted by the IRX −β relation
As discussed in Chapter 2, one way to calculate the infrared luminosity is by a rela-tion between the slope β and the ratio of infrared to ultraviolet luminosity. Using the SED model fitting program EAZY (Brammer et al., 2008), the slopes of all galaxies are measured individually. Table 5.1 shows average calculated values for β for each subsample. Using equation 2.10 the UV dust absorption centered at 1600 ˚A, A1600, is
derived and given in magnitudes. Integrating the individual EAZY spectral energy distributions results in the UV luminosity of each galaxy, from which the averaged values are given in the table. This leads us finally to the expected infrared luminosity using equation 2.9. The values in the last column of Table 5.1 are increased by 0.24 dex (Reddy et al., 2012) to account for the fact that the dust attenuation in the original equation of Meurer et al. (1999) is derived using a far-infrared luminosity given by LIR ≡ L(40−120µm) in stead of LIR ≡ L(8−1000µm) as what is used here.
For both fields the UV luminosity selected stacks A, B, C and D, show a trend between UV luminosity and β: the higher the luminosity the redder the slope β.
This results in a larger difference in IR luminosities between the stacks compared to the differences between the UV luminosities. If we compare the UV color selected stacked samples A1 and A2, we see that on average the red subsample A2 shows a slightly lower UV luminosity, but because of the higher absorption coefficient a higher IR luminosity. This proportionality holds for the UV color stacks of both GOODS-N and GOODS-S.
Sample hβi hA1600i hLU Vi hLIRi (mag) L L GOODS-S A -1.45 1.54 2.39 × 1010 2.68 × 1011 B -1.72 1.19 1.38 × 1010 9.92 × 1010 C -1.80 0.85 4.45 × 109 1.88 × 1010 D -1.85 0.76 2.18 × 109 7.85 × 109 A1 -1.73 0.99 2.64 × 1010 1.13 × 1011 A2 -1.17 2.10 2.12 × 1010 3.61 × 1011 GOODS-N A -1.40 1.63 2.32 × 1010 2.90 × 1011 B -1.61 1.23 1.25 × 1010 9.41 × 1010 C -1.78 0.88 3.90 × 109 1.76 × 1010 D -1.83 0.80 1.95 × 109 7.58 × 109 A1 -1.68 1.09 2.53 × 1010 1.57 × 1011 A2 -1.13 2.18 2.07 × 1010 4.78 × 1011
Table 5.1: Results of the β, A1600, LU V and LIR determinations using SED modeling (Brammer
et al., 2008) and the IRX − β relation (Meurer et al., 1999). The IR luminosities given in the last column are increased by 0.24 dex (Reddy et al., 2012) to account for the fact that the dust attenuation in the original equation of Meurer et al. (1999) is derived using a far-infrared luminosity given by LIR≡ L(40 − 120µm) in stead of LIR≡ L(8 − 1000µm) as is used here. The results for
UV luminosity stacks A, B, C and D show a redder slope for higher UV luminosities, whereas the UV color selected stacks A1 and A2 show a slightly lower UV luminosity for a redder slope. These trends are applicable on both fields.
5.1.2
Infrared luminosities derived by MIPS 24 µm and PACS
100 and 160 µm detections
Although the Monte Carlo simulation showed that there were no significant individ-ual detections of the B-dropout galaxies in the MIPS 24 µm and PACS 100 and 160
5.2. COMPARISON BETWEEN DUST ATTENUATIONS 45
µm bands, the stacking procedure increased the S/N and yield significant results for some subsamples, see Table 4.2. Fitting the stacked detections to the model SED calculated by Wuyts et al. (2008a) provides a method to convert from flux to lumi-nosity, for each infrared band individually. The results of this procedure are given in Table 5.2. For comparison, the predicted infrared luminosity by the IRX −β relation is again presented in the first column and is similar to the last column of Table 5.1. The error calculations are based on the bootstrap analysis that is performed on every stacked image. In case no significant detection was found, the 3σ upper limit is given.
In Figure 5.1 an SED of subsamples A1 (solid line) and A2 (dotted line) of the results of the 160 µm detections are presented, similar to Figure 2.4. We see that for our sample, the galaxies with a redder UV slope have more dust emission compared to the galaxies with blue slope, and this follows our expectation. Whether this is consistent with the IRX − β relation will be discussed in the next sections.
Figure 5.1: Wavelength (µm) versus Flux (mJy) SED plot of the UV slope selected samples A1 and A2, combined for GOODS-N and GOODS-S, of the 160 µm results. We see that galaxies with a redder UV slope have more dust emission compared to the galaxies with a blue slope.
5.2
Comparison between dust attenuations
The above gives the results of the dust-corrected infrared luminosities that are ob-tained by the two different methods. To compare our results of the dust attenuation
Sample LIR(U V ) LIR(24µm) LIR(100µm) LIR(160µm) L L L L GOODS-S A 2.68 × 1011 (9.28 ± 2.40) × 1011 (5.43 ± 1.73) × 1011 (2.41 ± 0.69) × 1011 B 9.92 × 1010 (3.39 ± 1.01) × 1011 (<2.43) × 1011 (1.24 ± 0.36) × 1011 C 1.88 × 1010 (8.66 ± 5.58) × 1010 (<1.82) × 1011 (1.06 ± 0.38) × 1011 D 7.85 × 109 (<1.92) × 1011 (<1.64) × 1011 (<8.71) × 1010 A1 1.13 × 1011 (4.05 ± 2.22) × 1011 (4.08 ± 1.83) × 1011 (2.29 ± 0.84) × 1011 A2 3.61 × 1011 (1.48 ± 0.45) × 1012 (6.88 ± 2.84) × 1011 (2.54 ± 1.26) × 1011 GOODS-N A 2.90 × 1011 (5.42 ± 1.61) × 1011 (3.41 ± 2.79) × 1011 (2.12 ± 1.03) × 1011 B 9.41 × 1010 (<2.69) × 1011 (<3.77) × 1011 (<1.89) × 1011 C 1.76 × 1010 (<2.08) × 1011 (<3.31) × 1011 (7.96 ± 0.61) × 1011 D 7.58 × 109 (<2.39) × 1011 (<3.61) × 1011 (<1.70) × 1011 A1 1.57 × 1011 (<7.27) × 1011 (<6.81) × 1011 (<2.94) × 1011 A2 4.78 × 1011 (9.44 ± 2.16) × 1011 (1.08 ± 0.51) × 1012 (3.56 ± 1.56) × 1011
Table 5.2: Results of IR luminosity as derived by the stacking analysis. The flux-to-luminosity conversion is performed by fitting the flux to a model SED from Wuyts et al. (2008a) for each IR band individually. The errors are the result of the bootstrap analysis that is performed on every stacked image. In case no significant detection was found, the 3σ upper limit is given. For comparison, the predicted infrared luminosity from Table 5.1 is shown in the first column.
with the theory, in this and the next sections, the results will be presented in IRX versus β diagrams, including the empirical IRX − β relation of Meurer et al. (1999). Because the 160 µm photometry is of the highest quality compared to the other bands, it will therefore give the most reliable LIR determination. Thereby, this band is of the longest wavelength, hence it requires the least extrapolation to calculate the total infrared luminosity. Therefore, we start with a review of the results obtained with this band. The results that will be discussed in this and the next section will only contain the most important results, based on subsamples and infrared observa-tions. For results of the entire sample at all wavelength we would like to refer the reader to the appendix.
In Figure 5.2 the IRX versus β plot of the highest luminosity subsample, divided in two bins based on UV color, A1 (blue) and A2 (red), are presented. The LIR determination is only based on the 160 µm detections. The points represent the weighted mean luminosities of the two fields for subsamples A1 and A2. In general,
5.3. COMPARING THE RESULTS TO OTHER SURVEYS 47
the figure shows that for galaxies with a redder slope, the dust attenuation is higher, which follows our expectations. Thereby, the LIR/LU V derived by IR detections is
consistent with the IRX − β relation of Meurer et al. (1999), within the error bars. Hence, the results suggest that the dust properties of this z ∼ 3.8 sample are similar to those of local starbursts.
LI R /L U V β
Figure 5.2: Dust attenuation LIR/LU V versus β plot, where the solid line represents the
theoret-ical IRX − β relation as derived by Meurer et al. (1999). The points match the UV color stacks, A1 (blue) and A2 (red) and are the results of the combination of the subsamples of GOODS-N and GOODS-S at 160 µm. The figure shows that for galaxies with a redder slope, the dust attenuation is higher, which follows our expectations. Thereby, the IRX −β relation provides a good estimation of the dust attenuation in comparison with these results.
5.3
Comparing the results to other surveys
A similar analysis at the same redshift range, but using significantly shallower data, has been performed by Lee et al. (2012), of UV-luminous star forming galaxies in the Bootes field of the NOAO Deep Wide-Field Survey. They divided the sample in three bins based on I-band magnitude, from which the results are added in Figure 5.3 (orange points). The triangle corresponds to the highest UV luminosity bin, the square to the middle bin, and the orange upper limit to the lowest luminosity stack.
