Chapter 1
Observations

1.1 FIR Background

The Far Infrared Absolute Spectrophotometer (FIRAS) on the Cosmic Background Explorer (COBE) satellite first detected the FIR extragalactic background radiation, i.e., the average FIR flux density received per area of sky. FIRAS measured this background with low angular resolution. The FIRAS measurements contain both galactic and extragalactic emission. Fixsen et al. (1998) extracted the extragalactic part of the FIR background radiation (see Fig. 1.1) by modeling the galactic foreground emission and subtracting it from the FIRAS data. They described the residual average extragalactic FIR background intensity as

(1.1)

where is frequency, ₀ = 3000 GHz, and B is the Planck function. The FIRAS results brought up the idea, that the extragalactic FIR background might consist of emission from dust enshrouded distant starbursts. If these starbursts were at high redshifts, then the implied star formation could dominate the average star formation rate of the early universe. Therefore it became of great importance to identify the objects which produce the extragalactic FIR background.

Figure 1.1: Top: Average intensity of the extragalactic background radiation derived from FIRAS data. The lines represent different approaches to remove the galactic foreground from the FIRAS spectra. The smooth line is the model from Fixsen et al. (1998). Bottom: The same model (thick line) with 1 errors (thin lines). The dashed lines represent a different approach by Puget et al. (1996). The crosses show DIRBE determinations by Hauser et al. (1998). The diamonds are the same data recalibrated by Fixsen et al. (1998).

1.2 Deep Field Surveys

Figure 1.2 shows a deep field map obtained with MAMBO at the IRAM 30m telescope. MAMBO is sensitive in the one mm atmospheric window, between ~210 and ~290 GHz, with an effective central frequency of 250 GHz (1.2 mm) for thermal spectra. As SCUBA, MAMBO was able to resolve the extragalactic FIR background into distinct sources. By now, about 100 sources were detected in the deep field maps, most of which have no optical counterpart to the sensitivity limit of 4-m class telescopes. This lack of optical counterparts may be caused by strong dust obscuration toward the massive starburst.

Figure 1.2: The largest MAMBO 1.2 mm deep field, which is centered on the low-redshift cluster Abell 2125. For this mosaic, 140 one-hour maps were observed. About 40 significant sources are seen with S250GHz > 1.5 mJy. (Bertoldi et al., 2000b)

The nature and the spectral energy distribution (SED) of the high redshift sources seen at (sub)mm wavelengths is not known, except for a few objects where optical counterparts were clearly identified or where measurements at different (F)IR wavelengths exist. Those objects show a thermal-like FIR spectrum. In the local universe we also find galaxies undergoing massive star formation which is highly obscured by dust. The SEDs of those objects are dominated by thermal dust emission in the FIR. The dust emission accounts for the bulk of the bolometric luminosity. The dust absorbs the light of the massive bright stars in the starbursts and re-emits the absorbed energy in the FIR. Such galaxies are known as as (ultra) luminous infrared galaxies ((U)LIRGs). Two of the most prominent and best studied objects of this class are Arp 220 (at redshift z = 0.018) and M82 (z = 0.000677; see Fig. 1.3). Galaxies of this type would be optically faint if they were at high redshifts, as the dust obscures most of the optical emission. These local starburst galaxies may be comparable to the galaxies seen in the MAMBO and SCUBA maps.

Figure 1.3: The right picture shows the heart of the starburst galaxy M82. It was taken with the NASA Hubble Space Telescope (HST) wide field planetary camera 2 (WFPC2) at optical wavelengths. The ongoing high rate of star formation is due to an encounter with its large galactic neighbor, M81. The picture at upper left shows the entire galaxy. The image was taken with the Kitt Peak National Observatory’s 0.9-meter telescope. The HST view is indicated by the white outline in the center.

Figure 1.4 shows the SEDs of Arp 220 and M82. The energy output is dominated by the dust emission in the FIR, mostly between 1 and 10 THz, i.e., 30 to 300 m. The characteristics of thermal dust emission are described in more detail in section 2.1.3. Arp 220 and M82 both show emission at radio wavelengths, consisting of synchrotron and free-free radiation, which mostly comes from supernova remnants. Many of the sources detected in the MAMBO Abell 2125 map lack an optical counterpart, but do have a radio counterpart. The ratios of mm to radio flux densities support the idea that these objects are starburst galaxies, since for star forming galaxies there is a good correlation between the FIR and radio flux density (see section 1.5). The mid-infrared (MIR) spectra of starburst galaxies show additional dust emission from polycyclic aromatic hydrocarbons (PAH). Absorption features are also evident, the strongest at ~ 10 m being caused by silicate dust grains. This strength of the absorption features can serve as a measure for the column density of absorbing dust. The bolometric luminosity (i.e., integrated over all frequencies) of M82 is 3.2 ^. 10¹⁰ L , and 2 ^. 10¹² L for Arp 220, where L = 3.826 ^. 10³³ erg s^-1 is the luminosity of the sun.

Figure 1.4: The spectral energy distribution of Arp 220 and M82. The SEDs are combined from data of ISO and taken from NASA extragalactic database (NED), as assembled by Pierre Cox.

As Fig. 1.5 reveals, in many cases ULIRGs are merging galaxies. The collision of galaxies can trigger massive star formation. The process of galaxy merging is part of the hierarchical structure formation that will be described in more detail in chapter 2.

Figure 1.5: ULIRGs observed with the WFPC2 of the HST at optical wavelengths. It seems that many of these ULIRGs are merging galaxies. Credits: NASA, Kirk Borne (Raytheon and NASA Goddard Space Flight Center, Greenbelt, Md.), Luis Colina (Instituto de Fisica de Cantabria, Spain), and Howard Bushouse and Ray Lucas (Space Telescope Science Institute, Baltimore, Md.)

1.3 Source Number Counts

The SCUBA detector at the James Clerk Maxwell telescope operates at an effective central frequency of 350 GHz (850 m) for thermal spectra. The deep field maps obtained by this instrument and by MAMBO reveal an increasing number of sources (see e.g. Tables 1.1 - 1.4). Having extracted the sources from the deep field maps, one can plot their brightness distribution. This was done for MAMBO (e.g. Bertoldi et al., 2000b) and for SCUBA (e.g. Scott et al., 2001) sources from a number of maps, and the resulting cumulative counts are shown in Fig. 1.6.

Figure 1.6: Cumulative number counts per solid angle of sources found in MAMBO and SCUBA deep field maps. The filled squares indicate the most recent SCUBA results, taken from Scott et al. (2001). The SCUBA counts for the lowest flux values (below 2 mJy) are derived from fields in which the source flux densities were amplified by gravitational lensing.

Many SCUBA surveys targeted dense, low-redshift galaxy clusters to take advantage of the gravitational lensing amplification provided by the cluster. The typical flux density enhancement of background sources is a factor 2 to 3. Many objects found in SCUBA maps would have been below the typical detection limit (~ 4 mJy) unless they were magnified through gravitational lensing. An example of lensed submm sources is shown in Fig. 1.7.

Figure 1.7: A true color image of Abell 1835, taken with the 5.1-m Hale Telescope at Palomar Observatory. The contours plotted show the 850 m SCUBA map. There are possible optical counterparts to at least four of the submm sources, but the brightest submm source has none. The submm sources are lensed by the Abell cluster. Taken from Ivison et al. (2000).

1.4 The k-Correction

Figure 1.8: The flux density of a ULIRG-like galaxy of given luminosity at different redshifts when observed at a fixed observing wavelength.

In Fig. 1.9 a model SED that mimics Arp 220 is shown at different redshifts. The flux density is calculated following eq. (A.28). For a fixed wavelength, the flux density does not decrease monotonically with redshift as one would expect from the increasing distance, because the flux density varies strongly with rest frame wavelength. Depending on which part of the SED comes into view at a redshift, the flux density varies on top of the decrease caused by the increasing distance. This effect is called the ”k-correction“.

Figure 1.8 shows the flux density observed at a given wavelength as function of redshift for a source with a SED like Arp 220. At 1.2 mm and 850 m the k-correction is negative, and the flux density remains roughly constant between z = 1 and 10. This allows nearly distance independent, sensitivity (i.e., luminosity) limited surveys over this redshift range.

In the optical and near-infrared the k-correction is positive, resulting in enhanced faintness with increasing redshift. In the MIR the k-correction is especially large due to the falling flank of the dust emission.

Figure 1.9: A SED model spectrum fitted to Arp 220 shifted to different wavelengths according to eq. (A.28). The dashed red vertical line indicates the observing frequency of MAMBO. The flux density remains nearly constant between z = 0.5 and z = 10.

1.5 Redshift Estimation and Source Distribution

For objects in the MAMBO and SCUBA deep field maps which have no bright optical counterparts it is difficult to determine the redshift, as optical or NIR spectroscopy is not possible in this cases. However, other methods may be used to estimate the redshifts. The major part of the energy re-emitted by dust comes from bright massive stars. Massive stars are continuously produced during a starburst, but after a relatively short period of 3-30 million years the massive stars die as supernovae. After several 10 Myr this results in an equilibrium between the birth and death of massive stars. Since the FIR luminosity comes from the massive stars and the radio luminosity comes from supernova remnants, the FIR and radio luminosities should have a nearly constant ratio during a continuous starburst.

Condon (1992) examined local galaxies whose radio flux is not dominated by an active galactic nucleus (AGN) and indeed found a tight correlation between the far infrared luminosity and the radio flux density (see Fig. 1.10). Based on this correlation, Carilli & Yun (1999, 2000) suggested a method to estimate the redshifts of the galaxies seen in the deep field maps, assuming that these objects have a similar correlation. They use a FIR to radio spectral index, which reflects the FIR to radio flux density ratio. This spectral index is defined as

(1.2)

where S() is the flux density at frequency , and ₁ and ₂ are the two frequencies between which the spectral index is evaluated.

Figure 1.10: The radio to FIR correlation for local starforming galaxies not dominated by an AGN (Condon, 1992).

Figure 1.11: The change of radio to mm spectral index with redshift. The unit of flux density is arbitrary, as the spectral index only depends on the flux ratio.

Since the flux density at (sub)mm wavelengths is approximately proportional to the FIR luminosity, and since from Condon’s relation the FIR luminosity is proportional to the 1.4 GHz flux density, the (sub)mm to radio spectral index should be similar for star forming galaxies. But it is not constant with redshift, as Fig. 1.11 illustrates. Assuming a slope for the radio SED and a slope of the dust emission part, one can derive the redshift from the measured spectral index. The dependence of the spectral index Carilli and Yun found is

(1.3)

where _radio = -0.8 for synchrotron emission (Condon, 1992) and _submm 3 - 4 for the dust emission (Carilli & Yun, 1999). Since not all galaxies have exactly the same SED, all quantities involved show some scatter. Carilli & Yun (2000) analyze the scatter of the spectral index, and they evaluate a median spectral index for local starburst galaxies. They derived the redshift by this spectral index for a few objects where spectroscopy was possible and compared their result to the redshift determined by spectroscopy. They found both redshifts to agree reasonably well. Due to the large scatter the method of redshift determination by the spectral index only gives a rough redshift estimate. If the radio emission of an object is not detected, this method gives a lower limit to its redshift.

I have collected the (sub)mm flux densities for the objects detected in the SCUBA and MAMBO deep fields and the corresponding 1.4 GHz radio fluxes from Very Large Array (VLA) maps (Tables 1.1 - 1.4). I evaluated the spectral index (or its lower limit) for these objects. Using the median spectral index from Carilli & Yun (2000) I determined the redshift (or its lower limit) for the objects. The results are stated in the tables 1.1 - 1.4 and in Figures 1.12 and 1.13.

From the estimated redshifts I derive the redshift distribution of the sources (see Fig. 1.14). This distribution shows that the objects in the MAMBO and SCUBA deep fields are mostly at redshifts z 1 - 3. The (sub)mm flux densities together with the high redshifts indicate that the sources have high bolometric luminosities, L_bol > 10¹¹L . The equilibrium between the formation of bright stars and their death results in a proportionality between the bolometric luminosity and the star formation rate of the star forming galaxy. The star formation rates derived from the flux densities and redshifts of the SCUBA and MAMBO sources are very high, of order 1000 M yr^-1.

Table 1.1: Redshifts estimated from the 350 to 1.4 GHz spectral index following Carilli and Yun’s method, for sources detected in SCUBA deep field surveys that also have radio detections. S350GHz S1.4GHz z Name [mJy] [Jy] SMMJ02399-0136 25.4 ± 0.5 526.0 ± 7.0 0.70-0.01+0.01 1.5 -0.6+0.9 SMMJ00266+1708 18.6 ± 0.5 100.0 ± 7.0 0.95-0.02+0.02 3.1 -1.2+2.2 SMMJ09429+4658 17.2 ± 0.5 32.0 ± 7.0 1.14-0.04+0.05 6.0 -3.0+6.0 SMMJ14009+0252 14.5 ± 0.5 529.0 ± 7.0 0.60-0.01+0.01 1.1 -0.5+0.7 SMMJ14011+0252 12.3 ± 0.5 115.0 ± 7.0 0.85-0.02+0.02 2.3 -0.9+1.5 SMMJ02399-0134 11.0 ± 0.5 500.0 ± 7.0 0.56-0.01+0.01 1.0 -0.4+0.6 SMMJ04433+0210 4.5 ± 0.5 70.0 ± 7.0 0.75-0.04+0.04 1.8 -0.8+1.3 123616.15/621513.7 5.4 ± 1.9 53.9 ± 8.4 0.83-0.10+0.09 2.2 -1.2+2.3 123618.33/621550.5 7.8 ± 1.6 151.0 ± 11.0 0.71-0.05+0.05 1.6 -0.8+1.2 123620.28/620844.1 33.0 ± 4.9 123.0 ± 10.2 1.01-0.04+0.04 3.8 -1.7+3.8 123621.22/621108.9 4.2 ± 2.9 52.6 ± 8.2 0.79-0.24+0.13 2.0 -1.4+2.5 123621.27/621708.4 7.5 ± 2.3 148.0 ± 11.0 0.71-0.08+0.06 1.6 -0.8+1.3 123622.65/621629.7 7.1 ± 1.7 70.9 ± 8.7 0.83-0.07+0.06 2.2 -1.0+2.0 123622.72/620945.9 2.2 ± 1.9 51.0 ± 8.2 0.68-0.39+0.14 1.4 -1.3+1.9 123629.13/621045.8 6.1 ± 2.2 81.4 ± 8.7 0.78-0.10+0.08 1.9 -1.0+1.8 123631.25/620957.8 3.0 ± 1.7 152.0 ± 10.9 0.54-0.16+0.09 0.9 -0.7+1.0 123635.59/621424.1 3.9 ± 3.8 87.8 ± 8.8 0.69-0.68+0.14 1.5 -1.5+1.9 123646.05/621448.7 10.7 ± 2.1 124.0 ± 9.8 0.81-0.05+0.05 2.1 -0.9+1.6 123646.70/621226.5 1.1 ± 0.6 72.0 ± 9.1 0.49-0.16+0.10 0.8 -0.7+0.9 123649.71/621312.8 1.0 ± 0.6 49.2 ± 7.9 0.55-0.19+0.12 1.0 -0.8+1.2 123655.77/620917.4 4.9 ± 3.5 64.2 ± 8.4 0.79-0.25+0.12 1.9 -1.4+2.4 123656.60/621207.6 2.5 ± 0.7 46.2 ± 7.9 0.72-0.09+0.08 1.6 -0.8+1.5 123656.91/621302.2 0.9 ± 0.6 49.5 ± 7.9 0.53-0.23+0.12 0.9 -0.8+1.1 123700.26/620909.8 11.9 ± 3.0 324.0 ± 18.0 0.65-0.06+0.05 1.3 -0.7+1.0 123701.57/621146.6 4.7 ± 2.1 128.0 ± 9.9 0.65-0.12+0.08 1.3 -0.8+1.2 123709.45/620837.7 5.1 ± 4.6 72.0 ± 8.8 0.77-0.44+0.14 1.9 -1.7+2.5 123709.77/620841.1 8.3 ± 4.5 67.9 ± 8.3 0.87-0.16+0.10 2.4 -1.5+3.0 LH850.1 10.5 ± 1.6 62.0 ± 13.0 0.93-0.06+0.07 2.9 -1.4+2.9 LH850.8 5.1 ± 1.3 130.0 ± 30.0 0.66-0.09+0.09 1.4 -0.8+1.3 LH850.12 6.2 ± 1.6 290.0 ± 40.0 0.55-0.08+0.07 1.0 -0.6+0.9 00266+1708 18.6 ± 0.5 94.0 ± 7.0 0.96-0.02+0.02 3.2 -1.3+2.4 12368+6212 7.0 ± 0.5 20.0 ± 7.0 1.06-0.07+0.09 4.4 -2.2+4.4 14009+0252 15.6 ± 0.5 529.0 ± 7.0 0.61-0.01+0.01 1.2 -0.5+0.7 14011+0252 14.6 ± 0.5 115.0 ± 7.0 0.88-0.02+0.02 2.5 -1.0+1.7 14171+5229 8.8 ± 0.5 120.0 ± 7.0 0.78-0.02+0.02 1.9 -0.8+1.2 S350GHz: Flux density at 350 GHz; S1.4GHz: Flux density at 1.4 GHz; : 350 to 1.4 GHz spectral index; z: redshift estimated using the Carilli & Yun method. Data taken from Barger et al. (2000); Smail et al. (2000); Fox et al. (2001); Dannerbauer et al. (2002).

Table 1.2: Lower redshift limits estimated from the 350 to 1.4 GHz spectral index following Carilli and Yun’s method, for sources detected in SCUBA deep field surveys that have no radio detection but upper limits to the radio flux density. Name S350 GHz S1.4 GHz z [mJy] [Jy] LH850.2 10.9 <280 >0.66 > 1.4 LH850.3 7.7 <160 >0.70 > 1.5 LH850.4 8.3 <120 >0.77 > 1.8 LH850.5 8.6 <160 >0.72 > 1.6 LH850.6 11.0 <120 >0.82 > 2.1 LH850.7 8.1 <240 >0.64 > 1.3 LH850.11 13.5 <160 >0.80 > 2.0 LH850.14 9.5 <240 >0.67 > 1.4 LH850.16 6.1 <120 >0.71 > 1.6 LH850.18 4.5 <120 >0.66 > 1.4 N2850.1 11.2 <300 >0.66 > 1.3 N2850.2 10.7 <300 >0.65 > 1.3 N2850.3 8.5 <300 >0.61 > 1.2 N2850.4 8.2 <330 >0.58 > 1.1 N2850.5 8.5 <250 >0.64 > 1.3 N2850.7 9.0 <250 >0.65 > 1.3 SMMJ22471-0206 9.2 < 65 >0.90 > 2.6 SMMJ02400-0134 7.6 < 33 >0.99 > 3.4 SMMJ04431+0210 7.2 < 70 >0.84 > 2.3 SMMJ00265+1710 6.1 <110 >0.73 > 1.6 SMMJ22472-0206 6.1 < 50 >0.87 > 2.4 SMMJ00266+1710 5.9 < 33 >0.94 > 3.0 SMMJ00267+1709 5.0 < 30 >0.93 > 2.9 S350GHz: Flux density at 350 GHz; S1.4GHz: Upper flux density limit at 1.4 GHz; : lower limit of the 350 to 1.4 GHz spectral index; z: lower redshift limit estimated using the Carilli & Yun method. Data taken from Smail et al. (2000); Fox et al. (2001).

Table 1.3: Redshifts estimated from the 250 to 1.4 GHz spectral index following Carilli and Yun’s method, for sources detected in MAMBO deep field surveys that also have radio detections. S250GHz S1.4GHz z Name [mJy] [Jy] LH-MM1 4.3 ± 0.5 62 ± 7 0.82-0.04+0.04 2.7 -1.0+1.7 LH-MM2 3.2 ± 0.5 82 ± 7 0.71-0.05+0.05 2.1 -0.8+1.3 LH-MM3 4.6 ± 0.5 48 ± 7 0.88-0.05+0.05 3.1 -1.2+2.1 LH-MM4 2.9 ± 0.5 46 ± 7 0.80-0.06+0.06 2.6 -1.1+1.8 NTT-1 5.7 ± 0.5 50 ± 7 0.91-0.04+0.05 3.4 -1.3+2.3 NTT-3 4.4 ± 0.5 44 ± 7 0.89-0.05+0.05 3.2 -1.3+2.3 NTT-4 2.7 ± 0.5 60 ± 7 0.73-0.06+0.06 2.3 -0.9+1.5 NTT-5 2.7 ± 0.5 60 ± 7 0.73-0.06+0.06 2.3 -0.9+1.5 NTT-6 2.0 ± 0.5 20 ± 7 0.89-0.11+0.13 3.2 -1.5+3.5 NTT-7 1.5 ± 0.5 90 ± 7 0.54-0.09+0.07 1.5 -0.7+1.1 NTT-8 2.4 ± 0.5 50 ± 7 0.75-0.07+0.07 2.3 -1.0+1.6 NTT-9 2.8 ± 0.5 40 ± 7 0.82-0.07+0.07 2.7 -1.1+2.0 NTT-11 5.2 ± 0.5 80 ± 7 0.81-0.04+0.04 2.6 -1.0+1.6 NTT-12 4.8 ± 0.5 90 ± 7 0.77-0.04+0.03 2.4 -0.9+1.4 NTT-13 3.0 ± 0.5 40 ± 7 0.83-0.07+0.07 2.8 -1.2+2.0 NTT-14 3.4 ± 0.5 65 ± 7 0.76-0.05+0.05 2.4 -0.9+1.5 NTT-17 2.2 ± 0.5 80 ± 7 0.64-0.07+0.06 1.8 -0.8+1.2 NTT-18 2.6 ± 0.5 50 ± 7 0.76-0.07+0.06 2.4 -1.0+1.7 NTT-20 6.4 ± 0.5 56 ± 7 0.91-0.04+0.04 3.4 -1.3+2.3 NTT-22 2.7 ± 0.5 50 ± 7 0.77-0.06+0.06 2.5 -1.0+1.7 A2125-01 4.3 ± 0.5 65 ± 7 0.81-0.04+0.04 2.6 -1.0+1.7 A2125-02 4.2 ± 0.5 83 ± 7 0.76-0.04+0.04 2.4 -0.9+1.4 A2125-05 5.2 ± 0.5 107 ± 7 0.75-0.03+0.03 2.3 -0.8+1.3 A2125-06 3.2 ± 0.5 103 ± 7 0.66-0.05+0.04 1.9 -0.8+1.2 A2125-07 3.0 ± 0.5 32 ± 7 0.88-0.07+0.08 3.1 -1.3+2.5 A2125-08 2.9 ± 0.5 51 ± 7 0.78-0.06+0.06 2.5 -1.0+1.7 A2125-09 3.6 ± 0.5 190 ± 7 0.57-0.04+0.03 1.6 -0.6+0.9 A2125-10 3.7 ± 0.5 59 ± 7 0.80-0.05+0.05 2.6 -1.0+1.7 A2125-11 3.3 ± 0.5 78 ± 7 0.72-0.05+0.05 2.2 -0.9+1.4 A2125-13 4.3 ± 0.5 38 ± 7 0.91-0.06+0.06 3.3 -1.3+2.5 A2125-14 3.6 ± 0.5 53 ± 7 0.81-0.05+0.05 2.7 -1.1+1.8 A2125-15 3.0 ± 0.5 138 ± 7 0.59-0.04+0.04 1.7 -0.7+1.0 S250GHz: Flux density at 250 GHz; S1.4GHz: Flux density at 1.4 GHz; : 250 to 1.4 GHz spectral index; z: redshift estimated using the Carilli & Yun method. Data taken from Bertoldi (2001).

Table 1.4: Lower redshift limits estimated from the 250 to 1.4 GHz spectral index following Carilli and Yun’s method, for sources detected in MAMBO deep field surveys that have no radio detection but upper limits to the radio flux density. Name S250 GHz S1.4 GHz z [mJy] [Jy] A2125-I 3.0 < 30 >0.89 > 3.2 A2125-II 3.0 < 30 >0.89 > 3.2 A2125-III 2.5 < 30 >0.85 > 2.9 A2125-IV 2.7 < 30 >0.87 > 3.0 A2125-V 2.5 < 30 >0.85 > 2.9 NTT-2 5.3 < 30 >1.00 > 4.1 NTT-23 2.5 < 30 >0.85 > 2.9 NTT-24 2.7 < 30 >0.87 > 3.0 NTT-25 2.7 < 30 >0.87 > 3.0 NTT-28 2.9 < 30 >0.88 > 3.1 NTT-29 3.7 < 40 >0.87 > 3.1 NDF-48 3.3 < 30 >0.91 > 3.3 NDF-b2 3.6 < 30 >0.92 > 3.5 S250GHz: Flux density at 250 GHz; S1.4GHz: Upper flux density limit at 1.4 GHz; : lower limit of the 250 to 1.4 GHz spectral index; z: lower redshift limit estimated using the Carilli & Yun method. Data taken from Bertoldi (2001).

Figure 1.12: The 250 to 1.4 GHz spectral index as function of redshift as derived by Carilli & Yun (2000) from a sample of local starburst galaxies (solid line). The dashed lines show the 1 scatter. The red crosses show the spectral index derived from the MAMBO mm- and VLA radio-flux densities (see Table 1.1). The blue arrows show the lower limits for sources without radio detection (Table 1.2). Figure 1.13: The redshift estimation by the 350 to 1.4 GHz spectral index, following Carilli & Yun (2000), for SCUBA detected sources (see Tables 1.3 and 1.4). The colors and symbols are similar to Fig. 1.12.

Figure 1.14: Redshift distribution of the sources from the MAMBO and SCUBA deep field surveys. The black line shows the objects detected at (sub)mm and radio wavelengths, which allows their redshift to be estimated from the correlation established by Carilli and Yun. The green line represents objects that have only an upper limit to their radio flux density, giving a lower limit to the redshift.

1.6 Conclusion

Millimeter and submillimeter deep field surveys were able to partially resolve the extragalactic FIR background into discrete sources. The nature of these sources however remains unclear. The lack of optical counterparts, their thermal FIR spectrum and their radio flux density suggest that the sources emit the bulk of their luminosity in the FIR and are comparable to local star forming galaxies, (U)LIRGs, although much more luminous. Galaxies of this class can be observed out to high redshifts due to the negative k-correction. The number counts and redshift distribution derived by the method Carilli and Yun developed, together with star formation rates derived from the bolometric luminosities of the MAMBO and SCUBA objects, indicate that the high redshift starburst galaxies may contribute a significant part to the star formation at early epochs of the universe. Since these galaxies are absent in optical surveys, the star formation history derived from optical data must be revised.

In this work I model a population of star forming galaxies at high redshifts. With this simulated population I try to reproduce the current FIR observations. I derive an average star formation rate density from the bolometric luminosities of the simulated objects as a function of redshift. I compare the results with the star formation rate densities derived from optical surveys.