Prospects for detecting CII emission during the Epoch of Reionization
We produce simulations of the atomic CII line emission in large sky fields in order to determine the current and future prospects for mapping this line during the high redshift epoch of reionization. We calculate the CII line intensity, redshift evolution and spatial fluctuations using observational relations between CII emission and the galaxy star formation rate (SFR) over the frequency range 200 - 300 GHz. We estimate an averaged intensity of in the redshift range . Observations of the CII emission in this frequency range will suffer contamination from emission lines at lower redshifts, in particular CO rotational lines. Using simulations, we estimated the CO contamination to be (originating from galaxies at ). Using detailed simulations of the CII and CO emission across a range of redshifts, we generate maps as a function of angle and frequency, fully taking into account this resolution and light cone effects. In order to reduce the foreground contamination we find that we should mask galaxies below redshifts with a CO(J:2-1) to CO(J:6-5) line flux density higher than or a AB magnitude lower than . We estimate that the additional continuum contamination originating in emission from stars and in dust, free-free, free-bound and two photon emission in the ISM is of the order of however it can be removed from observation due to the smooth evolution of this foreground with frequency. We also consider the possibility of cross correlating foreground lines with galaxy surveys in order to probe the intensity of the foregrounds. Finally, we discuss the expected constraints from two experiments capable of measuring the expected CII power spectrum.
Subject headings:cosmology: theory — diffuse radiation — intergalactic medium — large scale structure of universe
The epoch of reionization (EoR) is a fundamental stage in the history of large scale structure formation. The process of hydrogen ionization was fueled by radiation from the first galaxies which formed in overdense regions. Therefore, this process depends on a large set of astrophysical and cosmological parameters (Venkatesan 2000).
There are already several experiments in operation using low frequency telescopes, such as the Murchison Widefield Arrays (MWA) (Tingay et al. 2013), the Giant Metrewave Radio Telescope (GMRT) (Paciga et al. 2011), the Precision Array for Probing the Epoch of Reionization (PAPER) (Parsons et al. 2010) and the Low Frequency Array (LOFAR) (Rottgering et al. 2006) aimed at constraining this epoch through the measurement of the 21cm signal. Future experiments such as Phase II of HERA 111http://reionization.org and the Square Kilometre Array low frequency instrument (SKA1-LOW) (Mellema et al. 2013) should push this measurement to even higher redshifts.
One of the main challenges for probing the EoR with the 21 cm line is that observations will be contaminated by foregrounds several orders of magnitude higher than the signal (Shaver et al. 1999). Although the frequency smoothness of these foregrounds provides a way to remove them (Santos et al. 2005; Chapman et al. 2012), the combination with calibration errors and systematics complicates the foreground cleaning process.
Independent ways to measure this signal and to probe the reionization process are therefore required in order to ensure the validity of our measurements related to reionization.
In this work we analyse the use of CII intensity mapping both to probe the EoR during its final stages and to confirm and complement the 21 cm data. Although not resolving individual sources, the intensity mapping technique has the advantage of measuring all the emission in a given frequency band originating from a relatively large sky patch. This way, it is sensitive to radiation from faint sources and the diffuse IGM which at these high redshifts cannot be detected with other methods, but whose contribution to the total signal is often important (Gong et al. 2012; Silva et al. 2012). Compared to other techniques, intensity mapping has the advantage of providing three dimensional spatial information of the sources of emission that can be used to further understand the processes of structure formation. Intensity maps can also be used as cosmological probes since the fluctuations in the intensity of emission/absorption lines are correlated with the underlying dark matter density fluctuations (Carilli 2011). In particular, with CII, we can make maps of the sources of ionization, while the 21cm signal will simply be sensitive to the IGM.
We show the potential of CII intensity mapping by simulating mock observational cones of CII emission and its foregrounds at frequencies from 200 GHz to 300 GHz, taking into account the light cone effects. This allows us to test possible ways to reduce the foregrounds without erasing the signal. The main foregrounds in CII intensity maps from the EoR will be contamination from other far-infrared emission lines from lower redshifts, in particular emission from CO rotational transitions. CO emission from normal galaxies at is poorly constrained by observations. Therefore, in order to properly estimate the intensity of these lines and the contamination power spectra relative to CII observations, we used two independent methods. First we used the simulated galaxies catalog from the SAX-Sky simulation which uses a phenomenological model to calculate the luminosities of different CO transitions (Obreschkow et al. 2009a). We then confirmed our predictions using IR luminosity functions (LFs) and other observational data to estimate the relative intensities of the several CO transitions.
We find that CO contamination is dominated by bright sources and so it can be efficiently reduced by masking the pixels where radiation from these sources is observed. In order to apply this procedure we need a complementary experiment to measure CO emission from galaxies brighter than a given flux. This can be done with galaxy surveys targeting the CO emission, which would on its own be a powerful astrophysical probe on the conditions of the ISM. Alternatively the masking of the contaminant galaxies could be done with a CO tracer, easier to be observed, such as the SFR or the relative magnitude in a given filter.
We also explore the possibility of cross correlating CII and 21 cm maps in order to obtain maps of the EoR that are clean from foregrounds and systematics. This is possible since two lines emitted from the same redshift will be observed at different frequencies and so they will be contaminated mainly by uncorrelated foregrounds (Gong et al. 2012).
This paper is organized as follows: In Section 2 we describe how to theoretically estimate the CII emission. In Section 3 we describe the CII foregrounds. In Sections 4 and 5 we describe how we used simulations to generate the signal and the foregrounds. In the 5th Section we present the parameters of an experiment able to measure the CII signal and the CO signal in the 200 GHz to 300 GHz band and in Section 6 we discuss how to remove the CII foregrounds. We conclude with a discussion of the results obtained in Section 7.
2. Calculating CII emission
CII emission is originated in i) the interstellar medium (ISM), ii) Photodissociation regions (PDRs), iii) ionized regions (HII regions), iv) cold atomic gas or v) CO-dark molecular gas (regions in the boundary of molecular clouds with but without CO gas). Observations of the relative intensity of different emission lines have shown that the main source of CII emission is the dense PDRs located in the boundary of HII regions. PDRs are dense and warm regions of the ISM located between HII regions and molecular clouds. They contain mostly neutral gas, but due to their proximity from O, B stars or AGNs the physical and chemical properties of the gas are set by the strong far ultraviolet (FUV) field. The strong FUV to X-ray radiation that penetrates the PDR is absorbed by dust grains which emit electrons heating the gas, or by atoms with an energy threshold for ionization below the Lyman alpha limit such as carbon, oxygen and nitrogen. The FUV also causes transitions from atomic to molecular hydrogen and from ionized carbon to carbon monoxide (Hollenbach & Tielens 1997).
CII photons are emitted in PDRs as a cooling mechanism and so they are a consequence of pre-existing heat. CO-dark clouds are envelopes of dense gas with densities too low for carbon to be converted to CO, but which can be identified by their CII emission. The contribution from CO-dark clouds to the total CII budget is not yet clear but recent studies of our galaxy indicate that it can be high (up to ) (Pineda et al. 2013) under certain astrophysical conditions, more characteristic of the low redshift universe. Diffuse cold atomic gas can be characterized by its emission in the hydrogen 21 cm line and in the CII line. The intensity of emission in this gas phase will be proportional to the collisional rate which depends on the gas density and temperature and therefore also on FUV strength.
The carbon ionization energy is only 11.3 eV which is less than the 13.6 eV necessary to ionize hydrogen so at first we could expect, as was done in Gong et al. (2012), that all the carbon in HII regions would be ionized. There would then be a high emission in the CII 157m line since its excitation potential is only of 91 . Under this assumption most of the CII emission would come from the highest density locations inside HII regions. However this is not supported by observations: several observational maps of the spatial distribution of CII emission in galaxies indicate that the CII emission is mainly originating in PDRs and that HII regions contribute only a few of the total CII emission (Lebouteiller et al. 2012; Rigopoulou et al. 2014). There are studies which indicate a contribution from HII regions that can reach up to 30 of the total CII emission (Carral et al. 1994; Stacey et al. 1999; Aannestad & Emery 2003; Rigopoulou et al. 2013). However, these studies point out that most CII emission is originated in the low density HII regions. The more simple explanation for this unexpected result is that the carbon in the more dense places in HII regions is highly shielded from radiation by hydrogen and so almost all of the ionized carbon is located in low density regions.
The Herschel telescope and the SOFIA observatory were used to observe typical tracers of PDRs, HII regions and other galactic regions (Kaneda et al. 2013) and these observations showed that CII emission has a more complex spatial structure than most other infrared lines. In order to properly estimate the CII emission from a galaxy, it is necessary to observe it with high spatial resolution, which is not possible for most distant galaxies. Alternatively we can use the intensity mapping technique to measure the integrated CII emission from many galaxies.
2.1. Theoretical formulas to estimate CII emission
The intensity of CII emission is given theoretically (Gong et al. 2012) as:
where is the fraction of CII ions at the ground level , is the number density of once ionized carbon atoms, H(z) is the hubble parameter, is the spin temperature and (where is the frequency of the transition). The statistical weights are and and the Einstein spontaneous emission coefficient is .
As many of the parameters in Equation 1 are poorly known and cannot be directly obtained from observations we use an alternative formula, based on the halo model, to obtain the intensity of a line emitted from several galaxies in a relatively large volume. For this we made the simplification of assuming that the average luminosity of each of these galaxies is only a function of the mass of the dark matter halo which contains it and at most its redshift. The average intensity of a line is then given by:
where is the halo mass function (Sheth & Tormen 1999), is the halo mass, , , is the proper luminosity distance, is the comoving angular diameter distance and , where is the comoving distance and is the observed frequency. The relation between and the halo mass is physically based in the dependence of in the number density of CII atoms which should be proportional to the halo mass.
2.2. Calculating CII emission using observational based relations
The CII luminosity of a galaxy can be estimated from other observable quantities as long as there is a reasonable correlation between the two. For large volumes, since we integrate over several galaxies, it is even more reliable to use these observational relations to estimate the overall luminosity from these regions. CII emission is powered by FUV radiation and so there is a correlation between these two quantities which can be converted to a relation between CII and FIR luminosities given that in the star forming galaxies (which will dominate the signal) there is a known correlation between the FUV and FIR fluxes. The CII luminosity of a galaxy also depends on other astrophysical properties of the galaxy such as its metallicity, however the average ratio for nearby, late type galaxies and for is approximately constant (Boselli et al. 2002) and is given by:
This relation is also consistent with recent observations of high redshift galaxies (Stacey et al. 2010) and with observations of ULIRGS (), where a ratio of in the CII to FIR luminosities was found (Rigopoulou et al. 2014). In PDRs the same ratio is inversely proportional to the strength of the ambient radiation field , since is proportional to and depends weakly on (Kaufman et al. 1999). Therefore, this ratio is likely to slightly increase to low mass galaxies (up to ) and to decrease to high mass galaxies. The IR and the FIR luminosities are connected by the following relation:
The integrated IR luminosity, is related to the galaxies star formation rate () by the Kennicutt (1998) relation:
The connection between CII luminosity and the SFR can be easily understood in the case of CII emission arising from warm photodissociating regions, since in this case the FUV radiation ionizes the carbon in the outer layers of the photon-dominated molecular clumps which, in its turn emits CII with a luminosity proportional to the FUV flux which is linked to the galaxy SFR (de Looze et al. 2011). In HII regions the amount of ionized carbon should increase with the size of the region, which is proportional to the stellar radiation UV intensity. However, given that not all carbon is necessarily ionized at the same time in HII regions and that the CII luminosity of these regions also depends on the astrophysical conditions of the gas, one expects a considerable dispersion in the relation between CII luminosity from HII regions and the SFR. Alternative relations between the CII luminosity and the SFR, obtained using different galaxy datasets and using a SFR estimated from the infrared luminosity or from the H luminosity, can be found for example in Boselli et al. (2002), de Looze et al. (2011) or Sargsyan et al. (2012). All of the referred observational studies indicate that the ratio between CII and SFR is smaller for ultra-luminous galaxies although these galaxies account for no more than a few percent of the total emission, which justifies our use of a constant ratio.
The first five observations of star forming galaxies at detected by the ALMA experiment were published (see eg. Wang et al. (2013)). These galaxies have upper limits for the CII luminosity below what is predicted by Equation 2.2. However, their SFRs are above which puts them in the region where a CII deficit was already expected. Observations of typical star forming galaxies at , recently obtained with ALMA, show CII luminosities versus FIR ratios clearly above the usual values at z=0 (Capak et al. 2015). Also, for intensity calculations, according to our model, galaxies with SFRs above only represent around 20% of the total CII intensity and so when fitting the CII luminosity versus SFR relation in observational data we should take into account that less intense galaxies (which are too faint to be observed especially at high redshifts) have a large weight in the CII intensity and that they are more likely to have a more robust SFR ratio.
In order to obtain upper and lower bounds to our CII intensity estimation we decided to use 4 models for the versus SFR relation, to which we will refer to as: , , and . While Equation 2.2 corresponds to parameterization , parameterization corresponds to the recent fit to high redshift galaxies by De Looze et al. (2014) and parameterizations and correspond to fits to the galaxies in Figure 4. These models can all be parameterized as:
with the values for and presented in Table 1.
Here the CII intensity was estimated using Equation 2 with a CII luminosity given by Equation 7, converted into a CII luminosity versus halo mass relation. The conversion between SFR and halo mass was made using simulated galaxy catalogs post-processed by De Lucia & Blaizot (2007) and Guo et al. (2011) from the Millennium and Millennium II dark matter simulations (Springel et al. 2005; Boylan-Kolchin et al. 2009). We did not use an observational based relation since such a relation is not available for low halo masses and high redshifts. The galaxy SFR from the simulated catalogs is on average related to the mass of the dark matter halo containing the galaxy by:
The use of this formula results in the star formation rate density (SFRD) evolution shown in the right panel of Figure 1 assuming a dark matter halo mass range from to . The Millennium and Millennium II simulations only goes till a redshift of . However unless we want to consider unusual stars the relation for should be a good approximation for , if required.
2.3. Calculating CII emission using gas physics
The maximum possible upper value for the CII emission can be obtained assuming that all the carbon in the hot gas (typical HII regions) in a galaxy is ionized and therefore emitting in the CII line, such as was done in Gong et al. (2012). Here, we do a similar calculation but with an improved parameterization of the metallicity in the galaxies hot gas obtained using the Guo et al. (2011) galaxies catalog for low mass halos and the De Lucia & Blaizot (2007) galaxies catalog for high halo masses. The resulting relation between halo mass and metallicity in the hot gas component is shown in Figure 2. By analysing this figure we found that the metallicity in the lower mass halos of the De Lucia & Blaizot (2007) simulation is lower than the one found in the halos from the Guo et al. (2011) simulation, although these simulations used very similar prescriptions to determinate the galaxies metallicity. Since the Guo et al. (2011) simulation has a much higher mass resolution, we believe that their results are more reliable for the low luminosity halos, since the halos in the De Lucia & Blaizot (2007) galaxies catalog are only well resolved for masses above .
The average relation between and halo mass in the referred simulated galaxy catalogs can therefore, be parameterized in the form:
where at the redshift range 5.0 to 8.5 these parameters take the values: , , , , , , , and .
Assuming that all the carbon in the hot gas is ionized and that the carbon mass corresponds to a fraction of 21% of the total mass in metals (this is the same percentage of carbon found in the sun) we obtain . In reality only a fraction of the carbon in HII regions is ionized which can be easily included in these calculations. At large enough volumes the number density of CII atoms can be estimated from the halos mass using the formula:
where is the atomic carbon mass.
We can obtain an upper value for the intensity of CII emission in HII regions by replacing in Equation 1 the CII number density obtained from Equation 10. We estimated the CII number density by assuming that HII regions have an electronic temperature of K and an electronic density of (these values correspond to saturation emission values as obtained in Gong et al. (2012)).
In Figure 3 we show the CII intensity estimated assuming several models for the CII emission. The average intensity of CII emission in the redshift range shown is between for model and for model . The average CII intensity, obtained by averaging models to , between and is .
In Figure 4, the CII luminosity as a function of the SFR for the different methods described, is shown together with observational points of normal local galaxies from Malhotra et al. (2001) and with observational upper limits for high redshift galaxies. The observed high redshift galaxies, presented in this figure, have high SFRs which indicates that they are very massive and rare or that they have extreme SFRs/Mass ratios. In either case these galaxies have little effect on the overall CII intensity.
The CII luminosities from ionized regions, presented in Figure 4, were obtained by assuming that is linearly proportional to the halo mass and by determining the constant of proportionality between the two by imposing that Equations 2 and 1 give the same result. The relation between halo mass and SFR was assumed to follow Equation 4.
3. CII Foregrounds
The CII line emitted in the redshift range z 8.51 - 5.35 is observed at frequencies . CII is a far-infrared line and so CII intensity maps will be contaminated by other infrared lines and by infrared continuum emission from galaxies and from the IGM. In this section we show estimations for the contamination from all of these extra-galactic sources in the relevant observing frequency band. In addition we also consider contamination due to emission from our galaxy.
3.1. Contamination from line emission
The main contaminants in CII intensity maps will be emission lines from lower redshifts namely the , the
the and the CO rotation lines from transitions CO(2-1) and higher.
The and the lines are typical of PDRs while the line is typical of HII regions and so the SFR can be used to roughly estimate their intensity of emission such as in the CII case (see: section 3.5). The CO lines are emitted from molecular gas and their luminosities depend on several characteristics of the gas and so we carefully estimate their intensity of emission in the next section.
3.2. CO signal from simulations
CO rotation lines will be the main contaminants in CII intensity maps observed at frequencies 200 300 GHz. Since the luminosities of the several relevant CO transitions are poorly constrained observationally, we estimate their intensities using the CO fluxes in the simulated galaxy catalog from Obreschkow et al. (2009a) and confirm our results with a CO intensity calculated using only observational relations, when available. The Obreschkow et al. (2009a) catalog is available for halo masses above and provides astrophysical properties such as the CO fluxes for rotational transitions (1-0) to (10-9). The CO emission was estimated from the galaxies molecular gas content and from the ISM temperature using physically based prescriptions and assuming thermal equilibrium.
Each CO rotation line that is observed in the frequency range 200 - 300 GHz will come from the redshift range shown in Table 3. Note that for the CO(2-1), as is shown in Table 3, the minimum relevant redshift for this study is zero which corresponds to the line rest frequency.
The CO intensity can be estimated from its luminosity as:
where the sum in J (angular momentum) is a sum over the luminosities of the different rotation lines from CO(2-1) to CO(6-5) and . We do not account for higher CO transitions since according to this CO model the CO contamination in CII intensity maps is highly dominated by the lower CO transitions. We also justify our choice by arguing that the contamination from transitions (7 - 6) and higher is originated from high redshifts and so the lower metallicity of these galaxies is likely to result in a considerably low CO emission.
Using the simulated fluxes we parameterized the CO luminosity of galaxies as a function of halo mass for transitions CO(2-1) to CO(6-5) as:
Figure 5 shows the luminosity of the CO(2-1) transition as a function of halo mass, in the redshift range 0 to 0.15, obtained from the simulation.
Given that the minimum halo mass available in the Obreschkow et al. (2009a) galaxy catalog is not low enough for our study, we extrapolated the average CO luminosity to lower halo masses assuming that it is proportional to SFR at low masses. The CO luminosities were parameterized as a function of dark matter halo masses and not as a function of galaxy masses and therefore for high halo masses they include the contribution from a main galaxy and several satellite galaxies. This parameterization could also have been made as a function of IR luminosity or SFR, however, galaxies powered by active galactic nuclei have relatively small IR luminosities, small SFRs and high CO fluxes and so this population would have to be taken into account separately.
The theoretical average power spectra of CO contamination presented in Figure 7 for transitions CO(2-1) to CO(6-5) indicates that the dominant contamination will be due to the low-J CO transitions. However, the ratios of different CO lines were obtained by assuming a simple model with a single gas component in local thermodynamic equilibrium. This does not necessarily have to represent well the molecular gas conditions in all types of galaxies. A more recent work described in Lagos et al. (2011) and Lagos et al. (2012), attempts to estimate the luminosity of the several CO transitions using an improved method to estimate the molecular gas content in galaxies. This is based in a somewhat more detailed model of the gas properties, as compared to Obreschkow et al. (2009a), used to estimate the relation between CO emission and molecular gas content. The main difference in the results obtained by these two authors is that the Lagos et al. (2012) model predicts a smaller molecular content in galaxies for and higher ratios between the CO luminosities for higher transitions. These two corrections practically compensate themselves in terms of contamination in CII maps at the relevant frequencies for these study and so they should not have a significant effect in the validity of our predictions for intensity mapping. Even though there are limitations to the CO luminosities calculation made by Obreschkow et al. (2009a), observationally only the CO(1-0) line is well constrain at small redshifts () and in that case the CO LFs derived from the simulated galaxies catalog are compatible with observations. The few CO observations at suggest a number density of CO emitters higher than what is predicted by the Obreschkow model (Daddi et al. 2010; Tacconi et al. 2010; Aravena et al. 2012), however these observations are restricted to mainly the CO(2-1) transition from very high luminosity galaxies while for the relevant observed frequency range the CO emission is originated at , where the models are in better agreement.
3.3. CO signal from observations
An observational only based model to estimate the CO(1-0) luminosity is presented in Sargent et al. (2013) and so to support our conclusions we used this completely independent model to estimate the CO contamination in CII maps. The Sargent model estimates CO emission from a recent IR luminosity function at presented in Sargent et al. (2012) and with the observational relations between IR and CO luminosities presented in Sargent et al. (2013). The luminosity function (LF) is an useful way to put constraints on the overall luminosity of observed galaxies above a given luminosity limit characteristic of each survey. It corresponds to the number density of galaxies per luminosity interval as a function of luminosity. The LF is commonly plotted in units of number density per decade in luminosity , where dex accounts for the logarithmic variation of the luminosity for the bin used (). The Sargent IR LF for can be scaled with redshift using the factor in the galaxies luminosity and scaling the number density as for (for lower redshifts the number density is fixed).
The CO luminosities can be obtained from the IR LF using:
where for normal galaxies and for starbursts (Sargent et al. 2013). In Figure 6 the CO LF based in the Obreschkow et al. (2009b) model was obtained using a halo mass function and the CO luminosity parameterization from Equation 3.2. The two models shown in Figure 6 agree taking into account the uncertainty in the relation between the IR luminosity and CO(1-0) luminosity used in the observational CO model (showed as shaded regions). The uncertainties in the Sargent CO LFs are even higher if we take into account the error bars in the IR luminosity function, or the uncertainty in the passage from the CO(1-0) line to higher transitions.
Ratios between the luminosities of the CO(1-0) line and higher CO transitions (in units proportional to the surface brightness ) for different types of galaxies are available in Carilli & Walter (2013). In order to obtain observationally only based estimations for the LFs of the relevant CO transitions we used the Sargent CO(1-0) model plus the Carilli & Walter (2013) observational ratios: , , and which are appropriate for submillimeter galaxies. Since there is no available observational relation between transitions CO(6-5) and CO(1-0), we assumed that . For each transition the CO luminosity in  can be obtained using:
We will from now on refer to the observational CO luminosities predicted using the Sargent CO(1-0) LF plus the Carilli et al. ratios for CO transitions as the observational CO model. The main differences between the two CO models lies in the conversion ratios between the luminosity of the several transitions given that the average ratio in the Obreschkow simulation are , , , and at a redshift close to zero and slightly increase for higher redshifts. The flux ratios in the Obreschkow simulation are appropriate for regular galaxies, while for star bursts and quasars the ratios between fluxes of high CO transitions are much higher. Recent observationally based ratios for different CO transitions as a function of redshift can be found in Daddi et al. (2014). This study suggests that the relative contribution from high CO transitions relevant for our study is even smaller than what is predicted by the two models discussed here. That is, it should be easier to remove CO contamination from observational maps. Given the lack of observational measurements of fluxes of high CO transitions in normal galaxies, with masses below , the ratios between different CO transitions and the LFs from these lines are poorly constrained and this work can serve as motivation to plan an experiment especially designed to measure CO emission from several rotational transitions and their redshift evolution.
3.4. CO signal: intensity and power spectrum estimates
We will now show theoretical estimates for the intensity and the power spectra of CO contamination using the LFs obtained with the two CO methods. The CO intensity can be obtained by integrating over the CO LF for the luminosity range available for each line. Following Gong et al. (2012) the CO intensity is given by:
When calculating the power spectrum from a CII map contaminated by CO emission, the corresponding CO power spectrum will be rescaled from the original value at the CO emission redshift, both in amplitude and in terms of the wavelength. Following Gong et al. (2014) the contamination CO power spectra is given by:
where the clustering power spectra is given by:
The indexes or indicate whether we are referring to respectively the source (CII) or the foreground (CO) redshifts, is the comoving distance, is the three dimensional k vector at the redshift of the foreground line, is the matter power spectra and is the bias between the CO signal and dark matter.
The shot noise power spectra due to the discrete nature of galaxies is given by:
There are distortions in the observed power spectra in different directions due to redshift evolution of the signal. In theory these distortions could be used to differentiate between the signal and the foregrounds or to confirm if the foregrounds where effectively removed since in that case there should be no distortions observed (besides the known redshift-space distortions). However, in practice this would require an experiment with an extremely high resolution and so in this study we will only consider the spherical average power spectra. The foreground lines will contaminate the spherical average CII power spectra at .
Since we assume that there is a correlation between CO luminosity and dark matter halo mass then the bias between the overall CO emission and the underlying dark matter density field can be estimated from the halo bias () as:
where , and . The correct value for changes with the galaxy mass, assuming the values from the galaxies in the Obreschkow simulation we have for halos with and for higher mass halos. For the observationally based CO contamination power spectra we assume in our calculations. The estimated contamination power spectra of CO emission in CII maps observed in the frequency range 200 GHz to 300 GHz is shown in Figures 7 and 8 for respectively the Obreschkow CO model and the observational CO model.
3.5. Contamination from atomic emission lines
The m, the m and the m atomic emission lines are emitted from PDRs or from HII regions and so the luminosity of these lines is powered by stellar emission. Therefore it is expected to be correlated with the galaxies SFRs. The luminosity of these lines depends highly on the galaxies gas density and FUV flux (Kaufman et al. 1999). However, for a large number of galaxies, their luminosity densities scale with the FIR luminosity. We therefore used the observational ratios, presented in Table 5, taken from (Graciá-Carpio et al. 2011; Brauher et al. 2008; Ferkinhoff et al. 2011; Zhao et al. 2013), to estimate the lines luminosities ( stands for the average fraction of FIR emission of each line). The luminosity of these lines as a function of halo mass was then obtained using Equations 4, 5 and 8. The intensity of each line in the relevant range of 200 to 300 GHz, estimated using Equation 2 is shown in Table 5.
The average contamination from these lines is considerably below the CII intensity.
3.6. Contamination from continuum emission
The contamination from continuum emission can be estimated from the SFR and gas properties. The origins for the continuum emission considered here include: stellar continuum emission which escapes the galaxy, stellar emission reprocessed by the dust in the galaxy, free-free and free-bound continuum emission caused by interactions between free electrons and ions in the galaxies, and two photon emission originated during recombinations. Since continuum radiation (with the exception of some bands in stellar continuum radiation) observed in the frequency range 200 - 300 GHz will be emitted in the infrared band, it will not be absorbed by any of the main hydrogen lines or by dust and so we can assume that this radiation is not affected during its path towards us.
The intensity of contamination from all of the referred continuum sources of infrared emission is shown in Table 6 and the detailed calculations are presented in the appendix.
|Source of emission|
It is also expected that there is some contamination from the Milky Way which can be estimated from temperature maps of our galaxy for the relevant frequencies. Using temperature maps from Planck at frequencies , and we estimated that unless we were in the center of the Milky Way where the brightness temperature can reach 0.2 - 0.3 K, the average brightness temperature is well below K which corresponds to an observed intensity of to for 200 GHz and 300 GHz respectively.
The intensities in Table 6 show that the continuum contamination is above the CII signal however continuum emission can be fitted and efficiently subtracted from the observational maps.
4. Simulations of the observed signal
The CII mock observational cone was made using the following steps:
The same code was used to generate dark matter halo catalogs from the previously generated density field using the excursion set formalism and by sampling the halos directly from the density field. These catalogs were made for redshifts 5.3 to 8.5 with a redshift step of 0.1 and a halo mass range of to . At this point the halo properties contained in the catalogs included only the halo mass and its position in a three dimensional box with the size and resolution of the density field.
We randomly assigned astrophysical properties, such as SFR, from the De Lucia & Blaizot (2007) galaxies catalog, to the generated halos according only to the halos mass and redshift.
We added CII luminosities to the halo properties using the halos SFR versus CII luminosity relations shown in section 2.1, which resulted in four CII luminosity values for each halo, one for each of the , , and models.
In order to build the observational cones we made a box with 50 by cells which covers the frequency range 200 to 300 GHz and the field of view with steps of respectively 2 GHz and deg. The angular coordinates correspond to positions in right ascension (RA) and declination (DECL), where the center of the box (the cone rotation axis) is at RA = 0 and DECL = 0.
We filled the box with the halos by assuming that the halos z direction corresponds to the direction of the line of sight and that moving in this direction is equivalent to moving in redshift. Since the size of the halo catalogs in the z direction is smaller than the comoving distance from redshift 5.3 to 8.5 we piled the catalogs in order to cover all the needed distance range but we rotated the upper catalogs in order to not repeat structures in the line of sight direction. The initial position of the halos was assumed to be at the comoving distance at which emitted CII photons are observed at a frequency of 300 GHz (). The position of the halos was assumed to be at a distance (, ), where , which corresponds to a comoving distance and to an angular position in right ascension and declination of respectively:
Each comoving position was converted first to a redshift and then to an observed frequency using . The halos were then distributed in the cone according to their angular position and observed frequency. For each halo catalog at a redshift we only used the halos with a redshift lower than .
In each cell of the mock observing cone, the intensity was assumed to be given by a sum over the contribution from each galaxy as:
5. Simulations of the CO foreground contamination
The CO mock observational cones were made using the following steps:
A dark matter density field with a size of and a number of cells of was generated using the Simfast21 code.
The same code was used to generate dark matter halo catalogs from the previously generated density field using the excursion set formalism and by sampling the halos directly from the density field. These catalogs were made for redshifts 0 to 2.5 with a redshift step of 0.1 and a halo mass range of to . The halo properties contained in the catalogs include only the halo mass and position in a three dimensional box with the size and resolution of the density field.
We randomly assigned astrophysical properties, such as SFR, CO fluxes and visual absolute magnitudes, from the De Lucia & Blaizot (2007) and the Obreschkow et al. (2009a) simulated galaxy catalogs, to the halos (e.g. we allowed some randomness in the astrophysical properties for halos with same mass and redshift, using distributions from the SAX simulation).
We calculated the CO luminosity for each halo from its CO flux.
For each CO transition we built mock observing cones with intensities estimated as in the CII case and then we added the cones to obtain the total CO intensity.
In order to simulate the effect of the masking technique we made a mock observing cone with only the galaxies with CO fluxes above a given threshold. The pixels with at least one galaxy correspond to pixels that should be masked in order to decrease the CO contamination in CII observational maps and so we put to zero the corresponding pixels in the initial CO box and in the CII box. We also used the same technique with a limit in magnitudes in the AB system K filter () instead of a limit in CO flux.
A slice of a mock observational CII cone is shown in Figure 9. This figure shows that CII emission is not randomly distributed but that it follows the underlying density fluctuations.
One of the advantages of simulating mock observational cones is that we can directly add the signal and its contaminants to obtain a more realistic version of an observational intensity map. This is useful because it gives us better predictions of what an observational experiment will actually measure and how to relate the observed signal to the intrinsic signal which is where the scientific information really lies. The analysis of the information contained in these cones is mainly made using the power spectra of the target emission line and so we used slices in frequency (these slices correspond to the signal emission around a given redshift) from these cones to construct intensity maps in Cartesian coordinates, from which we calculated the signal power spectra. With this method we directly mapped the contaminants intensity spatial fluctuations into Cartesian coordinates at the signal redshift. This allowed us to directly obtain a contamination power spectra which is essential to determine the real degree of foreground contamination and to plan ways to clean observational maps.
The CII intensities obtained with these observing cones is shown in Table 7 together with the overall CO intensity from transitions (2-1) to (6-5) at the same observed frequencies. The results show that CO contamination will dominate observations especially for low frequencies.
6. Instrument parameters
The characteristics of an experiment able to measure the CII intensity and spatial fluctuations will now be briefly discussed.
|Instrument||CII-Stage I||CII-Stage II|
|Dish size ()|
|Survey area ()|
|Instantaneous FOV ()|
|Freq. range (GHz)||200 - 300||200 - 300|
|Frequency resolution (GHz)||2||0.4|
|Number of Spectrometers||32||64|
|Total number of bolometers||1600||16000|
|On-sky integration time (hr)||1000||2000|
|NEFD on sky ()||65||5|
We propose to use one of two similar setups, the first one (CII-Stage I) is appropriate for optimistic CII models (models with a high CII luminosity density) and the second one CII-Stage II has the minimum requirements to insure a CII power spectra detection in the case of a more pessimistic CII model. The choice of a setup for the CII experiment is mainly dependent on the evolution of the CII luminosity for high redshifts and so it can be updated when more high redshift CII observations are available.
The basic experiment proposed here (CII-Stage I) consists in using one stack of independent single beam, single polarization spectrometers, one stack for each polarization. Each of these spectrometers would contain several bolometers and each of the stacks would cover a line on the sky via a polarizing grid. The second stage experimental setup (CII-Stage II) is similar to the first one but covers a much larger area with a narrower spectra. The details of the proposed experimental setups are shown in Table 8. The angular resolution of the experiments is for CII-Stage I and for CII-Stage II, respectively.
7. Cleaning contamination from lower redshift emission lines
7.1. Pixel masking
As was shown in previous sections, the main line contaminants for the planned observations are CO rotation lines from low redshifts. Since the contamination from CO emission lines in the CII power spectra is high, we made CO flux cuts to study which galaxies are dominating the contamination and if they can be removed from the observational data by masking the pixels with the stronger contaminants.
Given that detecting galaxies with low CO fluxes can be very challenging, we also consider using a CO tracer easier to detect such as the SFR or the relative magnitude in a broad band filter such as the K filter (measured as magnitudes in the AB system in the K filter ) which is centered at 2190 nm and covers around 390 nm. The SFR can only be used as a CO tracer in star forming galaxies. Since there is also an intense CO emission in galaxies powered by active galactic nuclei, if we want to use SFR or infrared emission as a CO tracer we should use an additional tracer like observations in the visible band to target the active galactic nuclei.
In Figure 10 we can see that galaxies with a high CO flux also have relatively low magnitudes in the K band. Thus we estimated the cut necessary to reduce the power spectra of CO contamination.
We show in the bottom panels of Figure 11 that for the more optimistic CII models the power spectra of CO contamination can be efficiently reduced by removing from the observational maps contamination by galaxies with CO fluxes in one of the CO rotation lines higher than and that this can be done by masking less than 10 of the pixels for an experiment with a setup similar to the CII-Stage II experimental setup. In alternative the top panels of this figure show that masking in magnitudes is also possible and the necessary masking would require a cut of 22 in order to sufficiently decrease the power spectra of CO contamination predicted for a CII model like .
For CII models which yield lower intensities the cut would have to be of 23 or even higher which would make it impossible to apply the masking technique. The CO masking can be done with cuts in quantities like the CO flux, SFR, IR luminosity, magnitude in a given band or a combination of probes depending of the CO tracer experiments available. The masking cuts considered in this study are presented in Table 9 following the CII-Stage I or CII-Stage II experimental setups and assuming the Obreschkow CO model. The observational model would require masking CO galaxies till a flux cut of which corresponds to a masking percentage of or for the CII-Stage II and CII-Stage I experimental setups respectively.
|Flux/ cuts||CII-Stage I||CII-Stage II|
If we are able to measure CO luminosities of some galaxies to a high precision it will be possible to remove their intensity from each pixel instead of masking the pixel completely. This would reduce the masking percentage. However the number of galaxies which we can observe with the necessary precision to remove their contamination from observations accurately should be rather small. Also, in order to do this, the intensity of the galaxy would have to be above the “noise” in each of the pixels.
7.2. Cross correlating foregrounds
In this section we discuss the possibility to use cross correlation as a method to help removing CO foregrounds from CII maps and as a way to probe the degree of CO contamination remaining in CII maps after the masking technique has been applied.
7.2.1 Cross correlation with galaxy surveys
First, we consider cross correlating a CO line with the number density of galaxies.
As is shown in Figure 12 the intensity of CO emission in the CO(5-4) line is strongly correlated with the galaxies number density at the same redshift since they both trace the underlying dark matter density fluctuations.
Here we consider the case that the number density of galaxies is independently measured with a galaxy survey. The number density of
galaxies at a redshift z=1.4 can be cross-correlated with an observational intensity map of the CO(5-4) line centered
at the same redshift (obtained
from the 200 - 300 GHz observing cone) and the result will be proportional to the intensity fluctuations of the CO(5-4) line
even if the intensity map also contains CII and other CO lines.
This can be done for several foreground lines and redshifts to probe the degree of contamination by these lines.
7.2.2 Cross correlation between two CO lines
As can be observed in Table 3, in some cases there are two CO lines originated from the same redshift contaminating the observational maps at two different frequencies. For example, the CO(3-2) and the CO(4-3) emitted at a redshift of will be observed at frequencies of 288.2 GHz and 216.1 GHz respectively, and so they will contaminate CII intensity maps at redshifts 7.8 and 5.6.
As is shown in Figure 13 the cross correlation between observational maps with CII plus CO will be stronger than maps with just CII and so by cross correlating intensity maps before and after masking, we can confirm if the cleaning procedure was successful. Also, the existence of contamination from two lines emitted from the same redshift can in principle be implemented in algorithms to help removing the CO contamination, although that task is out of the objectives of this study.
8. Cross correlation between the HI and the CII lines
Both fluctuation in HI and in CII intensity maps are correlated with fluctuations in the underlying density field and so the spatial distribution of emission in these two lines is correlated. Therefore, the cross correlation power spectra of the the two lines gives a measure of their intensities.
Since CII is emitted from galaxies and HI is emitted from the IGM these two quantities are mostly negatively correlated at large scales. At small scales the correlation between CII and HI emission should be positive since they are both biased in overdense regions. However, we find no correlation in our simulations, which is probably due to the low intensity of 21 cm emission at theses scales.
In Figure 14 we show the cross power spectra between HI emission and two models for CII emission. The error bars shown in this figure were obtained with the HI 21 cm line experiment described in Table 10 and with the CII-Stage II instrument.
|FoV per station||6.55|
|effective area per stat.||355.04|
|bandwidth () BW||18||MHz|
|tot. int. time||200||hr|
|effective num. stat.||866|
In this paper we consider the possibility of applying the intensity mapping technique to the CII line at high redshifts in order to probe the EoR and galaxy properties in the early Universe. The ionized carbon CII 158 m line is one of the strongest emission lines in the spectra of star forming galaxies and so observing this line is one of the few possible ways to study very distant galaxies. Given the uncertainty in CII emission from high redshift galaxies we took into consideration four models for CII emission which cover the uncertainty in the relation between CII emission and SFR. We concluded that intensity mapping of the CII line during the end of the EoR is in the reach of today’s technology.
The intensity of the CII signal from to is likely to be between and although higher values would be possible if the SFRD is higher than the current predictions. In the local universe, CII emission from star-forming galaxies is a good probe of their SFR and so intensity mapping of this line should provide good constraints on the SFRD at high redshifts, even if the constant of proportionality between CII luminosity and SFR evolves with redshift. Although a reasonable dispersion in the CII emission versus SFR relation is expected, in intensity mapping studies, we are averaging the relation over thousands galaxies in each pixel, so that the total CII emission should be averaged by the SFRD. The CII intensity should be dominated by galaxies with luminosities below the threshold of galaxy surveys and so even if CII emission in bright galaxies is not a perfect tracer for star formation, it should provide good constraints in the SFRD. The CII line is also dependent in the ISM metallicity and although CII intensity maps cannot give strong constraints to this quantity they will provide a lower limit which will be on its own an improvement over current constraints of the gas metallicity at high redshifts. Note that redshift evolution of the metallicity can tell us about the characteristics of POP II and POP III stars which is also particularly important for Reionization studies.
Emission from CO rotation lines is going to be the main contaminant in CII observations and although the CO and CII intensities have a large uncertainty it is reasonably confirmed that some of the CO signal has to be removed from observations in order to recover the correct CII fluctuations. We estimated the CO intensity using two independent methods, one based in detailed simulations of gas conditions in galaxies and physical relations between CO transitions and other which uses only observational quantities and observational based relations between these quantities. Both these methods predict similar CO intensities. The current constraints in CO and CII emission indicate that the CO power spectra will be up to one order of magnitude higher than the CII power spectra. However we showed that the CO signal can be reduced at least as much, by masking the pixels contaminated by the galaxies with the brighter CO emission.
We described an experiment which is within reach of current technology and is able to measure the CII power spectra with enough resolution so that we can mask most of the CO contamination without erasing the CII signal. In order to identify the most luminous CO galaxies we propose to use a galaxy survey able to measure CO luminosities or a more modest survey able to detect the galaxies AB magnitudes in the K band, since this is a good tracer of CO luminosity. A galaxy survey able to measure CO luminosities of several transitions till a redshift of at least 2.5 would also provide the first LFs for CO transitions higher than the first CO rotational transition which would by it self be a valuable contribution to the study of gas conditions of galaxies.
If the CO contamination is too high and the masking technique is not enough to successfully clean the images or in order to confirm if the contamination was well removed, we can use cross correlations between different CO lines to estimate the intensity of their contamination. Even in the worst case scenario where the overall CO emission is a few times higher than what we have considered, we still would be able to remove CO to at least detect the CII signal with the proposed CII-Stage II experimental setup. Moreover cross correlation between intensity maps of CII and other lines from the same redshift will not suffer from line contamination.
Finally the CII line and the 21 cm line are expected to be strongly anticorrelated. By cross correlating CII and 21 cm maps, we will obtain a statistical estimate of the intensity of these signals independent of most foregrounds which can be a valuable asset in constraining Reionization.
MGS was also supported by the South African Square Kilometre Array Project and the South African National Research Foundation.
AC and YG acknowledge support from NSF CAREER AST-0645427 and AST-1313319 at UCI and also from the Keck Institute for Space Studies (KISS) subcontract for intensity mapping studies.
MBS was also a long Visiting Student at UCI, supported by NSF CAREER AST-0645427 and AST-1313319 and she thanks the Department of Physics and Astronomy at UCI for hospitality during her stay.
We thank Jamie Bock, Matt Bradford and the TIME team for useful discussions.
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In this appendix we summarize the key steps necessary to obtain the continuum foregrounds which will contaminate CII intensity maps in the
frequency range 200 - 300 GHz. This study includes contamination by stellar emission, dust emission, free-free and free-bound emission and finally
two photon emission.
.0.1 Stellar emission
The stellar luminosity at frequency is approximately given by the emissivity of a black body () integrated over the solid angle and the area of the stellar surface ():
For estimating the stellar radius () and for the star effective temperature () we used the formulas in (Cooray et al. 2012) for POP II stars and POP III stars. We calculated separately the emission from POP II and POP III stars assuming that the POP III stellar population evolution could be described using the error function. The error function is given by:
where we imposed that the POP III population ended at , that POP III stars are the dominant population for and that the POP III transition width is . A discussion for the choice of these values can be found at (Fernandez & Zaroubi 2013).
The observed stellar luminosity density is the sum of the luminosity density of POP II stars () and of POP III stars () given respectively by:
We integrated in stellar mass using a (Salpeter 1955) IMF (Initial Mass Function) with a mass range from 0.1 to 100 for POP II stars and a (Larson 1998) IMF with a mass range from 0.1 to 500 , and for POP III stars. In Equations 3 and 4, , corresponds to the maximum stellar mass of a star created at redshift which is still alive at z and is the normalization of the mass function in units of so that the total stellar mass coincides with the value that can be obtain with the star formation rate density in units of . For POP II and POP III stars is given respectively by:
The stellar emission contamination to the observed frequency is given by: