High-redshift cosmology with oxygen lines from H α surveys
MMNRAS , 1–9 (2020) Preprint 15 January 2020 Compiled using MNRAS L A TEX style file v3.0
High-redshift cosmology with oxygen lines from H α surveys Jos´e Fonseca , (cid:63) and Stefano Camera , , † Dipartimento di Fisica “G. Galilei”, Universit`a degli Studi di Padova, Via Marzolo 8, 35131 Padova, Italy INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Padova, Via Marzolo 8, 35131 Padova, Italy Dipartimento di Fisica, Universit`a degli Studi di Torino, Via P. Giuria 1, 10125 Torino, Italy INFN – Istituto Nazionale di Fisica Nucleare, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy INAF – Istituto Nazionale di Astrofisica, Osservatorio Astrofisico di Torino, Strada Osservatorio 20, 10025 Pino Torinese, Italy
ABSTRACT
A new generation of cosmological experiments will spectroscopically detect the H α linefrom emission-line galaxies (ELGs) at optical/near-infrared frequencies. Other emis-sion lines will also be present, which may come from the same H α sample or constitutea new galaxy sample altogether. Our goal is to assess the value, for cosmological in-vestigation, of galaxies at z (cid:38) α galaxy surveys and identifiable bythe highly redshifted ultra-violet and optical lines—namely the O ii line and the O iii doublet in combination with the H β line. We use state-of-the-art models of luminosityfunctions of astrophysical spectral lines to estimate the volumetric number density ofO iii +H β and O ii ELGs. We focus on a wavelength range which will be covered byplanned cosmological surveys. We study the constraining power of these high-redshiftgalaxy samples on cosmological parameters such as the amplitude of baryon acousticoscillations, H ( z ), D A ( z ), f σ ( z ), and bσ ( z ) for different survey designs. We presenta strong science case for extracting the O iii +H β sample, which we consider as an inde-pendent probe of the Universe in the redshift range 2 −
3. Moreover, we show that theO ii sample can be used to measure the baryon acoustic oscillations and the growthof structures above z = 3; albeit it may be shot-noise dominated, it will nonethe-less provide valuable tomographic information. Summarising, we discuss the scientificpotential of a sample of galaxies which, so far, has been mainly considered as a con-taminant in H α galaxy surveys. Our findings indicate that planed H α surveys shouldinclude the extraction of these oxygen-line samples in their pipeline, to enhance theirscientific impact on cosmology. Key words: large-scale structure of the Universe, cosmology: miscellaneous
Emission-line galaxies (ELGs), which are mainly star-forming galaxies, have UV and optical prominent linesthat we use to determine the redshift of each individualELG. Such lines include Ly α (121 . ii (372 . . iii (387 . β (486 . iii dou-blet (495 . . i (630 . ii (654 . . α (656 . ii (6717 nm and 6731 nm),and other weaker lines. H α is the strongest optical emis-sion line from star-forming galaxies, second only to Ly α inthe UV, and followed by the oxygen lines O iii and O ii . In (cid:63) [email protected] † [email protected] practice, N ii is nearly indistinguishable from H α and rep-resents only a minor contribution to the signal. It is thusnatural to choose H α when devising cosmological surveystargeting ELGs. But the H α line with a rest wavelength of656 . Euclid satellite (Laureijs et al.2011), which will take spectra of millions of ELGs to identifytheir redshift; the USA-led NASA WFIRST satellite (WideField Infrared Survey Telescope, Spergel et al. 2015); and an-other NASA mission called SPHEREx (Spectro-Photometerfor the History of the Universe, Epoch of Reionization, and c (cid:13) a r X i v : . [ a s t r o - ph . C O ] J a n J. Fonseca & S. Camera
Ices Explorer, Dor´e et al. 2014), which will complement theprevious two. The design of the satellites has been optimisedfor a wide range of scientific goals, including several trade-offs between sensitivity, surveyed area, wavelength coverage,available emission lines from ELGs and so on. This hasresulted into different sky area coverages and wavelengthranges in the optical and near-infrared bands, with someoverlap among them, which we summarise in Figure 1.Despite the prominence of the H α line, other emissionlines are used to identify the redshift of ELGs, as it is al-ready done by other ground-based spectroscopic galaxy sur-veys. This has been the case for past surveys such as SDSS(Strauss et al. 2002), WiggleZ (Blake et al. 2008), GAMA(Baldry et al. 2010), VIPERS (Scodeggio et al. 2018), andcurrent surveys such as DESI (Aghamousa et al. 2016).While SPHEREx will always have a complete set of linesto fully determine the redshift of a given galaxy, Euclid andWFIRST will only have a subset of these lines available (seeFigure 1).Let us take the example of
Euclid . Ly α will mainly comefrom redshifts well inside the epoch of reionisation and weexpect it to be sufficiently faint, such that it will not sub-stantially contaminate the sample. But the oxygen lines arestrong and high- z ELGs may contaminate the H α sample.Depending on the emitting redshift and experimental reso-lution, the O iii doublet, and H β will be indistinguishable sowe will bundle them together for simplicity. Even if the ex-periment provides enough wavelength resolution, these linesare close enough to be considered as a distinctive samplethat in practice increases the signal-to-noise ratio of detec-tion. Thus, in the observing window of Euclid , H α will seeELGs from z ∈ [0 . , . iii +H β will see them in therange z ∈ [1 . , . ii in the interval z ∈ [1 . , . α emitters as well as high-redshift galaxies identifiable by O iii +H β and/or O ii lines.The presence of these secondary samples is well known,including the fact that high redshift galaxies can be bemisidentified for H α emitters (and vice-versa). Line misiden-tification has already been pointed out by Addison et al.(2019) (see also Grasshorn Gebhardt et al. 2019), wherethey used the anisotropic power spectrum method (Gonget al. 2014) to estimate how the contaminated power spec-trum changes for a given ratio of misidentified galaxies. Butmisidentification will not happen for all high- z galaxies and,in principle, one will be able to constitute samples of galaxiesidentifiable by other lines. In fact, WFIRST plans to con-strain the BAO scale in the redshift range 2 < z < iii emission lines(Spergel et al. 2015). Grasshorn Gebhardt et al. (2019) alsoconsider the O iii sample centred at z = 2 .
32 contaminatedby the low- z H α sample. Addison et al. (2019) took a sim-ilar approach for a O iii sample centred in z = 1 . Euclid -like survey. Although the last two works focus on theeffects of line contamination, both of them neglect the po-tential contamination from O ii galaxies coming from evenhigher redshifts.But these works indicate the merit of looking for higherredshift star-forming ELGs using oxygen emission lines. Herewe will take a step back and reinterpret these ‘interlopers’as an independent secondary galaxy samples, which we willuse as a cosmological probe. We assume that one can clearly λ [ µ m] z EuclidSPHERExWFIRST H α O iii O iii H β O ii Ly α Figure 1.
Redshift of different emission lines as a function ofthe observed wavelength. Vertical lines indicate the wavelengthcoverage of different experiments:
Euclid (black dashed line),SPHEREx (blue dot-dashed line), and WFIRST (red dotted line). distinguish between emission lines. Indeed this discrimina-tion between O ii , O iii +H β , and H α can be possible usingprior information from a sister photometric survey, as wellas fainter lines such H β in the observed spectra. In addition,when two lines are present in the spectra, one can use priorknowledge of the line ratios O ii /O iii and O iii /H α to assesswhich pair of lines is the most probable one. Hence, in lightof the redshift ranges that each line can probe, one can ask ifwe can extend Euclid and WFIRST (excluding SPHEREx)to cosmological probes of high- z ELGs, and what is the meritof each individual sample for cosmology in the different red-shift ranges. Although this possibility was known, we havenot yet found clear studies of their cosmological performanceas tracers of the large-scale cosmic structure at z >
2. A pos-sible explanation for this is the lack of available observation-ally calibrated luminosity functions at higher redshifts. Re-cent results from the High- z Emission Line Survey (HiZELS,Geach et al. 2008) shed light on the redshift evolution ofELGs using the O ii and O iii +H β lines (Khostovan et al.2015). For recent semi-analytical works estimating the num-ber of ELGs that would be seen using H α and/or O iii lines,see Izquierdo-Villalba et al. (2019) and Zhai et al. (2019).These updated Schecter luminosity functions allow usto estimate the number density of observable high redshiftobjects for different flux thresholds. Based on these, we willcompute the signal-to-noise ratio of the first multipoles ofthe power spectrum for different flux thresholds. Further-more, we will assess and compare what kind of cosmologicalconstraints one obtains from different survey areas and fluxthresholds. We will show that the secondary high- z samplescomplement the information we obtain from low- z Universe,and present the case for them to be treated as independentcosmological samples. In fact, our results indicate that de-tailed studies of the precise number density estimations areneeded, as well as development of machinery to disentan-gle the several galaxy samples. These are a requirement for
MNRAS , 1–9 (2020) xtending H α galaxy surveys to higher redshifts Table 1.
Best-fit values for the O iii +H β and O ii luminosity functions from Khostovan et al. (2015).O iii +H β O ii Redshift 0 .
84 1 .
42 2 .
23 3 .
24 1 .
47 2 .
25 3 .
34 4 . φ ∗ − . +0 . − . − . +0 . − . − . +0 . − . − . +0 . − . − . +0 . − . − . +0 . − . − . +0 . − . − . +0 . − . log L ∗ . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . α − . − . − . − . − . − . − . − . proper calculations of the figure of merit of the secondary asa function of flux threshold and detection efficiency.The paper is organised as follows: in section 2 we esti-mate the number of observable ELGs at different redshiftsusing simple prescriptions from observationally calibratedluminosity functions and in section 3 we review the mul-tipole expansion of the power spectrum. In section 4 wepresent our main results such as signal-to-noise ratios forthe high-z ELGs multipole power spectrum and forecasts oftheir constraining power. We finish in section 5 discussionthe feasibility and potential of the high redshift ELG sample. As already discussed, emission lines other than H α will beredshifted within the observable wavelength range of H α galaxy surveys. The first natural approach to take is to con-sider each emission line as an individual sample. But thosesamples would have several overlapping galaxies and red-shifts. For example, the spectrometers of Euclid will workin the range [1 . µ m , µ m] while WFIRST in the range[0 . µ m , µ m], as shown in Figure 1. Hence, it is more nat-ural to break the ELG samples based on redshift ranges,rather than the line(s) used for the identification of the red-shift of the host galaxy. We can, therefore, subdivide theforeseeable ELG samples into three redshift ranges: • an ELG sample at z (cid:46) α line in combina-tion with other emission lines, which we call the H α sample; • an ELG sample in the range 2 (cid:46) z (cid:46) iii , H β and O ii mainly, which we will call the O iii +H β sample; • an ELG sample at 3 (cid:46) z (cid:46) . ii (alone orcombined with other NUV lines), which we will call the O ii sample.For the purpose of this paper, we will consider each sampleindependently and not a single ELG sample.We will estimate the observed number density ofO iii +H β and O ii galaxies using observationally calibratedSchecter luminosity functions which have the functionalform,Φ( L ) d (cid:18) LL ∗ (cid:19) = φ ∗ (cid:18) LL ∗ (cid:19) α e − L/L ∗ d (cid:18) LL ∗ (cid:19) . (1)The average comoving volumetric density of a particulartype of sources is given by n line [gal Mpc − ] ≡ d N line d V = (cid:90) L max /L ∗ L min /L ∗ d (cid:18) LL ∗ (cid:19) Φ ( L ) , (2)where the minimum luminosity is given by the flux thresh- z − − d N / d z / d Ω [ ga l d e g − ] H α Sobral+13H α Pozzetti+16O iii +H β Khostovan+15O ii Khostovan+15H α Zhai+19O iii
Zhai+19
Figure 2.
Estimates of the angular number density of ELGs as afunction of redshift of the H α sample, the O iii +H β sample and theO ii sample, for a flux threshold of F ∗ = 2 × − erg s − cm − .The estimates were obtained from the Schecter O iii +H β andO ii luminosity functions of Khostovan et al. (2015), Schecter H α luminosity functions of Sobral et al. (2013), modified Schecterluminosity function (Model 3) of Pozzetti et al. (2016) and theresults of Zhai et al. (2019). old F ∗ , i.e. L min ( z ) = 4 π D ( z ) F ∗ . L min is redshift depen-dent via the luminosity distance is D L ( z ) = (1 + z ) χ ( z ),where χ ( z ) is the radial comoving distance. The maximumluminosity, L max , can formally be infinite, although in prac-tice one cuts at a sufficiently large luminosity. This has lit-tle effect on the final estimate as the luminosity function isexponentially suppressed. Thus, the observed total surface number of objects per steradian is given byd N line d z dΩ [gal sr − ] = n line c D H ( z ) , (3)where the volume factor is given by the comoving angulardiameter distance D A (which for a flat universe is the sameas the comoving distance).For the Schecter luminosity function one only requires aset of observationally calibrated parameters { φ ∗ , L ∗ , α } fordifferent lines/types of galaxies. In Table 1, we summarisethe results for the O iii +H β and the O ii samples found byKhostovan et al. (2015) using HiZELS (Geach et al. 2008).In Figure 2, we plot the estimates for the angular redshiftdistribution of O iii +H β and O ii sources for a experimentalflux threshold of F ∗ = 2 × − erg s − cm − . The shaded MNRAS000
Estimates of the angular number density of ELGs as afunction of redshift of the H α sample, the O iii +H β sample and theO ii sample, for a flux threshold of F ∗ = 2 × − erg s − cm − .The estimates were obtained from the Schecter O iii +H β andO ii luminosity functions of Khostovan et al. (2015), Schecter H α luminosity functions of Sobral et al. (2013), modified Schecterluminosity function (Model 3) of Pozzetti et al. (2016) and theresults of Zhai et al. (2019). old F ∗ , i.e. L min ( z ) = 4 π D ( z ) F ∗ . L min is redshift depen-dent via the luminosity distance is D L ( z ) = (1 + z ) χ ( z ),where χ ( z ) is the radial comoving distance. The maximumluminosity, L max , can formally be infinite, although in prac-tice one cuts at a sufficiently large luminosity. This has lit-tle effect on the final estimate as the luminosity function isexponentially suppressed. Thus, the observed total surface number of objects per steradian is given byd N line d z dΩ [gal sr − ] = n line c D H ( z ) , (3)where the volume factor is given by the comoving angulardiameter distance D A (which for a flat universe is the sameas the comoving distance).For the Schecter luminosity function one only requires aset of observationally calibrated parameters { φ ∗ , L ∗ , α } fordifferent lines/types of galaxies. In Table 1, we summarisethe results for the O iii +H β and the O ii samples found byKhostovan et al. (2015) using HiZELS (Geach et al. 2008).In Figure 2, we plot the estimates for the angular redshiftdistribution of O iii +H β and O ii sources for a experimentalflux threshold of F ∗ = 2 × − erg s − cm − . The shaded MNRAS000 , 1–9 (2020)
J. Fonseca & S. Camera z d N / d z / d Ω [ ga l d e g − ] H α Sobral+13H α Pozzetti+16O iii +H β Khostovan+15O ii Khostovan+15H α Zhai+19O iii
Zhai+19
Figure 3.
Same as Figure 2 but for F ∗ = 5 × − erg s − cm − . areas represent the uncertainties in the number density fromthe luminosity function calibration errors. For comparison,we also include the estimates of the number of O iii numberof sources from Zhai et al. (2019) using simulations in com-bination with semi-analytical models. One can see that theexpected numbers of Zhai et al. (2019) are within the shadedarea given by Khostovan et al. (2015), although are system-atically lower in the deep survey. For completeness, we alsoshow the estimates for H α : from Sobral et al. (2013), whocalibrated a Schecter luminosity function using HiZELS;from Pozzetti et al. (2016), who also calibrated a modifiedSchecter luminosity function; and the semi-analytical esti-mates of Zhai et al. (2019). As expected, there is a hierarchyof the number of ELGs detected at the same flux limit, asO ii is known to be weaker than O iii , and the latter, in turn,weaker than H α . In Figure 3, we plot the expected num-bers but for a flux threshold of F ∗ = 5 × − erg s − cm − .Whilst Figure 2 can be regarded as the expected numbersfor a wide survey such as Euclid , Figure 3 can be understoodas the expected numbers in a much deeper survey.
For any biased tracer (like galaxies) of the underlying cosmiclarge-scale structure, the observed Fourier-space power spec-trum of its number density fluctuations can be expressed as P ( k ; z ) = (cid:2) b ( z ) + f ( z ) µ (cid:3) P m ( k, z ) + P shot ( z ) , (4)where the first term within square brackets is the lineargalaxy bias (assumed to be scale-independent), f ( z ) is thegrowth rate of density perturbations, µ is the cosine of theangle between the line-of-sight direction and the wave-vector k , and P m is the power spectrum of matter density fluctu-ations, which only depends on k = | k | because of homo-geneity and isotropy. The last term represents shot noise,due to galaxy number counts being a Poissonian samplingof the underlying continuous density field. The first term in Equation 4, which is the dominant one, is due to density fluc-tuations, whereas the second is the so-called redshift-spacedistortion (RSD) term. Finally, the shot-noise term is sim-ply given by the inverse of the volumetric number density ofsources of Equation 2, i.e. P shot = 1 n line . (5)For the rest of this analysis, we shall assume a com-mon bias prescription (see e.g. Amendola et al. 2013, for H α galaxies), b ( z ) = √ z, (6)since all the galaxies detected through the lines in consider-ation come from the same ELG sample. Despite this be-ing a crude approximation, we emphasise that the exactvalue of the bias does not affect substantially the resultswe present. Moreover, the exact determination of the biasof the O iii +H β and O ii samples is beyond the scope of thispaper.Since RSDs induce an anisotropy in the power spectrumgiven by the dependence of P on µ , it is better to rewritethe observed galaxy power spectrum in a Legendre multipoleexpansion. Hence, we have P ( k ; z ) = (cid:88) (cid:96) P (cid:96) ( k ; z ) L (cid:96) ( µ ) , (7)where L (cid:96) ( µ ) are the Legendre polynomials, and the coeffi-cients P (cid:96) ( k ) are uniquely dependent on the modules of thescale, k . The coefficients of the multipole expansion are thengiven by P (cid:96) ( k ; z ) = 2 (cid:96) + 12 (cid:90) − d µ P ( k ; z ) L (cid:96) ( µ ) . (8)Since P ( k ; z ) is even in µ , and the Legendre Polynomialshave the same parity of its multipole index, only the evenmultipoles of the power spectrum are different from zero. Ithas been shown that the lowest multipoles carry the bulk ofthe cosmological information. Therefore, we will only con-sider the first three non-zero multipoles, i.e. the monopole( (cid:96) = 0), the quadrupole ( (cid:96) = 2), and the hexadecapole( (cid:96) = 4). It is easy to show that they read P ( k ; z ) = (cid:20) b ( z ) + 23 b ( z ) f ( z ) + 15 f ( z ) (cid:21) P m ( k, z ) , (9) P ( k ; z ) = (cid:20) b ( z ) f ( z ) + 47 f ( z ) (cid:21) P m ( k, z ) , (10) P ( k ; z ) = 835 f ( z ) P m ( k, z ) . (11) Here, we explore the detectability of the cosmological sig-nal at high redshift—namely z (cid:39) In a given redshift bin z i , we define the signal-to-noise ratio(SNR) for the power spectrum, neglecting RSDs, asSNR( z i ) = (cid:118)(cid:117)(cid:117)(cid:116)(cid:88) j (cid:20) P ( k j , µ = 0; z i )∆ P ( k j , µ = 0; z i ) (cid:21) , (12) MNRAS , 1–9 (2020) xtending H α galaxy surveys to higher redshifts Table 2.
Cumulative signal-to-noise ratio for the power spectrum multipoles, SNR (cid:96) , for the various flux thresholds considered in thepaper. Note that these numbers refer to full-sky measurements: to get the value corresponding to a survey covering A survey steradians,it is sufficient to multiply the corresponding number by [ A survey / (4 π )] / . F ∗ H α O iii +H β O ii [erg cm − s − ] SNR (cid:96) =0 SNR (cid:96) =2 SNR (cid:96) =4 SNR (cid:96) =0 SNR (cid:96) =2 SNR (cid:96) =4 SNR (cid:96) =0 SNR (cid:96) =2 SNR (cid:96) =4 . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × . × − . × . × . × . × . × . × . × . × . × − where the uncertainty on the measurement of a given modeis∆ P ( k j , µ ; z i ) (cid:39) (cid:115) N k ( k j , z i ) [ P ( k j , µ ; z i ) + P shot ( z i )] . (13)The number of independent k -modes (omitting the redshiftdependence) on a scale k j , N k ( k j ), depends on the vol-ume of the survey. We follow the standard treatment andapproximate it to be N k ( k j ) (cid:39) k j ∆ kV survey / (2 π ), where∆ k = k min (cid:39) π/L and L is the smallest side of the sur-veyed volume. (Note that another common choice in the lit-erature is k min (cid:39) πV − / , which, however, overestimatesthe constraining power on the largest scales for volumes thatare not perfectly cubic.) Then, if follows that the sampledscales k j go from k min + ∆ k/ k max with ∆ k as a step. We also stress that these quanti-ties are all redshift-dependent, meaning that in fact we have k min ( z i ), ∆ k ( z i ), and k max ( z i ).To capture better the effect of RSDs, which induce ananisotropic pattern in the galaxy power spectrum, we alsocompute the SNR for Legendre multipoles, which readsSNR (cid:96) ( z i ) = (cid:118)(cid:117)(cid:117)(cid:116)(cid:34)(cid:88) j P (cid:96) ( k j ; z i )Cov − (cid:96)(cid:96) (cid:48) ( k j ; z i ) P (cid:96) (cid:48) ( k j ; z i ) (cid:35) (cid:96) = (cid:96) (cid:48) , (14)where we have introduced the covariance of the P (cid:96) ’s, viz.Cov (cid:96)(cid:96) (cid:48) ( k ; z ) =2 N k ( k, z ) (2 (cid:96) + 1)(2 (cid:96) (cid:48) + 1)2 (cid:90) − d µ [ P ( k, µ ; z )] L (cid:96) ( µ ) L (cid:96) (cid:48) ( µ ) . (15)Note that in the Gaussian approximation we adopted, themultipole covariance is still diagonal both in redshift and inscale, but it is not in multipole. Finally, the total SNR, foreither power spectrum or Legendre multipoles, is simply thesum in quadrature of the SNRs in each redshift bin.In Table 2 we present the cumulative signal-to-noise ra-tio for the power spectrum multipoles, SNR (cid:96) , for variousflux thresholds and the three ELG samples considered inour analysis. For simplicity, we consider a full-sky surveyand note that it is sufficient to rescale the numbers givenin the table by the quantity [ A survey / (4 π )] / , if one wantsto know the cumulative SNR (cid:96) of a survey covering a skyarea of A survey steradians. This happens because the mostrelevant effect of a change in survey area is the rescaling (in the direction perpendicular to the line of sight) of V survey in Equation 15—the third dimension, instead, is fixed bythe redshift-bin width. Albeit it is true that when the trans-verse size of the survey volume becomes smaller than theradial one, the k -binning also changes because of the redefi-nition of k min and, consequently, ∆ k ; but this effect is largelysubdominant compared to the overall linear dependence ofSNR (cid:96) ( z i ) upon [ A survey / (4 π )] / .As a take-home message from Table 2, we note all threeLegendre multipoles will be in principle detectable at highsignificance (i.e. signal-to-noise ratio larger than 10) evenfor the high-redshift O iii +H β and O ii samples. To guidethe reader’s eye, we highlight in the table in light/dark-greythe pairs of flux thresholds and multipoles for which the cu-mulative signal-to-noise ratio is smaller than 5 / falls within5 and 10; in other words, those configurations in which thestatistical power is insufficient / barely sufficient to detectthe signal. In other words, we could be able to detect themonopole and the quadrupole of the galaxy power spectrumup to redshift 3 −
4, extending significantly the reach ofthe H α mother survey. This is further explored and clar-ified in Figure 4, where the same full-sky but, this time,redshift-dependent SNR (cid:96) ( z i ) is shown for the three mainELG samples. Panels from top to bottom respectively referto the monopole, the quadrupole, and the hexadecapole. Ineach panel, line colours denote ELG samples (red for H α ,green for O iii +H β , and blue for O ii ), and from top to bot-tom we show results for flux thresholds F ∗ = 0 . , . , . , and 3 . − s − . Light/dark-grey areas denote the re-gions of limited/no detection, viz. 5 < SNR (cid:96) ( z i ) (cid:54)
10 andSNR (cid:96) ( z i ) (cid:54) In the previous section, we have shown how the cosmolog-ical signal from O iii +H β and O ii galaxies is in principledetectable. Now, we move on and discuss its value for cosmo-logical parameter estimation. To do so, we will now considerfive redshift-dependent cosmological parameters: • A BAO ( z i ), i.e. the amplitude of the baryon acoustic os-cillation (BAO) ‘wiggles’, defined as the amplitude of theoscillatory feature, f BAO ( k ), on top of a smooth, broad-band power spectrum, P smooth ( k ), according to P m ( k ) =[1 + A BAO f BAO ( k )] P smooth ( k ); • bσ ( z i ) ≡ f ( z i ) D ( z i ) σ , i.e. the value of the lineargalaxy bias multiplied by the square root of the overall nor- MNRAS000
10 andSNR (cid:96) ( z i ) (cid:54) In the previous section, we have shown how the cosmolog-ical signal from O iii +H β and O ii galaxies is in principledetectable. Now, we move on and discuss its value for cosmo-logical parameter estimation. To do so, we will now considerfive redshift-dependent cosmological parameters: • A BAO ( z i ), i.e. the amplitude of the baryon acoustic os-cillation (BAO) ‘wiggles’, defined as the amplitude of theoscillatory feature, f BAO ( k ), on top of a smooth, broad-band power spectrum, P smooth ( k ), according to P m ( k ) =[1 + A BAO f BAO ( k )] P smooth ( k ); • bσ ( z i ) ≡ f ( z i ) D ( z i ) σ , i.e. the value of the lineargalaxy bias multiplied by the square root of the overall nor- MNRAS000 , 1–9 (2020)
J. Fonseca & S. Camera S N R ℓ = S N R ℓ = H α O III + H β O II z S N R ℓ = Figure 4.
SNR (cid:96) ( z i ) as a function of redshift for the first threeLegendre multipoles of the galaxy power spectrum (red, green,and blue respectively for the H α , O iii +H β , and O ii sample). Linesfrom top to bottom (and corresponding markers) refer to fluxthresholds F ∗ = 0 . , . , . , . − s − . Dark- and light-grey areas denote regions of signal-to-noise ratios below 5 and 10,respectively. malisation of the matter power spectrum, σ , and the growthfactor, D ( z ); • fσ ( z i ) ≡ b ( z i ) D ( z i ) σ , i.e. the linear growth rate ofstructures, again factorising the redshift-dependent matterpower spectrum normalisation; • H ( z i ), i.e. the Hubble factor; • D A ( z i ), i.e. the angular diameter distance.We emphasise that each of the parameters described aboveis redshift dependent, meaning that we in fact constrain eachof them separately in each redshift bin, centred in z i .The aforementioned parameters form a parameter vec-tor ϑ ( z i ), for which we construct, in each redshift bin, aFisher matrix according to F αβ ( z i ) = 12 (cid:90) d µ (cid:88) j ∂ α P ( k j , µ ; z i ) ∂ β P ( k j , µ ; z i )[∆ P ( k j , µ ; z i )] , (16)where ∂ α is a short-hand notation for the partial derivativetaken with respect to ϑ α . Hence, the cumulative Fisher ma-trix, F , is the sum of the F ( z i ) in each redshift bin. Then,the marginal error on a parameter ϑ α is given by σ ϑ α = (cid:113) ( F − ) αα . (17)Figure 5 is a multi-panel plot summarising the rel-ative marginal errors on parameters, σ ϑ α /ϑ α , for all theparameters, the flux thresholds, the ELG samples andredshift bins, and the sky areas considered. In partic-ular: each row refer to a specific parameters, namely { bσ ( z i ) , H ( z i ) , D A ( z i ) , A BAO ( z i ) } from top to bottom;each column refer to a specific flux threshold, i.e. F ∗ =0 . , . , . , . − s − from left to right; red, green,and blue lines respectively refer to H α , O iii +H β , and O ii galaxies; and diamond, triangle, square, and circle markersrefer to (1 , , , × deg , respectively.The main conclusion one can draw from this plot is thatnot counter-intuitively, sensitivity is possibly more impor-tant than area for high-redshift observations. This is furtherdemonstrated in Figure 6, where we focus on the extractionof RSDs in terms of constraints on the redshift-dependentquantity fσ ( z ). We adopt the same colour code as beforefor the various ELG samples, and the two panels show fore-cast 1 σ marginal error bars on measurements of fσ ( z i ) ineach redshift bin, for a wide and shallow survey (left panel)or a narrow and deep survey (right panel). Clearly, mea-surements extracted from the original target, namely theH α -galaxy sample, are optimised for the former survey spec-ifications, with error bars 28 −
62% tighter than those ob-tained with the latter experimental configuration. It turnsout that a large area and a relatively larger flux thresholdis also better for RSD estimation from the O iii +H β sample,with error bars 67 −
94% smaller than for a narrow and deepsurvey. On the other hand, when it comes to the extractionof cosmological information from redshift 3 − ii galaxies,it is better to observe as much as thirty times a smaller skyarea, but with twice as deep a survey, which yields fσ ( z )measurements 38 −
25% more constrained.
We have generically used the locution ‘H α surveys’ for near-infrared space-based telescopes that will map galaxies posi-tions in particular sections of the sky. Despite the abuse ofterminology, the H α line will take a prominent role in thespectroscopic determination of the redshift of a given de-tected galaxy. Although the prospects to extend H α galaxysurveys up to z ∼ MNRAS , 1–9 (2020) xtending H α galaxy surveys to higher redshifts H α O III + H β O II σ b σ / b σ F * = / cm / s F * = / cm / s F * = / cm / s F * = / cm / s σ H / H σ D A / D A z σ A B A O / A B A O z z z Figure 5.
Relative 1 σ marginal errors on redshift-dependent parameters { bσ ( z ) , H ( z ) , D A ( z ) , A BAO ( z ) } from the clustering of galax-ies detected through different line emission: H α in red, O iii +H β in green, and O ii in blue. Circles, squares, triangles, and diamondsrespectively refer to survey areas of 1, 5, 15, and 30 in 10 deg , whereas the four columns illustrate the dependence of the constraintson the flux threshold, set to 0 .
5, 1 .
0, 2 .
0, and 3 . − s − from left to right. a strong assumption as one might think. A full treatmentof line identification is beyond the scope of this paper, butintuitively there are several ways to disentangle the contri-butions. For bright enough galaxies with several resolvableemission lines, misidentification will not be a problem. Evenwhen only one set of lines is visible, say H α and N ii (orO iii +H β ), then the line profiles will give an indication ofwhich is the correct set. In the case of O iii +H β , the spec-tral resolution R = 380 in combination with the equivalentwidth may be enough to identify the O iii doublet and the H β line separately. Another example of potential line confusionis when only a pair of strong lines are visible in the spectra.One might think that it would be H α and O iii , but using thepair separation, the equivalent width, and the ratio of thefluxes of the lines one can in principle determine if the paircorresponds to H α and O iii , or O iii and O ii (assuming thatH β is non-resolvable). In addition, the photometric samplecombined with the spectroscopic sample can be used to trainclassifiers to construct the three different ELG samples pro-posed here. Thus, instead of removing higher redshift ELGs from the H α sample, we propose for them to be consideras an entire new galaxy sample. It is therefore worth to usesimulated spectra and assess how these different approachescan provide O iii +H β and O ii samples. On the other hand,if the confusion limit is too high, and they cannot be disen-tangled, one has to include the anisotropic power spectrumin the forward modeling and marginalise for the proportionof contamination Addison et al. (2019), whilst fitting for thecosmological parameters.One may ask what is the scientific merit for cosmologyof these less numerous H α contaminants. Therefore, we fore-cast how much information would the O iii +H β and O ii sam-ple add to the standard set of cosmological parameters. Wehave shown that, despite worse constraining power than thelow- z H α sample, the secondary high- z samples can still pro-vide percent level constraints on the expansion rate, growth,and the amplitude of the BAOs. As the Universe is morelinear at higher redshifts, the reconstruction of the BAOis less demanding. Similarly, non-linearities only affect thepower spectrum at scales smaller than in the late Universe. MNRAS000
0, and 3 . − s − from left to right. a strong assumption as one might think. A full treatmentof line identification is beyond the scope of this paper, butintuitively there are several ways to disentangle the contri-butions. For bright enough galaxies with several resolvableemission lines, misidentification will not be a problem. Evenwhen only one set of lines is visible, say H α and N ii (orO iii +H β ), then the line profiles will give an indication ofwhich is the correct set. In the case of O iii +H β , the spec-tral resolution R = 380 in combination with the equivalentwidth may be enough to identify the O iii doublet and the H β line separately. Another example of potential line confusionis when only a pair of strong lines are visible in the spectra.One might think that it would be H α and O iii , but using thepair separation, the equivalent width, and the ratio of thefluxes of the lines one can in principle determine if the paircorresponds to H α and O iii , or O iii and O ii (assuming thatH β is non-resolvable). In addition, the photometric samplecombined with the spectroscopic sample can be used to trainclassifiers to construct the three different ELG samples pro-posed here. Thus, instead of removing higher redshift ELGs from the H α sample, we propose for them to be consideras an entire new galaxy sample. It is therefore worth to usesimulated spectra and assess how these different approachescan provide O iii +H β and O ii samples. On the other hand,if the confusion limit is too high, and they cannot be disen-tangled, one has to include the anisotropic power spectrumin the forward modeling and marginalise for the proportionof contamination Addison et al. (2019), whilst fitting for thecosmological parameters.One may ask what is the scientific merit for cosmologyof these less numerous H α contaminants. Therefore, we fore-cast how much information would the O iii +H β and O ii sam-ple add to the standard set of cosmological parameters. Wehave shown that, despite worse constraining power than thelow- z H α sample, the secondary high- z samples can still pro-vide percent level constraints on the expansion rate, growth,and the amplitude of the BAOs. As the Universe is morelinear at higher redshifts, the reconstruction of the BAOis less demanding. Similarly, non-linearities only affect thepower spectrum at scales smaller than in the late Universe. MNRAS000 , 1–9 (2020)
J. Fonseca & S. Camera z f σ ( z ) , 2.0 erg / cm / s z , 1.0 erg / cm / s Figure 6.
Relative 1 σ marginal errors on fσ ( z ) from the clustering of galaxies detected through different line emission: H α in red,O iii +H β in green, and O ii in blue, for two different surveys: on the left a lower sensitive but wide surveys (30000deg , F ∗ = 2 × − ergs − cm − ); on the right a narrow but more sensitive survey (1000deg , F ∗ = 1 × − erg s − cm − ). In addition to a tomographic study of the BAOs, a carefulidentification of the O iii +H β and O ii samples will allow forbetter tests of the growth and expansion rate up to a 1/5 ofthe size of the Universe. Current constraints from the high- z post-epoch of reionisation Universe come mainly from theLyman-alpha forest (see e.g. McDonald et al. 2006) or itscorrelations with Quasars (see e.g. Font-Ribera et al. 2014)or even its correlations with Damped Lyman-alpha systems(see e.g. Font-Ribera et al. 2012), although with less con-straining power. While the O iii +H β sample can give similarconstraints as the H α sample, the O ii is very sensitive to theflux threshold of the experiment (as it quickly becomes shot-noise dominated). Even when the sample is noise dominated,the potentially large volumes allow for a statistical detectionof the power spectrum. In the case of the O ii galaxy sample,we presented marginal errors without priors, but in fact wecan put strong priors on H and Ω m from other experiments(including the low redshift results from the same experi-ment), hence improving the constrains on fσ at z > given that H α galaxy surveys can in principle observe higherredshift ELGs using other emission lines, is it possible touse those to obtain complementary cosmological constraintsabove z > ? First we used recent state-of-the-art lumi-nosity functions to estimated the number density of ELGsdetectable using the O iii +H β set of lines and the O ii line.Despite the uncertainties inherited from the observation-ally calibrated luminosity functions and the fact that weassumed full observational efficiency, it seems possible tohave enough detectable galaxies for a signal-dominated mea-surement. In fact, we saw in Figure 4 that the monopolecumulative signal-to-noise ratio is well above 5, if not even10, for the three conceived samples, except for O ii in thefaintest threshold limit. In Figure 5, we showed the trade-offs between survey area and flux sensitivity, while for O ii ismore sensitive to the flux threshold, H α is more sensitive to the total sky area, as expected. Despite the technical detailsof future H α surveys, it is worth to account and identifyO iii +H β and O ii galaxies as they can increase substantiallythe overall of cosmological constraining power. More impor-tantly, these 2 samples will work as an anchor between cos-mic microwave background and local Universe constraints.It is therefore crucial to estimate properly the number den-sities of the secondary samples of O iii +H β and O ii , in orderto have true signal-to-noise estimates and figures-of-meritfor each survey. ACKNOWLEDGEMENTS
We thanks A. A. Khostovan for clarifications on the lumi-nosity functions. We thanks L. Guzzo and B. Granett foruseful discussion. JF is supported by the University of Paduaunder the STARS Grants programme CoGITO: Cosmologybeyond Gaussianity, Inference, Theory and Observations.SC is supported by the Italian Ministry of Education, Uni-versity and Research ( miur ) through Rita Levi Montalciniproject ‘ prometheus – Probing and Relating Observableswith Multi-wavelength Experiments To Help Enlighteningthe Universe’s Structure’, and by the ‘Departments of Ex-cellence 2018-2022’ Grant awarded by miur (L. 232/2016).
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