The Lyman-alpha forest power spectrum from the XQ-100 Legacy Survey
Vid Irši?, Matteo Viel, Trystyn A. M. Berg, Valentina D'Odorico, Martin G. Haehnelt, Stefano Cristiani, Guido Cupani, Tae-Sun Kim, Sebastian López, Sara Ellison, George D. Becker, Lise Christensen, Kelly D. Denny, Gábor Worseck, James S. Bolton
MMNRAS , 1–13 (2016) Preprint 8 February 2017 Compiled using MNRAS L A TEX style file v3.0
The Lyman-alpha forest power spectrum from the XQ-100Legacy Survey
Vid Iršič , (cid:63) , Matteo Viel , † , Trystyn A. M. Berg , Valentina D’Odorico ,Martin G. Haehnelt , Stefano Cristiani , , Guido Cupani , Tae-Sun Kim ,Sebastian López , Sara Ellison , George D. Becker , , Lise Christensen ,Kelly D. Denney , Gábor Worseck and James S. Bolton The Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste, Italy University of Washington, Department of Astronomy, 3910 15th Ave NE, WA 98195-1580 Seattle, USA INAF - Osservatorio Astronomico di Trieste, Via G. B. Tiepolo 11, I-34143 Trieste, Italy INFN - National Institute for Nuclear Physics, via Valerio 2, I-34127 Trieste, Italy Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 1A1, Canada Institute of Astronomy and Kavli Institute of Cosmology, Madingley Road, Cambridge CB3 0HA, UK Departamento de Astronomía, Universidad de Chile, Casilla 36-D, Santiago, Chile Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA Dark Cosmology Centre, Niels Bohr Institute, University of Copenhagen, Juliane Maries Vej 30, DK-2100 Copenhagen, Denmark Department of Astronomy, The Ohio State University, 140 West 18th Avenue, Columbus, OH 43210, USA Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany School of Physics and Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Accepted XXX. Received YYY; in original form ZZZ
ABSTRACT
We present the Lyman- α flux power spectrum measurements of the XQ-100 sample ofquasar spectra obtained in the context of the European Southern Observatory LargeProgramme "Quasars and their absorption lines: a legacy survey of the high redshiftuniverse with VLT/XSHOOTER". Using quasar spectra with medium resolutionand signal-to-noise ratio we measure the power spectrum over a range of redshifts z = 3 − . and over a range of scales k = 0 . − .
06 km − s . The results agree wellwith the measurements of the one-dimensional power spectrum found in the literature.The data analysis used in this paper is based on the Fourier transform and has beentested on synthetic data. Systematic and statistical uncertainties of our measurementsare estimated, with a total error (statistical and systematic) comparable to the one ofthe BOSS data in the overlapping range of scales, and smaller by more than forhigher redshift bins ( z > . ) and small scales ( k > .
01 km − s ). The XQ-100 dataset has the unique feature of having signal-to-noise ratios and resolution intermediatebetween the two data sets that are typically used to perform cosmological studies, i.e.BOSS and high-resolution spectra (e.g. UVES/VLT or HIRES). More importantly,the measured flux power spectra span the high redshift regime which is usually moreconstraining for structure formation models. Key words: cosmology: observations – (cosmology:) large-scale structure of theuniverse – (galaxies:) intergalactic medium – methods: data analysis
The absorption features blueward of the Lyman- α (Ly- α )emission line in the spectra of high-redshift quasars (QSOs) (cid:63) E-mail: [email protected] (VI) † E-mail: [email protected] (MV) are widely used as biased tracers of the density fluctuationsof a photo-ionized warm intergalactic medium (IGM), andare collectively known as the Ly- α forest (see Meiksin (2009);McQuinn (2015) for recent reviews).Although the first speculations and measurements weremade almost years ago (Gunn & Peterson 1965; Lynds1971), the physical picture of the Ly- α forest was established c (cid:13) a r X i v : . [ a s t r o - ph . C O ] F e b V. Iršič et al. in the 1990s by a detailed comparison of analytic calcula-tions (Bi & Davidsen 1997; Hui 1999; Viel et al. 2002) andnumerical simulations (Cen et al. 1994; Zhang et al. 1995;Miralda-Escudé et al. 1996; Hernquist et al. 1996; Theunset al. 1998, 2002) with observed absorption spectra (e.g. Kimet al. (2004)).In the last decade, a range of different statistics havebeen proposed (Schaye et al. 2000; Ricotti et al. 2000; The-uns & Zaroubi 2000; Theuns et al. 2002; Viel et al. 2005;Bolton et al. 2008; Lidz et al. 2010; Becker et al. 2011; Rudieet al. 2012; Garzilli et al. 2012; Bolton et al. 2012; Lee et al.2014; Iršič et al. 2013; Boera et al. 2014), and successfullyused, that focused on specific aspects (e.g. targeting cos-mology, temperature of the IGM, etc.). However, the mainquantity of choice when comparing observations with thetheoretical predictions has become the one-dimensional fluxpower spectrum P F ( k ) (Croft et al. 1999, 2002; Kim et al.2004; Viel et al. 2004; McDonald et al. 2005; Viel et al.2013a; Palanque-Delabrouille et al. 2013). This is becausethe flux power spectrum is tracing the actual fluctuations inthe observed forest, making it easy to understand systemat-ics and the noise properties. The flux power spectrum alsomore cleanly decouple the scales involved (e.g. fluctuationsdue to poor continuum fitting are restricted to large scales).Several measurements of the flux power spectrum havebeen performed in the last two decades, ranging from mea-surements on a few ten high-resolution, high signal-to-noiseratio QSO spectra (Vogt et al. 1994; Kim et al. 2004; Vielet al. 2004, 2013a) to measurements on many thousands ofQSO spectra with poor resolution and signal-to-noise (Yorket al. 2000; Dawson et al. 2013; McDonald et al. 2005;Palanque-Delabrouille et al. 2013). Taken together, thesemeasurements cover over three orders of magnitude in scale( k = 0 . − . − s ), however, they are either only cen-tered on large scales, or only on small scales, and no studyhas done a combined measurements of both.In this paper we present a new set of measurementsof the one-dimensional P F ( k ) on an intermediate data-set: a hundred QSO spectra with medium resolution ( ∼ −
20 km s − ) and medium signal-to-noise ratio ( S/N ∼ − ). The goal is to achieve measurements of both largeand small scales simultaneously and thus provide a bridgebetween the traditionally used data-sets probing either largeor small scales.The paper is structured as follows: in Sec. 2 we discussthe observational data used in our analysis, as well as thesynthetic data on which the data analysis procedure wastested. The various steps of the data analysis are describedin detail in Sec. 3. The final results are presented in Sec. 4and we conclude in Sec. 5. In this work we use 100 QSO spectra from the XQ-100Legacy Survey (López et al. 2016), observed with the X-Shooter spectrograph on the Very Large Telescope (Ver-net et al. 2011). These 100 quasars span the redshift range . < z < . .We limit ourselves to spectra obtained from the UVB and VIS spectrograph arms (see López et al. (2016) for moredetails), since the near-infrared spectral range gives us noinformation regarding the Ly- α forest. For each QSO spec-trum we merge the two spectral arms into one spectrum bya simple method. We re-bin the spectra onto a fixed wave-length grid with ∆ log λ = 3 × − (with λ in Å), which isthe larger of the two bin sizes of the individual arms. In theregion where the arms overlap we perform weighted aver-age of the flux, continuum and resolution element. We haveperformed a test where we treated each spectral arm as in-dependent quasar observation and the results showed thatthe effect of simple merging has negligible effect on the fluxpower spectrum measurements, at least at the scales wherewe are able to measure it.Since the weighting is done using the optimal inversevariance weights, any bad pixel that was determined to beso during pipeline reduction analysis is thus down-weighted.However, the subsequent merged spectra are also examinedby eye if they make sense and don’t have any pixels thatare obvious outliers. Using weighted merging of the armsalso ensures that the continuum transition from one armto the other is smooth. Whereas this introduces some falselarge scale fluctuations in the continuum was not thoroughlyexplored, however any such contributions would show up asexcess of continuum power, which we have investigated andverified it is very small (comparable to the noise levels), seeSec. 4.5.The resolution elements were taken to be constant perarm, with the values of and
11 km s − for UVB and VISarms, respectively.The continuum used in our analysis is based on cubicspline fits and is described in more detail in López et al.(2016).After the spectral arms have been merged we performadditional cuts on the data. First, we exclude pixels withnegative or zero flux errors as well as any bad pixels (withvery negative flux of f < − − , or as a flux over continuumlevel f/C < − ).Second, we mask regions around Damped Lyman- α (DLA) systems using the DLA sample provided by the sur-vey team (Sánchez-Ramírez et al. 2016). We do not use datawithin . equivalent widths from the center of the DLA.When measuring the flux power spectrum within theLy- α forest we only use the pixels within the − Årestframe wavelength range of each QSO spectrum. Thisrange is conservative in the sense that we do not probe theabsorption region close to the quasar Ly- α and Ly- β emis-sion lines (McDonald et al. 2005). Our data analysis pipeline was tested with synthetic datathat were generated exclusively for this work. We want togenerate a realistic flux field with a QSO redshift distribu-tion matching that of the observed data sample.First, we approximated the observed QSO redshift dis-tribution by binning the emission redshifts of the XQ-100sample into redshift bins, as shown in Fig. 1. To generatesynthetic QSO sample we have drawn their redshifts fromthis distribution. Figure 1 shows the distribution of and randomly drawn QSO redshifts from the distribu-tion given by the data. MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum z d N q d z XQ-100mock mock
Figure 1.
The QSO redshift distribution for XQ-100 data sample(red), for N Q = 5000 quasars of the synthetic data sample (blue),and for N Q = 100 quasars of a synthetic data sub-sample (green).name N Q pixel size/resolutionmock 5000 5000 XQ-100 valuesmock 100 100 XQ-100 values Table 1.
Different mock catalogues used in testing the data-analysis routine.
The various mock QSO catalogues used in this paperare presented in Table 1.In the next step we want to produce flux spectra alongthe line of sight of each QSO from the synthetic catalogues.To this end we use a suite of high resolution hydro-dynamicalsimulations of the intergalactic medium between redshifts < z < , with × particles in a h − Mpc box size(PRACE: Sherwood simulations - Bolton et al. (2016)). Theoutputs were produced with a redshift step of ∆ z = 0 . ina given redshift range, in the form of an extracted opticaldepth along randomly selected lines-of-sight.For each line-of-sight, and each redshift bin, the simu-lated optical depth is given on a velocity grid ( τ ( v ) ).First, we convert this to a grid of wavelengths ( λ ), orequivalently Ly- α absorption redshifts ( z = λ/λ α ), where λ α stands for Ly- α line ( . Å). The conversion is doneso that the mean absorption is assumed to happen at theredshift bin of the simulation output ( z s ) λ = λ α (1 + z s ) (cid:115) vc − vc , (1)where v is the velocity coordinate along the line-of-sightwithin a simulation box. Since the length of the absorp-tion spectrum along each line-of-sight, at a given redshift z s extends over the whole box size, and since the cosmologicalsimulations have periodic boundary conditions we make useof that to extend the signal also to negative velocities byperiodically repeating the spectrum from a simulation box.Thus, for a redshift bin z s the signal spans the redshift rangeof z s − ∆ z s < z < z s +∆ z s , where ∆ z s is simply the redshift length of the simulation box at a redshift z s . We choose toonly repeat the periodic signal once, since in the case of oursimulations the redshift difference between each z s and itsneighbours is less than z s .Second, we collect all the redshift outputs along eachline-of-sight into a single optical depth array. In principle themerging of the simulation boxes at different redshifts can bedone using a variety of methods (e.g. weighted interpolationbetween signals in neighbouring redshift bins). However weadopted the simplest method and order them, one after theother, by increasing simulation redshift, choosing simulationredshift bin with lower mean redshift in the areas of overlapbetween two simulation outputs.Such a construction allows us to have a line-of-sightextending over many redshifts, and thus mimicking the ob-served spectrum. There are, of course, a few shortcomingswe would like to point out.Most importantly, our basic ingredient is a spectrumextracted from a numerical simulation with a given box size.Hence, we will only be able to measure meaningful statisticson smaller scales. But we will be able to do so for eachredshift along a single line-of-sight.Secondly, such a construction has rather discrete jumpsin flux on the border between regions from simulation out-puts with different mean redshift. The artifacts in a spec-trum caused by such discrete jumps can be avoided by us-ing a more advanced technique of merging the simulationoutputs together along each line-of-sight, such as linear (orhigher order) interpolation. However, for our own tests onthe power spectrum, this did not play an important role,and thus we settled for the simplest merging.Thirdly, it is usually common to rescale the opticaldepth acquired from simulations at a given redshift, so thatthe mean flux in that redshift bin matches the observed one.Such re-scaling can be viewed as a correction of the UltraViolet background ionization rate from the simulations tomatch the observed mean flux (due to degeneracy betweenthe two). The increase (or decrease) in the optical depth isusually less than .We performed a similar correction, but on the opticaldepth along the entire constructed line-of-sight. The cor-rection factor had a redshift dependence, with redshift bin-ning matching that of the simulation output. The valueswere computed through iteration with the condition that themean flux computed along a specific line-of-sight matchesone from observations. For the purpose of testing the dataanalysis on synthetic data it did not matter what exactlyis the input observed mean flux, as long as we recover it.We chose to use one given by Palanque-Delabrouille et al.(2013).The last part in creating the synthetic data involvedtailoring the simulation output to a given survey specifica-tions: QSO redshift distribution, pixel-size, resolution andnoise properties.First, we assigned a QSO emission redshift to each line-of-sight, thus specifying what part of the redshift range fallsin the Ly- α forest region for that QSO spectrum. Quasarsused in this procedure were determined by the syntheticquasar catalogue.Each QSO spectrum was then rebinned with thesame wavelength bin size as in the XQ-100 observations( ∆ log λ = 3 × − ). MNRAS , 1–13 (2016)
V. Iršič et al. λ [ ˚ A] σ F ( λ ) stacked XQ-100noise model Figure 2.
Averaged flux errors of the XQ-100 sample (in red)compared to the noise model used in constructing the syntheticspectra (in blue).
A convolution was performed on each spectrum with aGaussian kernel with resolution element of
33 km s − . Sucha resolution element is larger than the one in XQ-100 surveybut for our purposes of testing the data analysis procedurethe exact number did not matter.In the end we also added noise to the spectrum. In prin-ciple adding noise after the convolution with the resolutionkernel only adds a component that is flux-independent (e.g.read-out noise). If the dominating contribution to the noisewere flux dependent (e.g.. Poisson noise) we could add it be-fore convolving with the resolution kernel. Both options weretested in the synthetic data and subsequent data analysis,but for most of the tests presented in the rest of the papersynthetic data has only flux-independent noise componentadded.To make sure that our data-analysis routines correctlyrecognize and subtract the noise we used a noise model thatis comparable to averaging the flux errors of the actual XQ-100 data. As shown in Fig. 2, the noise has a slight wave-length dependence towards the edges of the spectrum. Eventhough the scatter is not negligible, it was not modeled in thesynthetic data. The function we used to describe the noisemodel in the synthetic data is not a fit to the averaged fluxerrors. It is just a simple closed form function that exhibitsthe same large-scale wavelength-dependence behaviour. Wefound that for testing purposes of this paper such a modelwas sufficient.The very complicated flux error dependence comes fromtwo instrumental effects. First is that the flux error has along wavelength mode modulation, where it increases to-wards the edges of the observed spectral range, which co-incides with the edges of the CCD camera where the pixelsensitivity is lower than in the middle of the CCD. This isthe effect we wanted to capture in the model of the fluxerrors since a large mode fluctuations in real space of theflux errors might cause sharp features in the Fourier space.We wanted to make sure we access such a possibility onthe mock data, and understand any potential systematics it might cause. However, our error estimate did not showany weird behaviour compared to having a constant valueof flux error with wavelength. Second effect on the observedflux error that causes it to have a very complicated depen-dence was the small scale modulation, which is caused bylower sensitivity at the overlapping higher Echelle ordersof the spectrograph. We did not model such a small scalevariation in our mock catalogues, since our error estimateson both mock and real data would average over such smallscales.It should be noted that while the synthetic data in thispaper were designed for analysis of the flux power spectrum,they should be applicable to other flux statistics as well. In this section we describe the steps taken in the data anal-ysis procedure. The same strategy was adopted for both realand synthetic data in order to check for any systematic effectarising due to the analysis itself.The bulk of the analysis consists of the Fourier trans-forms of the input spectra, which is a method that has beenused extensively before, on similar data sets (Croft et al.1999, 2002; Kim et al. 2004; Viel et al. 2004, 2013a). Thismethod is used to measure the flux power spectrum of theLy- α forest. The measurements, of both real and syntheticdata, are in z − bins ( z = 3 . − . with step ∆ z = 0 . ) and k − bins ( k = 0 . − .
06 km − s , linearly binned withstep ∆ k = 3 × − km − s ). Using the provided continuum fits for each QSO spectrum( C ), we first divided the continuum of the XQ-100 spec-trum measurement ( f ). While we tested the robustness ofthe results by using different continuum models, we optedin the end for the official XQ-100 continuum fits describedin López et al. (2016). We did not fit the continuum at thesame time as the mean flux or the power spectrum. In thesynthetic data, the continuum was modeled as a constantequal to unity. For each line-of-sight we split the data into separate sub-samples ( z -bins) by measured redshift. Each pixel is assignedan absorption redshift which determines the redshift of thesub-sample it falls into. We perform this step, so that theFourier Transform used for the power spectrum analysis isperformed on the level of z -bins and not on the whole line-of-sight. This is foremost much easier to handle, since thescales of different mean redshifts are not mixed together. Itis also convenient to measure the power within a redshift binwhere the variation in wavelength is described by a velocitycoordinate only. This is an approximation, since measuringflux along a photons’ path gives a relation between redshiftand proper coordinate (or equivalently velocity coordinate).However the corrections are very small when measuring Ly- α power spectrum (McDonald et al. 2006; Iršič et al. 2016). MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum We perform an un-weighted average of the flux to obtainan estimate of the mean flux ( ¯ F = (cid:104) F (cid:105) = (cid:104) f/C (cid:105) ). A sam-ple average gives us an unbiased estimator of the true value,but underestimates the error on the average. To perform theunbiased weighted average the full variance would have tobe known (which is the sum of the error flux variance andvariance due to cosmic fluctuations). However, the cosmicvariance is not known at this stage in the data analysis.One option would be to measure the mean flux and its vari-ance together through a likelihood based iteration scheme,or compute the variance from the measured power spectrum.We opted for the latter, and simpler method. For each line-of-sight, and each z -bin we perform FourierTransform on a flux fluctuation field ( δ F = F/ ¯ F − ). Theflux power estimator is then given as a sum of the squaredFourier coefficients over all the pixels in all the z -bins alongall the lines-of-sight that contribute to the measured ( k, z ) bin: ˆ P tot ( k i , z j ) = 1 N ij (cid:88) n,m | δ F ( k n , z m ) | δ D ( k i − k n ) δ D ( z j − z m ) , (2)where N ij represents the number of pixels contributing tothe bin ( k i , z j ) . The sum goes over all the pixel pair config-urations with a wave number k n and redshift z m . We havedenoted the Dirac delta function as δ D .At this point we also correct the result for the effectsof finite pixel width and resolution element. Deconvolutionof the flux fluctuation field translates into simple division inthe Fourier space, thus δ F ( k n , z m ) = δ ( measured ) F ( k n , z m ) W ( k n ; p n,m , R n,m ) , (3)where p n,m is pixel width of pixel corresponding to bin( k n , z m ) and R n,m is resolution element of the same pixel.Both p and R are in velocity units. The pixel width p isconstant in both our data sets ( p = c ∆ log λ , with λ inÅ), whereas the resolution element can vary and is givenfor each pixel. In the synthetic data set, R is constant andequal to
33 km s − but in the real data set it varies between and
20 km s − due to different resolutions in differentspectral arms.The de-convolution kernel in Fourier space, W ( k ; p, R ) ,is a product of a Gaussian (Gaussian smoothing of the reso-lution element) and a Fourier transform of a square function(pixel width): W ( k ; p, R ) = e − k R sin ( kp )( kp ) . (4) In the subsection above we have explained how the total fluxpower spectrum is evaluated. However, this power describesboth fluctuations due to noise and the cosmological signal z ¯ F ( z ) mock 5000BOSS 2013Kim et al. 2007 Becker et al. 2012mock 100 Figure 3.
The mean transmitted flux as obtained from the syn-thetic data. In red we show results using mock QSO spec-tra and using mock QSO spectra (in blue). In black we plotthe standard observational results by Kim et al. (2007) (dashed),Becker et al. (2013) (dot-dashed) and Palanque-Delabrouille et al.(2013) (full line). The input to the mocks was the BOSS meanflux. The data points are shifted in redshift (by . ) to be readilydistinguishable. we are interested in. It is fair to assume that noise is un-correlated with the cosmological signal, and thus it can beremoved at the power spectrum level: P F ( k, z ) = P tot ( k, z ) − P N ( k, z ) . (5)We estimate the noise power by assuming that the P N ( k, z ) can be treated as constant in k , and its normaliza-tion for each redshift can be obtained through the varianceof the flux errors as a function of redshift. To that end wecompute the estimate of the flux error variance, at the stepwhen we compute the mean flux σ N ( z j ) = (cid:88) i σ F ( λ ( z i )) M j , (6)where M j is the number of pixels that correspond to a red-shift bin z j . The noise power is then given by ¯ F ( z ) σ N ( z ) = 1 π (cid:90) ∞ P N ( k, z ) dk ≈ π P N ( z ) ( k max − k min ) , (7)where k min = 0 for our choice of binning and k max is equalto Nyquist scale, which is the largest independent scale wemeasure through our Fourier Transform analysis.The estimate obtained through the above relation isused in our data analysis as the noise power. This methodhas been tested on synthetic data (see next Section) andprovides satisfactory results. In this section we present the results of the data analysisprocedure presented in this paper. First we show the results
MNRAS , 1–13 (2016)
V. Iršič et al. and tests of various methods and approximations used inthe analysis of the synthetic data. We then show the mainresults of this paper, performed on the XQ-100 sample ofQSO spectra. In the last subsection we discuss the way toobtain the estimate of the errors on the flux power spectrumbins.
First we apply the data analysis procedure to the syntheticcatalogue
QSO spectra in order to test for possible sys-tematic effects in our analysis. By using a larger number ofQSO spectra we hope to beat down the statistical fluctua-tions and proclaim the deviations that remain as systematicerrors.The measurements of the mean flux on synthetic dataare presented in Fig. 3. The input mean flux with which wehave calibrated the simulation outputs is plotted in full blackline (BOSS 2013 - Palanque-Delabrouille et al. (2013)). Redpoints with error-bars are measurement from the data anal-ysis procedure presented in this paper. The results agree wellwith the input version and suggests no important system-atic effects are present in this measurement. The analysiswas also repeated on a synthetic catalogue with only
QSOs. The results are plotted in green in Fig. 3, and agreewell with the
QSO spectra sample. Note however thatthe error-bars are very similar, and that is because they aredominated by the variance of flux fluctuations. As a com-parison, Fig. 3 also shows observed flux from two other sur-veys (Kim et al. (2007) and Becker et al. (2013); Viel et al.(2013a)) on a different sample of measured real data spectra.Next, the data analysis was tested on the measurementsof the flux power spectrum. Fig. 4 shows the results as afunction of scale ( k ) for three redshift bins ( z = 3 . - red, z = 3 . - blue and z = 4 . - green). The full lines representthe measurements performed on the synthetically generatedspectra as described in Sec. 2.2. For comparison we showthe flux power spectrum obtained by measuring it directlyon the simulation output at the specified redshifts (using5000 lines of sight), without going through the constructionprocedure of the synthetic data (dotted lines). The depar-tures from the input power spectrum at large scales are dueto insufficient number of lines-of-sight probing those scales.This is apparent from looking at the dashed-line in Fig. 4where the same analysis is performed on only QSO spec-tra. However, there are still some fluctuations present atsmaller scales that persist even when increasing the numberof QSO spectra in our analysis of the synthetic data. Fig. 5shows in greater detail the ratio between the recovered fluxpower from the synthetic data and simulation power spec-trum at those redshifts. The three colours still representthree redshift bins, but different line style show differenttests done in either the construction of the mock data orthe data analysis procedure.The dashed coloured lines (Fig. 5) show the effect of notcorrecting for the pixel width. The lines show the recoveredpower spectrum from the mocks, where no noise has beenadded ( P N = 0 ) and no convolution with the resolutionelement has been performed performed ( R = ∞ ). No cor-rections to noise, resolution or pixel width were added whenextracting the flux power from the mocks. The ratio is dif- k [km − s] k P αα ( k ) / π z = 3 . z = 3 . z = 4 . mock 5000mock 100PRACE Figure 4.
The flux power spectrum measured on the syntheticdata for (full lines) and (dashed lines) QSO spectra isshown. The three colours correspond to three (out of measured)redshift bins: z = 3 . (red), z = 3 . (blue) and z = 4 . (green).The dotted lines correspond to the power spectrum extractedfrom a simulation at that redshift. The error-bars are evaluatedusing bootstrap method (see Sec. 4.4 for details). ferent from unity because in the synthetic data the spectrawere rebinned using XQ-100 wavelength bin size, while theflux power spectrum from simulations was computed usingmuch finer binning.The dotted lines (Fig. 5) shows the effect of not correct-ing for the resolution element. The lines show the recoveredpower spectrum from the mocks with no noise ( P N = 0 ),but spectra were convolved with a Gaussian kernel with aresolution element R (see Sec. 2.2). However, no correctionto the resolution was made in the data analysis. Compar-ing with dashed lines, properly correcting for the resolutionhas much bigger impact on the recovered flux power thancorrecting for the pixel width.Additional tests were performed, where both noise( P N (cid:54) = 0 ) and resolution ( R ) were added to the syntheticdata, and while the data analysis corrected for the resolutionelement, no correction to the noise was added (dot-dashedcoloured lines in Fig. 5). Not correcting for the noise clearlyintroduces spurious power on small scales which increasesrapidly, while large scales remains unaffected.The last test (full lines in Fig. 5) shows the effect ofcorrecting the resolution element with slightly wrong value.We assume that our knowledge of the (synthetic) data res-olution element is of the order of few km s − (or roughly ). Both noise and XQ-100 pixel width were used in theconstruction of the mock sample, and both were as well cor-rected for in the power spectrum estimation. However theeffect of misestimating the resolution element translates intowrong power spectrum recovery on small scales. Deviationsof the flux power spectrum on small scales ( k ∼ .
05 km − s )are of order of − .On large scales tests agree nearly perfectly with eachother, which indicates that the fluctuations there are spe-cific to the data-set not the data-analysis routine, and thusof statistical nature. However on smaller scales the differ- MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum k [km − s] P F / P P R A C E ( k ) P N = 0 , R = ∞ → P ( k ) P N = 0 , R → P ( k, R = ∞ ) P N = 0 , R → P ( k, R ) P N = 0 , R → P ( k, R ) − P N Figure 5.
The ratio between flux power spectrum measured fromthe synthetic data (mock 5000) and the input simulation powerspectrum is reported. The colours again correspond to three red-shift bins (red - z = 3 . , blue - z = 3 . , green - z = 4 . ). Differentline styles correspond to different assumptions when generatingsynthetic data as well as different data analysis steps taken: P N - whether noise is added to the synthetic data, R - whether res-olution/pixel width were added; P ( k, R ) - whether in the dataanalysis resolution was corrected, and − P N whether noise wassubtracted (see text for details). z ¯ F ( z ) XQ-100 dataBecker et al. 2012BOSS 2013Kim et al. 2007
Figure 6.
The mean transmitted flux measured on the XQ-100 data sample (red points) using the data analysis and cuts asdescribed in Sec. 3 and 2.1. As a comparison we also plot resultsfor mean flux from Palanque-Delabrouille et al. (2013) (full blackline) and extrapolated values from Kim et al. (2007) (dashed blackline). The error bars on the mean flux were taken to be from thebootstrap covariance matrix. We also compare our results to themean flux measurements by Becker et al. (2013) (blue points).The difference comes from different continua estimation (see textfor details). ence to the simulation power are interpreted as correctingfor slightly wrong values of resolution element or pixel width(where resolution carries more weight). The differences areagain of the same order of magnitude ( − ) at the smallscale end of our measurements. Additional cause of these dif-ferences might be that no correction has been made in theanalysis regarding the aliasing of small scales approachingNyquist scale. To account for these systematic effects in ourdata analysis we use the results shown in full lines in Fig. 5to determine the systematic errors. The absolute differencebetween the models shown in Fig. 5 (full lines), and the ref-erence line of unity was used as a systematic error standarddeviation. This section contains the main results of the data analysisof the XQ-100 data sample. First we present the measure-ments of the mean transmitted flux as a function of redshift,in Fig. 6. The error bars were obtained using the method de-scribed in Sec. 3.3. As a comparison we also plot mean fluxfitting formulas from Palanque-Delabrouille et al. (2013) andKim et al. (2007). The mean flux measurements of XQ-100data agree well with Kim et al. (2007) up to redshift around . . The line for Kim et al. (2007) plotted in this paperis in fact an extrapolation of the fitting formula performedon lower redshift QSO spectra ( z < ). However comparingit to our results, it seems to be valid even at higher red-shifts. The difference in mean flux normalization betweenour results and Palanque-Delabrouille et al. (2013) is prob-ably due to different continuum fitting procedures. In Fig. 6we also compare to the results of the mean transmitted fluxof Becker et al. (2013). The difference is mainly due to differ-ent continuum fitting. Moreover the results by Becker et al.(2013) presented in this paper were rescaled to match lowerredshift measurements by Faucher-Giguère et al. (2008). Ourdata lacks the sufficiently low redshifts ( z = 2 − . ) to beused as rescaling of the results by Becker et al. (2013).The most important result of our paper is present inFig. 7. The figure shows the flux power spectrum, measuredon the XQ-100 sample of QSO spectra, as a function ofscale for three redshift bins from our analysis. All the stepsfrom the data analysis procedure were performed in orderto obtain the flux power values presented in this plot (seeTable A1 for full sample of measurements). We have alsosubtracted the metal power spectrum, measured within thesame data sample and extrapolated to lower redshifts (seeSec. 4.3). As a comparison the measurements of the BOSS2013 analysis are also plotted (Palanque-Delabrouille et al.2013) as well as overlapping redshift from high-redshift mea-surements (Becker et al. 2013). Since XQ-100 data sampleonly has QSO spectra, the flux power cannot be mea-sured at scales as large as BOSS analysis could. However,as predicted, due to higher resolution and signal-to-noise,smaller scales are measured. The error-bars of the flux powerused in this plot were estimated using a bootstrap covariancematrix of the data itself (see Sec. 4.4 for details) as well asthe systematic errors estimation using the method describedin Sec. 4.1. The XQ-100 flux power spectrum measurementspresented in this paper also agree remarkably well with thehigh-redshift measurements.
MNRAS000
MNRAS000 , 1–13 (2016)
V. Iršič et al. k [km − s] k P F ( k ) / π z = 3 . z = 3 . z = 4 . XQ-100 dataBOSS 2013HIRES 2013 @ z = 4 . Figure 7.
The flux power spectrum measurements of the XQ-100 data sample (circles). Full data analysis procedure described in Sec. 3was applied, as well as all the cuts to the data presented in Sec. 2.1. We have also subtracted the metal power spectrum (see Sec. 4.3).The error-bars used in this plot are a squared sum of both statistical errors (from bootstrap matrix estimation) and systematic errors(see Sec. 4.1). As a comparison measurements from Palanque-Delabrouille et al. (2013) (dots) and Viel et al. (2013a) (black triangles)are also plotted.
The flux power spectrum measured in this paper using thedata analysis presented in Sec. 3 contains the power comingfrom both Ly- α forest (predominantly) as well as a smallcontamination from the metals.Typically one can estimate the metal power spectrum inthe QSO spectra redwards of the Ly- α emission line, whereonly metal absorption is present (McDonald et al. 2005).The absorption due to metals is coming from mostly lowerredshifts, but if unidentified it contaminates the higher red-shift Ly- α forest. It is thus further assumed that the metalfluctuations are uncorrelated with the real Ly- α signal, andthat one can remove the effect of the metals by subtract-ing their power spectrum from the measured one. If higheraccuracy is desired further corrections can be added to thisapproach (Iršič & Slosar 2014). However, to measure the power spectrum redwards ofthe Ly- α emission line, for the same redshift range , whereflux power in the forest is measured, a secondary sample oflower redshift QSO spectra is needed. Since XQ-100 datasample only contains quasars at relatively high redshift,measurements of the metal power spectrum could only beachieved for the higher redshift bins, as shown in Fig. 8a.To measure the power we have adopted the restframe wave-length range of − Å in each QSO spectrum. As isevident from Fig. 8a the results are slightly noisy comparedto the metal power estimated in Palanque-Delabrouille et al.(2013).To estimate the Ly- α forest flux power for all redshiftswe have performed a simple extrapolation of the metal powerspectrum measurements. For each k -bin the value of metalpower remains roughly constant as a function of redshiftin the measurements of Palanque-Delabrouille et al. (2013). MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum k [km − s] P m ( k ) z = 3 . z = 4 . z = 4 . XQ-100 dataBOSS 2013SDSS 2005 (a) k -dependence z P m ( z ) k = 0 .
003 s km − k = 0 .
006 s km − k = 0 .
012 s km − XQ-100 dataBOSS 2013const. extrapol. (b) z -dependence Figure 8.
Left : The metal power spectrum measured in the restframe redshift range of − Å for three redshift bins: z = 3 . (red), z = 4 . (blue) and z = 4 . (green). Measurements of metal power spectrum by McDonald et al. (2005) (dot-dashed lines) andPalanque-Delabrouille et al. (2013) (dashed lines) are also plotted. Right : The measurements of the metal power spectrum as a functionof redshift, for three different k -modes: k = 0 .
003 km − s (red), k = 0 .
006 km − s (blue) and k = 0 .
012 km − s (green). The dashed linesshow the result by Palanque-Delabrouille et al. (2013). Previous measurements of metal power (dashed lines) indicate that the redshiftdependence can be approximated as roughly constant for each k -mode. Dotted lines show our result of such an approximation, which isalso used to extrapolate P m ( k, z ) to lower redshift bins. Using this information we averaged our P m ( k, z ) over thethree redshift measurements for each k -bin and used this asan extrapolation to lower redshifts. This is shown in Fig. 8b.Even though such an approximation is very rough, the valueof P m ( k, z ) is generally smaller or at best of the same orderas the statistical errors on our flux power spectrum mea-surements.To perform a more detailed analysis of the metal powerspectrum another sample of lower redshift quasars wouldbe needed, or individual metals contaminating the forestwould need to be identified. However, we believe that theresults would not change significantly and leave such a de-tailed analysis for future studies. To estimate the error-bars on the flux power spectrum theseparate QSO spectra contributions to the power spectrumwere bootstrapped by assuming each spectrum to be an inde-pendent measurement of the flux power (Slosar et al. 2011,2013; Iršič et al. 2013). We generated bootstrappedsamples of the input data-set and calculated the correspond-ing bootstrap covariance matrix.The method was applied first to the synthetic datasample, for mean flux as well as flux power spectrum mea-surements. Fig. 9a shows how the diagonal elements of thebootstrapped covariance matrix (bootstrap variance) forthe mean flux changes as a function of redshift. The rel-ative error on the mean flux from bootstrapped samplesis roughly constant. Different line styles correspond to us-ing or bootstrap samples, and the differences aresmall. Two colour schemes (magenta) and (green) corre- spond to estimating the error-bars on a mock 100 or 5000catalogues. The ratio between the two estimations is exactly (cid:112) N Q ( mock 5000 ) / (cid:112) N Q ( mock 100 ) , meaning that the vari-ance scales as expected with the number of QSO spectra inthe sample ( ∼ / (cid:112) N Q ). In red we plot the estimates of themean flux error-bars coming from the integrals over the full(signal + noise) power spectra at each redshift bin.Same analysis test was performed also on the flux powerspectrum variance estimation, as shown in Fig. 9b. Full linesand dot-dashed lines correspond to the bootstrapped sam-ples of mock 100 and mock 5000 QSO spectra respectively.The scaling of the variance holds in this case as well. Indashed lines we show the estimation of the systematic er-rors on the mean flux (see Sec. 4.1).The full bootstrap covariance matrix of the flux powerspectrum is shown in Fig. 10. The plots correspond tothe analysis done on mock 5000 (Fig. 10a) and mock 100(Fig. 10b) synthetic quasar catalogues. The covariance ma-trix in the plots was normalized (i.e. what is shown is C ij / (cid:112) C ii C jj ) so that the structure is readily discernible.Within one redshift bin the correlations between different k-bins are largely uncorrelated, with small correlation growingfrom large to small scales. However the correlations betweenadjacent redshift bins are quite large. This is a spurious re-sult of the way synthetic data are generated since up to twosimulation snapshots with successive redshift span roughlythe size of one redshift bin in the measurements. The struc-ture remains basically the same (albeit noisier) when com-paring the results obtained on only a QSO spectra.Finally, the same scheme was adopted on the XQ-100sample, and the results of the bootstrap covariance matrixare shown in Fig. 11. The correlation matrix is somewhat
MNRAS000
MNRAS000 , 1–13 (2016) V. Iršič et al. z σ ¯ F ( z ) / ¯ F ( z ) estimator N Q = 5000 N Q = 100 N B = 1000 N B = 100 (a) ¯ F variance k [km − s] σ P ( k ) ( k , z ) / P ( k , z ) z = 3 . z = 3 . z = 4 . σ sys N Q = 5000 N Q = 100 (b) P F variance Figure 9.
Left : The estimation of relative variance on the mean flux measurements of the synthetic data sample. In red is shown thevariance obtained through our data analysis (see Sec. 3.3), while magenta and green colours present the bootstrapped variance ofmock 100 and 5000 QSO spectra sample respectively. Dashed lines show the corresponding variance when only bootstrap sampleswere used.
Right : The estimation of the relative variance on the flux power spectrum measurements of the synthetic data sample. Threecolours correspond to three redshift bins: red - z = 3 . , blue - z = 3 . and green - z = 4 . . full and dot-dashed lines show the resultsobtained on mock 100 and 5000 QSO spectra samples respectively (both with bootstrap samples). In dotted lines the estimation ofthe systematic error is shown. noisy, which is to be expected comparing to the analysiswith varying number of input spectra performed on the syn-thetic data. The correlations with adjacent redshift bins arenegligible.Previous studies have shown, that bootstrapped covari-ance matrix underestimates the variance elements of the ma-trix by roughly (Kim et al. 2004; Palanque-Delabrouilleet al. 2013; Busca et al. 2013; Slosar et al. 2013; Iršič et al.2013). To compensate for that in order to achieve a con-servative estimation of the error-bars, the full bootstrappedcovariance matrix was multiplied by a factor of . . Since the absorption of the IGM at higher redshift becomesstronger, it becomes hard to provide an objective estimateof the continuum levels, due to inability to find transmissionregions in the Ly- α forest. Most attempts in the literatureregarding this issue assume that either the quasar intrinsicemission in the Ly- α forest region is unchanging from quasarto quasar and with redshift, or they model it on a quasar-by-quasar basis (Kim et al. 2004; McDonald et al. 2005;Palanque-Delabrouille et al. 2013; Viel et al. 2013b; Buscaet al. 2013; Slosar et al. 2013; Iršič et al. 2013).Nevertheless, the discussions and analysis on the topicin the literature agree that a change in the normalization ofthe continuum level in the Ly- α forest is perfectly degenerate with the mean transmitted flux estimations. On the otherhand, any large scale modulations of the continuum affectthe measurements of the correlations within the forest, butwhen working in Fourier space, they are confined to largescales.To estimate the possible contamination of the contin-uum power leaking into the flux power spectrum, we per-form a measurements of the bare continuum fits, as if theywere representing fluctuating absorption features of the Ly- α forest. This would be equivalent to averaging the continuaover all the lines-of-sight, to obtain an average and a statis-tical description of its fluctuations. Such an approach is avalid approximation in the limit for which we assume that allquasar continua follow the same shape (but different normal-ization due to different overall observed fluxes). The resultsof this simple model are shown in Fig. 12. The figure showsthe continuum power spectra for three different redshift bins(dot-dashed line), compared to the levels of the statisticalerrors (dashed line) on the measurements of the flux power(full line) . The continuum power spectra show a plateau-like feature towards smaller scales ( k > .
01 km − s ), in-creasing in power towards large scales ( k < .
01 km − s ), asexpected from previous analysis. The level of the continuumpower leaking into the total forest flux power is thus very The systematic errors estimated in Sec. 4.1 are comparable tothe statistical errors, and not shown in this figure.MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum z = 3.0 z = 3.2 z = 3.4 z = 3.6 z = 3.8 z = 4.0 z = 4.2z = 3.0z = 3.2z = 3.4z = 3.6z = 3.8z = 4.0z = 4.2 − . − . − . − . − . . . . . . . (a) mock 5000 z = 3.0 z = 3.2 z = 3.4 z = 3.6 z = 3.8 z = 4.0 z = 4.2z = 3.0z = 3.2z = 3.4z = 3.6z = 3.8z = 4.0z = 4.2 − . − . − . − . − . . . . . . . (b) mock 100 Figure 10.
The error correlation matrices of the flux power spectrum ( C ij / (cid:112) C ii C jj ). Top figure (10a) corresponds to the analysisdone on synthetic spectra, and bottom figure (10b) to the analysis on only synthetic spectra. The structure of the plot is thatwithin each labeled redshift bin, the k -bins follow in increasing order. See text for details. z = 3.0 z = 3.2 z = 3.4 z = 3.6 z = 3.8 z = 4.0 z = 4.2z = 3.0z = 3.2z = 3.4z = 3.6z = 3.8z = 4.0z = 4.2 − . − . − . − . − . . . . . . . Figure 11.
The error correlation matrix ( C ij / (cid:112) C ii C jj ) of theflux power spectrum measurements of the XQ-100 sample. Seetext for details. small, indeed it is comparable to the estimated noise power(dotted line).While we do not use this approach in our standard anal-ysis, it convinces us that the systematic errors due to the − − k [km − s] − − − − − k P F ( k ) / π z = 3 . z = 3 . z = 4 . XQ-100 datanoisecont σ stat Figure 12.
This figure shows the levels of the leaking continuumpower spectrum into the total measured Ly- α forest power spec-trum (dot-dashed lines). Compared to the statistical (and sys-tematic errors) evaluated in the previous sections of this paper(dashed lines), uncertainties due to continuum fitting are smallon the measurements of the power spectrum. The full forest fluxpower and the power spectrum of the noise are shown as a compar-ison (full lines and dotted lines, respectively). The three coloursrepresent three redshift bins: z = 3 . (red), z = 3 . (blue) and z = 4 . (green).MNRAS , 1–13 (2016) V. Iršič et al. continuum estimation, that would result into increased un-certainties on very large scales are much smaller than thestatistical and systematic errors on our measurements andcan thus be neglected. We caution that this is a simple esti-mation, and valid only for the data presented in this paper.
In this paper we have performed a Ly- α flux power spectrumanalysis on the XQ-100 sample of medium resolution,medium signal-to-noise QSO spectra in the redshift range . < z < . (López et al. 2016). The results are shownin Fig. 6 for the mean flux measurements, in Fig. 7 for theflux power spectrum measurements and in Fig. 11 for theestimation of the error correlations of the flux power.The resulting mean transmitted flux is in good agree-ment with previously measured mean flux by Kim et al.(2007) at lower redshifts. The redshift dependence showsslight deviations from the fitting formula in the Kim et al.(2007) paper at the higher redshift end, but it is still within − σ discrepancy.Measurements of the flux power spectrum cover therange of z = 3 . − . in redshift bins and k = 0 − .
06 km − s in k -mode bins. The results agree well withthe expectations that despite a small sample of QSO spec-tra, the higher values of spectral resolution and signal-to-noise ratio, allow for measurements of smaller scales thana large QSO number survey such as SDSS-III/BOSS (Daw-son et al. 2013). The total error bars on our measurements(combined statistical and systematic) are of the same or-der as those in BOSS analysis, specifically on small scales( k > .
01 km − s ). At higher redshifts ( z > . ) our errorbars are even smaller by more than .In the final analysis the official (and publicly available)XQ-100 Legacy Survey continuum fits were used. To consis-tently measure the mean flux (and flux power) a simulta-neous measurement of the quasar continua should be per-formed. However, wrong estimation of the continuum levelswould result in a slight change of normalization in the meanflux, while any long-range modulations of the continuum areabsorbed into large scales k -bins in the P F ( k ) measurements- and thus will not change the results on the medium to smallscales this experiment probes.Since many QSO spectra in the sample feature a DLA,these strong absorption system affect the flux power. In thecurrent analysis we have simply removed the pixels within . of the DLA equivalent width around the DLA centralabsorption redshift. However, with a more careful analy-sis DLA component could be removed from the spectraand thus additional wavelength ranges could be potentiallyadded to the flux power spectrum analysis to increase thefinal signal-to-noise in the P F ( k ) measurements. However,since the effect on the flux power seemed to be small and onlyaffected large-scale k -bins, a simpler approach was adoptedin the final analysis of the data.Through the use of a realistic synthetic QSO spectrasample, an estimation of the systematic error of our dataanalysis was obtained. However, for the larger part the sys-tematic error bars are below the statistical errors, obtainedthrough bootstrapping the data sample. This is valid atleast in the probed k -mode range. At larger scales, addi- tional contribution to systematic errors is introduced due toimperfect continuum fitting, while at small scales imperfectde-convolution of the resolution/pixel width contribution in-troduces significant obstacles. Last but not least, a FourierTransform analysis also introduces aliasing on small scaleswhich is difficult to correct for. For that reason such smallscales (just below Nyquist k -mode) were not measured inthe data analysis presented in this paper. We leave suchcorrections to subsequent analysis.Due to lack of lower-redshift quasars in the XQ-100 sam-ple, the contaminating metal power in the Ly- α forest wasonly measured in three highest redshift bins ( z = 3 . − . ).A simple and rough extrapolation was used to obtain an es-timate of the metal power at smaller redshifts. A separatestudy could be used to address this issue. We also point outthat if the metal power spectrum is measured sufficiently ac-curately at all redshifts, additional second order correctionsare known to be necessary to recover the Ly- α forest fluxpower (Iršič & Slosar 2014).The results on the flux power spectrum presented inthis paper have a great potential in putting additional con-straints on the cosmological parameters, as the measure-ments stretch between large and small scales, probed respec-tively by low-resolution large-quasar number surveys, and afew high-resolution, high signal-to-noise QSO spectra. Thepower in these intermediate scale range is sensitive to tothe small scale properties of the dark matter, as well as toreionization epoch through the Jeans scale measurements. ACKNOWLEDGEMENTS
We would like to warmly thank the ESO staff involved inthe execution of this Large Programme throughout all itsphases. VI is supported by US NSF grant AST-1514734. SLhas been supported by FONDECYT grant number 1140838and partially by PFB-06 CATA. VD, MV, SC acknowledgesupport from the PRIN INAF 2012 "The X-Shooter sam-ple of 100 quasar spectra at z ∼ . : Digging into cosmol-ogy and galaxy evolution with quasar absorption lines. SLEacknowledges the receipt of an NSERC Discovery Grant.MH acknowledges support by ERC ADVANCED GRANT320596 "The Emergence of Structure during the epoch ofReionization". The Dark Cosmology Centre is funded bythe Danish National Research Foundation. MV is supportedby ERC-StG "cosmoIGM". KDD is supported by an NSFAAPF fellowship awarded under NSF grant AST-1302093.JSB acknowledges the support of a Royal Society Univer-sity Research Fellowship. The hydrodynamical simulationsused in this work were performed with supercomputer timeawarded by the Partnership for Advanced Computing inEurope (PRACE) 8th Call. We acknowledge PRACE forawarding us access to the Curie supercomputer, based inFrance at the Tré Grand Centre de Calcul (TGCC). Thiswork also made use of the DiRAC High Performance Com-puting System (HPCS) and the COSMOS shared mem-ory service at the University of Cambridge. These are op-erated on behalf of the STFC DiRAC HPC facility. Thisequipment is funded by BIS National E-infrastructure cap-ital grant ST/J005673/1 and STFC grants ST/H008586/1,ST/K00333X/1. MNRAS , 1–13 (2016)
Q-100: Lyman-alpha forest power spectrum REFERENCES
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APPENDIX A: TABLE - MEASURED Ly- α FLUX POWER SPECTRUM
The last column P F ( k, z ) shows the total measured fluxpower spectrum, while the third column shows our esti-mate of the Ly- α forest power spectrum P α ( k, z ) , wherewe have subtracted the extrapolated metal power spectrum.The second-to-last column is measured metal power spec-trum, with a dash where no data could me measured withinthe XQ-100 data set. Statistical errors ( σ stat ) were obtainedusing bootstrap covariance matrix on the data. The sys-tematic errors were obtained through analysis on syntheticdata (see Sec. 4.1). The flux power spectrum and its co-variance matrix can be obtained from the following link:http://adlibitum.oats.inaf.it/XQ100survey/Data.html This paper has been typeset from a TEX/L A TEX file prepared bythe author.MNRAS , 1–13 (2016) V. Iršič et al.
Table A1.
Measured Ly- α flux power spectrum from XQ-100 data sample. All power spectrum (and error) columns are in [km s − ] units. The scale k is in [km − s] units. The columns are: mean redshift and scale of the power spectrum bin, estimated Ly- α forest fluxpower, measured metal and total flux power, as well as statistical and systematic errors. z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ] , 1–13 (2016) Q-100: Lyman-alpha forest power spectrum Table A1 – continued A table continued from the previous one z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ]000
Measured Ly- α flux power spectrum from XQ-100 data sample. All power spectrum (and error) columns are in [km s − ] units. The scale k is in [km − s] units. The columns are: mean redshift and scale of the power spectrum bin, estimated Ly- α forest fluxpower, measured metal and total flux power, as well as statistical and systematic errors. z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ] , 1–13 (2016) Q-100: Lyman-alpha forest power spectrum Table A1 – continued A table continued from the previous one z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ]000 , 1–13 (2016) V. Iršič et al.
Table A1 – continued A table continued from the previous one z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ] , 1–13 (2016) Q-100: Lyman-alpha forest power spectrum Table A1 – continued A table continued from the previous one z k [km − s] P α ( k, z ) [km s − ] σ stat [km s − ] σ sys [km s − ] P m ( k, z ) [km s − ] P F ( k, z ) [km s − ]000