arXiv subjects

K. Dolag

Publications and source records attributed to K. Dolag.

At least 109 records · Page 6Linked to original sources

arXiv2013

Numerical simulations of the possible origin of the two sub-parsec scale and counter-rotating stellar disks around SgrA*

We present a high resolution simulation of an idealized model to explain the origin of the two young, counter-rotating, sub-parsec scale stellar disks around the supermassive black hole SgrA* at the Center of the Milky Way. In our model, the collision of a single molecular cloud with a circum-nuclear gas disk (similar to the one observed presently) leads to multiple streams of gas flowing towards the black hole and creating accretion disks with angular momentum depending on the ratio of cloud and circum-nuclear disk material. The infalling gas creates two inclined, counter-rotating sub-parsec scale accretion disks around the supermassive black hole with the first disk forming roughly 1 Myr earlier, allowing it to fragment into stars and get dispersed before the second, counter-rotating disk forms. Fragmentation of the second disk would lead to the two inclined, counter-rotating stellar disks which are observed at the Galactic Center. A similar event might be happening again right now at the Milky Way Galactic Center. Our model predicts that the collision event generates spiral-like filaments of gas, feeding the Galactic Center prior to disk formation with a geometry and inflow pattern that is in agreement with the structure of the so called mini-spiral that has been detected in the Galactic Center.

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arXiv2013

Large-scale inhomogeneities of the intracluster medium: improving mass estimates using the observed azimuthal scatter

Using a set of hydrodynamical simulations of 62 galaxy clusters and groups we study the ICM of inhomogeneities, focusing on the ones on the large scale that, unlike clumps, are the most difficult to identify. To this purpose we introduce the concept of residual clumpiness, C_R, that quantifies the large-scale inhomogeneity of the ICM. After showing that this quantity can be robustly defined for relaxed systems, we characterize how it varies with radius, mass and dynamical state of the halo. Most importantly, we observe that it introduces an overestimate in the determination of the density profile from the X-ray emission, which translates into a systematic overestimate of 6 (12)% in the measurement of M_gas at R_200 for our relaxed (perturbed) cluster sample. At the same time, the increase of C_R with radius introduces also a ~2% systematic underestimate in the measurement of the hydrostatic-equilibrium mass (M_he), which adds to the previous one generating a systematic ~8.5% overestimate in f_gas in our relaxed sample. Since the residual clumpiness of the ICM is not directly observable, we study its correlation with the azimuthal scatter in the X-ray surface brightness of the halo and in the y-parameter profiles. We find that their correlation is highly significant (r_S = 0.6-0.7), allowing to define the azimuthal scatter measured in the X-ray surface brightness profile and in the y-parameter as robust proxies of C_R. After providing a function that connects the two quantities, we obtain that correcting the observed gas density profiles using the azimuthal scatter eliminates the bias in the measurement of M_gas for relaxed objects, which becomes (0+/-2)% up to 2R_200, and reduces it by a factor of 3 for perturbed ones. This method allows also to eliminate the systematics on the measurements of M_he and f_gas, although a significant halo to halo scatter remains. (abridged)

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arXiv2013

A numerical study of the effects of primordial non-Gaussianities on weak lensing statistics

While usually cosmological initial conditions are assumed to be Gaussian, inflationary theories can predict a certain amount of primordial non-Gaussianity which can have an impact on the statistical properties of the lensing observables. In order to evaluate this effect, we build a large set of realistic maps of different lensing quantities starting from light-cones extracted from large dark-matter only N-body simulations with initial conditions corresponding to different levels of primordial local non-Gaussianity strength $f_{\rm NL}$. Considering various statistical quantities (PDF, power spectrum, shear in aperture, skewness and bispectrum) we find that the effect produced by the presence of primordial non-Gaussianity is relatively small, being of the order of few per cent for values of $|f_{\rm NL}|$ compatible with the present CMB constraints and reaching at most 10-15 per cent for the most extreme cases with $|f_{\rm NL}|=1000$. We also discuss the degeneracy of this effect with the uncertainties due to the power spectrum normalization $σ_8$ and matter density parameter $Ω_{\rm m}$, finding that an error in the determination of $σ_8$ ($Ω_{\rm m}$) of about 3 (10) per cent gives differences comparable with non-Gaussian models having $f_{\rm NL}=\pm 1000$. These results suggest that the possible presence of an amount of primordial non-Gaussianity corresponding to $|f_{\rm NL}|=100$ is not hampering a robust determination of the main cosmological parameters in present and future weak lensing surveys, while a positive detection of deviations from the Gaussian hypothesis is possible only breaking the degeneracy with other cosmological parameters and using data from deep surveys covering a large fraction of the sky.

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arXiv2012

Planck intermediate results. X. Physics of the hot gas in the Coma cluster

We present an analysis of Planck satellite data on the Coma Cluster observed via the Sunyaev-Zeldovich effect. Planck is able, for the first time, to detect SZ emission up to r ~ 3 X R_500. We test previously proposed models for the pressure distribution in clusters against the azimuthally averaged data. We find that the Arnaud et al. universal pressure profile does not fit Coma, and that their pressure profile for merging systems provides a good fit of the data only at r R_500 than the mean pressure profile predicted by the simulations. The Planck image shows significant local steepening of the y profile in two regions about half a degree to the west and to the south-east of the cluster centre. These features are consistent with the presence of shock fronts at these radii, and indeed the western feature was previously noticed in the ROSAT PSPC mosaic as well as in the radio. Using Planck y profiles extracted from corresponding sectors we find pressure jumps of 4.5+0.4-0.2 and 5.0+1.3-0.1 in the west and southeast, respectively. Assuming Rankine-Hugoniot pressure jump conditions, we deduce that the shock waves should propagate with Mach number M_w=2.03+0.09-0.04 and M_se=2.05+0.25-0.02 in the West and Southeast, respectively. Finally, we find that the y and radio-synchrotron signals are quasi-linearly correlated on Mpc scales with small intrinsic scatter. This implies either that the energy density of cosmic-ray electrons is relatively constant throughout the cluster, or that the magnetic fields fall off much more slowly with radius than previously thought.

astro-ph.CO↗

arXiv2012

Planck intermediate results. VIII. Filaments between interacting clusters

About half of the baryons of the Universe are expected to be in the form of filaments of hot and low density intergalactic medium. Most of these baryons remain undetected even by the most advanced X-ray observatories which are limited in sensitivity to the diffuse low density medium. The Planck satellite has provided hundreds of detections of the hot gas in clusters of galaxies via the thermal Sunyaev-Zel'dovich (tSZ) effect and is an ideal instrument for studying extended low density media through the tSZ effect. In this paper we use the Planck data to search for signatures of a fraction of these missing baryons between pairs of galaxy clusters. Cluster pairs are good candidates for searching for the hotter and denser phase of the intergalactic medium (which is more easily observed through the SZ effect). Using an X-ray catalogue of clusters and the Planck data, we select physical pairs of clusters as candidates. Using the Planck data we construct a local map of the tSZ effect centered on each pair of galaxy clusters. ROSAT data is used to construct X-ray maps of these pairs. After having modelled and subtracted the tSZ effect and X-ray emission for each cluster in the pair we study the residuals on both the SZ and X-ray maps. For the merging cluster pair A399-A401 we observe a significant tSZ effect signal in the intercluster region beyond the virial radii of the clusters. A joint X-ray SZ analysis allows us to constrain the temperature and density of this intercluster medium. We obtain a temperature of kT = 7.1 +- 0.9, keV (consistent with previous estimates) and a baryon density of (3.7 +- 0.2)x10^-4, cm^-3. The Planck satellite mission has provided the first SZ detection of the hot and diffuse intercluster gas.

astro-ph.CO↗

arXiv2012

Planck Intermediate Results. V. Pressure profiles of galaxy clusters from the Sunyaev-Zeldovich effect

Taking advantage of the all-sky coverage and broad frequency range of the Planck satellite, we study the Sunyaev-Zeldovich (SZ) and pressure profiles of 62 nearby massive clusters detected at high significance in the 14-month nominal survey. Careful reconstruction of the SZ signal indicates that most clusters are individually detected at least out to R500. By stacking the radial profiles, we have statistically detected the radial SZ signal out to 3 x R500, i.e., at a density contrast of about 50-100, though the dispersion about the mean profile dominates the statistical errors across the whole radial range. Our measurement is fully consistent with previous Planck results on integrated SZ fluxes, further strengthening the agreement between SZ and X-ray measurements inside R500. Correcting for the effects of the Planck beam, we have calculated the corresponding pressure profiles. This new constraint from SZ measurements is consistent with the X-ray constraints from XMM-Newton in the region in which the profiles overlap (i.e., [0.1-1]R500), and is in fairly good agreement with theoretical predictions within the expected dispersion. At larger radii the average pressure profile is slightly flatter than most predictions from numerical simulations. Combining the SZ and X-ray observed profiles into a joint fit to a generalised pressure profile gives best-fit parameters [P0, c500, gamma, alpha, beta] = [6.41, 1.81, 0.31, 1.33, 4.13]. Using a reasonable hypothesis for the gas temperature in the cluster outskirts we reconstruct from our stacked pressure profile the gas mass fraction profile out to 3 x R500. Within the temperature driven uncertainties, our Planck constraints are compatible with the cosmic baryon fraction and expected gas fraction in halos.

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arXiv2012

Resolving infall caustics in dark matter halos

We have found that the phase-space of a dark matter particles assembling a galactic halo in cosmological N-body simulations has well defined fine grained structure. Recently accreted particles form distinctive velocity streams with high density contrast. For fixed observer position these streams lead to peaks in velocity distribution. Overall structure is close to that emerging in the secondary infall model.

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arXiv2012

Planck intermediate results. III. The relation between galaxy cluster mass and Sunyaev-Zeldovich signal

We examine the relation between the galaxy cluster mass M and Sunyaev-Zeldovich (SZ) effect signal D_A^2 Y for a sample of 19 objects for which weak lensing (WL) mass measurements obtained from Subaru Telescope data are available in the literature. Hydrostatic X-ray masses are derived from XMM-Newton archive data and the SZ effect signal is measured from Planck all-sky survey data. We find an M_WL-D_A^2 Y relation that is consistent in slope and normalisation with previous determinations using weak lensing masses; however, there is a normalisation offset with respect to previous measures based on hydrostatic X-ray mass-proxy relations. We verify that our SZ effect measurements are in excellent agreement with previous determinations from Planck data. For the present sample, the hydrostatic X-ray masses at R_500 are on average ~ 20 per cent larger than the corresponding weak lensing masses, at odds with expectations. We show that the mass discrepancy is driven by a difference in mass concentration as measured by the two methods, and, for the present sample, the mass discrepancy and difference in mass concentration is especially large for disturbed systems. The mass discrepancy is also linked to the offset in centres used by the X-ray and weak lensing analyses, which again is most important in disturbed systems. We outline several approaches that are needed to help achieve convergence in cluster mass measurement with X-ray and weak lensing observations.

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arXiv2012

Planck Intermediate Results. IV. The XMM-Newton validation programme for new Planck galaxy clusters

We present the final results from the XMM-Newton validation follow-up of new Planck galaxy cluster candidates. We observed 15 new candidates, detected with signal-to-noise ratios between 4.0 and 6.1 in the 15.5-month nominal Planck survey. The candidates were selected using ancillary data flags derived from the ROSAT All Sky Survey (RASS) and Digitized Sky Survey all-sky maps, with the aim of pushing into the low SZ flux, high-z regime and testing RASS flags as indicators of candidate reliability. 14 new clusters were detected by XMM, including 2 double systems. Redshifts lie in the range 0.2 to 0.9, with 6 clusters at z>0.5. Estimated M500 range from 2.5 10^14 to 8 10^14 Msun. We discuss our results in the context of the full XMM validation programme, in which 51 new clusters have been detected. This includes 4 double and 2 triple systems, some of which are chance projections on the sky of clusters at different z. We find that association with a RASS-BSC source is a robust indicator of the reliability of a candidate, whereas association with a FSC source does not guarantee that the SZ candidate is a bona fide cluster. Nevertheless, most Planck clusters appear in RASS maps, with a significance greater than 2 sigma being a good indication that the candidate is a real cluster. The full sample gives a Planck sensitivity threshold of Y500 ~ 4 10^-4 arcmin^2, with indication for Malmquist bias in the YX-Y500 relation below this level. The corresponding mass threshold depends on z. Systems with M500 > 5 10^14 Msun at z > 0.5 are easily detectable with Planck. The newly-detected clusters follow the YX-Y500 relation derived from X-ray selected samples. Compared to X-ray selected clusters, the new SZ clusters have a lower X-ray luminosity on average for their mass. There is no indication of departure from standard self-similar evolution in the X-ray versus SZ scaling properties. (abridged)

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arXiv2012

Planck intermediate results. VI: The dynamical structure of PLCKG214.6+37.0, a Planck discovered triple system of galaxy clusters

The survey of galaxy clusters performed by Planck through the Sunyaev-Zeldovich effect has already discovered many interesting objects, thanks to the whole coverage of the sky. One of the SZ candidates detected in the early months of the mission near to the signal to noise threshold, PLCKG214.6+37.0, was later revealed by XMM-Newton to be a triple system of galaxy clusters. We have further investigated this puzzling system with a multi-wavelength approach and we present here the results from a deep XMM-Newton re-observation. The characterisation of the physical properties of the three components has allowed us to build a template model to extract the total SZ signal of this system with Planck data. We partly reconciled the discrepancy between the expected SZ signal from X-rays and the observed one, which are now consistent at less than 1.2 sigma. We measured the redshift of the three components with the iron lines in the X-ray spectrum, and confirmed that the three clumps are likely part of the same supercluster structure. The analysis of the dynamical state of the three components, as well as the absence of detectable excess X-ray emission, suggest that we are witnessing the formation of a massive cluster at an early phase of interaction.

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arXiv2012

The pre-launch Planck Sky Model: a model of sky emission at submillimetre to centimetre wavelengths

We present the Planck Sky Model (PSM), a parametric model for the generation of all-sky, few arcminute resolution maps of sky emission at submillimetre to centimetre wavelengths, in both intensity and polarisation. Several options are implemented to model the cosmic microwave background, Galactic diffuse emission (synchrotron, free-free, thermal and spinning dust, CO lines), Galactic H-II regions, extragalactic radio sources, dusty galaxies, and thermal and kinetic Sunyaev-Zeldovich signals from clusters of galaxies. Each component is simulated by means of educated interpolations/extrapolations of data sets available at the time of the launch of the Planck mission, complemented by state-of-the-art models of the emission. Distinctive features of the simulations are: spatially varying spectral properties of synchrotron and dust; different spectral parameters for each point source; modeling of the clustering properties of extragalactic sources and of the power spectrum of fluctuations in the cosmic infrared background. The PSM enables the production of random realizations of the sky emission, constrained to match observational data within their uncertainties, and is implemented in a software package that is regularly updated with incoming information from observations. The model is expected to serve as a useful tool for optimizing planned microwave and sub-millimetre surveys and to test data processing and analysis pipelines. It is, in particular, used for the development and validation of data analysis pipelines within the planck collaboration. A version of the software that can be used for simulating the observations for a variety of experiments is made available on a dedicated website.

astro-ph.CO↗

arXiv2012

Planck Intermediate Results II: Comparison of Sunyaev-Zeldovich measurements from Planck and from the Arcminute Microkelvin Imager for 11 galaxy clusters

A comparison is presented of Sunyaev-Zeldovich measurements for 11 galaxy clusters as obtained by Planck and by the ground-based interferometer, the Arcminute Microkelvin Imager. Assuming a universal spherically-symmetric Generalised Navarro, Frenk & White (GNFW) model for the cluster gas pressure profile, we jointly constrain the integrated Compton-Y parameter (Y_500) and the scale radius (theta_500) of each cluster. Our resulting constraints in the Y_500-theta_500 2D parameter space derived from the two instruments overlap significantly for eight of the clusters, although, overall, there is a tendency for AMI to find the Sunyaev-Zeldovich signal to be smaller in angular size and fainter than Planck. Significant discrepancies exist for the three remaining clusters in the sample, namely A1413, A1914, and the newly-discovered Planck cluster PLCKESZ G139.59+24.18. The robustness of the analysis of both the Planck and AMI data is demonstrated through the use of detailed simulations, which also discount confusion from residual point (radio) sources and from diffuse astrophysical foregrounds as possible explanations for the discrepancies found. For a subset of our cluster sample, we have investigated the dependence of our results on the assumed pressure profile by repeating the analysis adopting the best-fitting GNFW profile shape which best matches X-ray observations. Adopting the best-fitting profile shape from the X-ray data does not, in general, resolve the discrepancies found in this subset of five clusters. Though based on a small sample, our results suggest that the adopted GNFW model may not be sufficiently flexible to describe clusters universally.

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arXiv2012

A divergence-cleaning scheme for cosmological SPMHD simulations

In magnetohydrodynamics (MHD), the magnetic field is evolved by the induction equation and coupled to the gas dynamics by the Lorentz force. We perform numerical smoothed particle magnetohydrodynamics (Spmhd) simulations and study the influence of a numerical magnetic divergence. For instabilities arising from divergence B related errors, we find the hyperbolic/parabolic cleaning scheme suggested by Dedner et al. 2002 to give good results and prevent numerical artifacts from growing. Additionally, we demonstrate that certain current Spmhd implementations of magnetic field regularizations give rise to unphysical instabilities in long-time simulations. We also find this effect when employing Euler potentials (divergenceless by definition), which are not able to follow the winding-up process of magnetic field lines properly. Furthermore, we present cosmological simulations of galaxy cluster formation at extremely high resolution including the evolution of magnetic fields. We show synthetic Faraday rotation maps and derive structure functions to compare them with observations. Comparing all the simulations with and without divergence cleaning, we are able to confirm the results of previous simulations performed with the standard implementation of MHD in Spmhd at normal resolution. However, at extremely high resolution, a cleaning scheme is needed to prevent the growth of numerical errors at small scales.

astro-ph.IM↗

arXiv2012

Planck Intermediate Results. I. Further validation of new Planck clusters with XMM-Newton

We present further results from the ongoing XMM-Newton validation follow-up of Planck cluster candidates, detailing X-ray observations of eleven candidates detected at a signal-to-noise ratio of 4.5<S/N<5.3 in the same 10-month survey maps used in the construction of the Early SZ sample. The sample was selected in order to test internal SZ quality flags, and the pertinence of these flags is discussed in light of the validation results. Ten of the candidates are found to be bona fide clusters lying below the RASS flux limit. Redshift estimates are available for all confirmed systems via X-ray Fe-line spectroscopy. They lie in the redshift range 0.19<z<0.94, demonstrating Planck's capability to detect clusters up to high z. The X-ray properties of the new clusters appear to be similar to previous new detections by Planck at lower z and higher SZ flux: the majority are X-ray underluminous for their mass, estimated using Y_X as mass proxy, and many have a disturbed morphology. We find tentative indication for Malmquist bias in the Y_SZ-Y_X relation, with a turnover at Y_SZ \sim 4 e-4 arcmin^2. We present additional new optical redshift determinations with ENO and ESO telescopes of candidates previously confirmed with XMM-Newton. The X-ray and optical redshifts for a total of 20 clusters are found to be in excellent agreement. We also show that useful lower limits can be put on cluster redshifts using X-ray data only via the use of the Y_X vs. Y_SZ and X-ray flux F_X vs. Y_SZ relations.

astro-ph.CO↗

arXiv2012

Toward Unbiased Galaxy Cluster Masses from Line of Sight Velocity Dispersions

We study the use of red sequence selected galaxy spectroscopy for unbiased estimation of galaxy cluster masses. We use the publicly available galaxy catalog produced using the semi-analytic model of De Lucia & Blaizot (2007) on the Millenium Simulation (Springel et al. 2005). We explore the impacts on selection using galaxy color, projected separation from the cluster center, and galaxy luminosity. We study the relationship between cluster mass and velocity dispersion and identify and characterize the following sources of bias and scatter: halo triaxiality, dynamical friction of red luminous galaxies and interlopers. We show that due to halo triaxiality the intrinsic scatter of estimated line of sight dynamical mass is about three times larger (30-40%) than the one estimated using the 3D velocity dispersion (~12%) and a small bias (~1%) is induced. We find evidence of increasing scatter as a function of redshift and provide a fitting formula to account for it. We characterize the amount of bias and scatter introduced by dynamical friction when using subsamples of red-luminous galaxies to estimate the velocity dispersion. We study the presence of interlopers in spectroscopic samples and their effect on the estimated cluster dynamical mass. Our results show that while cluster velocity dispersions extracted from a few dozen red sequence selected galaxies do not provide precise masses on a single cluster basis, an ensemble of cluster velocity dispersions can be combined to produce a precise calibration of a cluster survey mass observable relation. Currently, disagreements in the literature on simulated subhalo velocity dispersion mass relations place a systematic floor on velocity dispersion mass calibration at the 15% level in mass. We show that the selection related uncertainties are small by comparison, providing hope that with further improvements this systematic floor can be reduced.

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arXiv2012

Lensing and X-ray mass estimates of clusters (SIMULATION)

[Abridged] We present a comparison between weak-lensing (WL) and X-ray mass estimates of a sample of numerically simulated clusters. The sample consists on the 20 most massive objects at redshift z=0.25 and Mvir > 5 x 10^{14} Msun h^{-1}. They were found in a cosmological simulation of volume 1 h^{-3} Gpc^3, evolved in the framework of a WMAP-7 normalized cosmology. Each cluster has been resimulated at higher resolution and with more complex gas physics. We processed it thought Skylens and X-MAS to generate optical and X-ray mock observations along three orthogonal projections. The optical simulations include lensing effects on background sources. Standard observational tools and methods of analysis are used to recover the mass profiles of each cluster projection from the mock catalogues. Given the size of our sample, we could also investigate the dependence of the results on cluster morphology, environment, temperature inhomogeneity, and mass. We confirm previous results showing that WL masses obtained from the fit of the cluster tangential shear profiles with NFW functionals are biased low by ~ 5-10% with a large scatter (~10-25%). We show that scatter could be reduced by optimally selecting clusters either having regular morphology or living in substructure-poor environment. The X-ray masses are biased low by a large amount (~25-35%), evidencing the presence of both non-thermal sources of pressure in the ICM and temperature inhomogeneity, but they show a significantly lower scatter than weak-lensing-derived masses. The X-ray mass bias grows from the inner to the outer regions of the clusters. We find that both biases are weakly correlated with the third-order power ratio, while a stronger correlation exists with the centroid shift. Finally, the X-ray bias is strongly connected with temperature inhomogeneities.

astro-ph.CO↗

arXiv2012

Planck Early Results. II. The thermal performance of Planck

The performance of the Planck instruments in space is enabled by their low operating temperatures, 20K for LFI and 0.1K for HFI, achieved through a combination of passive radiative cooling and three active mechanical coolers. The scientific requirement for very broad frequency coverage led to two detector technologies with widely different temperature and cooling needs. Active coolers could satisfy these needs; a helium cryostat, as used by previous cryogenic space missions (IRAS, COBE, ISO, Spitzer, AKARI), could not. Radiative cooling is provided by three V-groove radiators and a large telescope baffle. The active coolers are a hydrogen sorption cooler (<20K), a 4He Joule-Thomson cooler (4.7K), and a 3He-4He dilution cooler (1.4K and 0.1K). The flight system was at ambient temperature at launch and cooled in space to operating conditions. The HFI bolometer plate reached 93mK on 3 July 2009, 50 days after launch. The solar panel always faces the Sun, shadowing the rest of Planck, andoperates at a mean temperature of 384K. At the other end of the spacecraft, the telescope baffle operates at 42.3K and the telescope primary mirror operates at 35.9K. The temperatures of key parts of the instruments are stabilized by both active and passive methods. Temperature fluctuations are driven by changes in the distance from the Sun, sorption cooler cycling and fluctuations in gas-liquid flow, and fluctuations in cosmic ray flux on the dilution and bolometer plates. These fluctuations do not compromise the science data.

astro-ph.IM↗

arXiv2011

Planck early results. VI. The High Frequency Instrument data processing

We describe the processing of the 336 billion raw data samples from the High Frequency Instrument (HFI) which we performed to produce six temperature maps from the first 295 days of Planck-HFI survey data. These maps provide an accurate rendition of the sky emission at 100, 143, 217, 353, 545 and 857 GHz with an angular resolution ranging from 9.9 to 4.4^2. The white noise level is around 1.5 μK degree or less in the 3 main CMB channels (100--217GHz). The photometric accuracy is better than 2% at frequencies between 100 and 353 GHz and around 7% at the two highest frequencies. The maps created by the HFI Data Processing Centre reach our goals in terms of sensitivity, resolution, and photometric accuracy. They are already sufficiently accurate and well-characterised to allow scientific analyses which are presented in an accompanying series of early papers. At this stage, HFI data appears to be of high quality and we expect that with further refinements of the data processing we should be able to achieve, or exceed, the science goals of the Planck project.

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