Planck2018 results

We present 353 GHz full-sky maps of the polarization fraction p, angle ψ, and dispersion of angles S of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of p decrease with increasing N_H. The uncertainty on the maximum polarization fraction, p_(max)=22.0% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between p and S is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of p, ψ, and S mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map S×p, looking for residual trends. While p decreases by a factor of 3--4 between N_H=10^(20) cm^(−2) and N_H=2×10^(22)cm^(−2), S×p decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of S×p with the dust temperature, even though in the diffuse ISM lines of sight with high p and low S tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on NH and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the p_(max) observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas.

J. Aumont | L. Montier | J. R. Bond | L. Toffolatti | J. J. Bock | B. P. Crill | J. E. Gudmundsson | M. Frailis | J. Borrill | A. Gruppuso | E. Hivon | G. Morgante | P. Natoli | F. Piacentini | M. Remazeilles | F. Cuttaia | O. Dor'e | M. Maris | S. Galeotta | M. Bersanelli | C. Burigana | N. Mandolesi | L. Pagano | W. C. Jones | G. Polenta | I. Ristorcelli | F. Perrotta | V. Guillet | G. Maggio | A. Moneti | J. D. McEwen | H. K. Eriksen | C. Dickinson | A. J. Banday | C. R. Lawrence | A. Mennella | P. B. Lilje | D. Herranz | B. D. Wandelt | E. Falgarone | J.-F. Cardoso | K. Ganga | I. K. Wehus | G. Lagache | P. Vielva | G. Helou | X. Dupac | J. P. Rachen | A. Zacchei | D. Maino | M. Douspis | C. Rosset | J. F. Mac'ias-P'erez | J. Delabrouille | S. Matarrese | A. Zonca | N. Krachmalnicoff | N. Vittorio | E. Calabrese | M. Tomasi | A. H. Jaffe | G. Patanchon | K. Ferriere | F. Levrier | H. C. Chiang | D. Tavagnacco | F. Boulanger | P. M. Lubin | R. Fernandez-Cobos | R. B. Barreiro | D. Scott | A. Ducout | R. Keskitalo | E. Franceschi | M. Le Jeune | C. Baccigalupi | J. M. Diego | M. Lattanzi | C. Sirignano | M. Kunz | H. Kurki-Suonio | V. Pettorino | A. Renzi | J. Cardoso | H. Kurki-Suonio | P. Lilje | C. Baccigalupi | K. Benabed | M. Kunz | G. Morgante | M. Douspis | J. Delouis | M. Frailis | A. Zacchei | A. Melchiorri | V. Pettorino | R. G'enova-Santos | J. Rubino-Mart'in | T. Ensslin | E. Hivon | A. Banday | F. Hansen | M. Reinecke | A. Lasenby | A. Challinor | B. Wandelt | F. Bouchet | S. Matarrese | J. Borrill | P. Bernardis | A. Jaffe | J. Bond | B. Crill | K. Ganga | W. Jones | F. Piacentini | G. Efstathiou | J. Diego | A. Moss | J. McEwen | Y. Fantaye | M. Ashdown | C. Lawrence | G. Helou | T. Kisner | H. Eriksen | F. Couchot | F. Boulanger | C. Dickinson | G. Green | J. Aumont | J. Bernard | M. Bersanelli | P. Bielewicz | M. Bucher | C. Burigana | R. Chary | H. Chiang | L. Colombo | F. Cuttaia | G. Zotti | J. Delabrouille | O. Dor'e | X. Dupac | E. Falgarone | F. Finelli | A. Fraisse | E. Franceschi | S. Galeotta | J. Gonz'alez-Nuevo | K. M. G'orski | S. Gratton | A. Gruppuso | S. Henrot-Versill'e | D. Herranz | E. Keihanen | R. Keskitalo | G. Lagache | J. Lamarre | M. Jeune | M. Liguori | M. L'opez-Caniego | P. Lubin | J. Mac'ias-P'erez | D. Maino | N. Mandolesi | A. Marcos-Caballero | M. Maris | P. Martin | E. Mart'inez-Gonz'alez | A. Mennella | M. Migliaccio | M. Miville-Deschênes | A. Moneti | P. Natoli | L. Pagano | D. Paoletti | B. Partridge | G. Patanchon | O. Perdereau | F. Perrotta | G. Polenta | J. Puget | J. Rachen | M. Remazeilles | A. Renzi | I. Ristorcelli | G. Rocha | C. Rosset | G. Roudier | M. Sandri | L. Spencer | R. Sunyaev | A. Suur-Uski | J. Tauber | D. Tavagnacco | L. Toffolatti | M. Tomasi | M. Tristram | J. Valiviita | B. Tent | P. Vielva | F. Villa | N. Vittorio | I. Wehus | A. Zonca | L. Vibert | E. Calabrese | F. Elsner | S. Galli | J. Gudmundsson | M. Lattanzi | M. Savelainen | Will Handley | N. Bartolo | J. Cardoso | C. Combet | E. D. Valentino | A. Ducout | M. Gerbino | T. Ghosh | Z. Huang | F. Levrier | G. Maggio | A. Mangilli | L. Salvati | T. Trombetti | L. Montier | K. Kiiveri | V. Lindholm | N. Mauri | L. Patrizii | C. Sirignano | G. Sirri | M. Tenti | Y. Akrami | Planck Collaboration N. Aghanim | M. Alves | A. Bracco | F. Vansyngel | M. Ballardini | S. Basak | R. Fernández-Cobos | A. Frolov | A. Karakci | J. Kim | N. Krachmalnicoff | Y.-Z. Ma | D. Molinari | S. Mottet | B. Ruiz-Granados | J. Carron | F. Forastieri | L. Polastri | W. Handley | K. Ferrière | V. Guillet | F. Villa | M. Sandri | M. Ashdown | M. Ballardini | N. Bartolo | S. Basak | K. Benabed | J.-P. Bernard | P. Bielewicz | F. R. Bouchet | A. Bracco | L. P. L. Colombo | C. Combet | P. de Bernardis | G. de Zotti | J.-M. Delouis | E. Di Valentino | G. Efstathiou | F. Elsner | T. A. Ensslin | Y. Fantaye | F. Finelli | A. A. Fraisse | A. Frolov | S. Galli | R. T. G'enova-Santos | M. Gerbino | T. Ghosh | J. Gonz'alez-Nuevo | F. K. Hansen | Z. Huang | E. Keihanen | J.-M. Lamarre | A. Lasenby | M. Liguori | M. L'opez-Caniego | A. Mangilli | P. G. Martin | E. Mart'inez-Gonz'alez | N. Mauri | A. Melchiorri | M. Migliaccio | M.-A. Miville-Deschenes | D. Molinari | A. Moss | D. Paoletti | J.-L. Puget | M. Reinecke | G. Rocha | G. Roudier | J. A. Rubino-Mart'in | B. Ruiz-Granados | L. Salvati | M. Savelainen | A.-S. Suur-Uski | J. A. Tauber | M. Tenti | T. Trombetti | J. Valiviita | M. Bucher | S. Gratton | R. Sunyaev | B. Van Tent | R.-R. Chary | M. I. R. Alves | A. Marcos-Caballero | J. Carron | F. Forastieri | W. Handley | K. Kiiveri | J. Kim | V. Lindholm | Y.-Z. Ma | L. Polastri | Y. Akrami | G. Green | F. Vansyngel | J. Bock | D. Scott | D. Scott | A. D. Rosa | D. Scott | G. Rocha | J. Bond | C. Lawrence | Y. Akrami | A.-S. Suur-Uski

[1]  Pekka Teerikorpi,et al.  Interstellar polarization at high galactic latitudes from distant stars VII. A complete map for southern latitudes b < −70 ◦ , 2004 .

[2]  G. W. Pratt,et al.  Planck intermediate results. XX. Comparison of polarized thermal emission from Galactic dust with simulations of MHD turbulence , 2014, 1405.0872.

[3]  V. Guillet,et al.  Dust models compatible with Planck intensity and polarization data in translucent lines of sight , 2017, 1710.04598.

[4]  P. Bastien,et al.  GRAIN ALIGNMENT IN STARLESS CORES , 2014, 1411.1031.

[5]  G. Lewis,et al.  Advanced Diagnostics for the Study of Linearly Polarized Emission. II. Application to Diffuse Interstellar Radio Synchrotron Emission , 2018, 1802.05403.

[6]  Carl Heiles 9286 Stars: An Agglomeration of Stellar Polarization Catalogs , 2000 .

[7]  J. Neveu,et al.  Statistics of the polarized submillimetre emission maps from thermal dust in the turbulent, magnetized, diffuse ISM , 2018, Astronomy & Astrophysics.

[8]  R. Ekers,et al.  Low-Mach-number turbulence in interstellar gas revealed by radio polarization gradients , 2011, Nature.

[9]  Jean-Francois Cardoso,et al.  Component separation with flexible models. Application to the separation of astrophysical emissions , 2008, 0803.1814.

[10]  Nicolas Ponthieu,et al.  Absolute calibration of the polarisation angle for future CMB B-mode experiments from current and future measurements of the Crab nebula , 2018, Astronomy & Astrophysics.

[11]  R. B. Barreiro,et al.  Planck 2018 results , 2018, Astronomy & Astrophysics.

[12]  A. Goodman,et al.  On the dispersion in direction of interstellar polarization , 1991 .

[13]  J. Cardoso,et al.  Foreground component separation with generalised ILC , 2011, 1103.1166.

[14]  V. Pavlidou,et al.  Searching for Inflationary B-modes: Can dust emission properties be extrapolated from 350 GHz to 150 GHz? , 2014, 1410.8136.

[15]  C. A. Oxborrow,et al.  Planck 2015 results. I. Overview of products and scientific results , 2015 .

[16]  N. Ysard,et al.  Separation of anomalous and synchrotron emissions using WMAP polarization data , 2008, 0802.3345.

[17]  Mapping the CMB sky: The BOOMERanG experiment , 1999, astro-ph/9911461.

[18]  California Institute of Technology,et al.  DISPERSION OF MAGNETIC FIELDS IN MOLECULAR CLOUDS. III. , 2011 .

[19]  Enzo Pascale,et al.  BALLOON-BORNE SUBMILLIMETER POLARIMETRY OF THE VELA C MOLECULAR CLOUD: SYSTEMATIC DEPENDENCE OF POLARIZATION FRACTION ON COLUMN DENSITY AND LOCAL POLARIZATION-ANGLE DISPERSION , 2015, 1509.05298.

[20]  R. B. Barreiro,et al.  Planck2018 results , 2018, Astronomy & Astrophysics.

[21]  John E. Vaillancourt,et al.  Interstellar Dust Grain Alignment , 2015 .

[22]  J. Greenstein,et al.  The Polarization of Starlight by Aligned Dust Grains. , 1951 .

[23]  R. B. Barreiro,et al.  Planck 2018 results. IX. Constraints on primordial non-Gaussianity , 2019, 1905.05697.

[24]  Simon Prunet,et al.  Statistical Properties of Galactic Starlight Polarization , 2001, astro-ph/0105023.

[25]  J. Soler,et al.  The magnetic environment of the Orion-Eridanus superbubble as revealed by Planck , 2017, 1712.03728.

[26]  C. B. Netterfield,et al.  AN IMPRINT OF MOLECULAR CLOUD MAGNETIZATION IN THE MORPHOLOGY OF THE DUST POLARIZED EMISSION , 2013, 1303.1830.

[27]  T. N. Gautier,et al.  A calculation of confusion noise due to infrared cirrus , 1992 .

[28]  H. Rix,et al.  Galactic reddening in 3D from stellar photometry – an improved map , 2018, 1801.03555.

[29]  A. Berdyugin,et al.  Interstellar polarization at high galactic latitudes from distant stars - VI. Extended polarization map and connection with the local spiral structure , 2002 .

[30]  D. S. Mathewson,et al.  Wavelength dependence of interstellar polarization and ratio of total to selective extinction. , 1975 .

[31]  G. W. Pratt,et al.  Planck intermediate results. XVII. Emission of dust in the diffuse interstellar medium from the far-infrared to microwave frequencies , 2013, 1312.5446.

[32]  C. A. Oxborrow,et al.  Planck intermediate results. XXIX. All-sky dust modelling with Planck, IRAS, and WISE observations , 2014, 1409.2495.

[33]  R. B. Barreiro,et al.  Planck intermediate results. LIV. Polarized dust foregrounds , 2018 .

[34]  G. W. Pratt,et al.  Planck intermediate results. XXI. Comparison of polarized thermal emission from Galactic dust at 353GHz with optical interstellar polarization , 2014 .

[35]  A. Berdyugin,et al.  Interstellar polarization at high galactic latitudes from distant stars. IV. A catalog of polarization data for the North Galactic Pole Area , 2001 .

[36]  R. B. Barreiro,et al.  Planck intermediate results. XLII. Large-scale Galactic magnetic fields , 2016, 1601.00546.

[37]  F. Boulanger,et al.  The Local Bubble: a magnetic veil to our Galaxy , 2018, 1803.05251.

[38]  A. Lazarian,et al.  A UNIFIED MODEL OF GRAIN ALIGNMENT: RADIATIVE ALIGNMENT OF INTERSTELLAR GRAINS WITH MAGNETIC INCLUSIONS , 2016, 1605.02828.

[39]  Pekka Teerikorpi,et al.  Interstellar polarization at high galactic latitudes from distant stars - VIII. Patterns related to the local dust and gas shells from observations of ~3600 stars , 2014 .

[40]  C. A. Oxborrow,et al.  Planck intermediate results XLIV. Structure of the Galactic magnetic field from dust polarization maps of the southern Galactic cap , 2016, 1604.01029.

[41]  R. B. Barreiro,et al.  Planck 2018 results , 2018, Astronomy & Astrophysics.

[42]  W. Stein Infrared radiation from interstellar grains. , 1966 .

[43]  G. Lewis,et al.  Advanced Diagnostics for the Study of Linearly Polarized Emission. I. Derivation , 2017, 1710.07377.

[44]  W. A. Hiltner,et al.  Polarization of Light From Distant Stars by Interstellar Medium. , 1949, Science.

[45]  J. Hough,et al.  The Efficiency of Grain Alignment in Dense Interstellar Clouds: a Reassessment of Constraints from Near-Infrared Polarization , 2007, 0711.2536.

[46]  G. W. Pratt,et al.  Planck intermediate results. XXXV. Probing the role of the magnetic field in the formation of structure in molecular clouds , 2015, 1502.04123.

[47]  Edward J. Wollack,et al.  Three Year Wilkinson Microwave Anistropy Probe (WMAP) Observations: Polarization Analysis , 2006, astro-ph/0603450.

[48]  The Millennium Arecibo 21 Centimeter Absorption-Line Survey. IV. Statistics of Magnetic Field, Column Density, and Turbulence , 2005, astro-ph/0501482.

[49]  J. L. Bourlot,et al.  The global dust SED: tracing the nature and evolution of dust with DustEM , 2010, 1010.2769.

[50]  D. Hartmann,et al.  The Milky Way in Molecular Clouds: A New Complete CO Survey , 2000, astro-ph/0009217.

[51]  C. A. Oxborrow,et al.  Planck intermediate results. XXI. Comparison of polarized thermal emission from Galactic dust at 353 GHz with interstellar polarization in the visible , 2014, 1405.0873.

[52]  Multiwavelength stellar polarimetry of the filamentary cloud IC5146. I. Dust properties , 2017, 1710.03899.

[53]  B. Wandelt,et al.  Statistical simulations of the dust foreground to cosmic microwave background polarization (Corrigendum) , 2017, Astronomy & Astrophysics.

[54]  G. W. Pratt,et al.  Planck intermediate results - XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes , 2014, 1409.5738.

[55]  Paul M. Brunet,et al.  The Gaia mission , 2013, 1303.0303.

[56]  C. A. Oxborrow,et al.  Planck2018 results , 2018, Astronomy & Astrophysics.

[57]  J S Hall,et al.  Observations of the Polarized Light From Stars. , 1949, Science.

[58]  S. Chatterjee,et al.  The Vertical Structure of Warm Ionised Gas in the Milky Way , 2008, Publications of the Astronomical Society of Australia.

[59]  G. W. Pratt,et al.  Planck intermediate results XXXII. The relative orientation between the magnetic field and structures traced by interstellar dust , 2014, 1409.6728.

[60]  J. Aumont,et al.  Planck intermediate results. XLVIII. Disentangling Galactic dust emission and cosmic infrared background anisotropies , 2016, 1605.09387.

[61]  B. G. Stewart,et al.  Point and interval estimation of the true unbiased degree of linear polarization in the presence of low signal-to-noise ratios , 1985 .

[62]  A FAR-INFRARED OBSERVATIONAL TEST OF THE DIRECTIONAL DEPENDENCE IN RADIATIVE GRAIN ALIGNMENT , 2015, 1509.08542.

[63]  R. B. Barreiro,et al.  Planck2018 results , 2020, Astronomy & Astrophysics.

[64]  B. Savage,et al.  A survey of interstellar H I from L-alpha absorption measurements. II , 1978 .

[65]  E. Abdikamalov,et al.  Polarization measurement analysis III. Analysis of the polarization angle dispersion function with high precision polarization data , 2016, 1608.07105.

[66]  M. Halpern,et al.  Five-Year Wilkinson Microwave Anisotropy Probe (WMAP1) Observations: Galactic Foreground Emission , 2008 .

[67]  R. B. Barreiro,et al.  Planck intermediate results: XXXIII. Signature of the magnetic field geometry of interstellar filaments in dust polarization maps , 2014, 1411.2271.

[68]  S. Masi,et al.  First detection of polarization of the submillimetre diffuse galactic dust emission by Archeops , 2003, astro-ph/0306222.

[69]  Jean-Francois Cardoso,et al.  Foreground component separation with generalised ILC , 2011, 1103.1166.

[70]  B. Andersson,et al.  OBSERVATIONS OF ENHANCED RADIATIVE GRAIN ALIGNMENT NEAR HD 97300 , 2010 .

[71]  D. Clemens,et al.  THE MAGNETIC FIELD OF CLOUD 3 IN L204 , 2014, 1407.3279.

[72]  C. A. Oxborrow,et al.  Planck intermediate results. XXXVIII. E- and B-modes of dust polarization from the magnetized filamentary structure of the interstellar medium , 2015, 1505.02779.

[73]  A. Lazarian,et al.  Radiative torques: analytical model and basic properties , 2007, 0707.0886.

[74]  A. Berdyugin,et al.  Research Note Interstellar polarization at high galactic latitudes from distant stars - V. First results for the South Galactic Pole , 2001 .

[75]  J. Bovy,et al.  Data analysis recipes: Fitting a model to data , 2010, 1008.4686.

[76]  R. B. Barreiro,et al.  Planck intermediate results - XXXIV. The magnetic field structure in the Rosette Nebula , 2015, 1501.00922.

[77]  S. Plaszczynski,et al.  A novel estimator of the polarization amplitude from normally distributed Stokes parameters , 2013, 1312.0437.

[78]  R. B. Barreiro,et al.  Planck 2018 results , 2018, Astronomy & Astrophysics.

[79]  B. Wandelt,et al.  Statistical simulations of the dust foreground to cosmic microwave background polarization (Corrigendum) , 2018, Astronomy & Astrophysics.

[80]  S. Plaszczynski,et al.  Polarization measurement analysis - I. Impact of the full covariance matrix on polarization fraction and angle measurements , 2014, 1406.6536.

[81]  G. W. Pratt,et al.  Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust , 2014, 1405.0871.

[82]  B. M. Gaensler,et al.  PROPERTIES OF INTERSTELLAR TURBULENCE FROM GRADIENTS OF LINEAR POLARIZATION MAPS , 2011, 1111.3544.

[83]  B. Kelly Some Aspects of Measurement Error in Linear Regression of Astronomical Data , 2007, 0705.2774.

[84]  G. Panopoulou,et al.  Local measurements of the mean interstellar polarization at high Galactic latitudes , 2018, Astronomy & Astrophysics.

[85]  D. Clarke,et al.  On the statistical behaviour of the position angle of linear polarization , 1993 .

[86]  G. W. Pratt,et al.  Planck 2013 results. XI. All-sky model of thermal dust emission , 2013, 1312.1300.

[87]  C. Heiles,et al.  The Millennium Arecibo 21 Centimeter Absorption-Line Survey. III. Techniques for Spectral Polarization and Results for Stokes V , 2004 .

[88]  R. B. Barreiro,et al.  Planck 2018 results , 2019, Astronomy & Astrophysics.

[89]  B. Draine INTERSTELLAR DUST GRAINS , 2003, astro-ph/0304489.

[90]  C. A. Oxborrow,et al.  Planck intermediate results. XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth , 2016, 1605.02985.

[91]  Jean-François Cardoso,et al.  Component Separation With Flexible Models—Application to Multichannel Astrophysical Observations , 2008, IEEE Journal of Selected Topics in Signal Processing.

[92]  P. Fischer,et al.  PROBING THE ROSETTE NEBULA STELLAR BUBBLE WITH FARADAY ROTATION , 2012, 1206.5173.

[93]  Paule Sonnentrucker,et al.  MOLECULAR HYDROGEN IN THE FAR ULTRAVIOLET SPECTROSCOPIC EXPLORER TRANSLUCENT LINES OF SIGHT: THE FULL SAMPLE , 2008 .

[94]  K. Gorski,et al.  HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , 2004, astro-ph/0409513.

[95]  J. Dickey,et al.  Infrared polarimetry and the galactic magnetic field. II: Improved models , 1992 .

[96]  D. Massa,et al.  An Analysis of the Shapes of Interstellar Extinction Curves. V. The IR-through-UV Curve Morphology , 2007, 0705.0154.

[97]  Albert Stebbins,et al.  Statistics of cosmic microwave background polarization , 1997 .

[98]  California Institute of Technology,et al.  Dispersion of Magnetic Fields in Molecular Clouds , 2008 .

[99]  G. W. Pratt,et al.  Planck 2015 results Special feature Planck 2015 results XII . Full focal plane simulations , 2016 .

[100]  A. Hanson,et al.  CHARTING THE INTERSTELLAR MAGNETIC FIELD CAUSING THE INTERSTELLAR BOUNDARY EXPLORER (IBEX) RIBBON OF ENERGETIC NEUTRAL ATOMS , 2015, 1510.04679.

[101]  L. Montier,et al.  Polarization measurements analysis II. Best estimators of polarization fraction and angle , 2014, 1407.0178.

[102]  C. A. Oxborrow,et al.  Planck 2013 results - VIII. HFI photometric calibration and mapmaking , 2013, 1303.5069.

[103]  J. Aumont,et al.  Planck2018 results , 2013, Astronomy & Astrophysics.

[104]  U. Seljak,et al.  An all sky analysis of polarization in the microwave background , 1996, astro-ph/9609170.

[105]  Peter G. Martin,et al.  Modelling and simulation of large-scale polarized dust emission over the southern Galactic cap using the GASS HI data , 2016, 1611.02418.

[106]  Astronomy,et al.  On the radiation driven alignment of dust grains: Detection of the polarization hole in a starless core , 2014, 1408.5133.

[107]  N. Ysard,et al.  Dust models post-Planck: constraining the far-infrared opacity of dust in the diffuse interstellar medium , 2015, 1506.07011.

[108]  Matthew A. Bershady,et al.  Linear Regression for Astronomical Data with Measurement Errors and Intrinsic Scatter , 1996, astro-ph/9605002.

[109]  E. Krugel The Physics of Interstellar Dust , 2002 .

[110]  Douglas P. Finkbeiner,et al.  MEASURING REDDENING WITH SLOAN DIGITAL SKY SURVEY STELLAR SPECTRA AND RECALIBRATING SFD , 2010, 1012.4804.