Gravitational Lensing of Distant Supernovae in Cold Dark Matter Universes

Ongoing searches for supernovae (SNe) at cosmological distances have recently started to provide large numbers of events with measured redshifts and apparent brightnesses. Compared to quasars or galaxies, Type Ia SNe represent a population of sources with well-known intrinsic properties and could be used to detect gravitational lensing even in the absence of multiple or highly distorted images. We investigate the lensing effect of background SNe due to mass condensations in three popular cold dark matter cosmologies (ΛCDM, OCDM, and SCDM) and compute lensing frequencies, rates of SN explosions, and distributions of arrival-time differences and image separations. If dark halos approximate singular isothermal spheres on galaxy scales and Navarro-Frenk-White profiles on group/cluster scales, and are distributed in mass according to the Press-Schechter theory, then about one of every 12 SNe at z ~ 1 will be magnified by Δm ≥ 0.1 mag (SCDM). The detection rate of SNe Ia with magnification Δm ≥ 0.3 is estimated to be of the order of a few events yr-1 deg-2 at maximum B light and IAB ≤ 25, 100 times smaller than the total rate expected at these magnitude levels. In the field, events magnified by more than 0.75 mag are 7 times less frequent; about one-fifth of them give rise to observable multiple images. While the time delay between the images is shorter than 3 days in ~25% of the cases (shorter than 30 days in 50%) (SCDM), a serious bias against the detection of small-separation events in ground-based surveys is caused by the luminosity of the foreground lensing galaxy. Because of the flat K-correction and wide luminosity function, Type II SNe dominate the number counts at IAB > 25 and have the largest fraction of lensed objects. The optimal survey sensitivity for Type Ia SNe magnified by Δm ≥ 0.75 mag is IAB ≈ 23. Magnification bias increases their incidence by a factor of 50 in samples with IAB ≤ 22, dropping to a factor of 3.5 at 24 mag. At faint magnitudes, the enhancement is larger for SNe II.

[1]  Yun Wang,et al.  Flux-averaging Analysis of Type Ia Supernova Data , 1999, astro-ph/9907405.

[2]  M. Bartelmann,et al.  The Core Structure of Galaxy Clusters from Gravitational Lensing , 1999, astro-ph/9905134.

[3]  A. Dekel,et al.  Formation of Structure in the Universe , 1999 .

[4]  P. Nugent,et al.  High-Redshift Supernovae in the Hubble Deep Field , 1999, astro-ph/9903229.

[5]  Ravi K. Sheth Giuseppe Tormen.  Large scale bias and the peak background split , 1999, astro-ph/9901122.

[6]  Yun Wang.  Supernova Pencil Beam Survey , 1998, astro-ph/9806185.

[7]  K. Tomita.  Angular Diameter Distances in Clumpy Friedmann Universes , 1998, astro-ph/9806047.

[8]  A. Ferrara,et al.  Gravitational Magnification of Population III Supernovae in Hierarchical Cosmological Models: Next Generation Space Telescope Perspectives , 1998, astro-ph/9806053.

[9]  P. Pellegrini,et al.  The Galaxy Luminosity Function at z ≤ 0.05: Dependence on Morphology , 1998, astro-ph/9805218.

[10]  R. Metcalf.  Gravitational lensing of high-redshift Type Ia supernovae: a probe of medium-scale structure , 1998, astro-ph/9803319.

[11]  M. Valle,et al.  On the evolution of the cosmic supernova rates , 1998, astro-ph/9803284.

[12]  G. Ellis,et al.  Lensing and caustic effects on cosmological distances , 1998, gr-qc/9801092.

[13]  I. Hook,et al.  Discovery of a supernova explosion at half the age of the Universe , 1997, Nature.

[14]  J. Holtzman,et al.  Cold dark matter variant cosmological models — I. Simulations and preliminary comparisons , 1997, astro-ph/9712142.

[15]  A. Riess,et al.  Snapshot Distances to Type Ia Supernovae: All in “One” Night's Work , 1997, astro-ph/9804065.

[16]  E. L. Wright,et al.  The COBE Diffuse Infrared Background Experiment Search for the Cosmic Infrared Background. IV. Cosmological Implications , 1997, astro-ph/9806129.

[17]  H. M. P. Couchman,et al.  Evolution of Structure in Cold Dark Matter Universes , 1997, astro-ph/9709010.

[18]  Alexei V. Filippenko,et al.  Optical spectra of supernovae , 1997 .

[19]  L. Pozzetti,et al.  The Star Formation History of Field Galaxies , 1997, astro-ph/9708220.

[20]  J. Bullock,et al.  The Cores of Dark Matter-dominated Galaxies: Theory versus Observations , 1997, astro-ph/9708176.

[21]  M. Bartelmann,et al.  Gravitational lensing of type Ia supernovae by galaxy clusters , 1997, astro-ph/9708120.

[22]  M. Rees,et al.  High-Redshift Supernovae and the Metal-Poor Halo Stars: Signatures of the First Generation of Galaxies , 1997, astro-ph/9701093.

[23]  H. Rix,et al.  A Survey for Large-Image Separation Lensed Quasars , 1996, astro-ph/9612159.

[24]  S. White,et al.  A Universal Density Profile from Hierarchical Clustering , 1996, astro-ph/9611107.

[25]  D. Long,et al.  A Robust Determination of the Time Delay in 0957+561A, B and a Measurement of the Global Value of Hubble's Constant , 1996, astro-ph/9610162.

[26]  P. Ruiz-Lapuente,et al.  SNe Ia: On the Binary Progenitors and Expected Statistics , 1996, astro-ph/9609078.

[27]  R. Cen,et al.  Effects of Weak Gravitational Lensing from Large-Scale Structure on the Determination of q0 , 1996, astro-ph/9607084.

[28]  William Press,et al.  A Precise Distance Indicator: Type Ia Supernova Multicolor Light-Curve Shapes , 1996, astro-ph/9604143.

[29]  I. Hook,et al.  The Type Ia Supernova Rate at z ~ 0.4 , 1996, astro-ph/9602125.

[30]  A. Kim,et al.  A GENERALIZED K CORRECTION FOR TYPE IA SUPERNOVAE: COMPARING R-BAND PHOTOMETRY BEYOND Z=0.2 WITH B, V, AND R-BAND NEARBY PHOTOMETRY , 1996 .

[31]  S. Cole,et al.  Using the evolution of clusters to constrain Omega , 1996, astro-ph/9601088.

[32]  N. Grogin,et al.  A New Model of the Gravitational Lens 0957+561 and a Limit on the Hubble Constant , 1995, astro-ph/9512156.

[33]  R. Carlberg,et al.  The Average Mass and Light Profiles of Galaxy Clusters , 1995, astro-ph/9512087.

[34]  Matthew Colless,et al.  Autofib Redshift Survey — I. Evolution of the galaxy luminosity function , 1995, astro-ph/9512057.

[35]  J. Primack,et al.  Cluster Cores, Gravitational Lensing, and Cosmology , 1995, astro-ph/9512063.

[36]  C. Kochanek.  Is there a cosmological constant , 1995, astro-ph/9510077.

[37]  R. Brandenberger.  Formation of structure in the universe , 1995, astro-ph/9508159.

[38]  O. Fèvre,et al.  The Canada-France Redshift Survey. VI. Evolution of the Galaxy Luminosity Function to Z approximately 1 , 1995, astro-ph/9507079.

[39]  D. Branch,et al.  The Effects of Inhomogeneities on Evaluating the Deceleration Parameter q$_0$ , 1995, astro-ph/9511108.

[40]  C. Kochanek.  Evidence for Dark Matter in MG 1654+134 , 1995 .

[41]  J. Tyson,et al.  Measurement of the mass profile of abell 1689 , 1995, astro-ph/9503119.

[42]  J. Villumsen.  Weak lensing by large-scale structure in open, flat and closed universes , 1995, astro-ph/9503011.

[43]  A. Fabian,et al.  Einstein Observatory evidence for the widespread baryon overdensity in clusters of galaxies , 1995, astro-ph/9502092.

[44]  C. Kochanek.  Gravitational Lensing Limits on Cold Dark Matter and Its Variants , 1994, astro-ph/9411082.

[45]  C. Kochanek.  The dynamics of luminous galaxies in isothermal halos , 1994 .

[46]  A. Schroeder,et al.  The Galactic supernova rate , 1994 .

[47]  S. Bergh,et al.  REDISCUSSION OF EXTRAGALACTIC SUPERNOVA RATES DERIVED FROM EVANS'S 1980-1988 OBSERVATIONS , 1994 .

[48]  S. Cole,et al.  Merger rates in hierarchical models of galaxy formation – II. Comparison with N-body simulations , 1994, astro-ph/9402069.

[49]  Andrew Gould,et al.  Proper Motions of MACHOs , 1994 .

[50]  C. Kochanek.  The Analysis of Gravitational Lens Surveys. II. Maximum Likelihood Models and Singular Potentials , 1993 .

[51]  Claudia Winge,et al.  SN 1992A : ultraviolet and optical studies based on HST, IUE and CTIO observations , 1993 .

[52]  H. Rix,et al.  Early type galaxies, dark halos, and gravitational lensing statistics , 1993 .

[53]  S. Tremaine,et al.  A family of models for spherical stellar systems , 1993, astro-ph/9309044.

[54]  M. Hamuy,et al.  K-CORRECTIONS FOR TYPE IA SUPERNOVAE , 1993 .

[55]  R. Narayan,et al.  The influence of core radius on gravitational lensing by elliptical lenses , 1993 .

[56]  M. Fukugita,et al.  Statistical properties of gravitational lenses with a nonzero cosmological constant , 1992 .

[57]  M. Jaroszyński,et al.  Gravitational lensing in a universe model with realistic mass distribution – II. Results , 1992 .

[58]  Nick Kaiser,et al.  Weak gravitational lensing of distant galaxies , 1992 .

[59]  M. Fukugita,et al.  Gravitational lensing frequencies: galaxy cross-sections and selection effects , 1991 .

[60]  R. Blandford,et al.  The distortion of distant galaxy images by large-scale structure , 1991 .

[61]  Joel R. Primack,et al.  Dynamical effects of the cosmological constant. , 1991 .

[62]  A. Babul,et al.  Gravitational lensing by smooth inhomogeneities in the Universe , 1991 .

[63]  Irwin I. Shapiro,et al.  New model for the 0957 + 561 gravitational lens system - Bounds on masses of a possible black hole and dark matter and prospects for estimation of H0 , 1991 .

[64]  Sidney van den Bergh,et al.  Revised supernova rates in Shapley-Ames galaxies , 1989 .

[65]  R. Blandford,et al.  The ring cycle: an iterative lens reconstruction technique applied to MG1131 + 0456 , 1989 .

[66]  B. Paczyński,et al.  Supernovae in luminous arcs , 1988 .

[67]  S. White,et al.  Gravitational lensing in a cold dark matter universe , 1988 .

[68]  P. Schneider,et al.  Gravitational lensing statistics of amplified supernovae , 1988 .

[69]  P. Schneider,et al.  Amplification and polarization of supernovae by gravitational lensing , 1987 .

[70]  S. Faber,et al.  Contraction of Dark Matter Galactic Halos Due to Baryonic Infall , 1986 .

[71]  J. Gott,et al.  The Statistics of gravitational lenses: The Distributions of image angular separations and lens redshifts , 1984 .

[72]  M. Postman,et al.  The morphology-density relation - The group connection , 1984 .

[73]  J. Ostriker,et al.  The statistics of gravitational lenses - Appaarent changes in the luminosity function of distant sources due to passage of light through a single galaxy , 1983 .

[74]  M. Rees,et al.  Cooling, dynamics and fragmentation of massive gas clouds: clues to the masses and radii of galaxies and clusters , 1977 .

[75]  J. Silk.  On the fragmentation of cosmic gas clouds. I. The formation of galaxies and the first generation of stars. , 1977 .

[76]  William H. Press,et al.  Formation of Galaxies and Clusters of Galaxies by Self-Similar Gravitational Condensation , 1974 .

[77]  R. C. Roeder,et al.  Distance-Redshift Relations for Universes with Some Intergalactic Medium , 1973 .

[78]  H. Bondi,et al.  The Gravitational Lens Effect , 1964 .

[79]  John C. Mather,et al.  Next Generation Space Telescope , 2000, Astronomical Telescopes + Instrumentation.

[80]  Christoph U. Keller.  NATIONAL OPTICAL ASTRONOMY OBSERVATORIES , 1999 .

[81]  B. Kaldeich-Schurmann.  The Next Generation Space Telescope: Science Drivers and Technological Challenges , 1998 .

[82]  Paul J. Steinhardt,et al.  The observational case for a low-density Universe with a non-zero cosmological constant , 1995, Nature.

[83]  J. Surdej,et al.  Gravitational lenses in the universe , 1993 .

[84]  J. Wheeler,et al.  The evolution of massive stars to explosion , 1993 .

[85]  R. Blandford,et al.  Cosmological Applications of Gravitational Lensing , 1992 .

[86]  V. Petrosian,et al.  Luminous arcs in clusters of galaxies , 1989 .

[87]  C. Heiles,et al.  Reddening estimates for galaxies in the Second Reference Catalog and the Uppsala General Catalog , 1984 .

[88]  C. Alcock.  Gravitational lenses , 1982, Nature.