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Selecting Supernovae for Cosmology Cosmic Co-Motion, Courant Cove, September 2010 Troels Haugbølle Niels Bohr International Academy – University of Copenhagen Collaborators: Bjarne Thomsen, Steen Hannestad

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Main Points With upcoming survey telescopes we will discover so many local supernovae that complete spectroscopic follow up of is unfeasible. To sample the peculiar velocity field, a regularly spaced distribution is advantageous, to avoid power leaking. Obtaining spectra for only a carefully selected subset gives the best constraints from the least observational investment.

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Peculiar Velocity Fields Velocity trace mass: v = - H f( m ) where is the density contrast, and f( m ) the growth factor The peculiar velocity field is sourced by the gravitational potential: It is directly dependent on the dark matter distribution

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Connecting the matter and velocity powerspectrum ● Velocity trace mass: v = - H f( m ) ● The angular velocity powerspectrum is related to the matter powerspectrum :

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Peculiar Velocity Fields ● Further away than ~80 Mpc h -1 cosmic variance is small enough, that we can constrain cosmological models ● Gravity sources the velocity field from density fluctuations on larger scales ● This is why peculiar velocities may be the best measure of 8 at z=0 The velocity field 90 Mpc h -1 away km/s The density field 90 Mpc h -1 away

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Upcoming surveys ● Lensing/asteroid surveys are better for local supernovae, than the high-z SNe surveys. They scan the sky continuously, and observe in many bands (typically 6). ● LSST saturates at m < or d < Mpc h -1 Pan-Starrs (4x)1.4Gp Hawaii Sky Mapper 256Mp 2010 Australia LSST 3.2Gp 2014 Chile Pan-Starrs

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Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Use the angular power spectrum of the peculiar velocity field as a tool for constraining cosmology

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Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Use the angular power spectrum of the peculiar velocity field as a tool for constraining cosmology

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Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Use the angular power spectrum of the peculiar velocity field as a tool for constraining cosmology

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Forecast ● The local supernova rate is approximately 1.2 x SN yr -1 h 3 Mpc -3 ● This gives potential Type Ia SN per year with distances less than 500 h -1 Mpc (z < 0.17) ● There will be light curves from survey telescopes, but precise redshifts are needed

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Forecast ● The local supernova rate is approximately 1.2 x SN yr -1 h 3 Mpc -3 ● This gives potential Type Ia SN per year with distances less than 500 h -1 Mpc (z < 0.17) ● There will be light curves from survey telescopes, but precise redshifts are needed ● A dedicated 1 m telescope would be able to take ~7000 spectra per year, or roughly 25% of the Type Ia SNe, assuming the survey telescopes covers half the sky

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Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Use the angular power spectrum of the peculiar velocity field as a tool for constraining cosmology

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Observational Strategy ● The precision we can measure the angular powerspectrum with depends crucially on the geometric distribution on the sphere ● Essentially power can “leak out” if there are big holes on the sky. ● We know where the SNe are before finding the redshift from the surveys

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Reconstructing the velocity PS - a geometric detour Random Points3072 Glass Points3072 “HealPix” Points12288 Random Points

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(figures thanks to Anja Weyant) Signal Power Leaking

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How to make a supernova survey Make Nbody sim Find density and velocity on a spherical shell Populate with Supernovae Calculate Angular PS Size of voids/ Max of matter PS Size of clusters

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...but there is more to it ● With a limited amount of SNe, we can only measure a limited part of the powerspectrum ● Algorithm: ● Given a set of Supernovae. Calculate powerspectrum

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...but there is more to it ● With a limited amount of SNe, we can only measure a limited part of the powerspectrum ● Algorithm: ● Given a set of Supernovae. Calculate powerspectrum ● Make N mock catalogues with same errors

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...but there is more to it ● With a limited amount of SNe, we can only measure a limited part of the powerspectrum ● Algorithm: ● Given a set of Supernovae. Calculate powerspectrum ● Make N mock catalogues with same errors ● Compare the mock powerspectra to the underlying powerspectrum ● This gives the shot noise + window function

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...but there is more to it ● With a limited amount of SNe, we can only measure a limited part of the powerspectrum ● Algorithm: ● Given a set of Supernovae. Calculate powerspectrum ● Make N mock catalogues with same errors ● Compare the mock powerspectra to the underlying powerspectrum ● This gives the shot noise + window function ● Subtract the error term from the observed powerspectrum

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● There are light curves, but we need precise redshifts ● A 1 m telescope can take 1 spectra in ~20 minutes ~7000 spectra per year ● It is not realistic to measure redshifts per year ● We need to optimize our observation strategy and only select “the right” supernovae Supernovae on a glass

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Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Use the angular power spectrum of the peculiar velocity field as a tool for constraining cosmology

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Connecting the matter and velocity powerspectrum Small scale amplitude 8

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Small scale amplitude or 8 ● Amplitude on large scales is fixed by the CMB ● 8 can be affected by ● Massive neutrinoes less power 256 Mpc h -1 Standard CDM 3 x 2.3 eV neutrinoes

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Small scale amplitude or 8 ● Amplitude on large scales is fixed by the CMB ● 8 can be affected by ● Massive neutrinoes less power ● Features / tilts in the primordial power spectrum

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Consequences for cosmology ● The overall amplitude depends on H f( m ) 8 This combination break degeneracies,and 8 can be constrained: Using 6 redshift bins (3 yrs of data, glass Sne), and a simple 2 analysis (with fixed H), we find a determination of 8 with 95% confidence

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● The overall amplitude depends on H f( m ) 8 This combination break degeneracies,and 8 can be constrained: Using 6 redshift bins (3 yrs of data, glass Sne), and a simple 2 analysis, we find a determination of 8 with 95% confidence Consequences for cosmology Glass SupernovaeAll Supernovae

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● Peculiar velocities or bulk flows can be measured using low redshift supernovae ● The peculiar velocity field is important to understand: ● It tells out about the structure of the local Universe ● It has to be corrected for in the Hubble diagram ● We can directly probe the gravitational potential, do Cosmology, and learn about the bias ● Upcoming survey telescopes will observe thousands of low redshift supernovae - but this potential can only be realized if time at support telescopes is allocated ● Optimizing the window function optimizes the science output ● We forecast that with 3 years of LSST data we can constrain 8 to roughly 5% Summary

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