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**Selecting Supernovae for Cosmology**

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

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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: Ñ v = - H f(Wm) where is the density contrast, and f(Wm) 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: Ñ v = - H f(Wm) 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 s8 at z=0 The velocity field 90 Mpc h-1 away -1100 1100 km/s The density field 90 Mpc h-1 away The dipole is maybe the best example

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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 Sky Mapper 256Mp 2010 Australia Pan-Starrs (4x)1.4Gp 2009+ Hawaii Pan-Starrs LSST 3.2Gp 2014 Chile

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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 LSST gives too many local SNe!

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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 1.2 x 10-4 SN yr-1 h3 Mpc-3**

The local supernova rate is approximately 1.2 x 10-4 SN yr-1 h3 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 1.2 x 10-4 SN yr-1 h3 Mpc-3**

The local supernova rate is approximately 1.2 x 10-4 SN yr-1 h3 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 -**

12288 Random Points 3072 “HealPix” Points 3072 Glass Points 3072 Random Points

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Power Leaking Signal (figures thanks to Anja Weyant)

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**How to make a supernova survey**

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

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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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Supernovae on a glass 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

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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 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(Wm) s8 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 Not using a glass gives you a skewed distribution, and much worse errors

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**Consequences for cosmology**

All Supernovae Glass Supernovae Consequences for cosmology The overall amplitude depends on H f(Wm) s8 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 Not using a glass gives you a skewed distribution, and much worse errors

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Summary 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% Not using a glass gives you a skewed distribution, and much worse errors

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