Bulk Flows, and Peculiar Velocities of Type Ia Supernovae Niels Bohr Summer Institute, August 2007 Troels Haugbølle Institute for Physics & Astronomy, Århus University Collaborators: Steen Hannestad, Bjarne Thomsen, (Århus) Jesper Sollerman, Johan Fynbo (DARK, NBI) Ariel Goobar, Edvard Mörtsell, (Stockholm)

Velocity Fields ● Velocity trace mass: In linear perturbation theory we have: (  k is the density contrast)

Velocity Fields ● Velocity trace mass. In linear perturbation theory we have: (  k is the density contrast) ● The peculiar velocity field is sourced by the gravitational potential: It is directly dependent on the dark matter distribution

Velocity Contra Density ● To measure the density we have to ● count standard objects ● take care not to miss any! ● Density is derived from number counts. ● Then put in the conversion from luminosity to mass, completeness, bias to dark matter etc ● The velocity field can be ● measured directly and sparsely ● There is no dark matter bias ● Problem: At large distances the Hubble Flow dominate. We need percent level precision

Velocity Fields ● Further away than ~100 Mpc h -1 cosmic variance is small, and we can constrain cosmological models ● Because of the extra k-factor the velocity field is smoother than the density field The velocity field 90 Mpc h -1 away km/s The density field 90 Mpc h -1 away

How to measure v r ● Requisites: The redshift of the host galaxy: z The luminosity distance or the apparent and absolute magnitudes: d L or m-M ● Traditionally used methods to obtain the distance include ● The Tully-Fisher relation ● Surface brightness fluctuations ● Fundamental plane ● They all have an intrinsic scatter of at least  m=

How to measure v r ● Requisites: The redshift of the host galaxy: z The luminosity distance or the apparent and absolute magnitudes: d L or m-M ● Traditionally used methods to obtain the distance include ● The Tully-Fisher relation ● Surface brightness fluctuations ● Fundamental plane ● They all have an intrinsic scatter of at least  m= ● With upcoming surveys Type Ia Supernovae will have an intrinsic scatter of  m=

Other factors apply to the luminosity distance at high redshift (Sugiura et al ‘99,Hui & Greene a-ph/ , Bonvin et al a-ph/ ) Light travels along geodesics, and is influenced by: ● The peculiar motion of the source and the observer, giving rise to a redshift. ● Gravitational lensing. It (de)magnifies the light rays and depends on the fluctuations in the gravitational potential ● Gravitational redshift ● An integrated effect from line-of-sight change in the potential (Sachs-Wolfe effect)

Other factors apply to the luminosity distance at high redshift (Sugiura et al ‘99,Hui & Greene a-ph/ , Bonvin et al a-ph/ ) Light travels along geodesics, and is influenced by: ● The peculiar motion of the source and the observer, giving rise to a redshift. ● Gravitational lensing. It (de)magnifies the light rays and depends on the fluctuations in the gravitational potential ● Gravitational redshift ● An integrated effect from line-of-sight change in the potential (Sachs-Wolfe effect) Important at low redshift & large scales Important at high redshift

Are we living in a Hubble Bubble? (Zehavi et al a-ph/ ) ● Used 44 SnIa ●  H = v r / d L ● Model suggest we are in an underdense region with radius of 70 Mpc h -1

Where are we flowing towards? (TH, et al a-ph/ ) ● Using 95 low-z SN Ia the dipole and the quadrupole at 60 Mpc h -1 is constrained: ● Dipole: 239 km/s towards Shapley ● Quadrupole: 512 km/s ● Higher multipoles cannot be constrained with current data

How big is the dipole? (Bonvin et al a-ph/ ) ● Use the same 44 SnIa ● As a test, given H 0, measure the CMB dipole ● Gives 405±192 km/s

How big is the dipole? (Bonvin et al a-ph/ ) ● Use the same 44 SnIa ● As a test, given H 0, measure the CMB dipole ● In the future: Given the CMB dipole amplitude |v 0 |, measure H(z) ● 100’s of SnIa’s needed for 30% error

Can we trust the local Hubble parameter? (Shi a-ph/ ,Shi MNRAS, 98 ) ● Used 20 SnIa (Upper plot) and 36 clusters with T-F relation ● Make CDM models that mimick the local density fields ● Run different cosmological scenarioes ● Compare! It is hard to see the difference, with current data. ● There is a 2% error on H 0 out to about 250 Mpc h -1 (z=0.08)

Errors from peculiar velocities when predicting cosmological parameters (Hui & Greene a-ph/ ) ● What is the signal in other applications here is the noise: ● The errors from peculiar velocities on different supernovaes are not independent, but correlated with the large scale structure SnFactory Snap + SnFactoryIntrinsic scatter only Large scale structure + systematics

Upcoming surveys ● Lensing/asteroid surveys are better for local supernovae. They scan the sky continuously, and observe in many bands Pan-Starrs 4x1.4Gp Hawaii Sky Mapper 256Mp 2008 Australia LSST 3.2Gp 2013 Chile

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift Goals GALAXIES DARK MATTER (from the millennium simulation)

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

Forecast ● The local supernova rate is approximately ● This gives potential Type Ia SN per year with distances less than 500 h -1 Mpc (z < 0.17) Typically peculiar velocities are ~ 400 km s -1 ● We want to look at the angular distribution as a function of distance. Binning in a reasonable manner we have 1100 SnIa at 60 h -1 Mpc with error  v r ~ 220 km s SnIa at 150 h -1 Mpc with error  v r ~ 550 km s SnIa at 350 h -1 Mpc with error  v r ~ 1300 km s -1

Forecast ● The local supernova rate is approximately ● This gives potential Type Ia SN per year with distances less than 500 h -1 Mpc (z < 0.17) ● There are light curves from survey telescopes, but precise redshifts are needed ● Follow up on Low redshift Type Ia Supernovae are not a priority

Forecast ● There are light curves, but precise redshifts are needed ● Low redshift Type Ia Supernovae are not a priority ● 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

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

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 beforehand from surveys

Observational Strategy ● The precision depends crucially on the geometric distribution on the sphere ● What is the optimal 25% of the SNe to observe, given a “semi-random” set ?

Observational Strategy ● The precision depends crucially on the geometric distribution on the sphere ● What is the optimal 25% of the SNe to observe, given a “semi-random” set ?

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

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

...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

...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

...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 error term

...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 error term ● Subtract the error term from the observed powerspectrum

Goals ● Predict how well we can probe the local velocity field, with upcoming supernovae surveys ● Design the optimal observational strategy to maximize science output ● Understand how the angular power spectrum of the peculiar velocity field can be used as a tool for ● constraining cosmology ● finding the (scale dependent) bias ● put limits on modified gravity ● removing scatter in the redshift- magnitude diagram at low redshift

Connecting the matter and velocity powerspectrum ● Velocity trace mass: ● The angular velocity powerspectrum is related to the matter powerspectrum:

Connecting the matter and velocity powerspectrum Small scale amplitude   8

Connecting the matter and velocity powerspectrum ● Many cosmological parameters are already probed efficiently by other means ● CMB, LSS, High redshift SnIa, BAO, Cluster density, BBN all give strong bounds on: ● But! Peculiar velocities probe DM potential directly. It is very sensitive to the amplitude: ● Weak lensing give similar limits, but different systematics

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 2.3 eV neutrinoes

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

Consequences for cosmology ● The overall amplitude depends on   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 ● Current 95% limits are ~20% (Pike & Hudson astro-ph/ )

● The overall amplitude depends on   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 ● Current 95% limits are ~20% (Pike & Hudson astro-ph/ ) Consequences for cosmology Glass SupernovaeAll Supernovae Weak Lensing (a-ph/ )

● 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 supuernovae - but this potential can only be realised if time at support telescopes is allocated ● We forecast that with 3 years of LSST data we can constrain  8 to roughly 5% Summary