Type Ia Supernovae on a glass: The bread and butter of peculiar velocities Lunch meeting Aarhus, March 2007 Troels Haugbølle Institute for Physics & Astronomy, Århus University Collaborators:Steen Hannestad, Bjarne Thomsen

Goals of our project ● 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

Velocity Fields ● Velocity trace mass: ● The peculiar velocity field is sourced by the gravitational potential: It is directly dependent on the dark matter dist  No bias! ● Further away than ~100 Mpc h -1 cosmic variance is small, and we can constrain cosmological models! The velocity field 30 Mpc awayThe density field 30 Mpc away km/s

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 ● Good, since there are few SnIa’s ● At large distances the Hubble Flow dominate

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

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

Upcoming surveys ● The change in apparent magnitude with redshift is used to constrain the cosmology. Many surveys will be done the next couple of years. (Hui & Greene a-ph/ )

Upcoming surveys ● Unfortunately surveys have small FOV, and are designed for high redshift SNe. In fact weak lensing/asteroid surveys are better for local supernovae. They scan the sky continuously, and observe in many bands (typically 6) Pan-Starrs Sky Mapper 4x1.4Gp Mp 2008 Hawaii Australia LSST 3.2Gp 2013 Chile

Forecast ● We know the local supernova rate ● This gives Type Ia SN per year inside a distance of 500 h -1 Mpc 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 ● We know the local supernova rate ● This gives Type Ia SN per year inside a distance of 500 h -1 Mpc ● There are light curves, but we need precise redshifts ● Low redshift Type Ia Supernovae are not a priority ● We need to do it ourselves ● It is not realistic to measure redshifts per year.

How to make a supernova survey Make Nbody sim Find density and velocity on a spherical shell Populate with Supernovae Calculate Power spectrum

...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

Supernovae on a glass ● We know the local supernova rate ● This gives Type Ia SN per year inside a distance of 500 h -1 Mpc ● There are light curves, but we need precise redshifts ● Low redshift Type Ia Supernovae are not a priority ● We need to do it ourselves ● It is not realistic to measure redshifts per year.

Goals of our project ● 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 tool for constraining cosmology

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

Connecting the matter and velocity powerspectrum ● We can find the average amplitude between l=5-20 ● It is free of cosmic variance

Consequences for cosmology ● The overall amplitude depends on   This combination break degeneracies,and   8 can be constrained ● The form of the velocity powerspectrum is directly related to the shape parameter ● The amplitude and shape at l=5-20 is not affected much by cosmic variance ● Success depends on proper observational strategy - can I have a glass, please?

Other factors apply to the lumi- nosity 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 lumi- nosity 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 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

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

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

The lowest multipoles and the local universe ● The lowest multipoles of the angular powerspectrum are easy to understand ● The monopole gives the contraction/expansion ● The dipole measures average flow ● The quadrupole represents the first shear mode

The peculiar velocity at higher redshifts and the cosmic web Timeline in movie To give a feeling for the cosmic large scale structure I will show you two movies, where we slowly zoom out and see structure further and further away Distance to the observer

The peculiar velocity at higher redshifts and the cosmic web

The angular powerspectrum Size of voids Size of clusters