Measuring the local Universe with peculiar velocities of Type Ia Supernovae MPI, August 2006 Troels Haugbølle Institute for Physics & Astronomy, Århus University Collaborators:Steen Hannestad, Bjarne Thomsen

Goals of our project ● Predict how many type Ia supernovae are needed to probe the local velocity field reliably ● Compute the error bars from cosmic variance and compare to the intrinsic and observational errors on type Ia supernova explosions ● Understand how the angular power spectrum of the peculiar velocity field can be used to put constraints on the cosmological parameters

Velocity Fields ● Velocity trace mass: v(r) ~ H 0  m 0.6  (r)/  ● The local flow tells us about the local gravity field, and the attraction towards structures further away ● At higher redshifts we can constrain the cosmology 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, etc ● The velocity field can be ● measured directly and sparsely ● Good, since there are few SnIa’s ● We have to take care of bias though.

How to measure v r ● Requisites: The redshift z 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 z 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= ● In the last 10 years we have had a new kid in town ● Type Ia supernovae ● They have a scatter of  m= , and it will decrease

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 (LSST may get 1000’s of low redshift SnIa). (Hui & Greene a-ph/ )

How to measure v r Given the magnitude or the luminosity distance and the redshift We can calculate the luminosity distance and relate to v r

How to measure v r Given the magnitude or the luminosity distance and the redshift We can calculate the luminosity distance and relate to v r Given by CMB

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

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 Limits of the approach: ● Use linear theory for the large scale structure to predict levels of error from peculiar velocities in supernovae data ● Assume supernovaes to be distributed uniformely on the sky SnFactory Snap + SnFactory

Goals of our project ● Predict how many type Ia supernovae are needed to probe the local velocity field reliably ● Compute the error bars from cosmic variance and compare to the intrinsic and observational errors on type Ia supernova explosions ● Understand how the angular power spectrum of the peculiar velocity field can be used to put constraints on the cosmological parameters

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

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 lowest multipoles and the local universe ● In the near future the Supernova Factory should detect 300 supernovae at z= and the SDSSII will detect up to 200 supernovae in the redshift range z= ● We have made a Monte Carlo simulation asuming 300 SnIa’s, to find the error on  m as a function of redshift. Method ● Given a redshift z ● Find 300 SnIa ● Compute multipoles ● Repeat 500 times ● (Do it for 27 different observers) Assume SnF with 100 SnIa In each redshift bin. Then  m intrinsic = 0.1/√100=0.01  m error =  m Cosmic Var =  m Monopole = 0.03  m Dipole =  m Quadrupole = { { Errors Signal

The lowest multipoles and the local universe ● In real life we have to combine the supernovae at different redshift in shells. Then it is important to correct for the change in  m, which goes like z -1. By multiplying by the redshift, we factor out the distance dependence Redshift Redshift x  m

The lowest multipoles and the local universe ● Summary ● Peculiar velocities from upcoming low redshift Supernova surveys is a promising tool to understand ther local large scale structure ● With the Supernova Factory we will detect the dipole and put limits on the evolution with redshift ● The monopole and the quadrupole will be detected

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

The angular powerspectrum

Consequences for cosmology ● The cluster abundance and amplitude depends strongly on  8    8 can be constrained if we can detect the higher multipoles ● The overall amplitude is inversely proportional to the Hubble parameter H(z):  H(z) together with  m gives us the the equation of state for the dark energy ● The form of the powerspectrum is related to  m