1. 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

2. 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.

3. 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

4. Connecting the matter and velocity powerspectrum
Velocity trace mass: Ñ  v = - H f(Wm) 
The angular velocity powerspectrum is related to the matter powerspectrum :

5. 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

6. 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

7. 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!

8. 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

9. 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

10. 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

11. 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

12. 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

13. 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

14. Reconstructing the velocity PS - a geometric detour -
12288 Random Points
3072 “HealPix” Points
3072 Glass Points
3072 Random Points

15. Power Leaking
Signal
(figures thanks to Anja Weyant)

16. 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

17. ...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

18. ...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

19. ...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

20. ...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

21. 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

22. 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

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

24. 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

25. 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

26. 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

27. 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

28. 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