SNe Ia growth-rate measurements with Rubin-LSST simulations: intrinsic scatter systematics

$f{\sigma }_8$: a probe for gravity and dark energy

How to estimate velocities from SNe Ia?

The intrinsic scatter of SNe Ia

We know that intrinsic scatter has a color dependance!

In this work we will consider 4 models of intrinsic scatter:

• Random achromatic scatter
  Unrealistic
• The G10 model (Guy et al. 2010): $\sim 70\mathrm{\%}$ achromatic / $\sim 30\mathrm{\%}$ chromatic
  Historically used (Pantheon, Pantheon+)
• The C11 model (Chotard et al. 2011): $\sim 30\mathrm{\%}$ achromatic / $\sim 70\mathrm{\%}$ chromatic
  Historically used (Pantheon, Pantheon+)
• The BS21 model (Brout et al. 2021) with its parameters fitted in Popovic et al. 2023 (P23): dust-based model
  Currently favored by data (DES 5 year)

Why is SNe Ia intrinsic scatter a concern?

Intrinsic scatter is the most important systematic for the DES 5 year analysis of the dark energy equation of state parameter $w$ (Vincenzi et al. 2024).

Rubin-LSST Simulations

We used the SNANA software (Kessler et al. 2009) to simulate the 10 years of the Rubin-LSST survey!

Simulation of the SN Ia hosts

8 mocks cut from the (2 Gpc $h^{-1}$)${}^3$ box of the Uchuu UniverseMachine galaxy catalog (Ishiyama et al. 2021, Aung et al. 2023)

We simulated SN Ia parameters correlations with their host properties:

• SN Ia rate - Host mass correlation from Wiseman et al. 2021
• SN Ia parameters - Host mass correlation from Popovic et al. 2021

The SNe Ia simulated sample

$N_{\text{SN}}\sim O(50000)$

Building the Hubble diagram

Hubble diagram of SNe Ia:

x-axis: $z_{\mathrm{obs}}$ of the hosts

y-axis: distance modulus $\mu =5\log (d_L/10\text{ pc})=m-M$

Standard Method:

${\mathit{\mu }}_{\mathbf{obs}}={\mathit{m}}_{\mathit{B}}-(M_B-\alpha {\mathit{x}}_{\mathbf{1}}+\beta \mathit{c}+{\mathbf{\Delta }}_{\mathit{M}}({\mathbf{M}}_{\mathrm{host}};\gamma ))$

${\mathit{\sigma }}_{\mathit{\mu }}^2={\mathit{\sigma }}_{\mathbf{obs}}^2+{{\sigma }_{\mathrm{int}}}^2$

$M_B$, $\alpha$, $\beta$, $\gamma$ and ${\sigma }_{\mathrm{int}}$ will be fitted along $f{\sigma }_8$

BBC method:

${\mathit{\mu }}_{\mathbf{obs}\mathbf{,}\mathbf{BBC}}={\mathit{m}}_{\mathit{B}}-(M_B-\alpha {\mathit{x}}_{\mathbf{1}}+\beta \mathit{c}+{\mathbf{\Delta }}_{\mathit{M}}({\mathbf{M}}_{\mathrm{host}};\gamma ))+{\delta }_{\mathrm{corr}.}$

${\mathit{\sigma }}_{\mathit{\mu }}^2={\mathit{\sigma }}_{\mathbf{obs}}^2+{{\sigma }_{\mathrm{int}}}^2$

${\delta }_{\mathrm{corr}.}$ is obtained by:

• Running an extra-large simulations ($\sim 40\times$ LSST) and fitting the hubble diagram
• Binning over the parameters $p=\{z_{\mathrm{obs}},x_1,c,M_{\mathrm{host}}\}$
• Computing the correction in each cell ${\delta }_{\mathrm{corr}.}={⟨{\mu }_{\mathrm{obs}}-{\mu }_{\mathrm{fid}}⟩}_{\mathrm{cell}}$
• Interpolate over the cells to obtain ${\delta }_{\text{corr.}}(p)$

$M_B$, $\alpha$, $\beta$, $\gamma$ and ${\sigma }_{\mathrm{int}}$ are fitted prior to $f{\sigma }_8$

Fitting for $f{\sigma }_8$

We fit for $f{\sigma }_8$ using the Maximum likelihood method with the FLIP package (see Corentin' talk)

Calibration of ${\sigma }_u$

Empirical damping introduced in Koda et al. 2014: $D_u=\text{sinc}(k{\sigma }_u)$

From a fit of true vel. from randomly sampled galaxies of the Uchuu simulation we found ${\sigma }_u\simeq 21\text{Mpc }{h}^{-1}$

Results: Estimated velocities

We only consider SNe Ia at $0.02<z<0.1$, $N_{\text{SN}}\sim 8000$

Results: $f{\sigma }_8$ fit for different scatter model

• True vel. fit: unbiased, ${\sigma }_{f{\sigma }_8}\sim 5\mathrm{\%}$
• RND - Similar results: ${\sigma }_{f{\sigma }_8}\sim 13\mathrm{\%}$
• G10 - Similar results: ${\sigma }_{f{\sigma }_8}\sim 12\mathrm{\%}$
• C11 - Similar results: ${\sigma }_{f{\sigma }_8}\sim 10\mathrm{\%}$
• P23 - Standard fit: ${\sigma }_{f{\sigma }_8}\sim 14\mathrm{\%}$
  P23 - BBC fit: ${\sigma }_{f{\sigma }_8}\sim 10\mathrm{\%}$

Results for P23 are biased by $\sim -20\mathrm{\%}$ due to non-gaussianity!

Results: adding the B21 variations covariance

Bias correction re-run for variations of BS21 parameters => new covariance term $${\text{C}}_{ij}^{\mu \mu ,\mathrm{int}.\mathrm{scat}.}=\mathrm{\Delta }{\mu }_i^{\mathrm{BS}21}\mathrm{\Delta }{\mu }_j^{\mathrm{BS}21}+\frac{1}{3}\sum _{p=1}^3\mathrm{\Delta }{\mu }_i^{\mathrm{P}23,p}\mathrm{\Delta }{\mu }_j^{\mathrm{P}23,p}$$ (from Vincenzi et al. 2024)

Results: the ${\sigma }_u$ systematic

$\mathrm{\Delta }{\sigma }_u\sim 18.5-23.5\text{ Mpc }{h}^{-1}$ ⇨ ${\sigma }_{f{\sigma }_8}^{{\sigma }_u}\sim 6\mathrm{\%}$

Conclusion

• Estimated PVs are unbiased using the BBC method compared to the standard method
• Correlations between hosts and SNe don't seems to bias $f{\sigma }_8$
• The BS21 model leads to non-gaussianity that bias the measurements of $f{\sigma }_8$
• The uncertainty on the parameters of BS21 are not a major systematic for $f{\sigma }_8$
• The parameter ${\sigma }_u$ is correlated with $f{\sigma }_8$ and we estimated the amplitude of this systematic to be $\sim 6\mathrm{\%}$

What's next?

• Is the BS21 model correct? Will we see this non-gausianity in data?
• Can we get rid of ${\sigma }_u$?

Full $f{\sigma }_8$ results

${\sigma }_u$ syst. for G10

BS21 equations