Systematic errors in the measurement of neutrino masses due to baryonic feedback processes: Prospects for stage IV lensing surveys

We examine the importance of baryonic feedback effects on the matter power spectrum on small scales and the implications for the precise measurement of neutrino masses through gravitational weak lensing. Planned large galaxy surveys such as the Large Synoptic Sky Telescope and Euclid are expected to measure the sum of neutrino masses to extremely high precision, sufficient to detect nonzero neutrino masses even in the minimal mass normal hierarchy. We show that weak lensing of galaxies, while being a very good probe of neutrino masses, is extremely sensitive to baryonic feedback processes. We use publicly available results from the Overwhelmingly Large Simulations project to investigate the effects of active galactic nuclei feedback, the nature of the stellar initial mass function, and gas cooling rates on the measured weak lensing shear power spectrum. Using the Fisher matrix formalism and priors from $\mathrm{CMB}+\mathrm{BAO}$ data, we show that, when one does not account for feedback, the measured neutrino mass may be substantially larger or smaller than the true mass, depending on the dominant feedback mechanism, with the mass error $|\mathrm{\Delta }{m}_{\nu }|$ often exceeding the mass $m_{\nu }$ itself. We also consider gravitational lensing of the cosmic microwave background (CMB) and show that it is not sensitive to baryonic feedback on scales $\ell <2000$, although CMB experiments that aim for sensitivities $\sigma (m_{\nu })<0.02\mathrm{eV}$ will need to include baryonic effects in modeling the CMB lensing potential. A combination of CMB lensing and galaxy lensing can help break the degeneracy between neutrino masses and baryonic feedback processes. We conclude that future large galaxy lensing surveys such as Large Synoptic Sky Telescope and Euclid can only measure neutrino masses accurately if the matter power spectrum can be measured to similar accuracy.

Figure 1

The square of the baryon bias, $b^2(k)=P_{\text{full}}(k)/P_{\mathrm{DM}}(k)$, for redshifts $z=0$, 1, 2, 3. The black (solid), red (dashed), and blue (dotted) curves show the effect of baryonic feedback on the matter power spectrum, for feedback models 1, 2, and 3, respectively. Feedback model 1 includes AGN feedback (labeled AGN in Ref. [27]). Feedback model #2 accounts for a top-heavy IMF and extra SN energy (labeled DBLIMFV1618 in Ref. [27]), while feedback model 3 has no SN feedback and cooling by primordial elements only (labeled NOSN-NOZCOOL in Ref. [27]). As expected, the model with AGN feedback (model 1) shows the largest damping in the power spectrum on small scales at $z=0$. The model with no metal cooling or SN feedback (model 3) shows a boost in the power spectrum on small scales due to contraction of halos.

Figure 2

Left: The weak lensing power spectrum for source redshifts $z=0.2$, 1.0, and 3.0, assuming $m_{\nu }=0.3\mathrm{eV}$. Only the autopower spectra are shown. The black curves assume feedback model 1, the blue curves are plotted for feedback model 2, and the red curves are for feedback model 3. Also shown are expected error bars for an LSST-like or Euclid-like instrument (for feedback model 1), with bin size $\mathrm{\Delta }\ell =50$ for $\ell <1000$, and $\mathrm{\Delta }\ell =100$ otherwise. The error bars are large for small $z$ because of low volume and for large $z$ because of low flux. Right: Fractional change in the shear autopower spectrum for $z=1.0$: $\mathrm{\Delta }{C}_{\ell }=[C_{\ell }-C_{\ell }(\text{ref})]/C_{\ell }(\text{ref})$, where the reference model has no feedback and assumes a neutrino mass of 0.3 eV. The magenta curve considers a smaller neutrino mass $m_{\nu }=0.2\mathrm{eV}$. The shaded area represents the error for $z=1.0$.

Figure 3

Expected statistical error in the measurement of neutrino masses, assuming multipoles up to ${\ell }_{\max }$ can be measured. The redshift range is divided into one bin (black, solid) of size $\mathrm{\Delta }z=2.5$, three bins (red, dashed) with each bin of size $\mathrm{\Delta }z=0.8$, and five bins (blue dotted) with bin size $\mathrm{\Delta }z=0.5$. There is one power spectrum with one bin, six power spectra with three bins, and fifteen power spectra with five bins.

Figure 4

Bias in the estimated neutrino mass from weak lensing assuming LSST parameters, relative to the assumed neutrino mass. Source galaxies in the redshift range $0<z<2.5$ are divided into five bins. The bias, or systematic error, is due to ignoring baryonic feedback. The four panels show the bias $\mathrm{\Delta }{m}_{\nu }$ for assumed neutrino masses $m_{\nu }=0.4$, 0.3, 0.2, 0.1 eV. The three curves are plotted for feedback models 1, 2, and 3. Note that the Fisher matrix formalism is not reliable when $|\mathrm{\Delta }{m}_{\nu }|>m_{\nu }$.

Figure 5

Bias, or systematic error in the estimated neutrino mass, compared to the statistical error, for $m_{\nu }=0.3\mathrm{eV}$. The bias is huge compared to the statistical error, even exceeding $100\sigma (m_{\nu })$ (although the results are not valid when $|\mathrm{\Delta }{m}_{\nu }|>m_{\nu }$), implying that a precise measurement of $m_{\nu }$ is not possible unless the matter power spectrum is known to similar accuracy.

Figure 6

Bias in the cosmological parameters $\overrightarrow{\theta }=\{{\mathrm{\Omega }}_{\mathrm{b}}{h}^2,{\mathrm{\Omega }}_{\mathrm{c}}{h}^2,h,A_{\mathrm{s}},n_{\mathrm{s}}\}$ (relative to the mean values) due to ignoring feedback. The shaded band shows the fractional statistical error. While $\mathrm{\Delta }{\theta }_i\ll {\theta }_i$, the bias is still large compared to the statistical error.

Figure 7

Comparison of an LSST-like survey ($z_0=0.92$, $f_{\text{sky}}=0.5$, $50\text{galaxies}/{\mathrm{arcmin}}^2$) with a DES-like survey ($z_0=0.60$, $f_{\text{sky}}=0.1$, $10\text{galaxies}/{\mathrm{arcmin}}^2$), for feedback model 2, and $m_{\nu }=0.3\mathrm{eV}$.

Figure 8

Expected errors in the neutrino mass from CMB lensing, assuming $f_{\text{sky}}=0.5$ and cosmic variance error bars. The magenta curve shows the statistical error in $m_{\nu }$, while the black (solid), red (dashed), and blue (dotted) curves show the systematic error due to feedback models 1, 2, and 3. The true neutrino mass was set to 0.1 eV. For all models, the systematic error is smaller than the statistical error.