Diffuse Supernova Neutrino Background

• Diffuse Supernova Neutrino Background is the cumulative flux of neutrinos released by all core-collapse supernovae across cosmic time, including both visible and invisible explosions.
• Synoptic surveys now reduce uncertainty in the cosmic supernova rate, enabling precise models that connect DSNB measurements with key neutrino spectral properties.
• DSNB observations serve as a unique probe of stellar evolution and neutrino physics, constraining the fraction of invisible supernovae and testing neutrino flavor conversion models.

The diffuse supernova neutrino background (DSNB) is the integrated flux of (anti)neutrinos produced by all core-collapse supernovae (CCSNe), including both optically visible and “invisible” events, since the onset of stellar activity in the universe. In the 10–26 MeV energy regime, the DSNB constitutes the dominant extra-terrestrial flux expected on Earth, providing a unique cumulative probe of massive star death, stellar evolution, and supernova neutrino physics. Precision characterization of the DSNB links astrophysical and cosmological history with the microscopic properties of neutrinos and is a key objective for future neutrino observatories.

1. Definition and Theoretical Context

The DSNB is fundamentally the superposition of all (anti)neutrinos released from core-collapse supernovae across cosmic time, excluding the rare Galactic events that are resolved as individual bursts. Every core-collapse supernova, regardless of whether it results in a bright optical transient or collapse to a black hole without an accompanying explosion, emits ∼10^58 neutrinos, carrying away virtually the entirety of the progenitor’s gravitational binding energy. Individual CCSNe are too distant to be detected as discrete sources; the sum over cosmic history manifests as a diffuse, quasi-isotropic MeV neutrino flux.

Quantitatively, the DSNB flux per neutrino flavor and per unit energy at Earth, φₙᵤ(ε), is given by the cosmological line-of-sight integral:

$$\phi_\nu(\epsilon) = c \int_0^\infty (1+z) \left| \frac{dt}{dz} \right| R(z) N_\nu[(1+z)\epsilon]\,dz$$

with:

• $c$: speed of light
• $z$: source redshift
• $|dt/dz| = [ (1+z) H(z) ]^{-1}$
• $$H(z) = H_0 \sqrt{ \Omega_m(1+z)^3 + \Omega_\Lambda }$$
• $R(z)$: cosmic core-collapse supernova rate (CSNR)
• $N_\nu[(1+z)\epsilon]$: time-integrated emitted (anti)neutrino spectrum per CCSN, redshifted from emission energy to observed energy
• $$N_\nu(\epsilon) = \mathcal{E}_\nu \frac{120}{7\pi^4} \frac{\epsilon^2}{T_\nu^4} \frac{1}{e^{\epsilon/T_\nu} + 1 }$$

Here, $\mathcal{E}_\nu$ is the canonical energy emitted per flavor (typically $\sim 5 \times 10^{52}$ erg), and $T_\nu$ is the effective neutrino temperature, a parameter sensitive to the underlying supernova physics.

2. Cosmic Supernova Rate and the Role of Synoptic Surveys

The normalization of the DSNB is controlled by the cosmic supernova rate (CSNR), $R(z)$, which reflects the massive star death rate and is closely tied to the cosmic star formation rate due to the short lifetimes of massive progenitors. Historically, the uncertainty in $R(z)$—dominated by the absolute normalization—has been as large as ±40%, strongly limiting the predictive power for the DSNB.

Wide-field synoptic sky surveys (LSST, Pan-STARRS, DES) are designed to continuously monitor large swathes of the sky for transient events. By directly counting CCSNe and mapping their rate as a function of redshift up to $z \sim 1$, these surveys will reduce the uncertainty in the CSNR normalization to ±5% or better, with the error budget dominated by systematics. The shape of $R(z)$ is already relatively well constrained; the challenge previously was the absolute scale. Direct event counting eliminates biases (e.g., due to dust obscuration, survey depth, or galaxy selection) and, for the first time, will allow for a model-independent normalization of the CCSN history—substantially enhancing the reliability of DSNB predictions.

Critically, the cosmic volume accessible to these surveys ($z \lesssim 1$) encompasses ∼87% of progenitors responsible for high-significance DSNB detection in the 10–26 MeV range due to redshift-dependent energy downgrading.

3. Predictive Power for Neutrino Physics

The DSNB offers a uniquely global probe of supernova neutrino emission complements to rare Galactic bursts. With survey-based supernova history reducing the CSNR uncertainty to about 5%, the high-energy tail ($\gtrsim$20 MeV) of the DSNB becomes highly sensitive to the assumed neutrino spectral shape—especially the effective temperature $T_\nu$—because the inverse beta decay cross section rises steeply with energy.

Comparative models, e.g., for $T_\nu = 4, 6, 8$ MeV, predict distinguishable DSNB signals; with previous uncertainties, these differences were undetectable. High-precision (∼5%) DSNB normalization will thus allow next-generation neutrino detectors (e.g., Gd-doped Super-Kamiokande) to test supernova explosion physics and neutrino spectral properties including possible flavor transformations in the supernova environment.

The DSNB’s energy spectrum also has the potential to discriminate among different theoretical scenarios for neutrino flavor evolution, including MSW and collective effects, should deviations from canonical predictions be observed.

4. Revealing Invisible Supernovae

A critical aspect of the DSNB is its inclusiveness: all CCSNe contribute, not only those producing bright optical transients. This encompasses:

• Supernovae rendered optically “invisible” due to extreme host-galaxy dust extinction.
• Direct black hole formation events or “failed” explosions that yield little or no observable electromagnetic signal.

Such events may have enhanced neutrino emission relative to standard CC SNe and contribute a non-negligible fraction to the DSNB. Estimates of the invisible supernova fraction have a wide permissible range: 10% in standard models, but up to 50% given current observational and theoretical uncertainties. By comparing the DSNB measured via neutrino detectors—the sum over all collapses—to the sum over optically detected collapses (from synoptic surveys), any significant excess in the DSNB would strongly suggest an additional population of invisible or failed events. Quantifying this invisible fraction is crucial to understanding the true fate distribution of massive stars and the frequency of failed explosions.

5. DSNB Modeling and Mathematical Formalism

The precise modeling of the DSNB combines:

• The CSNR $R(z)$ obtained via synoptic surveys,
• Individual event spectra $N_\nu(\epsilon)$ parameterized by Fermi–Dirac forms with zero chemical potential,
• Redshift integration accounting for cosmological expansion and energy shift,
• Detector cross section and response for event-rate predictions (e.g., inverse beta decay: $\bar{\nu}_e + p \rightarrow e^+ + n$).

This yields the measurable event spectrum:

$$\frac{dN_e}{dE_e}(E_e) = N_p\, \sigma(E_\nu)\, \int_0^\infty (1+z)\, \phi[E_\nu(1+z)]\, R(z)\, |c\, dt/dz|\, dz$$

with $E_e$ the detected positron energy, $N_p$ the number of free protons (e.g., in SK), and $\sigma(E_\nu)$ the inverse beta decay cross section.

With improved astrophysical constraints on $R(z)$ and $N_\nu(\epsilon)$, theoretical predictions for the DSNB flux and spectrum gain close-to-experiment precision.

6. Implications for Cosmology and Stellar Evolution

The synergy between synoptic surveys and neutrino observatories transforms the DSNB from a theoretical curiosity into a rigorous test of cosmic history and stellar evolution:

• Measurement of the DSNB spectrum enables calibration of the CSNR and cross-validation of the cosmic star formation history.
• The high-statistics energy spectrum opens a channel for constraining the invisible supernova fraction, informing models of black hole formation and progenitor mass thresholds.
• “Excess” neutrino flux—beyond what can be explained by optically recorded SNe—quantifies the contribution from highly extinguished or failed SNe, directly impacting our understanding of heavy element enrichment, galaxy evolution, and baryonic feedback into the intergalactic medium.
• The DSNB serves as a laboratory for neutrino physics, including tests of flavor conversion, spectral distortions, and potentially new physics if significant discrepancies with predictions persist after all astrophysical uncertainties are minimized.

7. Outlook for Near-Future Observations

With synoptic synoptic surveys soon delivering high-precision CSNR data and detector upgrades such as Gd-doping of Super-Kamiokande providing background-rejection necessary for robust DSNB searches, the major limiting astrophysical uncertainties in DSNB prediction will be constrained to a few percent level. The accessible $z<1$ volume contains the vast majority of the observable DSNB signal, ensuring that the survey-based method captures the relevant source population.

This will allow for:

• Rigorous empirical tests of the absolute DSNB flux and its energy-dependence,
• Disentanglement of underlying neutrino spectra and emission mechanisms,
• Empirical bounds on the rate of optically undetectable core collapses.

Precision DSNB measurements, tightly linked to synoptic survey results, thus represent a nexus of cosmology, stellar astrophysics, and neutrino physics, with the potential to resolve outstanding problems in each domain and to provide new insights into the fate of massive stars across cosmic time (Lien et al., 2010).