Photon and neutrino fluxes from spheroidal dwarf galaxies in a decaying DM model

This paper investigates indirect detection signatures of a decaying scalar singlet dark matter candidate, calculating predicted gamma-ray and neutrino fluxes from the Milky Way and 14 dwarf spheroidal galaxies to demonstrate that observable signals are possible within specific parameter spaces consistent with cosmological constraints.

The Gist

The Cosmic Ghost Hunt: A Simple Explanation

Imagine the universe is a giant, dark room filled with invisible furniture. We know this furniture is there because we can see the floorboards bending under its weight (that's gravity), but we can't see the furniture itself. This invisible stuff is Dark Matter.

For decades, scientists have been trying to catch a glimpse of this "ghost" by building super-sensitive traps (direct detection) or smashing particles together to see if the ghost pops out (colliders). But so far, the traps are empty, and the ghosts haven't shown up.

This paper proposes a new way to hunt for the ghost: Instead of waiting for it to bump into us, let's wait for it to die.

1. The "Gravity-Only" Ghost

The authors suggest a specific type of dark matter that is incredibly shy. It doesn't talk to normal matter (like atoms or light) at all, except through gravity.

Think of this dark matter particle as a very old, heavy stone floating in space. Because it's so old and heavy, it's unstable. Eventually, it will crumble apart. But here's the twist: it doesn't crumble because of a chemical reaction or a collision. It crumbles because gravity itself is pulling it apart.

In this model, the "stone" (Dark Matter) has a lifespan longer than the age of the universe, but it does eventually decay. When it breaks, it shatters into pieces we can see: Gamma rays (super-energetic light) and Neutrinos (ghostly particles that pass through everything).

2. The Hunting Grounds: The Milky Way and "Dwarf Galaxies"

To find these decay products, the scientists looked at two places:

• The Milky Way: Our home galaxy. It's like a big city with a lot of traffic (dark matter).
• Dwarf Spheroidal Galaxies (dSphs): These are tiny, faint galaxies orbiting ours. They are like quiet, empty villages.

Why look at the quiet villages?
In the big city (Milky Way), there's a lot of background noise—stars exploding, gas clouds, and other cosmic events that create gamma rays and neutrinos. It's hard to hear a whisper in a crowded stadium.
In the quiet villages (dSphs), there are almost no stars or gas. It's a silent library. If you hear a whisper there, you know it's coming from the dark matter, not from a noisy star.

The paper calculated that even though these villages are small, they are so packed with dark matter that the signal from their decay is actually just as loud as the signal from our own galaxy's center.

3. The "Flashlight" and the "Ghost"

The authors ran simulations to see what happens when these dark matter particles decay.

• The Flashlight (Gamma Rays): When the dark matter breaks, it shoots out high-energy light. The scientists calculated how bright this light would be for different sizes of dark matter particles (from 10 GeV to 1 TeV).
• The Ghost (Neutrinos): It also shoots out neutrinos. These are like ghosts that can walk through the Earth without stopping. To catch them, we need giant detectors like IceCube (a telescope buried in the ice at the South Pole).

The Results:
The paper found that if the dark matter is heavy (around 1,000 times the mass of a proton) and decays at a specific rate, our current telescopes might actually see it.

• The Sweet Spot: The best chance to see this signal is if the dark matter is heavy (1 TeV) and the "gravity connection" is strong enough to let it decay relatively quickly (though still taking billions of years).
• The Noise: For lighter particles, the signal is too weak to see with current technology. It's like trying to hear a mouse squeak in a hurricane.

4. The Big Picture: Why This Matters

This paper is a hopeful sign for the "Indirect Detection" team.

• The Problem: We haven't found dark matter yet, and the usual suspects (WIMPs) are looking less likely.
• The Solution: Maybe dark matter isn't a particle that bumps into us; maybe it's a particle that slowly fades away, leaving a trail of gamma rays and neutrinos.
• The Future: The authors say that while we might not see this today, the next generation of telescopes (like KM3NeT, which is being built underwater) will be 46% better at catching these signals.

The Analogy Summary

Imagine you are trying to find a specific type of rare, invisible bird in a forest.

• Old Method: You set up a net to catch the bird when it flies by. (Direct Detection). Result: No birds caught.
• New Method (This Paper): You realize the bird is dying of old age and dropping its feathers. You don't look for the bird; you look for the feathers (Gamma rays and Neutrinos) falling from the sky.
• Where to look: You check the big city park (Milky Way) and the quiet backwoods (Dwarf Galaxies). You realize the backwoods are actually better because there are no other birds dropping feathers to confuse you.
• Conclusion: If you have a big enough net (a powerful telescope) and wait long enough, you might just catch a feather and finally prove the bird exists.

In short: This paper says, "Stop looking for the ghost in the mirror; look for the footprints it leaves behind as it fades away. We might just be able to see them soon."

Technical Summary

1. Problem Statement

The nature of Dark Matter (DM) remains unresolved despite extensive direct detection efforts (e.g., XENONnT, LZ, PandaX), which have increasingly constrained the parameter space for Weakly Interacting Massive Particles (WIMPs). The absence of direct signals has shifted focus toward indirect detection methods, specifically searching for secondary products (gamma rays, neutrinos) from DM annihilation or decay.

This paper addresses a specific gap: the lack of conclusive results in WIMP models has motivated the exploration of purely gravitational DM models. In these scenarios, DM interacts with the Standard Model (SM) exclusively through gravity (or Planck-suppressed operators), naturally evading direct detection constraints. The authors investigate a decaying DM scenario where a scalar singlet DM candidate decays into SM particles via a non-minimal gravitational coupling. The study focuses on calculating the resulting photon and neutrino fluxes from the Milky Way and 14 dwarf spheroidal galaxies (dSphs) to determine their observability.

2. Methodology

Theoretical Framework

• Model: The authors utilize a model extending the Standard Model with a real scalar singlet field ($\phi$) stabilized by a $Z_2$ global symmetry.
• Decay Mechanism: Stability is broken in curved spacetime via a non-minimal coupling to the Ricci scalar ($R$). The interaction Lagrangian is defined as $\mathcal{L}_\xi = -\xi R F(\phi, X)$, where $\xi$ is the coupling constant.
• Conformal Transformation: The action is transformed from the Jordan frame to the Einstein frame using a Weyl transformation $\Omega^2(\phi) = 1 + 2\xi M \kappa^2 \phi$. This generates effective tree-level interactions between the DM field and SM fields (fermions, Higgs, gauge bosons).
• Decay Channels: At the electroweak scale, the dominant decay channels considered are:
  • $\phi \to f\bar{f}$ (fermions)
  • $\phi \to hh$ (Higgs bosons)
  • $\phi \to VV$ (gauge bosons $W, Z$)
• Mass Range: The study focuses on DM masses ($m_\phi$) in the electroweak scale: 10 GeV, 500 GeV, and 1 TeV.

Astrophysical Calculation

• Targets: The authors analyzed the Milky Way (MW) halo and 14 dwarf spheroidal galaxies (dSphs) (e.g., Bootes I, Segue I, Ursa Major II).
• Flux Calculation: The differential flux ($d\Phi/dE$) is calculated using the standard formula:
  $$\frac{d\Phi_X}{d\Omega dE} = \frac{r_s}{4\pi} \frac{\rho_0}{M_{DM}} \frac{1}{D} \sum_f \Gamma_f \frac{dN_f^X}{dE}$$
  where $D$ is the astrophysical "D-factor" (line-of-sight integral of DM density).
• Tools:
  • CLUMPY: Used to compute the D-factors for the specific density profiles of the dSphs and the MW.
  • Numerical Integration: Used to compute differential fluxes and total event rates.
• Event Rate Estimation: The number of detectable events ($\mu_s$) was estimated assuming a detector with an effective area of 1 km² and an exposure time of 1 year.
  • Neutrinos: Neutrino oscillations were explicitly calculated to determine the flux of muon neutrinos arriving at Earth from the source flavors.
  • Gamma Rays: Calculated directly from the decay spectra.

3. Key Contributions

1. Gravitational Portal Implementation: The paper provides a concrete phenomenological analysis of a decaying DM model where the decay is induced solely by non-minimal gravitational coupling, bypassing the need for new gauge interactions.
2. Comparative Flux Analysis: It offers a direct comparison of signal strengths between the Milky Way and a specific set of 14 dSphs, demonstrating that their D-factors and resulting fluxes are of the same order of magnitude.
3. Benchmark Scenarios: The study presents results for three benchmark masses (10 GeV, 500 GeV, 1 TeV) and three coupling strengths ($\xi = 10^{-10}, 10^{-13}, 10^{-16}$), mapping the parameter space against current and future experimental sensitivities.
4. Oscillation Inclusion: The neutrino analysis rigorously includes flavor oscillation effects ($\nu_\mu \to \nu_\mu, \nu_e \to \nu_\mu, \nu_\tau \to \nu_\mu$) to predict the observable muon neutrino flux at Earth.

4. Results

Flux and Event Rates

• Milky Way vs. dSphs: The computed gamma-ray and neutrino fluxes from the MW and dSphs are comparable. The D-factors for the studied dSphs are similar to the MW, validating dSphs as robust targets for this specific decay model.
• Dependence on Parameters:
  • Coupling ($\xi$): The signal scales strongly with $\xi$. The strongest signals occur at $\xi = 10^{-10}$.
  • Mass ($m_\phi$):
    • 1 TeV: Produces the highest flux for $\xi = 10^{-10}$.
    • 10 GeV: Despite lower mass, the flux can be significant for large $\xi$, but the event rate drops drastically for smaller $\xi$.
• Event Counts (1 km², 1 year):
  • Best Case ($m_\phi = 1$ TeV, $\xi = 10^{-10}$):
    • MW: ~4,000 neutrino events (5–10 GeV).
    • dSphs: ~300–3,000 neutrino events (5–10 GeV).
    • Gamma Rays: High event counts, with the best scenario yielding 1–10,000 events (5–10 GeV) for dSphs.
  • Worst Case ($\xi = 10^{-16}$): Event rates drop significantly; detecting a single event could require years of data, particularly for lower masses.
• Target Specifics: Among dSphs, Segue I, Ursa Major II, and Leo II yield the highest neutrino counts due to their high dark matter densities.

Energy Spectra

• The energy spectra for both photons and neutrinos exhibit a decreasing behavior with energy.
• Lower-energy particles (5–10 GeV range) are more abundant and thus more likely to be detected than high-energy (TeV) particles in this specific model.

5. Significance and Conclusions

• Viability of Gravitational DM: The study confirms that decaying DM models driven by gravitational portals are phenomenologically viable. The predicted signals fall within the reach of current and next-generation indirect detection experiments, particularly for coupling values $\xi \geq 10^{-13}$.
• Experimental Outlook:
  • Neutrino Telescopes: Experiments like IceCube and the upcoming KM3NeT are highlighted as crucial. KM3NeT is projected to increase detectable events by up to 46% compared to current setups.
  • Complementarity: Neither gamma rays nor neutrinos show a clear dominance; both channels offer comparable sensitivity. This suggests a multi-messenger approach is optimal.
• Constraints: The results suggest that future experiments could constrain the parameter space of gravitational decaying DM, specifically testing lifetimes $\tau \gtrsim 10^{24}$ s.
• Limitations: The current analysis is restricted to two-body decay channels. At higher masses, multi-body decays may become relevant, requiring more complex computational tools.

In summary, the paper demonstrates that even in the absence of direct WIMP interactions, decaying dark matter coupled via gravity can produce observable photon and neutrino signatures, making dwarf spheroidal galaxies and the Milky Way halo prime targets for next-generation neutrino and gamma-ray observatories.