⚛️ phenomenology

Thermal Emission of Dark Photons from Earth's Core

This paper estimates constraints on the kinetic mixing parameter of sub-eV dark photons produced by thermal emission from Earth's core, demonstrating that current experiments like SENSEI and DAMIC-M already limit this parameter space while the proposed Oscura experiment could improve sensitivity by two to three orders of magnitude.

Original authors: Hooman Davoudiasl

Published 2026-06-26

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Hooman Davoudiasl

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the Earth's core not just as a ball of hot metal, but as a giant, glowing furnace. For decades, scientists have looked at stars like our Sun to see if they leak out invisible particles called "dark photons." But stars are incredibly hot and dense—like trying to hear a whisper in a jet engine.

This paper suggests we should look at a quieter, cooler place: the center of our own planet. The author, Hooman Davoudiasl, proposes that the Earth's core might be leaking these invisible particles, too. Here is the breakdown of the idea, using simple analogies.

The Invisible "Ghost" Particle

Think of the Dark Photon as a "ghost" version of the light we can see.

The Real Thing: Regular photons are particles of light. They interact with everything that has an electric charge (like electrons).
The Ghost: Dark photons are similar, but they live in a "hidden sector" of the universe. They don't usually talk to our world.
The Connection: However, there is a tiny, weak "leak" between the hidden world and our world. The paper calls this leak $\epsilon$ (epsilon). Imagine it as a very thin, almost invisible bridge. If the bridge is wide enough, ghost particles can sneak over into our world and be detected.

The Earth as a Factory

The Earth's core is made mostly of iron and is incredibly hot (about 6,000 Kelvin).

The Process: Just as a hot stove glows and emits light, the hot iron in the Earth's core is constantly jiggling its electrons. Because of that tiny "bridge" ( $\epsilon$ ), some of this energy is converted into dark photons instead of regular light.
The Escape: These dark photons are so light and ghost-like that they don't get stuck in the rock. They zip right out of the Earth's core, travel through the crust, and reach the surface without losing much energy. It's like a ghost walking straight through a wall.

Two Ways to Catch the Ghost

The paper looks at two different ways to figure out if these particles exist and how strong that "bridge" ( $\epsilon$ ) is.

1. The "Cooling Down" Test (Earth Core Cooling)

Imagine you have a cup of hot coffee. If you leave it alone, it cools down. But if you have a secret, super-efficient straw sucking heat out of it, it will cool down much faster than physics says it should.

The Logic: If the Earth is leaking too many dark photons, it would be losing heat faster than we observe.
The Result: The author calculated how much heat the Earth could lose this way. They found that while this method sets some limits, the Earth isn't cooling fast enough to rule out the current theories. It's a bit like checking the coffee cup and realizing, "Well, it's not cooling too fast, so the straw might be there, but we can't prove it's not there just by looking at the temperature."

2. The "Direct Catch" Test (Listening for the Ghost)

This is where the paper gets exciting. Instead of watching the Earth cool, the author suggests we listen for the ghosts arriving at the surface.

The Setup: There are ultra-sensitive detectors on Earth (like SENSEI and DAMIC-M) designed to catch dark matter. They usually look for dark matter floating in space.
The Twist: The author realized these same detectors could catch the dark photons coming from the Earth itself. It's like realizing a microphone designed to hear a distant bird could also hear a whisper coming from the floorboards right beneath it.
The Discovery: When the author applied the data from these existing experiments to the Earth's dark photon leak, they found that these experiments are already constraining the theory. They have already ruled out some possibilities that scientists thought were still open.

The Future: The "Super-Microphone"

The paper also looks ahead to a proposed experiment called Oscura.

The Analogy: If SENSEI and DAMIC-M are like a standard microphone, Oscura is a super-sensitive recording studio microphone.
The Potential: The author estimates that Oscura could be 100 to 1,000 times more sensitive than current experiments. If built, it could detect these Earth-leaking dark photons even if the "bridge" ( $\epsilon$ ) is incredibly thin—far thinner than anything we can test right now.

The Bottom Line

The paper argues that the Earth's core is a unique, "Goldilocks" laboratory—hot enough to produce these particles, but cool enough to be different from the extreme conditions of stars.

What they found: Current experiments (SENSEI and DAMIC-M) are already telling us that if these dark photons exist, they are very weakly connected to our world.
What they hope for: A future experiment (Oscura) could potentially see these particles, opening a new window into the "hidden sector" of the universe, all by listening to the heat of our own planet.

The author admits their calculations are a "rough sketch" (like a map drawn from memory) and that a more detailed map of the Earth's core is needed for precise numbers. However, the sketch is detailed enough to suggest that this is a promising path for future discovery.

Technical Summary: Thermal Emission of Dark Photons from Earth's Core

Problem Statement
The paper investigates the potential for the Earth's hot core to act as a source of light dark photons ( $\gamma_d$ ) in the sub-eV mass regime ( $m_{\gamma_d} \lesssim 0.1$ eV). While stellar cores (e.g., the Sun) are standard astrophysical sources for constraining dark sector physics, the Earth's core offers a distinct environment characterized by lower temperatures ( $\sim 5000-6000$ K) and high densities ( $\sim 10$ g cm $^{-3}$ ). The authors aim to determine if thermal emission from this "intermediate" environment can provide competitive constraints on the kinetic mixing parameter $\epsilon$ , which governs the coupling between the dark photon and the Standard Model (SM) electromagnetic current.

Methodology
The authors employ a simplified model of the Earth's core, treating it as a system of iron (Fe) with a solid inner core ( $r_{in} \approx 1220$ km, $T_{in} \approx 6000$ K) and a molten outer core ( $r_{out} \approx 3480$ km, $T_{out} \approx 5000$ K). Electrons in this iron system are modeled as a degenerate Fermi gas with a Fermi energy $E_F \approx 10.34$ eV.

The analysis proceeds through two primary channels:

Thermal Emission Formalism: The authors adapt existing formalisms for resonant thermal emission from a plasma (originally derived for the Sun) to the Earth's degenerate electron gas. The power per unit volume for longitudinal mode emission is given by:
$\frac{dP_L}{dV} \approx \frac{1}{4\pi} \frac{\epsilon^2 m_{\gamma_d}^2 \omega_p^3}{e^{\omega_p/T} - 1}$
where $\omega_p$ is the plasma frequency. The authors address the discrepancy between the naive plasma frequency derived from total electron density ( $\sim 15$ eV) and experimental values ($3.5-5.0$ eV) by considering that only electrons near the Fermi surface contribute to optical scattering, effectively reducing the relevant electron density. Two values for $\omega_p$ are tested: 3.5 eV and 5.0 eV.
Constraint Derivation:
- Earth Core Cooling: The total emitted power ( $P_L^{tot}$ ) is calculated by integrating over the core volume. This is compared against the Earth's total cooling rate ( $L_\oplus \sim 10^{19}$ erg s $^{-1}$ ). The condition $P_L^{tot} < L_\oplus$ provides an upper bound on $\epsilon$ .
- Direct Detection Recasting: The authors recast results from dark matter direct detection experiments (SENSEI and DAMIC-M) that utilize skipper-CCD technology. These experiments search for the absorption of dark matter particles by electrons. The authors equate the flux of dark photons emitted by the Earth's core to the flux of dark matter assumed in these experiments, allowing them to translate experimental exclusion limits on $\epsilon$ (for DM masses equal to $\omega_p$ ) into constraints on the Earth-emitted dark photon flux.

Key Contributions and Results

Cooling Constraints: The study calculates that the Earth's thermal emission of dark photons is constrained by geophysical cooling limits. However, the resulting bounds on $\epsilon$ are found to be weaker than existing constraints from other sources (such as stellar cooling or laboratory experiments) for the mass range considered.
Direct Detection Bounds: By recasting data from SENSEI and DAMIC-M, the authors demonstrate that these experiments already probe new parameter space for dark photons emitted by the Earth's core. Specifically:
- For $m_{\gamma_d} = \omega_p = 3.5$ eV, SENSEI constrains $\epsilon \lesssim 3 \times 10^{-13}$ and DAMIC-M constrains $\epsilon \lesssim 6 \times 10^{-14}$ .
- For $m_{\gamma_d} = \omega_p = 5.0$ eV, SENSEI constrains $\epsilon \lesssim 0.8 \times 10^{-13}$ and DAMIC-M constrains $\epsilon \lesssim 2 \times 10^{-14}$ .
Future Projections: The paper projects the sensitivity of the proposed Oscura experiment. Depending on the assumed plasma frequency ( $\omega_p$ ), Oscura could reach values of $\epsilon$ two to three orders of magnitude below current bounds. For $\omega_p = 5.0$ eV, the projected reach is $\epsilon \lesssim 2 \times 10^{-17}$ , representing a significant improvement over current limits.

Significance and Claims
The paper positions the Earth's core as a unique, "intermediate" source for dark photon production, bridging the gap between laboratory conditions and extreme stellar environments. While the authors acknowledge that the Earth's cooling argument does not currently yield the strongest constraints, the primary significance lies in the recasting of direct detection experiments.

The authors claim that current results from SENSEI and DAMIC-M already constrain dark photon parameter space relevant to Earth-core emission. Furthermore, they argue that future experiments like Oscura have the potential to explore regions of parameter space that are currently unprobed, specifically for dark photon masses around $10^{-4}$ to $5$ eV (depending on the specific $\omega_p$ assumption). The authors emphasize that their treatment is an exploratory approximation; they suggest that more detailed analyses of the Earth's core profile, thermal properties, and experimental considerations are necessary for precise phenomenological results, but their findings provide sufficient motivation to pursue such refinements.