⚛️ general relativity

Effect of dark matter on galactic black hole ringdown waveforms and shadows

This paper calculates that while a dark matter halo has a negligible effect on the ringdown waveforms and shadows of supermassive black holes like M87*, a surrounding dark matter spike produces a significantly larger, potentially detectable impact that existing Event Horizon Telescope observations are nearly sensitive enough to confirm or rule out.

Original authors: Ramin G. Daghigh, Gabor Kunstatter

Published 2026-09-02

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CC BY 4.0

Original authors: Ramin G. Daghigh, Gabor Kunstatter

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

Deep in the centers of most galaxies, including our own, lie supermassive black holes, objects so dense that their gravity traps even light. Surrounding these cosmic giants is a vast, invisible cloud of dark matter, a substance that does not emit or reflect light but reveals itself through its gravitational pull. While astronomers have long mapped the large-scale distribution of this dark matter in galactic halos, a more concentrated structure has been theorized to exist right at the core: a "spike." This spike is a region where dark matter is packed much more tightly around the black hole than in the wider halo. Understanding the difference between a diffuse halo and a dense spike is crucial because each would warp space and time in a distinct way, potentially leaving a unique fingerprint on the signals these black holes send out.

Two primary ways exist to observe these black holes and test the nature of their surroundings. First, when a black hole is disturbed, perhaps by merging with another, it rings like a bell, sending out ripples in spacetime known as gravitational waves. The way these waves fade away, called the ringdown, carries information about the black hole's mass and the environment it sits in. Second, the Event Horizon Telescope has captured images of the "shadow" of a black hole, a dark silhouette caused by light bending around the event horizon. The size of this shadow is determined by the geometry of space near the black hole. If a dense spike of dark matter exists, it should subtly alter both the sound of the gravitational ringdown and the apparent size of the shadow.

In a recent study, researchers Ramin G. Daghigh and Gabor Kunstatter set out to calculate exactly how a dark matter spike versus a dark matter halo would affect these two observable features, focusing specifically on the supermassive black hole at the center of the galaxy M87. Their work addresses a critical detail often overlooked in previous calculations: the perspective of the observer. They found that if one calculates the effects using the time measured by an observer sitting close to the black hole, the influence of the dark matter appears small. However, when the calculation is corrected to reflect the time measured by a distant observer on Earth, the effect becomes dramatically larger. This difference arises because the extra mass of the dark matter slows down time relative to the distant observer, a phenomenon known as gravitational redshift. This redshift acts as a dominant factor, stretching the gravitational waves and making the black hole's shadow appear larger.

The team performed detailed simulations to compare the impact of a dense spike against a more spread-out halo of the same total mass. They modeled the spike using a density profile that rises sharply near the black hole, while the halo was modeled using a standard distribution profile found in elliptical galaxies like M87. Their results showed that the dense spike produces a significant change in the gravitational wave signal, altering the ringdown waveform in a way that could theoretically be detected by future instruments. In contrast, the spread-out halo, even with the same total mass, produces a negligible effect on the waveform as long as its distribution scale matches current observational expectations. The halo's mass is too far away from the black hole to cause the same strong redshift effect that the concentrated spike does.

Regarding the shadow of the black hole, the researchers calculated how much the presence of a dark matter spike would enlarge the dark silhouette seen by the Event Horizon Telescope. They found that for the estimated density of a spike around M87, the shadow would appear about 0.1 percent larger than it would in a universe without dark matter. While this seems tiny, it is remarkably close to the precision of current measurements. The authors noted that existing observations are within an order of magnitude of being able to detect or rule out the presence of such a spike. If the density of the spike is slightly higher than current estimates, or if we observe an even more massive black hole, the enlargement of the shadow could become large enough to be confirmed by the next generation of telescope observations.

The study also clarified a subtle but important point about the physics of these environments. The researchers examined two different assumptions about how dark matter particles might push against each other: one where the pressure is the same in all directions, and another where the pressure is zero in the direction pointing toward the black hole but exists in other directions. They found that for the specific density profiles expected in these galactic cores, both assumptions lead to the same geometric result for the spacetime around the black hole. This means that the uncertainty about the internal pressure of dark matter does not significantly change the prediction for how the shadow or the gravitational waves would look.

Ultimately, the paper suggests that the search for dark matter spikes is not just a theoretical exercise but a potentially observable reality. The key lies in listening to the gravitational waves from massive black holes with the correct perspective. By accounting for the redshift caused by the extra mass of the dark matter, the signal of a spike becomes much clearer. If gravitational waves from a black hole similar to M87* can be detected with sufficient precision, they could provide the first direct evidence of a dark matter spike, offering a new window into the invisible matter that shapes our universe. Until then, the shadow of M87* remains a tantalizing target, with current data hovering just on the edge of being able to reveal the presence of this dense, invisible cloud.

Technical Summary: Effect of Dark Matter on Galactic Black Hole Ringdown Waveforms and Shadows

Problem Statement
Dark matter (DM) halos are known to surround supermassive black holes (SMBHs) at galactic centers, with theoretical proposals suggesting the existence of dense "spikes" at the cores of these halos. While recent pulsar timing arrays (NANOGrav, PPTA, EPTA, CPTA) have detected a stochastic gravitational-wave background likely originating from SMBH binaries, the ability to resolve individual ringdown waveforms or precise shadow measurements remains limited. Previous studies have investigated the impact of DM spikes on gravitational waves and shadows, but often utilized the Schwarzschild time coordinate of the central black hole (measured by an observer between the horizon and the inner spike radius) rather than the proper time of an asymptotic stationary observer. This paper addresses the discrepancy in calculating the observable effects of DM distributions (specifically spikes and halos) on ringdown waveforms and photon ring shadows, emphasizing the critical role of reference frame choice and redshift factors.

Methodology
The authors employ a general relativistic framework to model the spacetime geometry of a black hole surrounded by extended matter distributions.

Metric Derivation: The study solves the Tolman-Oppenheimer-Volkoff (TOV) equations for a spherically symmetric static metric. Two pressure assumptions are considered:
- Isotropic pressure: $p_r = p_t$ .
- Anisotropic pressure: Zero radial pressure ( $p_r = 0$ ) with non-zero tangential pressure.
  The authors demonstrate that for the density profiles of interest (DM spikes and halos), the pressure term is negligible in determining the metric geometry, yielding effectively identical results for both assumptions.
Reference Frame and Redshift: A key methodological step involves integrating the metric function $\mu(r)$ from the inner boundary of the matter shell ( $r_{in}$ ) outward. The authors highlight that previous works often fixed the time coordinate to the Schwarzschild time of the vacuum region inside the spike. In contrast, this paper derives the metric relative to an asymptotic observer at infinity. This introduces a constant redshift factor $C$ (where $C > 1$ ), relating the Schwarzschild time $t$ to the asymptotic proper time $\tilde{t}$ via $\tilde{t} = \sqrt{C}t$ .
Waveform Calculation: The quasi-normal mode (QNM) wave equation is solved for massless scalar perturbations. The potential $V(r)$ is derived for the metric. The authors show that the wave equation is covariant under the time rescaling, meaning the waveform shape is preserved but stretched in time by the factor $\sqrt{C}$ when viewed by an asymptotic observer.
Specific Models:
- DM Spikes: Modeled using an adiabatically formed density profile $\rho \propto r^{-\gamma_{sp}}$ with $\gamma_{sp} = 7/3$ , applied to Sgr A* and M87*.
- DM Halos: Modeled using the Hernquist density profile, typical for elliptical galaxies like M87, with anisotropic pressure ( $p_r=0$ ). An analytic solution for the metric is derived for this profile.
Shadow Calculation: The shadow radius is calculated using null geodesics. The authors derive the relationship between the impact parameter at infinity and the observed shadow radius, incorporating the redshift factor $C$ .

Key Contributions and Results

Dominance of Redshift: The primary contribution is the demonstration that the dominant effect of a DM spike on the ringdown waveform, as seen by an asymptotic observer, is an overall time dilation (redshift) factor $\sqrt{C}$ . Previous calculations using the interior Schwarzschild time significantly underestimated this effect.
Spike vs. Halo:
- Spikes: For the DM spike surrounding M87*, the redshift factor $C$ is significant enough to alter the ringdown waveform in a potentially detectable way. The effect is orders of magnitude more significant than that of a standard halo.
- Halos: For a Hernquist-profile halo, the impact on the QNM potential and ringdown waveform is negligible unless the scale radius of the halo is unrealistically small (within a few orders of magnitude of the black hole mass). If the halo distribution scale aligns with observational expectations, the redshift effect is minimal.
Waveform Detectability: The authors calculate ringdown waveforms for Sgr A* and M87*. They find that for M87*, a DM spike with a density roughly 8.4 times the expected value produces a visible change in the ringdown waveform in the asymptotic frame. This suggests that future gravitational wave detections from massive galactic black holes could constrain DM spike parameters.
Shadow Size: The presence of a DM spike increases the black hole shadow radius by a factor of $\sqrt{C}$ . For M87*, using density bounds from previous literature, the predicted increase in shadow size is of the order of 0.1%. This corresponds to a diameter enlargement of approximately 0.2% (derived from $C \approx 1.004$ ).
Comparison with Observations: The paper notes that the predicted increase in shadow size is just one order of magnitude smaller than the proposed error bars of recent Event Horizon Telescope (EHT) measurements (which have reduced error bars to ~1%). This implies that current or near-future EHT data could potentially detect or rule out the presence of a DM spike of the estimated density.

Significance and Claims
The paper claims that accurate modeling of DM effects on black hole observables requires expressing results in the frame of an asymptotic stationary observer to correctly account for redshift. The authors conclude that:

The impact of a DM spike on ringdown waveforms is significantly larger than previously estimated when viewed from infinity, potentially making it detectable in future gravitational wave observations of massive black holes (comparable to or larger than M87*).
The effect of a standard DM halo on these waveforms is negligible for realistic distribution scales.
Existing EHT observations of black hole shadows are approaching the sensitivity required to detect the subtle (order of 0.1%) enlargement of the shadow caused by a DM spike, offering a potential observational test for the existence of such spikes.

The authors maintain a modest tone regarding the immediate detection, noting that while the effect is theoretically significant and potentially within reach of current technology, it relies on specific density assumptions and the ability to measure waveforms or shadow sizes with high precision. They do not propose new experiments but rather interpret the potential of existing and upcoming data (NANOGrav, EHT) in light of their corrected theoretical framework.

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