Do Pulsars surf on waves of dark matter?

Title: The second data release from the European Pulsar Timing Array VI. Challenging the ultralight dark matter paradigm

Authors: Clemente Smarra, Boris Goncharov, Enrico Barausse, J. Antoniadis, S. Babak, A.-S. Bak Nielsen, C. G. Bassa, A. Berthereau, M. Bonetti, E. Bortolas, P. R. Brook, M. Burgay, R. N. Caballero, A. Chalumeau, D. J. Champion, S. Chanlaridis, S. Chen, I. Cognard, G. Desvignes, M. Falxa, R. D. Ferdman, A. Franchini, J. R. Gair, E. Graikou, J.-M. Grießmeier, L. Guillemot, Y. J. Guo, H. Hu, F. Iraci, D. Izquierdo-Villalba, J. Jang, J. Jawor, G. H. Janssen, A. Jessner, R. Karuppusamy, E. F. Keane, M. J. Keith, M. Kramer, M. A. Krishnakumar, K. Lackeos, K. J. Lee, K. Liu, Y. Liu, A. G. Lyne, J. W. McKee, R. A. Main, M. B. Mickaliger, I. C. Niţu, A. Parthasarathy, B. B. P. Perera, D. Perrodin, A. Petiteau, N. K. Porayko, A. Possenti, H. Quelquejay Leclere, A. Samajdar, S. A. Sanidas, A. Sesana, G. Shaifullah, L. Speri, R. Spiewak, B. W. Stappers, S. C. Susarla, G. Theureau, C. Tiburzi, E. van der Wateren, A. Vecchio, V. Venkatraman Krishnan, J. Wang, L. Wang, and Z. Wu

First Author’s Institution: International School for Advanced Studies, Via Bonomea 265, Trieste, Italy and INFN, Sezione di Trieste; Institute for Fundamental Physics of the Universe, Via Beirut 2, Trieste, Italy

Status: Published in Physical Review Letters [refereed version is free to read here until the end of 2023]

Our Universe is positively thrumming, and so was the astrophysics community when members of the International Pulsar Timing Array (IPTA) made coordinated announcements in June of this year revealing signals consistent with a statistically random or stochastic gravitational wave background. The data behind the announcement and some of their implications are described in more detail in these bites. For the purposes of today’s bite, we’ll wander a bit further afield: what does this same data say about dark matter in our galaxy?

Stellar lighthouses as galactic clocks

Before understanding what the IPTA has to do with dark matter, we should understand what it has to do with…well, pulsars! Pulsars are neutron stars with two important jobs: to rotate and emit jets of light.

The first is achieved in the process of becoming a neutron star: somewhere in the Universe, a supernova explodes, turning a massive star that’s run its course into a neutron star and giving it a lot of spin in the process. This can make pulsars reach extremely steady periods of a few seconds or even down to milliseconds! Pulsars also have strong magnetic fields which serve to align jets of particles along the two magnetic poles of the star, but generally not with the axis of spin. This means the jets will “pulse” along the line of sight as the spin turns one of the jets towards the Earth, earning pulsars both their name and their standard description as ‘stellar lighthouses.’ 

Together, these two properties make pulsars extraordinary clocks, as the time of arrival (TOA) of a pulsar’s light is very strictly set by the speed of light and distance between us and the pulsar. This is particularly true of pulsars with periods on the order of milliseconds (MSPs), as they are less prone to being disturbed by astrophysical events like accretion which can affect the period of their slower-spinning siblings. This means that any change in the TOA from these pulsars is likely to be due to a change in the travel time—and, therefore, distance—to our detectors. The IPTA member collaborations use this fact to look for gravitational waves, which are one way to alter the distance traversed by the pulsars’ photons. Today, we are considering a totally different way of changing the path of their light.  

Surf’s up!

Pulsars are stars, and so live embedded in a galaxy; in fact, most of the ones we know live in our own galaxy. Our galaxy, in turn, lives in its own dark matter halo. While we have a general idea of the shape of this halo, we know very little about the dark matter that makes it up. One option is called Fuzzy Dark Matter (FDM): a dark matter candidate so light (around 10-22 eV) that we no longer describe it with a bunch of individual particles but as one wavefunction predicting where large numbers of particles are likely to be, similar to the hydrogen atom in quantum mechanics. The exact mass of the dark matter also sets its ‘correlation length’—aka, the distance over which the wavefunction evolves in unison. This “wavy” behavior of FDM makes its gravitational potential oscillate periodically, pulling the pulsars slightly closer then farther away from the Earth like buoys out on a sea with waves. 

The authors of today’s paper are members of the European Pulsar Timing Array (EPTA) who decided to look for evidence for FDM in the EPTA data. To do this, there are three important distances to consider: the average distance between the pulsars (the buoys in this analogy), the average distance between the pulsars and the Earth (the distance of buoys to the shore, where the observer is standing), and the correlation length of FDM (the size of the wave). The first two are known quantities from the PTA dataset; the last is unknown but depends on the mass of the FDM particle, so testing which distances are allowed by the data gives us exclusions on possible particle masses. When comparing the lengths, there are three options:

  • If the correlation length of FDM is the smallest of the three, the pulsars are riding different waves, and so their movement is uncorrelated
  • If the correlation length is larger than the pulsar-pulsar or pulsar-Earth distances, but smaller than the part of the halo we know about from rotation curves (about 20 kpc). This is analogous to the wave being larger than the distance between the buoys or from the buoys to the shore, but smaller than the distance to the horizon. This means the dark matter halo’s density and the pulsar data aren’t being measured over quite the same patch of sky, leading to slightly different statistics in the analysis. The authors call this case pulsar-correlated
  • If the correlation length is larger than the other two lengths and stretches beyond 20 kpc; in other words, the entire swath of the sea we can observe is affected by one really big wave. In this case, the two patches of the sky benign analyzed are the same, and the movement of the buoys is fully correlated

Analyzing the EPTA dataset with each of these assumptions in mind yielded the results illustrated in Fig. 1. Rather than fully ruling out FDM in certain mass ranges, the authors put limits on the maximum percentage of dark matter that could be FDM. For masses between 10-24 and 10-23.7 eV,  that percentage is only around 30%; for masses up to 10-23.3 eV, it’s closer to 70%. Above that mass, FDM is not constrained by current PTA data, and FDM is free to ride its wave into the sunset…for now. 

A figure showing two plots. On the left, the mass of the FDM particle is on the horizontal axis, while the amplitude of perturbations in on the vertical axis. The measured density of dark matter is plotted as a diagonal straight line. There are two data lines from previous papers (marked PPTA Bayes 2018 and NANOGrav 2018) that don't dip below the dark matter line, and so don't constrain the dark matter. The three cases presented in this bite - correlated, uncorrelated, and pulsar-correlated - do dip below the dark matter line at a mass of around 10^-23.3 eV. 

On the right, the horizontal axis is the same but the vertical axis now shows relative density of dark matter that could be FDM over all dark matter. The three cases in this paper are presented: the pulsar-correlated case falls below the line where all of dark matter could be FDM around 10^-23.3 eV, while the other two dip below around 10^-23.2. For masses smaller than that, the lines show that FDM can be between 30% and 70% of dark matter at most, depending on the exact mass.
Figure 1: The bottom axes show the mass of the particle, while the top axes show the corresponding oscillation frequency of the FDM gravitational potential (our “wave”). Figure 1 in the paper.
Left: The vertical axis shows the amplitude of oscillation in previous searches for FDM (green dashed, red dotted), the three cases outlined above in the current data (blue, orange, brown), and the observed dark matter density (purple, dashed). Where the three full lines dip below the purple, the two data sets are in tension so FDM is unlikely to be 100% of the dark matter present. 
Right: The vertical axis shows the ratio of dark matter that could be FDM and the total dark matter present, essentially equivalent to dividing the colored lines in the right figure with the purple dashed line. The horizontal dotted line shows where 100% of dark matter is FDM. All three colored lines have crossed above that threshold for particle masses above 10-23.3 eV, meaning that EPTA data is consistent with FDM in that region. 

Astrobite edited by William Lamb

Featured image credit: Luna Zagorac (The original pulsar data inside the surfboard is in “Radio Observations of the Pulse Profiles and Dispersion Measures of Twelve Pulsars,” by Harold D. Craft, Jr. )

About Luna Zagorac

I am a cosmology postdoc at the Perimeter Institute in Canada, thinking about all things non-baryonic, weird, and interdisciplinary. I got my PhD in physics from Yale University in 2022, where I was also a Franke Fellow in the Natural Sciences & Humanities working on a project on Egyptian archaeoastronomy, another passion of mine. When I’m not writing code or deciphering glyphs, I can usually be found reading, doodling, or drinking coffee.

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