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A Multi-Wavelength Investigation of the Radio-Loud Supernova PTF11qcj and its Circumstellar Environment

We present the discovery, classification, and extensive panchromatic (from radio to X-ray) follow-up observations of PTF11qcj, a supernova (SN) discovered by the Palomar Transient Factory (PTF). Our observations with the Karl G. Jansky Very Large Array show that this event is radio-loud: PTF11qcj reached a radio peak luminosity comparable to that of the famous gamma-ray-burst-associated SN 1998bw (L (sub 5 gigahertz) approximates 10 (sup 29) ergs per second per hertz). PTF11qcj is also detected in X-rays with the Chandra Observatory, and in the infrared band with Spitzer. Our multi-wavelength analysis probes the SN interaction with circumstellar material. The radio observations suggest a progenitor mass-loss rate of approximately 10 (sup -4) the mass of the sun per year times (v (sub omega) divided by 1000 kilometers per second), and a velocity of approximately 0.3-0.5 c (the speed of light in a vacuum) for the fastest moving ejecta (at around 10 days after explosion). However, these estimates are derived assuming the simplest model of SN ejecta interacting with a smooth circumstellar wind, and do not account for possible inhomogeneities in the medium and asphericity of the explosion. The radio data show deviations from such a simple model, as well as a late-time re-brightening. The X-ray flux from PTF11qcj is compatible with the high-frequency extrapolation of the radio synchrotron emission (within the large uncertainties). A light echo from pre-existing dust is in agreement with our infrared data. Our pre-explosion data from the PTF suggest that a precursor eruption of absolute magnitude M (sub r) approximately equal to -13 mag may have occurred approximately 2.5 years prior to the SN explosion. Overall, PTF11qcj fits the expectations from the explosion of a Wolf-Rayet star. Precursor eruptions may be a feature characterizing the final pre-explosion evolution of such stars.

Radio↗

New Horizons in Cosmology with Spectral Distortions of the Cosmic Microwave Background

Following the pioneering observations with COBE in the early 1990s, studies of the cosmic mi- crowave background (CMB) have primarily focused on temperature and polarization anisotropies. CMB spectral distortions – tiny departures of the CMB energy spectrum from that of a perfect blackbody – provide a second, independent probe of fundamental physics, with a reach deep into the primordial Universe. The theoretical foundation of spectral distortions has seen major advances in recent years, highlighting the immense potential of this emerging field. Spectral distortions probe a fundamental property of the Universe – its thermal history – thereby providing additional insight into processes within the cosmological standard model(I) (CSM) as well as new physics beyond. Spectral distortions are an important tool for understanding inflation and the nature of dark matter. They shed new light on the physics of recombination and reionization, both prominent stages in the evolution of our Universe, and furnish critical information on baryonic feedback processes, in addition to probing primordial correlation functions at scales inaccessible to other tracers. In principle the range of signals is vast: many orders of magnitude of discovery space can be explored by detailed observations of the CMB energy spectrum. Several CSM signals are predicted and provide clear experimental targets that are observable with present-day technology. Confirmation of these signals would extend the reach of the CSM by orders of magnitude in physical scale as the Universe evolves from the initial stages to its present form. Their absence would pose a huge theoretical challenge, immediately pointing to new physics. Here, we advocate for a dedicated effort to measure CMB spectral distortions at the largest angular scales (greater than approximately 1°) within the ESA Voyage 2050 Program. We argue that an L-class mission with a pathfinder would allow a precise measurement of all the expected CSM distortions. With an M-class mission, the primordial distortions (created at z >~ 10(exp 3)) would still be detected at modest significance, while the late-time distortions will continue to be measured to high accuracy. Building on the heritage of COBE/FIRAS, a spectrometer that consists of multiple, cooled (approximately equal to 0.1 K), absolutely-calibrated Fourier Transform Spectrometers (FTS) with wide frequency coverage (ν approximately equal to 10 GHz to a few x THz) and all-sky spectral sensitivity at the level of 0.1 0.5 Jy/sr would be the starting point for the M-class option. A scaled and further optimized version of this concept is being envisioned as the L-class option. Such measurements can only be done from space and would deliver hundreds of absolutely-calibrated maps of the Universe at large scales, opening numerous science opportunities for cosmology and astrophysics. This will provide independent probes of inflation, dark matter and particle physics, recombination and the energy output of our Universe from at late times, turning the long-standing spectral distortion limits of COBE/FIRAS into clear detections.

Chluba, J.↗

Discovery of Highly Blueshifted Broad Balmer and Metastable Helium Absorption Lines in a Tidal Disruption Event

We report the discovery of nonstellar hydrogen Balmer and metastable helium absorption lines accompanying a transient, high-velocity (0.05c) broad absorption line (BAL) system in the optical spectra of the tidal disruption event (TDE) AT2018zr (z = 0.071). In the Hubble Space Telescope UV spectra, absorption of high- and low-ionization lines is also present at this velocity, making AT2018zr resemble a low-ionization BALQSO. We conclude that these transient absorption features are more likely to arise in fast outflows produced by the TDE than absorbed by the unbound debris. In accordance with the outflow picture, we are able to reproduce the flat-topped Hα emission in a spherically expanding medium without invoking the typical prescription of an elliptical disk. We also report the appearance of narrow (~1000 kms(exp −1)) N III λ4640, He II λ4686, Hα, and Hβ emission in the late-time optical spectra of AT2018zr, which may be a result of UV continuum hardening at late times, as observed by Swift. Including AT2018zr, we find a high association rate (three out of four) of BALs in the UV spectra of TDEs. This suggests that outflows may be ubiquitous among TDEs and less sensitive to viewing angle effects compared to QSO outflows.

Hung, T.↗

Spitzer Microlensing of MOA-2016-BLG-231L: A Counter-rotating Brown Dwarf Binary in the Galactic Disk

We analyze the binary microlensing event MOA-2016-BLG-231, which was observed from the ground and from Spitzer. The lens is composed of very-low-mass brown dwarfs (BDs) with M(1)= 21(+12, -5) M(J) and M(2)=9(+5. -2) M(J), and it is located in the Galactic disk D(L)=2.85(+0.88, -0.50) kpc. This is the fifth binary brown dwarf discovered by microlensing, and the BD binary is moving counter to the orbital motion of disk stars. Constraints on the lens physical properties come from late-time, non-caustic-crossing features of the Spitzer light curve. Thus, MOA-2016-BLG-231 shows how Spitzer plays a crucial role in resolving the nature of BDs in binary BD events with short timescales (≲10 days).

Sun-Ju Chung↗

Discovery of a Fast Iron Low-ionization Outflow in the Early Evolution of the Nearby Tidal Disruption Event AT 2019qiz

We report the results of ultraviolet (UV) and optical photometric and spectroscopic analysis of the tidal disruption event (TDE) AT 2019qiz. Our follow-up observations started <10 days after the source began to brighten in the optical and lasted for a period of six months. Our late-time host-dominated spectrum indicates that the host galaxy likely harbors a weak active galactic nucleus. The initial Hubble Space Telescope (HST) spectrum of AT 2019qiz exhibits an iron and low-ionization broad absorption line (FeLoBAL) system that is seen for the first time in a TDE. This spectrum also bears a striking resemblance to that of Gaia16apd, a superluminous supernova. Our observations provide insights into the outflow properties in TDEs and show evidence for a connection between TDEs and engine-powered supernovae at early phases, as originally suggested by Metzger & Stone (2016). In a time frame of 50 days, the UV spectra of AT 2019qiz started to resemble those of previous TDEs with only high-ionization BALs. The change in UV spectral signatures is accompanied by a decrease in the outflow velocity, which began at 15,000 km/s and decelerated to ~ 10,000 km/s. A similar evolution in the Ha emission-line width further supports the speculation that the broad Balmer emission lines are formed in TDE outflows. In addition, we detect narrow absorption features on top of the FeLoBAL signatures in the early HST UV spectrum of AT 2019qiz. The measured H I column density corresponds to a Lyman-limit system, whereas the metal absorption lines (such as N V, C IV, Fe II, and Mg II) are likely probing the circumnuclear gas and interstellar medium in the host galaxy.

Tiara Hung↗

A Year in the Life of GW 170817: The Rise and Fall of a Structured Jet from a Binary Neutron Star Merger

We present the results of our year-long afterglow monitoring of GW 170817, the first binary neutron star merger detected by Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) and Advanced Virgo. New observations with the Australian Telescope Compact Array and the Chandra X-ray Telescope were used to constrain its late-time behaviour. The broad-band emission, from radio to X-rays, is well-described by a simple power-law spectrum with index β ∼ 0.585 at all epochs. After an initial shallow rise ∝t0.9, the afterglow displayed a smooth turnover, reaching a peak X-ray luminosity of LX ≈ 5 × 1039 erg s−1 at 160 d, and has now entered a phase of rapid decline, approximately ∝t−2. The latest temporal trend challenges most models of choked jet/cocoon systems, and is instead consistent with the emergence of a relativistic structured jet seen at an angle of ≈22◦ from its axis. Within such model, the properties of the explosion (such as its blast wave energy EK ≈ 2 × 1050 erg, jet width θc ≈ 4◦, and ambient density n ≈ 3 × 10−3 cm−3) fit well within the range of properties of cosmological short gamma-ray bursts.

Acceleration of particles↗

The case for a high-redshift origin of GRB100205A

The number of long gamma-ray bursts (GRBs) known to have occurred in the distant Universe (z>5) is small (∼15); however, these events provide a powerful way of probing star formation at the onset of galaxy evolution. In this paper, we present the case for GRB100205A being a largely overlooked high-redshift event. While initially noted as a high-z candidate, this event and its host galaxy have not been explored in detail. By combining optical and near-infrared Gemini afterglow imaging (at t < 1.3 d since burst) with deep late-time limits on host emission from the Hubble Space Telescope, we show that the most likely scenario is that GRB100205A arose in the range 4 < z<8. GRB100205A is an example of a burst whose afterglow, even at ∼1 h post burst, could only be identified by 8-m class IR observations, and suggests that such observations of all optically dark bursts may be necessary to significantly enhance the number of high-redshift GRBs known.

A A Chrimes↗

Caltech–NRAO Stripe 82 Survey (CNSS). III. The First Radio-discovered Tidal Disruption Event, CNSS J0019+00

We present the discovery of a nuclear transient with the Caltech–NRAO Stripe 82 Survey (CNSS), a dedicated radio transient survey carried out with the Karl G.Jansky Very Large Array (VLA). This transient, CNSS J001947.3+003527, exhibited a turn-on over a timescale of <~1 yr, increasing in flux density at 3 GHz from <0.14 mJy in 2014 February to 4.4 ± 0.1 mJy in 2015 March, reaching a peak luminosity of 5 x 10^28 erg s-1 Hz-1 around 2015 October. The association of CNSS J0019+00 with the nucleus (Gaia and our very-long baseline interferometry positions are consistent to within 1 pc) of a nearby S0 Seyfert galaxy at 77 Mpc, together with the radio spectral evolution, implies that this transient is most likely a tidal disruption event (TDE). Our equipartition analysis indicates the presence of a ∼15,000 km s−1 outflow, having energy ∼1049 erg. We derive the radial density profile for the circumnuclear material in the host galaxy to be proportional to R−2.5. All of these properties suggest resemblance with radio-detected thermal TDEs like ASASSN-14li and XMMSL1 J0740-85. No significant X-ray or optical emission is detected from CNSS J0019+00, although this may simply be due to the thermal emission being weak during our late-time follow-up observations. From the CNSS survey we have obtained the first unbiased measurement of the rate of radio TDEs, R(>500μJy) of about 2 × 10−3 deg−2, or equivalently a volumetric rate of about 10 Gpc−3 yr−1. This rate implies that all-sky radio surveys such as the VLA Sky Survey and those planned with ASKAP, will find many tens of radio TDEs over the next few years.

M M Anderson↗

Evidence for Late-stage Eruptive Mass Loss in the Progenitor to SN2018gep, a Broad-lined Ic Supernova: Pre-explosion Emission and a Rapidly Rising Luminous Transient

We present detailed observations of ZTF18abukavn (SN2018gep), discovered in high-cadence data from the Zwicky Transient Facility as a rapidly rising (1.4 ± 0.1 mag/hr) and luminous (M(g,peak) = -20 mag) transient. It is spectroscopically classified as a broad-lined stripped-envelope supernova (Ic-BL SN). The high peak luminosity (L(bol) ≳ 3 x 10^(44) erg/s), the short rise time (t = 3 days rise in g band), and the blue colors at peak (g–r ~ -0.4) all resemble the high-redshift Ic-BL iPTF16asu, as well as several other unclassified fast transients. The early discovery of SN2018gep (within an hour of shock breakout) enabled an intensive spectroscopic campaign, including the highest-temperature (T(eff) ≳ 40,000 K) spectra of a stripped-envelope SN. A retrospective search revealed luminous (M(g) ~ M(r) ≈ -14 mag) emission in the days to weeks before explosion, the first definitive detection of precursor emission for a Ic-BL. We find a limit on the isotropic gamma-ray energy release E(γ,iso) < 4.9 x 10^(48) erg, a limit on X-ray emission L(X) < 10^(40) erg/s, and a limit on radio emission vL(v) ≲ 10^(37) erg/s. Taken together, we find that the early (<10 days) data are best explained by shock breakout in a massive shell of dense circumstellar material (0.02 Mꙩ) at large radii (3 x 10^(14) cm) that was ejected in eruptive pre-explosion mass-loss episodes. The late-time (>10 days) light curve requires an additional energy source, which could be the radioactive decay of Ni-56.

Anna Y. Q. Ho↗

IQ Collaboratory. II. The Quiescent Fraction of Isolated, Low-mass Galaxies across Simulations and Observations

We compare three major large-scale hydrodynamical galaxy simulations (EAGLE, Illustris-TNG, and SIMBA) by forward modeling simulated galaxies into observational space and computing the fraction of isolated and quiescent low-mass galaxies as a function of stellar mass. Using SDSS as our observational template, we create mock surveys and synthetic spectroscopic and photometric observations of each simulation, adding realistic noise and observational limits. All three simulations show a decrease in the number of quiescent, isolated galaxies in the mass range M * = 10 9−10 M ꙩ , in broad agreement with observations. However, even after accounting for observational and selection biases, none of the simulations reproduce the observed absence of quiescent field galaxies below M * = 10 9 M ꙩ . We find that the low-mass quiescent populations selected via synthetic observations have consistent quenching timescales, despite an apparent variation in the late-time star formation histories. The effect of increased numerical resolution is not uniform across simulations and cannot fully mitigate the differences between the simulations and the observations. The framework presented here demonstrates a path toward more robust and accurate comparisons between theoretical simulations and galaxy survey observations, while the quenching threshold serves as a sensitive probe of feedback implementations.

Claire M. Dickey↗

First Demonstration of Early Warning Gravitational-wave Alerts

Gravitational-wave observations became commonplace in Advanced LIGO-Virgo's recently concluded third observing run. 56 nonretracted candidates were identified and publicly announced in near real time. Gravitational waves from binary neutron star mergers, however, remain of special interest since they can be precursors to high-energy astrophysical phenomena like γ-ray bursts and kilonovae. While late-time electromagnetic emissions provide important information about the astrophysical processes within, the prompt emission along with gravitational waves uniquely reveals the extreme matter and gravity during—and in the seconds following—merger. Rapid communication of source location and properties from the gravitational-wave data is crucial to facilitate multimessenger follow-up of such sources. This is especially enabled if the partner facilities are forewarned via an early warning (pre-merger) alert. Here we describe the commissioning and performance of such a low-latency infrastructure within LIGO-Virgo. We present results from an end-to-end mock data challenge that detects binary neutron star mergers and alerts partner facilities before merger. We set expectations for these alerts in future observing runs.

Ryan Magee↗

Spitzer’s Last Look at Extragalactic Explosions: Long-Term Evolution of Interacting Supernovae

Here we present new, yet final, mid-infrared (mid-IR) data for supernovae (SNe) based on measurements with the Spitzer Space Telescope. Comparing our recent 3.6 and 4.5 μm photometry with previously published mid-IR and further multiwavelength data sets, we were able to draw some conclusions about the origin and heating mechanism of the dust in these SNe or in their environments, as well as about possible connection with circumstellar matter (CSM) originating from pre-explosion mass-loss events in the progenitor stars. We also present new results regarding both certain SN classes and single objects. We highlight the mid-IR homogeneity of SNe Ia-CSM, which may be a hint of their common progenitor type and of their basically uniform circumstellar environments. Regarding single objects, it is worth highlighting the late-time interacting Type Ib SNe 2003gk and 2004dk, for which we present the first-ever mid-IR data, which seem to be consistent with clues of ongoing CSM interaction detected in other wavelength ranges. Our current study suggests that long-term mid-IR follow-up observations play a key role in a better understanding of both pre- and post-explosion processes in SNe and their environments. While Spitzer is not available anymore, the expected unique data from the James Webb Space Telescope, as well as long-term near-IR follow-up observations of dusty SNe, can bring us closer to the hidden details of this topic.

Supernovae↗

DECADE+DES Y3 Weak Lensing Mass Map: A 13,000 deg$^2$ View of Cosmic Structure from 270 Million Galaxies

We present the largest galaxy weak lensing mass map of the late-time Universe, reconstructed from 270 million galaxies in the DECADE and DES Year 3 datasets, covering 13,000 square degrees. We validate the map through systematic tests against observational conditions (depth, seeing, etc.), finding the map is statistically consistent with no contamination. The large area covered by the mass map makes it a well-suited tool for cosmological analyses, cross-correlation studies and the identification of large-scale structure features. We demonstrate its potential by detecting cosmic filaments directly from the mass map for the first time and validating them through their association with galaxy clusters selected using the Sunyaev-Zeldovich effect from Planck and ACT DR6.

Gatti, M. [Chicago U., KICP] (ORCID:00000001613487↗

SPT-3G D1: A Measurement of Secondary Cosmic Microwave Background Anisotropy Power

We report new measurements of millimeter-wave temperature power spectra in the angular multipole range $1700 \le \ell \le 11,000$ (wavelengths $13^\prime \gtrsim λ\gtrsim 2^\prime$). We use two years of data in three observing bands centered near 95, 150, and 220 GHz from the SPT-3G receiver on the South Pole Telescope that cover a 1646 deg$^2$ region of the Southern sky. Using the measured power spectra, we present constraints on the thermal and kinematic Sunyaev-Zel'dovich (SZ) effects, radio galaxies, and cosmic infrared background (CIB). We find that inferred SZ powers are dependent on the detailed modeling of the thermal SZ-CIB correlation, and to a lesser extent on the assumed angular dependence of the SZ spectra. We report constraints for simulation-based model templates as well as fits where the angular dependencies of the SZ and CIB power spectra are allowed to vary. In the latter case at $\ell=3000$, we find thermal SZ power at 143 GHz of $D_{3000}^{\rm tSZ} = 4.91\pm0.37\, μ{\rm K}^2$ and kinematic SZ power of $D_{3000}^{\rm kSZ} =1.75\pm0.86\, μ{\rm K}^2$. We use the measured kinematic SZ power to estimate the duration of reionization, noting that the reionization inferences are sensitive to the model choices and assumed level of homogeneous kinematic SZ power from the late-time universe. We find a 95% limit on the duration from an ionization fraction of 25% to 75% of $Δ^{50} z_{\rm re} <\,3.8$ based on a semi-analytic model, or a limit on the duration from an ionization fraction of 5% to 95% of $Δ^{90} z_{\rm re} <\,6.1$ based on the AMBER simulations.

Chaubal, P. [Melbourne U.]↗

Dynamical Dark Energy Imprints in the Lyman-Alpha Forest

The nature of dark energy (DE) remains elusive, even though it constitutes the dominant energy-density component of the Universe and drives the late-time acceleration of cosmic expansion. By combining measurements of the expansion history from baryon acoustic oscillations, supernova surveys, and cosmic microwave background data, the Dark Energy Spectroscopic Instrument (DESI) Collaboration has inferred that the DE equation of state may evolve over time. The profound implications of a time-variable, ``dynamical" DE (DDE) that departs from a cosmological constant motivate the need for independent observational tests. In this work, we use cosmological hydrodynamical simulations of structure formation to investigate how DDE affects the properties of the Lyman-Alpha ``forest'' of absorption features produced by neutral hydrogen in the cosmic web. We find that DDE models consistent with the DESI constraints induce a spectral tilt in the forest transmitted flux power spectrum, imprinting a scale- and redshift-dependent signature relative to standard Lambda-CDM cosmologies. These models also yield higher intergalactic medium temperatures and reduced Lyman-Alpha opacity compared to Lambda-CDM. We discuss the observational implications of these trends as potential avenues for independent confirmation of DDE.

Garza, Diego [UC, Santa Cruz, Inst. Part. Phys.] (↗

Constraining GREA, an alternative theory accounting for the present cosmic acceleration

The origin of the Universe's late-time accelerated expansion remains unknown. The General Relativistic Entropic Acceleration (GREA) theory offers a compelling alternative to $Λ$CDM, attributing cosmic acceleration to entropy growth associated with cosmic and black hole horizons, without invoking a cosmological constant. We test GREA against the latest DESI DR2 Baryon Acoustic Oscillations (BAO), multiple Type Ia supernova compilations (Union3, Pantheon$\texttt{+}$, DES-SN5YR), and cosmic microwave background (CMB) distance measurements. While GREA is not nested within $Λ$CDM, it achieves a comparable goodness-of-fit, highlighting its potential as a theoretically motivated framework that circumvents some of the fine-tuning issues of the standard $Λ$CDM cosmology. We find that the best-fit model features a transient phantom crossing at $z \lesssim 2$, with $w_a\equiv \mathrm{d} w(a=1)/\mathrm{d}a \simeq-0.3$, in good agreement with observations. However, its present-day value $w_0\equiv w(z=0)$ is tightly constrained to be $w_0\simeq-1$. Upcoming low-redshift (i.e. $z < 1$) cosmological probes, from both background and perturbations, will offer promising avenues for further exploring the viability of the GREA theory.

Calderon, R. [Prague, Inst. Phys.] (ORCID:00000002↗

Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $Ω_\text{m}=0.312^{+0.018}_{-0.024}$, $σ_8=0.777\pm 0.024$, $S_8\equiv σ_8 \sqrt{Ω_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $Ω_\text{m}=0.353^{+0.025}_{-0.031}$, $σ_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$σ$), and in significant tension with results from eROSITA clusters (2.9$σ$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.

Aymerich, G. [Orsay, IAS; AIM, Saclay] (ORCID:0009↗

Neutrinos as Dark Matter

Active neutrinos in standard cosmology were ruled out as a dark matter candidate in the 1980's. The reason is twofold: they are too light to account for the observed energy density of dark matter in the Universe, and their relativistic nature would spoil structure formation. In this note we suggest that an enhanced density of cold Standard Model active neutrinos today could behave effectively as dark matter, avoiding constraints from recombination and structure formation. Such an enhancement could be produced, for instance, by late-time decays of a light scalar field that is not in thermal equilibrium with the plasma. This mechanism is testable through the detection of the Cosmic Neutrino Background (C$\nu$B), which could have an average cosmological energy density a factor of $\sim 100-200$ times larger than expected in $\Lambda$CDM. The postulated light neutrinophilic scalar field may be observable, with Yukawa couplings in the range $y \sim 5 \times 10^{-16}-10^{-12}$. A scenario preferred by structure formation constraints is that the scalar is a Majoron, and the neutrinos have an inverted mass hierarchy.

Cline, James M. [McGill U.] (ORCID:000000017437419↗