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1. Strongly Lensed Supermassive Black Hole Binaries as Nanohertz Gravitational-wave Sources

   https://doi.org/10.3847/1538-4357/ace16f  

   Khusid, Nicole M.; Mingarelli, Chiara M.; Natarajan, Priyamvada; Casey-Clyde, J. Andrew; Barnacka, Anna (September 2023, The Astrophysical Journal)

   Abstract Supermassive black hole binary systems (SMBHBs) should be the most powerful sources of gravitational waves (GWs) in the universe. Once pulsar timing arrays (PTAs) detect the stochastic GW background from their cosmic merger history, searching for individually resolvable binaries will take on new importance. Since these individual SMBHBs are expected to be rare, here we explore how strong gravitational lensing can act as a tool for increasing their detection prospects by magnifying fainter sources and bringing them into view. Unlike for electromagnetic waves, when the geometric optics limit is nearly always valid, for GWs the wave-diffraction-interference effects can become important when the wavelength of the GWs is larger than the Schwarzchild radius of the lens, i.e., $M_{\mathrm{lens}}\sim {10}^8{\left(\frac{f}{\mathrm{mHz}}\right)}^{-1}{M}_{\odot }$. For the GW frequency range explored in this work, the geometric optics limit holds. We investigate GW signals from SMBHBs that might be detectable with current and future PTAs under the assumption that quasars serve as bright beacons that signal a recent merger. Using the black hole mass function derived from quasars and a physically motivated magnification distribution, we expect to detect a few strongly lensed binary systems out toz≈ 2. Additionally, for a range of fixed magnifications 2 ≤μ≤ 100, strong lensing adds up to ∼30 more detectable binaries for PTAs. Finally, we investigate the possibility of observing both time-delayed electromagnetic signals and GW signals from these strongly lensed binary systems—that will provide us with unprecedented multi-messenger insights into their orbital evolution. 

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2. The NANOGrav 15 yr Data Set: Chromatic Gaussian Process Noise Models for Six Pulsars

   https://doi.org/10.3847/1538-4357/ad5291  

   Larsen, Bjorn; Mingarelli, Chiara_M F; Hazboun, Jeffrey S; Chalumeau, Aurélien; Good, Deborah C; Simon, Joseph; Agazie, Gabriella; Anumarlapudi, Akash; Archibald, Anne M; Arzoumanian, Zaven; et al (August 2024, The Astrophysical Journal)

   Abstract Pulsar timing arrays (PTAs) are designed to detect low-frequency gravitational waves (GWs). GWs induce achromatic signals in PTA data, meaning that the timing delays do not depend on radio frequency. However, pulse arrival times are also affected by radio-frequency-dependent “chromatic” noise from sources such as dispersion measure (DM) and scattering delay variations. Furthermore, the characterization of GW signals may be influenced by the choice of chromatic noise model for each pulsar. To better understand this effect, we assess if and how different chromatic noise models affect the achromatic noise properties in each pulsar. The models we compare include existing DM models used by the North American Nanohertz Observatory for Gravitational waves (NANOGrav) and noise models used for the European PTA Data Release 2 (EPTA DR2). We perform this comparison using a subsample of six pulsars from the NANOGrav 15 yr data set, selecting the same six pulsars as from the EPTA DR2 six-pulsar data set. We find that the choice of chromatic noise model noticeably affects the achromatic noise properties of several pulsars. This is most dramatic for PSR J1713+0747, where the amplitude of its achromatic red noise lowers from ${\log }_{10}{A}_{\mathrm{RN}}=-{14.1}_{-0.1}^{+0.1}$to $-{14.7}_{-0.5}^{+0.3}$, and the spectral index broadens from ${\gamma }_{\mathrm{RN}}={2.6}_{-0.4}^{+0.5}$to ${\gamma }_{\mathrm{RN}}={3.5}_{-0.9}^{+1.2}$. We also compare each pulsar's noise properties with those inferred from the EPTA DR2, using the same models. From the discrepancies, we identify potential areas where the noise models could be improved. These results highlight the potential for custom chromatic noise models to improve PTA sensitivity to GWs. 

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3. Host galaxy demographics of individually detectable supermassive black-hole binaries with pulsar timing arrays

   https://doi.org/10.1088/1361-6382/ad9131  

   Cella, Katharine; Taylor, Stephen R; Zoltan_Kelley, Luke (December 2024, Classical and Quantum Gravity)

   Abstract Massive black hole binaries (MBHBs) produce gravitational waves (GWs) that are detectable with pulsar timing arrays. We determine the properties of the host galaxies of simulated MBHBs at the time they are producing detectable GW signals. The population of MBHB systems we evaluate is from theIllustriscosmological simulations taken in tandem with post processing semi-analytic models of environmental factors in the evolution of binaries. Upon evolving to the GW frequency regime accessible by pulsar timing arrays, we calculate the detection probability of each system using a variety of different values for pulsar noise characteristics in a plausible near-future International Pulsar Timing Array dataset. We find that detectable systems have host galaxies that are clearly distinct from the overall binary population and from most galaxies in general. With conservative noise factors, we find that host stellar metallicity, for example, peaks at $\sim 2Z_{\odot }$as opposed to the total population of galaxies which peaks at $\sim 0.6Z_{\odot }$. Additionally, the most detectable systems are much brighter in magnitude and more red in color than the overall population, indicating their likely identity as large ellipticals with diminished star formation. These results can be used to develop effective search strategies for identifying host galaxies and electromagnetic counterparts following GW detection by pulsar timing arrays. 

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4. On the overlap reduction function of pulsar timing array searches for gravitational waves in modified gravity

   https://doi.org/10.1088/1361-6382/ad9881  

   Cordes, Nina; Mitridate, Andrea; Schmitz, Kai; Schröder, Tobias; Wassner, Kim (December 2024, Classical and Quantum Gravity)

   Abstract Pulsar timing array (PTA) searches for gravitational waves (GWs) aim to detect a characteristic correlation pattern in the timing residuals of galactic millisecond pulsars. This pattern is described by the PTA overlap reduction function (ORF) ${\mathrm{\Gamma }}_{ab}\left({\xi }_{ab}\right)$, which is known as the Hellings–Downs (HD) curve in general relativity (GR). In theories of modified gravity, the HD curve often receives corrections. Assuming, e.g. a subluminal GW phase velocity, one finds a drastically enhanced ORF in the limit of small angular separations between pulsaraand pulsarbin the sky, ${\xi }_{ab}\to 0$. In particular, working in harmonic space and performing an approximate resummation of all multipole contributions, the auto correlation coefficientΓ_aaseems to diverge. In this paper, we confirm that this divergence is unphysical and provide an exact and analytical expression forΓ_aain dependence of the pulsar distanceL_aand the GW phase velocity $v_{\mathrm{ph}}$. In the GR limit and assuming a large pulsar distance, our expression reduces to ${\mathrm{\Gamma }}_{aa}=1$. In the case of subluminal phase velocity, we show that the regularization of the naive divergent result is a finite-distance effect, meaning thatΓ_aascales linearly withfL_a, wherefis the GW frequency. For superluminal phase velocity (subluminal group velocity), which is relevant in the case of massive gravity, we correct an earlier analytical result forΓ_ab. Our results pave the way for fitting modified-gravity theories with nonstandard phase velocity to PTA data, which requires a proper understanding of the auto correlation coefficientΓ_aa. 

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5. Answers to frequently asked questions about the pulsar timing array Hellings and Downs curve

   https://doi.org/10.1088/1361-6382/ad4c4c  

   Romano, J D; Allen, B (July 2024, Classical and Quantum Gravity)

   Abstract We answer frequently asked questions (FAQs) about the Hellings and Downs correlation curve—the ‘smoking-gun’ signature that pulsar timing arrays (PTAs) have detected gravitational waves (GWs). Many of these questions arise from inadvertently applying intuition about the effects of GWs on LIGO-like detectors to the case of pulsar timing, where not all of it applies. This is because Earth-based detectors, like LIGO and Virgo, have arms that are short (km scale) compared to the wavelengths of the GWs that they detect ( $\approx {10}^2$–10⁴km). In contrast, PTAs respond to GWs whose wavelengths (tens of light-years) are much shorter than their arms (a typical PTA pulsar is hundreds to thousands of light-years from Earth). To demonstrate this, we calculate the time delay induced by a passing GW along an Earth-pulsar baseline (a ‘one-arm, one-way’ detector) and compare it in the ‘short-arm’ (LIGO-like) and ‘long-arm’ (PTA) limits. This provides qualitative and quantitative answers to many questions about the Hellings and Downs curve. The resulting FAQ sheet should help in understanding the ‘evidence for GWs’ recently announced by several PTA collaborations. 

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