More Like this

1. Calculation of the Coulomb Self-Energy of a Spherical Surface with Uniform Surface Charge Density Using the Fourier Transform Method

   https://doi.org/10.1142/S2661339522500159  

   Ciftja, Orion (September 2022, The Physics Educator)

   Undergraduate students in upper levels of physics or engineering programs learn the theory of Fourier series and integral transform method from mathematics courses. Nevertheless, they rarely see the application of such a method to solving problems in calculus-based physics courses that deal with topics such as electrostatics or magnetism. In this work, we illustrate the utility of the Fourier transform method by considering and solving via such a technique a representative problem that arises in electrostatics. The chosen case study is that of a spherical surface with uniform surface charge density and the calculation of its electrostatic Coulomb self-energy. By solving this problem by using the Fourier transform technique we also draw attention to the pedagogical aspects of the treatment. In particular, we stress the point that the Fourier transform method should be treated at more depth in calculus-based physics courses for undergraduate students. 

   more » « less
2. Coulomb self-energy of a solid hemisphere with uniform volume charge density

   https://doi.org/10.1142/S0217984923500185  

   Ciftja, Orion (May 2023, Modern Physics Letters B)

   Calculation of the Coulomb self-energy of a solid hemisphere with uniform volume charge density represents a very challenging task. This system is an interesting example of a body that lacks spherical symmetry though it can be conveniently dealt with in spherical coordinates. In this work, we explain how to calculate the Coulomb self-energy of a solid hemisphere with uniform volume charge density by using a method that relies on the expansion of the Coulomb potential as an infinite series in terms of Legendre polynomials. The final result for the Coulomb self-energy of a uniformly charged solid hemisphere turns out to be quite simple. 

   more » « less
3. TDCOSMO: IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles

   https://doi.org/10.1051/0004-6361/202038861  

   Birrer, S.; Shajib, A. J.; Galan, A.; Millon, M.; Treu, T.; Agnello, A.; Auger, M.; Chen, G. C.-F.; Christensen, L.; Collett, T.; et al (November 2020, Astronomy & Astrophysics)

   null (Ed.)

   The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H 0 = 73.3 −1.8 +1.7 km s −1 Mpc −1 , describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H 0 . We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H 0 . Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H 0 = 74.5 −6.1 +5.6 km s −1 Mpc −1 . Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H 0 = 67.4 −3.2 +4.1 km s −1 Mpc −1 . This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H 0 . While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H 0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H 0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data. 

   more » « less
4. Dust Drift Timescales in Protoplanetary Disks at the Cusp of Gravitational Instability

   https://doi.org/10.3847/1538-4357/ad83cd  

   Williams, Jonathan_P; Painter, Caleb; Anderson, Alexa_R; Ribas, Alvaro (November 2024, The Astrophysical Journal)

   Abstract Millimeter emitting dust grains have sizes that make them susceptible to drift in protoplanetary disks due to the difference between their orbital speed and that of the gas. The characteristic drift timescale depends on the surface density of the gas. By comparing disk radius measurements from Atacama Large Millimeter/submillimeter Array CO and continuum observations at millimeter wavelengths, the gas surface density profile and dust drift time can be self-consistently determined. We find that profiles which match the measured dust mass have very short drift timescales, an order of magnitude or more shorter than the stellar age, whereas profiles for disks that are on the cusp of gravitational instability, defined via the minimum value of the Toomre parameter, $Q_{\min }\sim 1-2$, have drift timescales comparable to the stellar lifetime. This holds for disks with masses of dust ≳5M_⊕across a range of absolute ages from less than 1 Myr to over 10 Myr. The inferred disk masses scale with stellar mass as $M_{\mathrm{disk}}\approx M_{*}/5Q_{\min }$. This interpretation of the gas and dust disk sizes simultaneously solves two long standing issues regarding the dust lifetime and exoplanet mass budget, and suggests that we consider millimeter wavelength observations as a window into an underlying population of particles with a wide size distribution in secular evolution with a massive planetesimal disk. 

   more » « less
5. Coupled Disk-star Evolution in Galactic Nuclei and the Lifetimes of QPE Sources

   https://doi.org/10.3847/1538-4357/ad639e  

   Linial, Itai; Metzger, Brian_D (September 2024, The Astrophysical Journal)

   Abstract A modest fraction of the stars in galactic nuclei fed toward the central supermassive black hole (SMBH) approach on low-eccentricity orbits driven by gravitational-wave radiation (extreme mass ratio inspiral (EMRI)). In the likely event that a gaseous accretion disk is created in the nucleus during this slow inspiral (e.g., via an independent tidal disruption event (TDE)), star–disk collisions generate regular short-lived flares consistent with the observed quasiperiodic eruption (QPE) sources. We present a model for the coupled star-disk evolution, which self-consistently accounts for mass and thermal energy injected into the disk from stellar collisions and associated mass ablation. For weak collision/ablation heating, the disk is thermally unstable and undergoes limit-cycle oscillations, which modulate its properties and lead to accretion-powered outbursts on timescales of years to decades, with a time-averaged accretion rate ∼0.1Ṁ Edd. Stronger collision/ablation heating acts to stabilize the disk, enabling roughly steady accretion at the EMRI-stripping rate. In either case, the stellar destruction time through ablation, and hence the maximum QPE lifetime, is ∼10²–10³yr, far longer than fallback accretion after a TDE. The quiescent accretion disks in QPE sources may at the present epoch be self-sustaining and fed primarily by EMRI ablation. Indeed, the observed range of secular variability broadly matches those predicted for collision-fed disks. Changes in the QPE recurrence pattern following such outbursts, similar to that observed in GSN 069, could arise from temporary misalignment between the EMRI-fed disk and the SMBH equatorial plane as the former regrows its mass after a state transition. 

   more » « less