We have obtained optical and near-infrared spectra of candidate members of the star-forming clusters IC 348 and NGC 1333. We classify 100 and 42 candidates as new members of the clusters, respectively, which brings the total numbers of known members to 478 and 203. We also have performed spectroscopy on a large majority of the previously known members of NGC 1333 in order to provide spectral classifications that are measured with the same scheme that has been applied to IC 348 in previous studies. The new census of members is nearly complete for K s < 16.8 at A J < 1.5 in IC 348 and for K s < 16.2 at A J < 3 in NGC 1333, which correspond to masses of 0.01 M ⊙ for ages of 3 Myr according to theoretical evolutionary models. The faintest known members extend below these completeness limits and appear to have masses of ∼0.005 M ⊙ . In extinction-limited samples of cluster members, NGC 1333 exhibits a higher abundance of objects at lower masses than IC 348. It would be surprising if the initial mass functions of these clusters differ significantly given their similar stellar densities and formation environments. Instead, it is possible that average extinctions are lower for less massive members of star-forming clusters, in which case extinction-limited samples could be biased in favor of low-mass objects in the more heavily embedded clusters like NGC 1333. In the H-R diagram, the median sequences of IC 348 and NGC 1333 coincide with each other for the adopted distances of 300 and 235 pc, which would suggest that they have similar ages. However, NGC 1333 is widely believed to be younger than IC 348 based on

Previous studies have found that ∼1deg2 fields surrounding the stellar aggregates in the Taurus star-forming region exhibit a surplus of solar-mass stars relative to denser clusters like IC348 and the Orion Nebula Cluster. To test whether this difference reflects mass segregation in Taurus or a variation in the initial mass function, we have performed a survey for members of Taurus across a large field (∼40 deg 2 ) that was imaged by the Sloan Digital Sky Survey (SDSS). We obtained optical and near-infrared spectra of candidate members identified with those images and the Two Micron All Sky Survey, as well as miscellaneous candidates that were selected with several other diagnostics of membership. We have classified 22 of the candidates as new members of Taurus, which includes one of the coolest known members (M9.75). Our updated census of members within the SDSS field shows a surplus of solar-mass stars relative to clusters, although it is less pronounced than in the smaller fields toward the stellar aggregates that were surveyed for previously measured mass functions in Taurus. In addition to spectra of our new members, we include in our study near-IR spectra of roughly half of the known members of Taurus, which are used to refine their spectral types and extinctions. We also present an updated set of near-IR standard spectra for classifying young stars and brown dwarfs at M and L types.

Although the gravitational waves observed by advanced LIGO and Virgo are consistent with compact binaries in a quasi-circular inspiral prior to coalescence, eccentric inspirals are also expected to occur in Nature. Due to their complexity, we currently lack ready-to-use, analytic waveforms in the Fourier domain valid for sufficiently high eccentricity, and such models are crucial to coherently extract weak signals from the noise. We here take the first steps to derive and properly validate an analytic waveform model in the Fourier domain that is valid for inspirals of arbitrary orbital eccentricity. As a proof-of-concept, we build this model to leading post-Newtonian order by combining the stationary phase approximation, a truncated sum of harmonics, and an analytic representation of hypergeometric functions. Through comparisons with numerical post-Newtonian waveforms, we determine how many harmonics are required for a faithful (matches above 99%) representation of the signal up to orbital eccentricities as large as 0.9. As a first byproduct of this analysis, we present a novel technique to maximize the match of eccentric signals over time of coalescence and phase at coalescence. As a second byproduct, we determine which of the different approximations we employ leads to the largest loss in match, which could be used to systematically improve the model because of our analytic control. The future extension of this model to higher post-Newtonian order will allow for an accurate and fast phenomenological hybrid that can account for arbitrary eccentricity inspirals and mergers.PACS numbers: 04.30.-w,04.25.-g,04.25.Nx 1 The post-Newtonian approximation is one in which the field equations are solved assuming small velocities and weak gravitational fields in an expansion in powers of ( v c ), where v is the orbital velocity and c is the speed of light [20]. By nPN order we mean an expansion to order (v/c) 2n . arXiv:1807.07163v1 [gr-qc]

In [1], we developed a parameterized post-Einsteinian (ppE) model for the evolution of gravitational wave (GW) bursts from highly eccentric binary systems in time-frequency space. We here correct a few mistakes in some ingredients of the model. I. KEPLER PROBLEM IN THE PPE FORMALISMAs part of the computation of a ppE burst model, we considered an effective one body description for binary systems with generic modifications to the Newtonian potential. We claimed that the Newtonian potential within a generic modified theory of gravity can be written as shown in Eq. (B1) of [1], where the corrections scale as M/r p , with M the total mass of the binary and r p the pericenter distance of the binary. While the derivations in Appendix B of [1] are self-consistent, this scaling of the corrections is not suitable for some modified theories. We here generalize the results of this appendix to allow the model to apply to a wider set of theories.For equatorial orbits, the corrections to the Newtonian kinetic energy and gravitational potential within a modified theory of gravity may be written aswhere µ is the reduce mass of the binary, (α,β,γ) are amplitude parameters that depend on the coupling constants of the theory, and (ã,b,c) ∈ R that control the post-Newtonian (PN With this potential, we now compute the corrections to orbital quantities necessary to construct the ppE burst model, namely the orbital energy, angular momentum, period, and pericenter velocity. Let us begin by considering the Lagrangian for the binary within an effective one-body formalism. At leading (Newtonian) PN order, the Lagrangian for equatorial orbits may be written as L = T − U , with T = (1/2)µ(ṙ 2 + r 2φ2 ) + δT and U = −µM/r + δU . This Lagrangian admits two conserved quantities associated with the orbital energy and angular momentum, specificallyBy studying the turning points (ṙ = 0) of Eq. (3), and writing E = E N + δE and L = L N + δL, we findwith the Newtonian energy and angular momentum (E N , L N ) given in Eqs. (5.2) and (5.3) in [2], andThese deformations can be related to the generic deformation for the energy and angular momentum given in nonlinearity of the point particle Lagrangian, higher order terms in the velocity can couple to the modifications to the metric. Here, we are only concerned with the leading order terms, i.e. those that scale as v 2 × (α,β,γ). arXiv:1404.0092v3 [gr-qc] 2 Oct 20172 Eqs. (27) and (28) where LO stands for the leading-order term in a PN expansion. Now, let us consider the orbital period within our ppE formalism. In order to do this, it is useful to parametrize the radius of the orbit aswhere p = r p (1 + e) is the semi-latus rectum of the orbit and ψ increases monotonically by 2π from one pericenter passage to the next. The reason for this parametrization is that, in general, any deformation to the Newtonian potential will cause the orbits to precess [3], and as a result, the orbit will return to pericenter when φ = 2π + O (M/r p ). Using ψ to parameterize the orbit allows us to avoid complications from ...

While there has been much success in understanding the orbital dynamics and gravitational wave emission of eccentric compact binaries in the post-Newtonian formalism, some problems still remain. The largest of these concerns hereditary effects: non-linear phenomena related to the scattering off of the background curved spacetime (tails) and to the generation of gravitational waves by gravitational waves (memory). Currently, these hereditary effects are only known numerically for arbitrary eccentricity through infinite sums of Bessel functions, with closed-form, analytic results only available in the small eccentricity limit. We here calculate, for the first time, closed-form, analytic expressions for all hereditary effects to third post-Newtonian order in binaries with arbitrary eccentricity. For the tails, we first asymptotically expand all Bessel functions in high eccentricity and find a superasymptotic series for each enhancement factor, accurate to better than 10 −3 relative to post-Newtonian numerical calculations at all eccentricities. We further improve the small-eccentricity behavior of the superasymptotic series by generating hyperasymptotic expressions for each enhancement factor, typically accurate to better than 10 −8 at all eccentricities. For the memory, we discuss its computation within the context of an osculating approximation of the binary's orbit and the difficulties that arise. Our closed-form analytic expressions for the hereditary fluxes allow us to numerically compute orbital phases that are identical to those found using an infinite sum of Bessel functions to double numerical precision.