A Gaussian process framework for modelling instrumental systematics: application to transmission spectroscopy

Transmission spectroscopy, which consists of measuring the wavelength-dependent absorption of starlight by a planet's atmosphere during a transit, is a powerful probe of atmospheric composition. However, the expected signal is typically orders of magnitude smaller than instrumental systematics, and the results are crucially dependent on the treatment of the latter. In this paper, we propose a new method to infer transit parameters in the presence of systematic noise using Gaussian processes, a technique widely used in the machine learning community for Bayesian regression and classification problems. Our method makes use of auxiliary information about the state of the instrument, but does so in a non-parametric manner, without imposing a specific dependence of the systematics on the instrumental parameters, and naturally allows for the correlated nature of the noise. We give an example application of the method to archival NICMOS transmission spectroscopy of the hot Jupiter HD 189733, which goes some way towards reconciling the controversy surrounding this dataset in the literature. Finally, we provide an appendix giving a general introduction to Gaussian processes for regression, in order to encourage their application to a wider range of problems.Comment: 6 figures, 1 table, accepted for publication in MNRA

X-Ray Observations of Black Widow Pulsars

We describe the first X-ray observations of five short orbital period ($P_B < 1$ day), $\gamma$-ray emitting, binary millisecond pulsars. Four of these, PSRs J0023+0923, J1124$-$3653, J1810+1744, and J2256$-$1024 are `black-widow' pulsars, with degenerate companions of mass $\ll0.1 M_{\odot}$, three of which exhibit radio eclipses. The fifth source, PSR J2215+5135, is an eclipsing `redback' with a near Roche-lobe filling $\sim$0.2 solar mass non-degenerate companion. Data were taken using the \textit{Chandra X-Ray Observatory} and covered a full binary orbit for each pulsar. Two pulsars, PSRs J2215+5135 and J2256$-$1024, show significant orbital variability while PSR J1124$-$3653 shows marginal orbital variability. The lightcurves for these three pulsars have X-ray flux minima coinciding with the phases of the radio eclipses. This phenomenon is consistent with an intrabinary shock emission interpretation for the X-rays. The other two pulsars, PSRs J0023+0923 and J1810+1744, are fainter and do not demonstrate variability at a level we can detect in these data. All five spectra are fit with three separate models: a power-law model, a blackbody model, and a combined model with both power-law and blackbody components. The preferred spectral fits yield power-law indices that range from 1.3 to 3.2 and blackbody temperatures in the hundreds of eV. The spectrum for PSR J2215+5135 shows a significant hard X-ray component, with a large number of counts above 2 keV, which is additional evidence for the presence of intrabinary shock emission and is similar to what has been detected in the low-mass X-ray binary to millisecond pulsar transition object PSR J1023+0038.Comment: 8 pages, 6 figures, 2 tables, submitted to Ap

Dyson-Schwinger Equations - aspects of the pion

The contemporary use of Dyson-Schwinger equations in hadronic physics is exemplified via applications to the calculation of pseudoscalar meson masses, and inclusive deep inelastic scattering with a determination of the pion's valence-quark distribution function.Comment: 4 pages. Contribution to the Proceedings of ``DPF 2000,'' the Meeting of the Division of Particles and Fields of the American Physical Society, August 9-12, 2000, Department of Physics, the Ohio State University, Columbus, Ohi

New insights into ultraluminous X-ray sources from deep XMM-Newton observations

The controversy over whether ultraluminous X-ray sources (ULXs) contain a new intermediate-mass class of black holes (IMBHs) remains unresolved. We present new analyses of the deepest XMM-Newton observations of ULXs that address their underlying nature. We examine both empirical and physical modelling of the X-ray spectra of a sample of thirteen of the highest quality ULX datasets, and find that there are anomalies in modelling ULXs as accreting IMBHs with properties simply scaled-up from Galactic black holes. Most notably, spectral curvature above 2 keV in several sources implies the presence of an optically-thick, cool corona. We also present a new analysis of a 100 ks observation of Holmberg II X-1, in which a rigorous analysis of the temporal data limits the mass of its black hole to no more than 100 solar masses. We argue that a combination of these results points towards many (though not necessarily all) ULXs containing black holes that are at most a few 10s of solar mass in size.Comment: 5 pages, 2 figures, to appear in the proceedings of "The X-ray Universe 2005", San Lorenzo de El Escorial (Spain), 26-30 September 200

New biostratigraphic, magnetostratigraphic and isotopic insights into the Middle Eocene Climatic Optimum in low latitudes

The Middle Eocene Climatic Optimum (MECO) was a warming event that interrupted the long-term Eocene cooling trend. While this event is well documented at high southern and mid-latitudes, it is poorly known from low latitudes and its timing and duration are not well constrained because of problems of hiati, microfossil preservation and weak magnetic polarity in key sedimentary sections. Here, we report the results of a study designed to improve the bio-, magneto- and chemostratigraphy of the MECO interval using high-resolution records from two low-latitude sections in the Atlantic Ocean, Ocean Drilling Program (ODP) Sites 1051 and 1260. We present the first detailed benthic foraminiferal stable isotope records of the MECO from the low latitudes as well as the biostratigraphic counts of Orbulinoides beckmanni and new magnetostratigraphic results. Our data demonstrate a ~ 750 kyr-long duration for the MECO characterized by increasing δ13C and decreasing δ18O, with minimum δ18O values lasting ~ 40 kyr at 40.1 Ma coincident with a short-lived negative δ13C excursion. Thereafter, δ18O and δ13C values recover rapidly. The shift to minimum δ18O values at 40.1 Ma is coincident with a marked increase in the abundance of the planktonic foraminifera O. beckmanni, consistent with its inferred warm-water preference. O. beckmanni is an important Eocene biostratigraphic marker, defining planktonic foraminiferal Zone E12 with its lowest and highest occurrences (LO and HOs). Our new records reveal that the LO of O. beckmanni is distinctly diachronous, appearing ~ 500 kyr earlier in the equatorial Atlantic than in the subtropics (40.5 versus 41.0 Ma). We also show that, at both sites, the HO of O. beckmanni at 39.5 Ma is younger than the published calibrations, increasing the duration of Zone E12 by at least 400 kyr. In accordance with the tropical origins of O. beckmanni, this range expansion to higher latitudes may have occurred in response to sea surface warming during the MECO and subsequently disappeared with cooling of surface waters

Pion electromagnetic form factor at spacelike momenta

A novel method is employed to compute the pion electromagnetic form factor, F_\pi(Q^2), on the entire domain of spacelike momentum transfer using the Dyson-Schwinger equation (DSE) framework in quantum chromodynamics (QCD). The DSE architecture unifies this prediction with that of the pion's valence-quark parton distribution amplitude (PDA). Using this PDA, the leading-order, leading-twist perturbative QCD result for Q^2 F_\pi(Q^2) underestimates the full computation by just 15% on Q^2>~8GeV^2, in stark contrast with the result obtained using the asymptotic PDA. The analysis shows that hard contributions to the pion form factor dominate for Q^2>~8GeV^2 but, even so, the magnitude of Q^2 F_\pi(Q^2) reflects the scale of dynamical chiral symmetry breaking, a pivotal emergent phenomenon in the Standard Model.Comment: 5 pages, 2 figures. To appear in Phys. Rev. Let