Spontaneous emission of radiation

“Spontaneous emission of radiation” calculates the rate of spontaneous electric-dipole emission of a photon by an excited atom or molecule. The calculation proceeds by using basic quantum mechanics (i.e. not using the short cuts of Chapter 19); it uses quantum electrodynamics but is not, on that account, particularly difficult. A 2p–1s transition in hydrogen is used as exemplar; the radiation is elliptically polarized. The spectral line profile (lineshape function) is approximately Lorentzian, but has a high-frequency cut-off, needed to prevent the power radiated from diverging. A radiation-induced frequency shift is negligible. The width of the line profile agrees with the Einstein A-coefficient. A high-frequency cut-off is shown to apply similarly in the derivation of Golden Rule Number Two.

Measuring and characterizing the line profile of HARPS with a laser frequency comb

Aims. We study the 2D spectral line profile of the High Accuracy Radial Velocity Planet Searcher (HARPS), measuring its variation with position across the detector and with changing line intensity. The characterization of the line profile and its variations are important for achieving the precision of the wavelength scales of 10−10 or 3.0 cm s−1 necessary to detect Earth-twins in the habitable zone around solar-like stars. Methods. We used a laser frequency comb (LFC) with unresolved and unblended lines to probe the instrument line profile. We injected the LFC light – attenuated by various neutral density filters – into both the object and the reference fibres of HARPS, and we studied the variations of the line profiles with the line intensities. We applied moment analysis to measure the line positions, widths, and skewness as well as to characterize the line profile distortions induced by the spectrograph and detectors. Based on this, we established a model to correct for point spread function distortions by tracking the beam profiles in both fibres. Results. We demonstrate that the line profile varies with the position on the detector and as a function of line intensities. This is consistent with a charge transfer inefficiency effect on the HARPS detector. The estimate of the line position depends critically on the line profile, and therefore a change in the line amplitude effectively changes the measured position of the lines, affecting the stability of the wavelength scale of the instrument. We deduce and apply the correcting functions to re-calibrate and mitigate this effect, reducing it to a level consistent with photon noise.

An optical spectroscopic and polarimetric study of the microquasar binary system SS 433

Aims. Our aim is to study the mass transfer, accretion environment, and wind outflows in the SS 433 system, concentrating on the so-called stationary lines. Methods. We used archival high-resolution (X-shooter) and low-resolution (EMMI) optical spectra, new optical multi-filter polarimetry, and low-resolution optical spectra (Liverpool Telescope), spanning an interval of a decade and a broad range of precessional and orbital phases, to derive the dynamical properties of the system. Results. Using optical interstellar absorption lines and H I 21 cm profiles, we derive E(B − V) = 0.86 ± 0.10, with an upper limit of E(B − V) = 1.8 ± 0.1 based on optical Diffuse Interstellar Bands. We obtain revised values for the ultraviolet and U band polarizations and polarization angles (PA), based on a new calibrator star at nearly the same distance as SS 433 that corrects the published measurement and yields the same PA as the optical. The polarization wavelength dependence is consistent with optical-dominating electron scattering with a Rayleigh component in U and the UV filters. No significant phase modulation was found for PA while there is significant variability in the polarization level. We fortuitously caught a flare event; no polarization changes were observed but we confirm the previously reported associated emission line variations. Studying profile modulation of multiple lines of H I, He I, O I, Na I, Si II, Ca II, Fe II with precessional and orbital phase, we derive properties for the accretion disk and present evidence for a strong disk wind, extending published results. Using transition-dependent systemic velocities, we probe the velocity gradient of the wind, and demonstrate that it is also variable on timescales unrelated to the orbit. Using the rotational velocity, around 140 ± 20 km s−1, a redetermined mass ratio q = 0.37 ± 0.04, and masses MX = 4.2 ± 0.4 M⊙, MA = 11.3 ± 0.6 M⊙, the radius of the A star fills – or slightly overfills – its Roche surface. We devote particular attention to the O I 7772 Å and 8446 Å lines, finding that they show different but related orbital and precessional modulation and there is no evidence for a circumbinary component. The spectral line profile variability can, in general, be understood with an ionization stratified outflow predicted by thermal wind modeling, modulated by different lines of sight through the disk produced by its precession. The wind can also account for an extended equatorial structure detected at long wavelength.

FIESTA – disentangling stellar variability from exoplanets in the Fourier domain

ABSTRACT We propose a new analysis methodology – FourIEr phase SpecTrum Analysis (FIESTA, or $\mathit {\Phi }$ESTA) – for the study of spectral line profile variability in Fourier space. The philosophy of $\mathit {\Phi }$ESTA is highlighted in its interpretation of a line deformation as various shifts of the composing Fourier modes. With this ability, $\mathit {\Phi }$ESTA excels in distinguishing the effects of a bulk shift in a line profile, from changes in a line profile shape. In other words, it can distinguish a radial velocity shift due to orbiting companions like planets, from an apparent radial velocity shift due to stellar variability (often referred to as ‘jitter’). Most importantly, it can quantify the radial velocity impact of stellar jitter on each epoch. Our simulations show that (compared to a model that does not account for stellar activity), $\mathit {\Phi }$ESTA can almost triple the fraction of planets recovered with orbital parameters measured to within 10 per cent of their input parameters, when extracting a 2 m s−1 amplitude planetary signal in the midst of ∼2 m s−1 amplitude starspot jitter for high signal-to-noise ratio (>200 pixel−1) data. $\mathit {\Phi }$ESTA can also be used to identify stellar activity related periods in a periodogram analysis and classify relative amplitudes of stellar jitter and planetary signals, with examples for the analysis of HARPS data of the active star HD 224789 and the active planet-host star HD 103720. In the end, we demonstrate that $\mathit {\Phi }$ESTA’s framework is working as well as other activity indicators in correlating with stellar jitter.

Effect of the Ions on the Electron Collision Operator through Electronic Trajectory Modification

We investigate the ion effect on the broadening of the spectral line profile by the free electrons collisions with the emitters in plasmas. We only considered the weak collisions’ contribution. This effect has a consequence on the trajectories of the free electrons through the electric microfield created by the ions of the plasma. Thanks to the Meijer’s functions, the calculation of the electronic Stark broadening is precisely established.