Joint Bayesian Estimation of Quasar Continua and the Lyman-Alpha Forest Flux Probability Distribution Function

We present a new Bayesian algorithm making use of Markov Chain Monte Carlo sampling that allows us to simultaneously estimate the unknown continuum level of each quasar in an ensemble of high-resolution spectra, as well as their common probability distribution function (PDF) for the transmitted Ly$\alpha$ forest flux. This fully automated PDF regulated continuum fitting method models the unknown quasar continuum with a linear Principal Component Analysis (PCA) basis, with the PCA coefficients treated as nuisance parameters. The method allows one to estimate parameters governing the thermal state of the intergalactic medium (IGM), such as the slope of the temperature-density relation $\gamma-1$, while marginalizing out continuum uncertainties in a fully Bayesian way. Using realistic mock quasar spectra created from a simplified semi-numerical model of the IGM, we show that this method recovers the underlying quasar continua to a precision of $\simeq7\%$ and $\simeq10\%$ at $z=3$ and $z=5$, respectively. Given the number of principal component spectra, this is comparable to the underlying accuracy of the PCA model itself. Most importantly, we show that we can achieve a nearly unbiased estimate of the slope $\gamma-1$ of the IGM temperature-density relation with a precision of $\pm8.6\%$ at $z=3$, $\pm6.1\%$ at $z=5$, for an ensemble of ten mock high-resolution quasar spectra. Applying this method to real quasar spectra and comparing to a more realistic IGM model from hydrodynamical simulations would enable precise measurements of the thermal and cosmological parameters governing the IGM, albeit with somewhat larger uncertainties given the increased flexibility of the model.Comment: 21 pages (+ Appendix), accepted at Ap

The Opacity of the Intergalactic Medium Measured Along Quasar Sightlines at z∼6z\sim 6

We publicly release a new sample of $34$ medium resolution quasar spectra at $5.77\leq z_{\rm em}\leq6.54$ observed with the Echellette Spectrograph and Imager (ESI) on the Keck telescope. This quasar sample represents an ideal laboratory to study the intergalactic medium (IGM) during the end stages of the epoch of reionization, and constrain the timing and morphology of the phase transition. For a subset of $23$ of our highest signal-to-noise ratio spectra (S/N$>7$, per $10\,{\rm km\,s^{-1}}$ pixel), we present a new measurement of the Lyman-$\alpha$ (Ly$\alpha$) forest opacity spanning the redshift range $4.8\lesssim z\lesssim6.3$. We carefully eliminate spectral regions that could be causing biases in our measurements due to additional transmitted flux in the proximity zone of the quasars, or extra absorption caused by strong intervening absorption systems along the line of sight. We compare the observed evolution of the IGM opacity with redshift to predictions from a hydrodynamical simulation with uniform ultraviolet background (UVB) radiation, as well as two semi-numerical patchy reionization models, one with a fluctuating UVB and another with a fluctuating temperature field. Our measurements show a steep rise in opacity at $z\gtrsim5.0$ and an increased scatter and thus support the picture of a spatially inhomogeneous reionization process, consistent with previous work. However, we measure significantly higher optical depths at $5.3\lesssim z\lesssim5.7$ than previous studies, which reduces the contrast between the highest opacity Gunn-Peterson troughs and the average opacity trend of the IGM, which may relieve some of the previously noted tension between these measurements and reionization models.Comment: accepted for publication at Ap

The Circular Velocity Curve of the Milky Way from 55 to 2525 kpc

We measure the circular velocity curve $v_{\rm c}(R)$ of the Milky Way with the highest precision to date across Galactocentric distances of $5\leq R \leq 25$ kpc. Our analysis draws on the $6$-dimensional phase-space coordinates of $\gtrsim 23,000$ luminous red-giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be $v_{\rm c}(R_{\odot}) = (229.0\pm0.2)\rm\,km\,s^{-1}$ with systematic uncertainties at the $\sim 2-5\%$ level. We find that the velocity curve is gently but significantly declining at $(-1.7\pm0.1)\rm\,km\,s^{-1}\,kpc^{-1}$, with a systematic uncertainty of $0.46\rm\,km\,s^{-1}\,kpc^{-1}$, beyond the inner $5$ kpc. We exclude the inner $5$ kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a non-axisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy's dark halo mass within the virial radius to be $M_{\rm vir} = (7.25\pm0.26)\cdot 10^{11}M_{\odot}$ and a local dark matter density of $\rho_{\rm dm}(R_{\odot}) = 0.30\pm0.03\,\rm GeV\,cm^{-3}$.Comment: Accepted for publication in ApJ. All data can be downloaded here: https://doi.org/10.5281/zenodo.146805

Unravelling 13 Billion Years of Cosmic History with Spectroscopic Studies: From the Milky Way to the Epoch of Reionization

In this thesis we trace the cosmic history from the Epoch of Reionization to the local universe by means of several spectroscopic studies. In the first part, we analyze $34$ quasar spectra at $5.8\lesssim z_{\rm em}\lesssim 6.5$ and measure the redshift evolution of the opacity of the intergalactic medium (IGM) within the Ly$\alpha$ as well as the Ly$\beta$ forest to set new constraints on the timing and morphology of the reionization epoch. We find evidence for an extended reionization process down to $z\sim 5$, and, while the observed scatter in the Ly$\alpha$ forest optical depth can be well reproduced by current state-of-the-art simulations including spatial fluctuations in the temperature field or the ultraviolet background, we find a strong mismatch between simulations and observations in the Ly$\beta$ forest opacity, suggesting an inversion of the thermal state of the post-reionization IGM. We also measure the sizes of the quasars' proximity zones, which are regions of enhanced ionization in the vicinity of the quasars, ionized by their own radiation. We find a dependency of the proximity zone sizes to the quasars' lifetime, which presents a novel method to estimate the lifetime of individual quasars, providing unprecedented constraints on the formation and growth of supermassive black holes in the early universe. We discover three quasars with very short lifetimes, i.e. $t_{\rm Q}\sim 10^4-10^5$~yr, that pose significant challenges to all current black hole formation theories. In the second part of this thesis we explore the structure and dynamics of the Milky Way. We develop a new data-driven model to determine precise parallaxes by combining multi-band photometry and spectroscopy to make global kinematic maps of our Galaxy from $\gtrsim 45,000$ luminous red giant stars with only $\lesssim 10\%$ parallax uncertainties. Our map extends to Galactocentric distances of $25$~kpc, well beyond the reach of parallax estimates by the \textit{Gaia} mission. Making use of these new spectrophotometric parallaxes, we determine the most precise measurement to date of the circular velocity curve of the Milky Way over a wide range of Galactocentric distances. Based on Jeans modeling in an axisymmetric gravitational potential we find that the velocity curve is gently but significantly declining

Spectrophotometric parallaxes with linear models: Accurate distances for luminous red-giant stars

With contemporary infrared spectroscopic surveys like APOGEE, red-giant stars can be observed to distances and extinctions at which Gaia parallaxes are not highly informative. Yet the combination of effective temperature, surface gravity, composition, and age - all accessible through spectroscopy - determines a giant's luminosity. Therefore spectroscopy plus photometry should enable precise spectrophotometric distance estimates. Here we use the APOGEE-Gaia-2MASS-WISE overlap to train a data-driven model to predict parallaxes for red-giant branch stars with $0<\log g\leq2.2$ (more luminous than the red clump). We employ (the exponentiation of) a linear function of APOGEE spectral pixel intensities and multi-band photometry to predict parallax spectrophotometrically. The model training involves no logarithms or inverses of the Gaia parallaxes, and needs no cut on the Gaia parallax signal-to-noise ratio. It includes an L1 regularization to zero out the contributions of uninformative pixels. The training is performed with leave-out subsamples such that no star's astrometry is used even indirectly in its spectrophotometric parallax estimate. The model implicitly performs a reddening and extinction correction in its parallax prediction, without any explicit dust model. We assign to each star in the sample a new spectrophotometric parallax estimate; these parallaxes have uncertainties of a few to 15 percent, depending on data quality, which is more precise than the Gaia parallax for the vast majority of targets, and certainly any stars more than a few kpc distance. We obtain 10-percent distance estimates out to heliocentric distances of $20\,$kpc, and make global maps of the Milky Way's disk.Comment: Submitted to ApJ, comments are welcome. All data can be downloaded here: https://doi.org/10.5281/zenodo.146805