Nonparametric Methods in Astronomy: Think, Regress, Observe -- Pick Any Three

Telescopes are much more expensive than astronomers, so it is essential to minimize required sample sizes by using the most data-efficient statistical methods possible. However, the most commonly used model-independent techniques for finding the relationship between two variables in astronomy are flawed. In the worst case they can lead without warning to subtly yet catastrophically wrong results, and even in the best case they require more data than necessary. Unfortunately, there is no single best technique for nonparametric regression. Instead, we provide a guide for how astronomers can choose the best method for their specific problem and provide a python library with both wrappers for the most useful existing algorithms and implementations of two new algorithms developed here.Comment: 19 pages, PAS

Object Classification in Astronomical Multi-Color Surveys

We present a photometric method for identifying stars, galaxies and quasars in multi-color surveys, which uses a library of >65000 color templates. The method aims for extracting the information content of object colors in a statistically correct way and performs a classification as well as a redshift estimation for galaxies and quasars in a unified approach. For the redshift estimation, we use an advanced version of the MEV estimator which determines the redshift error from the redshift dependent probability density function. The method was originally developed for the CADIS survey, where we checked its performance by spectroscopy. The method provides high reliability (6 errors among 151 objects with R<24), especially for quasar selection, and redshifts accurate within sigma ~ 0.03 for galaxies and sigma ~ 0.1 for quasars. We compare a few model surveys using the same telescope time but different sets of broad-band and medium-band filters. Their performance is investigated by Monte-Carlo simulations as well as by analytic evaluation in terms of classification and redshift estimation. In practice, medium-band surveys show superior performance. Finally, we discuss the relevance of color calibration and derive important conclusions for the issues of library design and choice of filters. The calibration accuracy poses strong constraints on an accurate classification, and is most critical for surveys with few, broad and deeply exposed filters, but less severe for many, narrow and less deep filters.Comment: 21 pages including 10 figures. Accepted for publication in Astronomy & Astrophysic

NICMOS Imaging of a Damped Lyman-alpha Absorber at z=1.89 toward LBQS 1210+1731 : Constraints on Size and Star Formation Rate

We report results of a high-resolution imaging search (in rest frame H-$\alpha$ and optical continuum) for the galaxy associated with the damped Lyman-$\alpha$ (DLA) absorber at $z=1.892$ toward the $z_{em}=2.543$ quasar LBQS 1210+1731, using HST/NICMOS. After PSF subtraction, a feature is seen in both the broad-band and narrow-band images, at a projected separation of 0.25\arcsec from the quasar. If associated with the DLA, the object would be $\approx 2-3$ $h_{70}^{-1}$ kpc in size with a flux of $9.8 \pm 2.4$ $\mu$Jy in the F160W filter, implying a luminosity at $\lambda_{central}=5500$ {\AA} in the rest frame of $1.5 \times 10^{10}$ $h_{70}^{-2}$ L$_{\odot}$ at $z=1.89$, for $q_{0}=0.5$. However, no significant H-$\alpha$ emission is seen, suggesting a low star formation rate (SFR) (3 $\sigma$ upper limit of 4.0 $h_{70}^{-2}$ M$_{\odot}$ yr$^{-1}$), or very high dust obscuration. Alternatively, the object may be associated with the host galaxy of the quasar. H-band images obtained with the NICMOS camera 2 coronagraph show a much fainter structure $\approx 4-5$ $h_{70}^{-1}$ kpc in size and containing four knots of continuum emission, located 0.7\arcsec away from the quasar. We have probed regions far closer to the quasar sight-line than in most previous studies of high-redshift intervening DLAs. The two objects we report mark the closest detected high-redshift DLA candidates yet to any quasar sight line. If the features in our images are associated with the DLA, they suggest faint, compact, somewhat clumpy objects rather than large, well-formed proto-galactic disks or spheroids.Comment: 52 pages of text, 19 figures, To be published in Astrophysical Journal (accepted Dec. 8, 1999

The Lyman-alpha Forest Power Spectrum from the Sloan Digital Sky Survey

We measure the power spectrum, P_F(k,z), of the transmitted flux in the Ly-alpha forest using 3035 high redshift quasar spectra from the Sloan Digital Sky Survey. This sample is almost two orders of magnitude larger than any previously available data set, yielding statistical errors of ~0.6% and ~0.005 on, respectively, the overall amplitude and logarithmic slope of P_F(k,z). This unprecedented statistical power requires a correspondingly careful analysis of the data and of possible systematic contaminations in it. For this purpose we reanalyze the raw spectra to make use of information not preserved by the standard pipeline. We investigate the details of the noise in the data, resolution of the spectrograph, sky subtraction, quasar continuum, and metal absorption. We find that background sources such as metals contribute significantly to the total power and have to be subtracted properly. We also find clear evidence for SiIII correlations with the Ly-alpha forest and suggest a simple model to account for this contribution to the power. While it is likely that our newly developed analysis technique does not eliminate all systematic errors in the P_F(k,z) measurement below the level of the statistical errors, our tests indicate that any residual systematics in the analysis are unlikely to affect the inference of cosmological parameters from P_F(k,z). These results should provide an essential ingredient for all future attempts to constrain modeling of structure formation, cosmological parameters, and theories for the origin of primordial fluctuations.Comment: 92 pages, 45 of them figures, submitted to ApJ, data available at http://feynman.princeton.edu/~pmcdonal/LyaF/sdss.htm

Detection of Ly\beta auto-correlations and Ly\alpha-Ly\beta cross-correlations in BOSS Data Release 9

The Lyman-$\beta$ forest refers to a region in the spectra of distant quasars that lies between the rest-frame Lyman-$\beta$ and Lyman-$\gamma$ emissions. The forest in this region is dominated by a combination of absorption due to resonant Ly$\alpha$ and Ly$\beta$ scattering. When considering the 1D Ly$\beta$ forest in addition to the 1D Ly$\alpha$ forest, the full statistical description of the data requires four 1D power spectra: Ly$\alpha$ and Ly$\beta$ auto-power spectra and the Ly$\alpha$-Ly$\beta$ real and imaginary cross-power spectra. We describe how these can be measured using an optimal quadratic estimator that naturally disentangles Ly$\alpha$ and Ly$\beta$ contributions. Using a sample of approximately 60,000 quasar sight-lines from the BOSS Data Release 9, we make the measurement of the one-dimensional power spectrum of fluctuations due to the Ly$\beta$ resonant scattering. While we have not corrected our measurements for resolution damping of the power and other systematic effects carefully enough to use them for cosmological constraints, we can robustly conclude the following: i) Ly$\beta$ power spectrum and Ly$\alpha$-Ly$\beta$ cross spectra are detected with high statistical significance; ii) the cross-correlation coefficient is $\approx 1$ on large scales; iii) the Ly$\beta$ measurements are contaminated by the associated OVI absorption, which is analogous to the SiIII contamination of the Ly$\alpha$ forest. Measurements of the Ly$\beta$ forest will allow extension of the usable path-length for the Ly$\alpha$ measurements while allowing a better understanding of the physics of intergalactic medium and thus more robust cosmological constraints.Comment: 26 pages, 10 figures; matches version accepted by JCA

The intergalactic medium thermal history at redshift z=1.7--3.2 from the Lyman alpha forest: a comparison of measurements using wavelets and the flux distribution

We investigate the thermal history of the intergalactic medium (IGM) in the redshift interval z=1.7--3.2 by studying the small-scale fluctuations in the Lyman alpha forest transmitted flux. We apply a wavelet filtering technique to eighteen high resolution quasar spectra obtained with the Ultraviolet and Visual Echelle Spectrograph (UVES), and compare these data to synthetic spectra drawn from a suite of hydrodynamical simulations in which the IGM thermal state and cosmological parameters are varied. From the wavelet analysis we obtain estimates of the IGM thermal state that are in good agreement with other recent, independent wavelet-based measurements. We also perform a reanalysis of the same data set using the Lyman alpha forest flux probability distribution function (PDF), which has previously been used to measure the IGM temperature-density relation. This provides an important consistency test for measurements of the IGM thermal state, as it enables a direct comparison of the constraints obtained using these two different methodologies. We find the constraints obtained from wavelets and the flux PDF are formally consistent with each other, although in agreement with previous studies, the flux PDF constraints favour an isothermal or inverted IGM temperature-density relation. We also perform a joint analysis by combining our wavelet and flux PDF measurements, constraining the IGM thermal state at z=2.1 to have a temperature at mean density of T0/[10^3 K]=17.3 +/- 1.9 and a power-law temperature-density relation exponent gamma=1.1 +/- 0.1 (1 sigma). Our results are consistent with previous observations that indicate there may be additional sources of heating in the IGM at z<4.Comment: 15 pages, 14 figures, matches version accepted for publication on MNRA

Short-timescale Fluctuations in the Difference Light Curves of QSO 0957+561A,B: Microlensing or Noise?

From optical R band data of the double quasar QSO 0957+561A,B, we made two new difference light curves (about 330 days of overlap between the time-shifted light curve for the A image and the magnitude-shifted light curve for the B image). We observed noisy behaviours around the zero line and no short-timescale events (with a duration of months), where the term event refers to a prominent feature that may be due to microlensing or another source of variability. Only one event lasting two weeks and rising - 33 mmag was found. Measured constraints on the possible microlensing variability can be used to obtain information on the granularity of the dark matter in the main lensing galaxy and the size of the source. In addition, one can also test the ability of the observational noise to cause the rms averages and the local features of the difference signals. We focused on this last issue. The combined photometries were related to a process consisting of an intrinsic signal plus a Gaussian observational noise. The intrinsic signal has been assumed to be either a smooth function (polynomial) or a smooth function plus a stationary noise process or a correlated stationary process. Using these three pictures without microlensing, we derived some models totally consistent with the observations. We finally discussed the sensitivity of our telescope (at Teide Observatory) to several classes of microlensing variability.Comment: MNRAS, in press (LaTeX, 14 pages, 22 eps figures

Quasar accretion disk sizes from continuum reverberation mapping in the DES standard-star fields

Measurements of the physical properties of accretion disks in active galactic nuclei are important for better understanding the growth and evolution of supermassive black holes. We present the accretion disk sizes of 22 quasars from continuum reverberation mapping with data from the Dark Energy Survey (DES) standard star fields and the supernova C fields. We construct continuum lightcurves with the \textit{griz} photometry that span five seasons of DES observations. These data sample the time variability of the quasars with a cadence as short as one day, which corresponds to a rest frame cadence that is a factor of a few higher than most previous work. We derive time lags between bands with both JAVELIN and the interpolated cross-correlation function method, and fit for accretion disk sizes using the JAVELIN Thin Disk model. These new measurements include disks around black holes with masses as small as $\sim10^7$ $M_{\odot}$, which have equivalent sizes at 2500\AA \, as small as $\sim 0.1$ light days in the rest frame. We find that most objects have accretion disk sizes consistent with the prediction of the standard thin disk model when we take disk variability into account. We have also simulated the expected yield of accretion disk measurements under various observational scenarios for the Large Synoptic Survey Telescope Deep Drilling Fields. We find that the number of disk measurements would increase significantly if the default cadence is changed from three days to two days or one day.Comment: 33 pages, 24 figure

The host galaxies and black-hole:galaxy mass ratios of luminous quasars at z~4

We present and analyse the deepest, high-quality Ks-band images ever obtained of luminous quasars at z~4, in an attempt to determine the basic properties of their host galaxies less than 1 Gyr after the first recorded appearance of black holes with Mbh > 10^9 Msol. To maximise the robustness of our results we have carefully selected two SDSS quasars at z~4. These quasars are representative of the most luminous quasars known at this epoch but they also, crucially, lie within 40 arcsec of comparably-bright foreground stars (required for accurate PSF definition), and have redshifts which ensure line-free Ks-band imaging. The data were obtained in excellent seeing (<0.4-arcsec) at the ESO VLT with integration times of ~5.5 hours per source. Via carefully-controlled separation of host-galaxy and nuclear light, we estimate the luminosities and stellar masses of the host galaxies, and set constraints on their half-light radii. The quasar host galaxies have K-band luminosities similar to radio galaxies at comparable redshifts, suggesting that these quasar hosts are also among the most massive galaxies in existence at this epoch. However, the quasar hosts are a factor ~5 smaller than the host galaxies of luminous low-redshift quasars. We estimate the stellar masses of the z~4 host galaxies to lie in the range 2-10x10^11 Msol, and use the CIV emission line in the Sloan spectra to estimate the masses of their black holes. The results imply a black-hole:host-galaxy mass ratio Mbh:Mgal~0.01-0.05. This is an order of magnitude higher than typically seen in the low-redshift Universe, and is consistent with existing evidence for a systematic growth in this mass ratio with increasing redshift, at least for objects selected as powerful AGN.Comment: 10 pages, 6 figure