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Register a new userSelection Functions in Astronomical Data Modeling, with the Space Density of White Dwarfs as Worked Example
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Statistical studies of astronomical data sets, in particular of cataloged properties for discrete objects, are central to astrophysics. One cannot model those objects population properties or incidences without a quantitative understanding of the conditions under which these objects ended up in a catalog or sample, the samples selection function. As systematic and didactic introductions to this topic are scarce in the astrophysical literature, we aim to provide one, addressing generically the following questions: What is a selection function? What arguments $vec{q}$ should a selection function depend on? Over what domain must a selection function be defined? What approximations and simplifications can be made? And, how is a selection function used in `modelling? We argue that volume-complete samples, with the volume drastically curtailed by the faintest objects, reflect a highly sub-optimal selection function that needlessly reduces the number of bright and usually rare objects in the sample. We illustrate these points by a worked example, deriving the space density of white dwarfs (WD) in the Galactic neighbourhood as a function of their luminosity and Gaia color, $Phi_0(M_G,B-R)$ in [mag$^{-2}$pc$^{-3}$]. We construct a sample of $10^5$ presumed WDs through straightforward selection cuts on the Gaia EDR3 catalog, in magnitude, color, parallax, and astrometric fidelity $vec{q}=(m_G,B-R,varpi,p_{af})$. We then combine a simple model for $Phi_0$ with the effective survey volume derived from this selection function $S_C(vec{q})$ to derive a detailed and robust estimate of $Phi_0(M_G,B-R)$. This resulting white dwarf luminosity-color function $Phi_0(M_G,B-R)$ differs dramatically from the initial number density distribution in the luminosity-color plane: by orders of magnitude in density and by four magnitudes in density peak location.
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The growing field of large-scale time domain astronomy requires methods for probabilistic data analysis that are computationally tractable, even with large datasets. Gaussian Processes are a popular class of models used for this purpose but, since the computational cost scales, in general, as the cube of the number of data points, their application has been limited to small datasets. In this paper, we present a novel method for Gaussian Process modeling in one-dimension where the computational requirements scale linearly with the size of the dataset. We demonstrate the method by applying it to simulated and real astronomical time series datasets. These demonstrations are examples of probabilistic inference of stellar rotation periods, asteroseismic oscillation spectra, and transiting planet parameters. The method exploits structure in the problem when the covariance function is expressed as a mixture of complex exponentials, without requiring evenly spaced observations or uniform noise. This form of covariance arises naturally when the process is a mixture of stochastically-driven damped harmonic oscillators -- providing a physical motivation for and interpretation of this choice -- but we also demonstrate that it can be a useful effective model in some other cases. We present a mathematical description of the method and compare it to existing scalable Gaussian Process methods. The method is fast and interpretable, with a range of potential applications within astronomical data analysis and beyond. We provide well-tested and documented open-source implementations of this method in C++, Python, and Julia.
White dwarfs (WDs) embedded in gaseous disks of active galactic nucleus (AGNs) can rapidly accrete materials from the disks and grow in mass to reach or even exceed the Chandrasekhar limit. Binary WD (BWD) mergers are also believed to occur in AGN accretion disks. We study observational signatures from these events. We suggest that mass-accreting WDs and BWD mergers in AGN disks can lead to thermonuclear explosions that drive an ejecta shock breakout from the disk surface and power a slow-rising, relatively dim Type Ia supernova (SN). Such SNe Ia may be always outshone by the emission of the AGN disk around the supermassive black hole (BH) with a mass of $M_{rm SMBH}gtrsim 10^8,M_odot$. Besides, accretion-induced collapses (AICs) of WDs in AGN disks may occur sometimes, which may form highly-magnetized millisecond neutron stars (NSs). The subsequent spin-down process of this nascent magnetar can deposit its rotational energy into the disk materials, resulting in a magnetar-driven shock breakout and a luminous magnetar-powered transient. We show that such an AIC event could power a rapidly evolving and luminous transient for a magnetic field of $Bsim10^{15},{rm G}$. The rising time and peak luminosity of the transient, powered by a magnetar with $Bsim10^{14},{rm G}$, are predicted to have similar properties with those of superluminous supernovae. AIC events taking place in the inner parts of the disk around a relatively less massive supermassive BHs ($M_{rm SMBH}lesssim10^8,M_odot$) are more likely to power the transients that are much brighter than the AGN disk emission and hence easily to be identified.
Classification of transient and variable light curves is an essential step in using astronomical observations to develop an understanding of their underlying physical processes. However, upcoming deep photometric surveys, including the Large Synoptic Survey Telescope (LSST), will produce a deluge of low signal-to-noise data for which traditional labeling procedures are inappropriate. Probabilistic classification is more appropriate for the data but are incompatible with the traditional metrics used on deterministic classifications. Furthermore, large survey collaborations intend to use these classification probabilities for diverse science objectives, indicating a need for a metric that balances a variety of goals. We describe the process used to develop an optimal performance metric for an open classification challenge that seeks probabilistic classifications and must serve many scientific interests. The Photometric LSST Astronomical Time-series Classification Challenge (PLAsTiCC) is an open competition aiming to identify promising techniques for obtaining classification probabilities of transient and variable objects by engaging a broader community both within and outside astronomy. Using mock classification probability submissions emulating archetypes of those anticipated of PLAsTiCC, we compare the sensitivity of metrics of classification probabilities under various weighting schemes, finding that they yield qualitatively consistent results. We choose as a metric for PLAsTiCC a weighted modification of the cross-entropy because it can be meaningfully interpreted. Finally, we propose extensions of our methodology to ever more complex challenge goals and suggest some guiding principles for approaching the choice of a metric of probabilistic classifications.
For years, the standard procedure to measure radial velocities (RVs) of spectral observations consisted in cross-correlating the spectra with a binary mask, that is, a simple stellar template that contains information on the position and strength of stellar absorption lines. The cross-correlation function (CCF) profiles also provide several indicators of stellar activity. We present a methodology to first build weighted binary masks and, second, to compute the CCF of spectral observations with these masks from which we derive radial velocities and activity indicators. These methods are implemented in a python code that is publicly available. To build the masks, we selected a large number of sharp absorption lines based on the profile of the minima present in high signal-to-noise ratio (S/N) spectrum templates built from observations of reference stars. We computed the CCFs of observed spectra and derived RVs and the following three standard activity indicators: full-width-at-half-maximum as well as contrast and bisector inverse slope.We applied our methodology to CARMENES high-resolution spectra and obtain RV and activity indicator time series of more than 300 M dwarf stars observed for the main CARMENES survey. Compared with the standard CARMENES template matching pipeline, in general we obtain more precise RVs in the cases where the template used in the standard pipeline did not have enough S/N. We also show the behaviour of the three activity indicators for the active star YZ CMi and estimate the absolute RV of the M dwarfs analysed using the CCF RVs.
Milky Way dwarf satellites are unique objects that encode the early structure formation and therefore represent a window into the high redshift Universe. So far, their study was conducted using electromagnetic waves only. The future Laser Interferometer Space Antenna (LISA) has the potential to reveal Milky Way satellites in gravitational waves emitted by double white dwarf (DWD) binaries. We investigate gravitational wave (GW) signals detectable by LISA as a possible tool for the identification and characterisation of the Milky Way satellites. We use the binary population synthesis technique to model the population of DWDs in dwarf satellites and we assess the impact on the number of LISA detections when making changes to the total stellar mass, distance, star formation history and metallicity of satellites. We calibrate predictions for the known Milky Way satellites on their observed properties. We find that DWDs emitting at frequencies $gtrsim 3,$mHz can be detected in Milky Way satellites at large galactocentric distances. The number of these high frequency DWDs per satellite primarily depends on its mass, distance, age and star formation history, and only mildly depends on the other assumptions regarding their evolution such as metallicity. We find that dwarf galaxies with $M_star>10^6,$M$_{odot}$ can host detectable LISA sources with a number of detections that scales linearly with the satellites mass. We forecast that out of the known satellites, Sagittarius, Fornax, Sculptor and the Magellanic Clouds can be detected with LISA. As an all-sky survey that does not suffer from contamination and dust extinction, LISA will provide observations of the Milky Way and dwarf satellites galaxies valuable for Galactic archaeology and near-field cosmology.
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