A New Algorithm For Difference Image Analysis

In the context of difference image analysis (DIA), we present a new method for determining the convolution kernel matching a pair of images of the same field. Unlike the standard DIA technique which involves modelling the kernel as a linear combination of basis functions, we consider the kernel as a discrete pixel array and solve for the kernel pixel values directly using linear least-squares. The removal of basis functions from the kernel model is advantageous for a number of compelling reasons. Firstly, it removes the need for the user to specify such functions, which makes for a much simpler user application and avoids the risk of an inappropriate choice. Secondly, basis functions are constructed around the origin of the kernel coordinate system, which requires that the two images are perfectly aligned for an optimal result. The pixel kernel model is sufficiently flexible to correct for image misalignments, and in the case of a simple translation between images, image resampling becomes unnecessary. Our new algorithm can be extended to spatially varying kernels by solving for individual pixel kernels in a grid of image sub-regions and interpolating the solutions to obtain the kernel at any one pixel.Comment: MNRAS Letters Accepte

Integrating Temporal and Spectral Features of Astronomical Data Using Wavelet Analysis for Source Classification

Temporal and spectral information extracted from a stream of photons received from astronomical sources is the foundation on which we build understanding of various objects and processes in the Universe. Typically astronomers fit a number of models separately to light curves and spectra to extract relevant features. These features are then used to classify, identify, and understand the nature of the sources. However, these feature extraction methods may not be optimally sensitive to unknown properties of light curves and spectra. One can use the raw light curves and spectra as features to train classifiers, but this typically increases the dimensionality of the problem, often by several orders of magnitude. We overcome this problem by integrating light curves and spectra to create an abstract image and using wavelet analysis to extract important features from the image. Such features incorporate both temporal and spectral properties of the astronomical data. Classification is then performed on those abstract features. In order to demonstrate this technique, we have used gamma-ray burst (GRB) data from the NASA's Swift mission to classify GRBs into high- and low-redshift groups. Reliable selection of high-redshift GRBs is of considerable interest in astrophysics and cosmology.Comment: Accepted and Published in 2015 IEEE Applied Imagery Pattern Recognition Workshop (AIPR), Imaging: Earth and Beyond (Washington DC, October 13-15, 2015) Conference Proceeding

Variations of the Selective Extinction Across the Galactic Bulge - Implications for the Galactic Bar

We propose a new method to investigate the coefficient of the selective extinction, based on two band photometry. This method uses red clump stars as a means to construct the reddening curve. We apply this method to the OGLE color-magnitude diagrams to investigate the variations of the selective extinction towards various parts of the Galactic bulge. We find that $A_{_V}/E_{_{V-I}}$ coefficient is within the errors the same for $l=\pm 5\deg$ OGLE fields. Therefore, the difference of $\sim 0.37\;mag$ in the extinction adjusted apparent magnitude of the red clump stars in these fields (Stanek et al.~1994, 1995) cannot be assigned to a large-scale gradient of the selective extinction coefficient. This strengthens the implication of this difference as indicator of the presence of the bar in our Galaxy. However using present data we cannot entirely exclude the possibility of $\sim 0.2\;mag/mag$ variations of the selective extinction coefficient on the large scales across the bulge.Comment: submitted to ApJ Letters, 10 pages, gziped PostScript with figures included; also available through WWW at http://www.astro.princeton.edu/~library/prep.htm

Measurements of streaming motions of the Galactic bar with Red Clump Giants

We report a measurement of the streaming motion of the stars in the Galactic bar with the Red Clump Giants (RCGs) using the data of the Optical Gravitational Lensing Experiment II (OGLE-II). We measure the proper motion of 46,961 stars and divide RCGs into bright and faint sub-samples which on average will be closer to the near and far side of the bar, respectively. We find that the far-side RCGs (4,979 stars) have a proper motion of \Delta ~ 1.5 +- 0.11 mas yr^{-1} toward the negative l relative to the near-side RCGs (3,610 stars). This result can be explained by stars in the bar rotating around the Galactic center in the same direction as the Sun with v_b ~ 100 km s^{-1}. In the Disc Star (DS) and Red Giant (RG) samples, we do not find significant difference between bright and faint sub-samples. For those samples \Delta \~ 0.3 +- 0.14 mas yr^{-1} and ~ 0.03 +- 0.14 mas yr^{-1}, respectively. It is likely that the average proper motion of RG stars is the same as that of the Galactic center. The proper motion of DSs with respect to RGs is ~ 3.3 mas yr^{-1} toward positive l. This value is consistent with the expectations for a flat rotation curve and Solar motion with respect to local standard of rest. RGs have proper motion approzimately equal to the average of bright and faint RCGs, which implies that they are on average near the center of the bar. This pilot project demonstrates that OGLE-II data may be used to study streaming motions of stars in the Galactic bar. We intend to extend this work to all 49 OGLE-II fields in the Galactic bulge region.Comment: 7 pages, 9 figures, submitted to MNRA

Machine-z: Rapid Machine Learned Redshift Indicator for Swift Gamma-ray Bursts

Studies of high-redshift gamma-ray bursts (GRBs) provide important information about the early Universe such as the rates of stellar collapsars and mergers, the metallicity content, constraints on the re-ionization period, and probes of the Hubble expansion. Rapid selection of high-z candidates from GRB samples reported in real time by dedicated space missions such as Swift is the key to identifying the most distant bursts before the optical afterglow becomes too dim to warrant a good spectrum. Here we introduce "machine-z", a redshift prediction algorithm and a "high-z" classifier for Swift GRBs based on machine learning. Our method relies exclusively on canonical data commonly available within the first few hours after the GRB trigger. Using a sample of 284 bursts with measured redshifts, we trained a randomized ensemble of decision trees (random forest) to perform both regression and classification. Cross-validated performance studies show that the correlation coefficient between machine-z predictions and the true redshift is nearly 0.6. At the same time our high-z classifier can achieve 80% recall of true high-redshift bursts, while incurring a false positive rate of 20%. With 40% false positive rate the classifier can achieve ~100% recall. The most reliable selection of high-redshift GRBs is obtained by combining predictions from both the high-z classifier and the machine-z regressor.Comment: Accepted to the Monthly Notices of the Royal Astronomical Society Journal (10 pages, 10 figures, and 3 Tables