Changeset 40695 for trunk/doc/release.2015/ps1.diffs/diffs.tex
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trunk/doc/release.2015/ps1.diffs/diffs.tex
r40577 r40695 63 63 \section{Introduction} 64 64 65 The age of synoptic surveys has come. As optical (and other 66 wavelength) telescopes are surveying ever increasing areas to ever 67 fainter flux limits with multiple repeats, there is a growing interest 68 in the study of transient phenomena. This technological progress is 69 well matched with the current scientific emphases on large samples of 70 supernovae (SN), microlenses, asteroids, and other transients and 71 variable sources. 65 The past three decades have seen the increasing importance of 66 time-domain surveys in astronomy. These include asteroid searches 67 such as the Lincoln Near-Earth Asteroid Research 68 \citep[LINEAR][]{2000Icar..148...21S}, the Lowell Observatory 69 Near-Earth Object Search \citep[LONEOS,][]{1995DPS....27.0110B}, the 70 Catalina Sky Survey \citep{2003DPS....35.3604L}, and ATLAS 71 \citep{2018PASP..130f4505T}; microlensing surveys such as MACHO 72 \citep{1993ASPC...43..291A} and Optical Gravitational Lens Experiment 73 \citep[OGLE,][]{1992AcA....42..253U}; and searches for supernovae and 74 other transient sources such as ASAS-SN \citep{2014ApJ...788...48S}, the 75 Palomar Transient Factory \citep[PTF,][]{2009PASP..121.1395L}, and the Robotic Optical 76 Transient Search Experiment \citep[ROTSE-I,][]{2000ApJ...542..251A}. 77 78 The Pan-STARRS Observatory \citep{chambers2017} has been a leader in 79 the searches for both explosive transient / supernova and potentially 80 hazardous asteroids. According to the statistics maintained by David 81 Bishop\footnote{http://www.rochesterastronomy.org/snimages/archives.html}, 82 since 2009, 40\% of all supernova have been discovered by 83 Pan-STARRS\,1. Similarly, 24\% of all Near Earth Objects (NEOs) 84 discovered to date have been found by 85 Pan-STARRS\footnote{https://cneos.jpl.nasa.gov/stats/site\_all.html}. 86 Since 2014, when Pan-STARRS shifted its primary mission to the search 87 for NEOs, this fraction has increased to 41\%. Both of these search 88 programs use nightly observations to hunt for features which have 89 changed, either between multiple images in a single night or between 90 the current image and an archival reference image. 72 91 73 92 PSF-matched image differencing\footnote{We eschew the popular term … … 88 107 of the convolution kernel as a linear combination of basis functions, 89 108 which allows the least-squares problem to be reduced to a matrix 90 equation. \citet{2000A &AS..144..363A} showed how this can be expanded109 equation. \citet{2000AAS..144..363A} showed how this can be expanded 91 110 to allow spatial variation of the kernel across the images. Of 92 111 course, the basis functions used for the kernel may be completely … … 137 156 basis functions, $g_i(x,y) k_i(u,v)$, where the inclusion of 138 157 $g_i(x,y)$ allows for spatial variation of the kernel. In order to 139 enforce conservation of flux \citep[following][]{2000A &AS..144..363A},158 enforce conservation of flux \citep[following][]{2000AAS..144..363A}, 140 159 we specify that all of the kernel basis functions have zero sum, 141 160 $\sum_{u,v} k_i(u,v) = 0\ \forall i$. This may be achieved by scaling … … 161 180 $\chi^2$ between wide and narrow kernels. Setting $c_i \equiv 0$ and 162 181 $p_i \equiv 0$ reduces the above equation to the 163 \citet{2000A &AS..144..363A} formalism, but with the normalisation182 \citet{2000AAS..144..363A} formalism, but with the normalisation 164 183 ($b_0$) included explicitly. In practise, the above sum will only be 165 184 over small regions (known as ``stamps''), and if we assume that the 166 185 spatial variation is not large, then we can simply use the coordinates 167 186 of the stamp centres for the $g_i(x,y)$; this allows a faster 168 calculation \citep{2000A &AS..144..363A}.187 calculation \citep{2000AAS..144..363A}. 169 188 170 189 To simplify the equation, we write … … 199 218 other special polynomial for the $f_i(x,y)$ and $g_i(x,y)$ is simple 200 219 and convenient. The kernel basis function sets of 201 \citet{1998ApJ...503..325A} and \citet{2000A &AS..144..363A} are220 \citet{1998ApJ...503..325A} and \citet{2000AAS..144..363A} are 202 221 \begin{equation} 203 222 g_i(x,y) k_i'(u,v) = \psi_i x^\ell y^m u^p v^q \exp((u^2+v^2)/2s_i^2) … … 338 357 \subsection{Stamps} 339 358 340 The choice of stamps is key to successful PSF-matching --- the 341 convolution kernel is only as good as the stamps used to construct it. 342 We use a merged list of sources from photometry of the two input 343 images as the basis of our stamps list. Sources with a flag 344 indicating that it is anything other than a pristine astrophysical 345 source are excluded. At the present time, we make no effort to select 346 sources of a particular color or range of colors. 359 Since we restrict the analysis of the kernel required for PSF matching 360 to the small ``stamps'' centered on bright stars, the choice of stamps 361 is key to successful PSF-matching. The convolution kernel is only as 362 good as the stamps used to construct it. We use a merged list of 363 sources from photometry of the two input images as the basis of our 364 stamps list. Sources with a flag indicating that it is anything other 365 than a pristine astrophysical source are excluded. At the present 366 time, we make no effort to select sources of a particular color or 367 range of colors. 347 368 348 369 We exclude sources with any masked pixels that would affect the … … 490 511 progressive software packages producing \citep[e.g., 491 512 SWarp:][]{2002ASPC..281..228B} and using \citep[e.g., 492 SExtractor:][]{1996A &AS..117..393B} weight maps to characterise the513 SExtractor:][]{1996AAS..117..393B} weight maps to characterise the 493 514 noise over the image. Because of simplicity and lower calculation 494 515 cost relative to weights or standard deviations, we prefer to … … 993 1014 \clearpage 994 1015 \bibliographystyle{apj} 995 \bibliography{apj-jour,references} 1016 %\bibliography{apj-jour,references} 1017 \input{diffs.bbl} 996 1018 997 1019 \end{document}
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