Index: trunk/doc/release.2015/ps1.calibration/calibration.tex =================================================================== --- trunk/doc/release.2015/ps1.calibration/calibration.tex (revision 40602) +++ trunk/doc/release.2015/ps1.calibration/calibration.tex (revision 40614) @@ -1,4 +1,4 @@ -\documentclass[10pt,preprint]{aastex} -% \documentclass[iop,floatfix]{emulateapj} +% \documentclass[10pt,preprint]{aastex} +\documentclass[iop,floatfix]{emulateapj} % \pdfoutput=1 @@ -101,5 +101,5 @@ of the Pan-STARRS\,1 $3\pi$ Survey. The photometric goals were to reduce the systematic effects introduced by the camera and detectors, -and to place all of the observations into a photometric system with +and to place all of the observations onto a photometric system with consistent zero points over the entire area surveyed, the \approx 30,000 square degrees north of $\delta = -30$\degrees. The @@ -115,7 +115,4 @@ \section{Introduction}\label{sec:intro} - -\note{list all ID\_IMAgE, ID\_MEAS, ID\_OBJ, ID\_SECF flags from libdvo/include/dvo.h and identify how they are set; make tables} - From May 2010 through March 2014, the Pan-STARRS Science Consortium @@ -175,10 +172,10 @@ contained only average information resulting from the many individual images obtained by the $3\pi$ Survey observations. A second data -release, DR2, was made available \note{20 January 2019}. DR2 provides +release, DR2, was made available 28 January 2019. DR2 provides measurements from all of the individual exposures, and include an improved calibration of the PV3 processing of that dataset. This is the fifth in a series of seven papers describing the -Pan-STARRS1 Surveys, the data reduction techiques and the resulting +Pan-STARRS1 Surveys, the data reduction techniques and the resulting data products. This paper (Paper V) describes the final calibration process, and the resulting photometric and astrometric quality. @@ -195,5 +192,5 @@ %Pan-STARRS Data Processing Stages \citet[][Paper II]{magnier2017.datasystem} -describes how the various data processing stages are organised and implemented +describes how the various data processing stages are organized and implemented in the Imaging Processing Pipeline (IPP), including details of the the processing database which is a critical element in the IPP infrastructure . @@ -288,14 +285,16 @@ Astronomical objects are detected and characterized in the stack images. The details of the analysis of the sources in the stack -images are discussed in \cite{magnier2017.analysis}, but in brief these include -PSF photometry, along with a range of measurements driven by the goals -of understanding the galaxies in the images. Because of the -significant mask fraction of the GPC1 focal plane, and the varying -image quality both within and between exposures, the effective PSF of -the PS1 stack images is highly variable. The PSF varies significantly -on scales as small as a few to tens of pixels, making accurate PSF -modelling essentially infeasible. The PSF photometry of sources in -the stack images is thus degraded significantly compared to the -quality of the photometry measured for the individual chip images. +images are discussed in \cite{magnier2017.analysis}, but in brief +these include PSF photometry, along with a range of measurements +driven by the goals of understanding the galaxies in the images. +Because of the significant mask fraction of the GPC1 focal plane, and +the varying image quality both within and between exposures, the +effective PSF of the PS1 stack images (often including more than 10 +input exposures taken in different conditions) is highly variable. +The PSF varies significantly on scales as small as a few to tens of +pixels, making accurate PSF modelling essentially infeasible. The PSF +photometry of sources in the stack images is thus degraded +significantly compared to the quality of the photometry measured for +the individual chip images. To recover most of the photometric quality of the individual chip @@ -311,6 +310,5 @@ fluxes from the individual warp images are averaged, a reliable measurement of the faint source flux is determined. The details of -this analysis are described in detail in Magnier et al -\cite{magnier2017.analysis}. +this analysis are described in detail in \cite{magnier2017.analysis}. The data products from the chip photometry, stack photometry, and @@ -320,5 +318,5 @@ photometric and astrometric calibrations. In this article, we discuss the photometric calibration of the individual exposures, the stacks, -and the warp imags. We also discuss the astrometric calibration of +and the warp images. We also discuss the astrometric calibration of the individual exposures and the stack images. @@ -332,5 +330,5 @@ each chip: a simple TAN projection as described by \cite{2002AA...395.1077C} is used to relate sky coordinates to a -cartesian tangent-plane coordinate system. A pair of low-order +Cartesian tangent-plane coordinate system. A pair of low-order polynomials are used to relate the chip pixel coordinates to this tangent-plane coordinate system. The transforming polynomials are of @@ -352,5 +350,5 @@ accuracy consists of a set of connected solutions for all chips in a single exposure. This model also uses a TAN projection to relate the -sky coordinates to a locally cartesian tangent plane coordinate system. +sky coordinates to a locally Cartesian tangent plane coordinate system. A set of polynomials is then used to relate the tangent plane coordinates to a `focal plane' coordinate system, $L,M$: @@ -363,5 +361,5 @@ across the field of the camera. Since these effects are smooth across the field of the camera, a single pair of polynomials can be used for -each exposure. Like in the chip analysis about, the \ippprog{psastro} +each exposure. Like in the chip analysis above, the \ippprog{psastro} code restricts the exponents with the rule $i + j <= N_{\rm order}$ where the order of the fit, $N_{\rm order}$, may be 1 to 3, under the @@ -392,6 +390,4 @@ \end{eqnarray} -\note{does this section need more? does this section need to be moved?} - %% Include a description of the WCS keywords used to represent the fit elements? @@ -476,5 +472,5 @@ if too many reference stars are chosen, there is a higher chance of a false-positive match, especially as many of the reference stars may -not be detected in the GPC1 image. The seletion of the reference +not be detected in the GPC1 image. The selection of the reference stars includes a limit on the brightest and faintest magnitudes of the stars selected. @@ -537,5 +533,5 @@ The astrometry solution from the cross correlation step above is again -used to selected matches between the reference stars and observed +used to select matches between the reference stars and observed stars in the image. The matching radius starts off quite large, and a series of fits is performed to generate the transformation between @@ -586,5 +582,5 @@ the current best set of transformations. These fits start with low order (1) and large matching radius. As the iterations proceed, the -radius is reduced and the order is allowed to increaes, up to 3rd +radius is reduced and the order is allowed to increase, up to 3rd order for the final iterations. @@ -610,6 +606,7 @@ calibration was based on a reference catalog generated from \PSONE\ photometry, this methods was no longer needed. Note that we -do not include an airmass correction in this zero point analysis: the -airmass correction is folded into the observed zero point. The zero +do not fit for the airmass slope in this analysis. The nominal +airmass slope is used for each filter; any deviation from the nominal +value is effectively folded into the observed zero point. The zero point may be measured separately for each chip or as a single value for the entire exposure; the latter option was used for the PV3 @@ -687,5 +684,5 @@ \code{X} in both cases is one of {$grizy$}. % -Table~\ref{tab:tab:object_mask_values} lists the flags specific to an +Table~\ref{tab:object_mask_values} lists the flags specific to an object as a whole. These values are stored in the DVO database field \code{Average.flags} and are exposed in PSPS in @@ -875,15 +872,16 @@ Photometric nights are selected and all other exposures are ignored. -Each night is allowed to have a single fitted zero point and a single -fitted value for the airmass extinction coefficient per filter. The -zero points and extinction terms are determined as a least squares -minimization process using the repeated measurements of the same stars -from different nights to tie nights together. Flat-field corrections -are also determined as part of the minimization process. In the -original (PV1) ubercal analysis, \cite{2012ApJ...756..158S} determined -flat-field corrections for $2\times 2$ sub-regions of each chip in the -camera and four distinct time periods (``seasons''). Later analysis -(PV2) used an $8\times8$ grid of flat-field corrections to good -effect. +Each night is allowed to have a single fitted zero point +(corresponding to the sum $zp_{\rm nominal} + M_{cal}$ below) and a +single fitted value for the airmass extinction coefficient ($K_{\rm + \lambda}$) per filter. The zero points and extinction terms are +determined as a least squares minimization process using the repeated +measurements of the same stars from different nights to tie nights +together. Flat-field corrections are also determined as part of the +minimization process. In the original (PV1) ubercal analysis, +\cite{2012ApJ...756..158S} determined flat-field corrections for +$2\times 2$ sub-regions of each chip in the camera and four distinct +time periods (``seasons''). Later analysis (PV2) used an $8\times8$ +grid of flat-field corrections to good effect. The ubercal analysis was re-run for PV3 by the Harvard group. For the @@ -952,7 +950,7 @@ DVO internal representation in which the zero point of each image is split into three main components: -\[ +\begin{equation} zp_{\rm total} = zp_{\rm nominal} + M_{cal} + K_{\rm \lambda}(\sec \zeta - 1) -\] +\end{equation} where $zp_{\rm nominal}$ and $K_{\rm \lambda}$ are static values for each filter representing respectively the nominal zero point and the @@ -978,5 +976,6 @@ \hline \hline -{\bf Filter} & {\bf Zero Point (Raw)} & {\bf Zero Point (Calspec)} & {\bf Airmass Slope} \\ +{\bf Filter} & {\bf Zero Point} & {\bf Zero Point} & {\bf Airmass Slope} \\ + & {\bf (Raw)} & {\bf (Calspec)} & \\ \hline \gps & 24.563 & 24.583 & 0.147 \\ @@ -995,7 +994,7 @@ tables, it also updates the individual measurements associated with those images. In the DVO database schema, the normalized instrumental -magnitude, $M_{\rm inst} = -2.5log_{10} (DN / sec) + 25.0$ are stored -for each measurement. The value of 25.0 is an arbitrary (but fixed) -constant offset to place the instrumental magnitudes into +magnitude, $M_{\rm inst} = -2.5log_{10} (DN / sec)$ is stored +for each measurement, with an arbitrary (but fixed) +constant offset of 25 to place the modified instrumental magnitudes into approximately the correct range. Associated with each measurement are two correction magnitudes: $M_{\rm cal}$ and $M_{\rm flat}$, along @@ -1009,7 +1008,7 @@ (`relative') magnitude is determined from the stored database values as: -\[ -M_{\rm rel} = M_{\rm inst} - 25.0 + zp_{\rm ref} + M_{\rm cal} + M_{\rm flat} + K_\lambda (sec \zeta - 1). -\] +\begin{equation} +M_{\rm rel} = M_{\rm inst} + zp_{\rm ref} + M_{\rm cal} + M_{\rm flat} + K_\lambda (sec \zeta - 1). +\end{equation} The calibration offsets, $M_{\rm cal}$ and $M_{\rm flat}$, represent the per-exposure zero point correction and the slowly-changing @@ -1045,11 +1044,13 @@ are related by arithmetic magnitude offsets which account for effects such as the instrumental variations and atmospheric attenuation. -\[ +\begin{equation} M_{rel} = m_{inst} + ZP + M_{cal} -\] +\end{equation} From the collection of measurements, we can generate an average magnitude for a single star (or other object): -\[ M_{ave} = \frac{\sum_i M_{rel,i} w_i}{\sum_i w_i} \] +\begin{equation} + M_{ave} = \frac{\sum_i M_{rel,i} w_i}{\sum_i w_i} +\end{equation} We find that the color difference of the different chips can be ignored, and set the color-trend slope to 0.0. Note that we only use @@ -1063,5 +1064,8 @@ finding the best mean magnitudes for all objects and the best $M_{\rm cal}$ offset for each exposure: -\[ \chi^2 = \sum_{i,j} (m_{inst}[i,j] + ZP + K \zeta + M_{clouds}[i] - M_{ave}[j]) w_{i,j} / \sum_{i,j} w_{i,j} \] +\begin{equation} + \chi^2 = \frac{\sum_{i,j} (m_{inst}[i,j] + ZP + K \zeta + + M_{clouds}[i] - M_{ave}[j]) w_{i,j}}{\sum_{i,j} w_{i,j}} +\end{equation} If everything were fitted at once and allowed to float, this system of @@ -1087,5 +1091,5 @@ We attempt to exclude these poor measurements in advance by rejecting measurements which the photometric analysis has flagged the result as -suspcious. We reject detections which are excessively masked; these include +suspicious. We reject detections which are excessively masked; these include detections which are too close to other bright objects, diffraction spikes, ghost images, or the detector edges. However, these @@ -1133,6 +1137,11 @@ % \note{do we drop this when calculating the final mean mags?} % \note{do I need to present the math?} -\[ \mu = \frac{\sum m_i w_i \sigma_i^{-2}}{\sum w_i \sigma_i^{-2}} \] -\[ \sigma_\mu = \frac{\sum w_i^2 \sigma_i^{-2}}{(\sum w_i \sigma_i^{-2})^2} \] +\begin{equation} + \mu = \frac{\sum m_i w_i \sigma_i^{-2}}{\sum w_i \sigma_i^{-2}} +\end{equation} +\begin{equation} + \sigma_\mu = \frac{\sum w_i^2 \sigma_i^{-2}}{(\sum w_i + \sigma_i^{-2})^2} +\end{equation} The calculation of the relative photometry zero points is performed @@ -1158,5 +1167,5 @@ \begin{center} \begin{minipage}{0.85\linewidth} - \includegraphics[width=\textwidth,clip]{{pics/photflat.example}.png} + \includegraphics[width=\textwidth,clip]{{pics/photflat.example.sm}.png} \end{minipage} \hspace{-2.75in} @@ -1170,5 +1179,5 @@ The iterations described above (calculate mean magnitudes, calculate zero points, calculate new measurements) are -peformed on each of the 73 region hosts in parallel. However, between +performed on each of the 73 region hosts in parallel. However, between certain iteration steps, the region hosts must share some information. After mean object magnitudes are calculated, the region hosts must @@ -1185,5 +1194,5 @@ the 73 region hosts. A process is then launched on each of the region hosts which is responsible for managing the image calibration analysis -on that host. These processes in turn make an intial request of the +on that host. These processes in turn make an initial request of the photometry information (object and measurement) from the 100 parallel DVO partition machines. In practice, the processes on the the region @@ -1211,8 +1220,8 @@ analysis. -\begin{figure}[htbp] +\begin{figure*}[htbp] \begin{center} %width=\hsize - \includegraphics[height=\vsize,clip]{{pics/allsky.photom.sigma}.png} + \includegraphics[height=\vsize,clip]{{pics/allsky.photom.sigma.sm}.png} \caption{\label{fig:allsky.photom.sigma} Consistency of photometry measurements across the sky. Each panel shows a map of the @@ -1223,5 +1232,5 @@ single-measurement errors for bright stars.} \end{center} -\end{figure} +\end{figure*} %% \note{need to discuss the process of setting the final mean magnitudes} @@ -1307,5 +1316,5 @@ for photometry tied to the PSF model and a second for the aperture-like measurements (total aperture magnitudes, Kron magnitude, -cicular fixed-radius aperture magnitudes). This split is needed +circular fixed-radius aperture magnitudes). This split is needed because of the limited quality of the stack PSF photometry due to the highly variable PSF in the stacks. Aperture magnitudes, however, are @@ -1326,5 +1335,5 @@ \subsection{Photometry Calibration Quality} -Figure~\ref{fig:allsky.photom.sigma} shows the standard devitions of +Figure~\ref{fig:allsky.photom.sigma} shows the standard deviations of the mean residual photometry for bright stars as a function of position across the sky. For each pixel in these images, we selected @@ -1365,5 +1374,5 @@ Once the image photometric calibrations (zero points and flat-field -corrections) have been determined and applied to the measuremetns from +corrections) have been determined and applied to the measurements from each image, we can calculate the best average photometry for each object. We calculate average magnitudes for the chip photometry; for @@ -1398,7 +1407,7 @@ The ranking values are defined as follows: \begin{itemize} -\item {\bf rank 0 :} perfect measurment (no quality concerns) +\item {\bf rank 0 :} perfect measurement (no quality concerns) \item {\bf rank 1 :} PSF ``perfect pixel'' quality factor (\code{PSF_QF_PERFECT}) $< 0.85$. \code{PSF_QF_PERFECT} measures the PSF-weighted fraction of pixels which are not masked \citep[see][]{magnier2017.analysis}. -\item {\bf rank 2 :} Photometry analysis flag field (\code{photFlags}) has one of the ``poor quality'' bits raised. These bits are listed below; OR-ed together they have the hexideciaml value \code{0xe0440130} +\item {\bf rank 2 :} Photometry analysis flag field (\code{photFlags}) has one of the ``poor quality'' bits raised. These bits are listed below; OR-ed together they have the hexadecimal value \code{0xe0440130} \begin{itemize} \item {\tt PM\_SOURCE\_MODE\_POOR = 0x00000010} : Fit succeeded, but with low-S/N or high-Chisq @@ -1419,5 +1428,5 @@ \code{PSF_QF} measures the PSF-weighted fraction of pixels which are not masked as ``bad'', but may be ``suspect''. Bad values are - blank, highly non-linear or non-responsibe; suspect pixels include + blank, highly non-linear or non-responsive; suspect pixels include those pixels on ghosts, diffraction spikes, bright star bleeds, and the mildly-saturated cores of bright stars. Suspect values may have @@ -1440,5 +1449,5 @@ %% IMAGE_OFFSET = 2.0 mag %% IMAGE_SCATTER = 0.075 mag -\item {\bf rank 6 :} Photometry analysis flag field (\code{photFlags}) has one of the ``bad quality'' bits raised. These bits are listed below; OR-ed together they have the hexideciaml value \code{0x1003bc88} +\item {\bf rank 6 :} Photometry analysis flag field (\code{photFlags}) has one of the ``bad quality'' bits raised. These bits are listed below; OR-ed together they have the hexadecimal value \code{0x1003bc88} \begin{itemize} \item {\tt PM\_SOURCE\_MODE\_FAIL = 0x00000008} : Non-linear fit failed (non-converge, off-edge, run to zero) @@ -1469,5 +1478,5 @@ Rank values are assigned exclusively starting from the highest values: -if a measurements satisfieds the rule for \eg, rank 6, it will not be +if a measurements satisfies the rule for \eg, rank 6, it will not be tested for ranks 5 and lower. After all measurements have been assigned a ranking value, the set of all measurements with the common @@ -1512,11 +1521,11 @@ error, is used to modify the standard weight. We use a Cauchy function to define a new weight: -\[ +\begin{equation} \omega^\prime = \frac{\omega}{1 + r^2} -\] +\end{equation} using -\[ +\begin{equation} r = \frac{F_o - F_i}{\sigma} -\] +\end{equation} where $F_o$ is the average magnitude (or flux for forced-warp photometry), $F_i$ is the measured magnitude (or flux), $\sigma$ is @@ -1562,5 +1571,5 @@ bootstrap-resampled measurement of the error may be artificially small. We record the maximum of the bootstrap-sampling error and the -formal error from the weighted average calculation. The minimumn and +formal error from the weighted average calculation. The minimum and maximum of the unclipped values are also recorded for the chip photometry. @@ -1646,5 +1655,5 @@ from the same skycell for each object. Also note that a faint object, near the detection limit of the stack, may be detected on a -secondary skycell but not (due to statistical flucuations) be detected +secondary skycell but not (due to statistical fluctuations) be detected on the corresponding primary skycell. Thus it is expected that some objects may be lacking any primary detections. @@ -1702,10 +1711,10 @@ \includegraphics[width=\hsize,clip]{{pics/KHexample}.png} \caption{\label{fig:KHexample} Illustration of the Koppenh\"ofer Effect - on chip XY04. In each plot, the solid line shows the measured + on chip XY04. {\bf Bottom left} X-direction before correction. The solid line shows the measured mean residual for stars detected on this chip as a function of the - instrumental magnitude / FWHM$^2$. {\bf bottom left} X-direction before correction. -{\bf bottom right} Y-direction before correction. -{\bf top left} X-direction after correction. -{\bf top right} Y-direction after correction. } + instrumental magnitude / FWHM$^2$. +{\bf Bottom right} Y-direction before correction. +{\bf Top left} X-direction after correction. +{\bf Top right} Y-direction after correction. } \end{center} \end{figure*} @@ -1716,8 +1725,8 @@ \caption{\label{fig:KHmap} Map of the amplitude of the Koppenh\"ofer Effect on chips across the focal plane. In the - affected chips, bright stars are up to 0.2 \note{arcsec} deviant - from their expected positions. {\bf bottom left} X-direction before - correction. {\bf bottom right} Y-direction before correction. {\bf - top left} X-direction after correction. {\bf top right} + affected chips, bright stars are up to 0.2 arcsec deviant + from their expected positions. {\bf Bottom left} X-direction before + correction. {\bf Bottom right} Y-direction before correction. {\bf + Top left} X-direction after correction. {\bf Top right} Y-direction after correction.} \end{center} @@ -1762,6 +1771,6 @@ The Koppenh\"ofer Effect was first identified in February 2011 by Johannes Koppenh\"ofer (MPE) as part of the effort to search for -planet transists in the Stellar Transit Survey data. He noticed that -the astromety of bright stars and faint stars disagreed on overlapping +planet transits in the Stellar Transit Survey data. He noticed that +the astrometry of bright stars and faint stars disagreed on overlapping chips at the boundary between the STS fields. After some exploration, it was determined that the X coordinate of the brightest stars was @@ -1832,5 +1841,5 @@ angle. For each filter, we determine the DCR trend as a function of the difference between the star color and the reference star color, -using the red or blue color approriate to the particular filter, times +using the red or blue color appropriate to the particular filter, times the tangent of the zenith distance. Figure~\ref{fig:DCRexample} shows the DCR trend for the 5 filters \grizy, as well as the measured @@ -1849,5 +1858,5 @@ The amplitude of the DCR trend in the five filters is $(g,r,i,z,y) = (0.010, 0.001, -0.003, -0.017, -0.021)$ arcsec airmass$^{-1}$ -magntiude$^{-1}$. We saturate the DCR correction if the term $color +magnitude$^{-1}$. We saturate the DCR correction if the term $color TAN (\zeta)$ for a given measurement is outside a range where the DCR correction is well measured. The maximum DCR correction applied @@ -1859,5 +1868,5 @@ \begin{figure*}[htbp] \begin{center} - \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.gri}.png} + \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.gri.sm}.png} \caption{\label{fig:astroflat.gri} High-resolution astrometric flat-field correction images for $gri$.} \end{center} @@ -1866,5 +1875,5 @@ \begin{figure*}[htbp] \begin{center} - \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.zy}.png} + \includegraphics[width=0.85\textwidth,clip]{{pics/astroflat.zy.sm}.png} \caption{\label{fig:astroflat.zy} High-resolution astrometric flat-field correction images for $zy$.} \end{center} @@ -1891,5 +1900,5 @@ The dominant pattern in the astrometric residual is roughly a series of concentric rings. The pattern is similar to the pattern of the -focal surface residuals measured by \cite{onaka.spie}, which also has +focal surface residuals measured by \cite{2008SPIE.7014E..0DO}, which also has a concentric series of rings with similar spacing. The ``tent'' in the center of the focal surface is reflected in these astrometry @@ -1961,5 +1970,5 @@ per-measurement position errors. -Figure~\ref{fig:allsky.astrom.sigma} shows the standard devitions of +Figure~\ref{fig:allsky.astrom.sigma} shows the standard deviations of the mean residual astrometry in $(\alpha,\delta)$ for bright stars as a function of position across the sky. For each pixel in these @@ -1997,8 +2006,6 @@ than the \approx 17 mas value in that earlier analysis. We attribute this degradation to the noise introduced by the astrometric -flat-field. - -\note{This noise has been addressed for the DR2 release of the - individual measurement data. show updated maps and residuals} +flat-field. This noise has been addressed for the DR2 release +of the individual measurement data. \begin{figure}[htbp] @@ -2039,5 +2046,5 @@ The initial analysis of the PV2 astrometry used the 2MASS positions as -an inertial constraint: the 2MASS coordiates were included in the +an inertial constraint: the 2MASS coordinates were included in the calculation of the mean positions for the objects in the database, with weight corresponding to the reported astrometric errors. In this @@ -2064,5 +2071,5 @@ and PS1 epoch (\approx 2012). Since we are fitting the image calibrations without fitting for the proper motions of the stars, we -are in essencence forcing those stars to have proper motions of 0.0. +are in essence forcing those stars to have proper motions of 0.0. The background quasars would then be observed to have proper motions corresponding to the proper motions of the reference stars, but in the @@ -2080,5 +2087,5 @@ star mean position is then translated to the expected position at the epoch of that image. The image calibration is then performed relative -to these predicted postions. This process naturally accounts for the +to these predicted positions. This process naturally accounts for the proper motion of the reference stars. In order to make the calibrations consistent with the observed coordinates of an external @@ -2089,5 +2096,5 @@ In order to perform this analysis, we need estimated distances for -every reference star used in the analysis. Green et al (REF) +every reference star used in the analysis. \cite{2014ApJ...783..114G} performed SED fitting for 800M stars in the 3$\pi$ region using PV2 data. The goal of this work was to determine the 3D structure of the @@ -2104,5 +2111,5 @@ and Solar motion parameters ($U_{\rm sol}, V_{\rm sol}, W_{\rm sol}$) = (9.32, 11.18, 7.61) km sec$^{-1}$ as determined by -\cite{1997MNRAS.291..683F} using Hipparcos data. Proper motions are +\cite{1997MNRAS.291..683F} using Hipparchus data. Proper motions are determined from the following: \begin{eqnarray} @@ -2112,5 +2119,5 @@ \mu^{\rm sol}_{b} & = & \frac{(U \cos(l) + V \sin(l)) \sin(b) - W \cos(b)}{d} \end{eqnarray} -where $d$ is the distance and $l,b$ are the Galactic coordintes of the +where $d$ is the distance and $l,b$ are the Galactic coordinates of the star. Note that the proper motion induced by %% \note{some reference for this?} @@ -2179,5 +2186,5 @@ to $g-r$ and $g-i$ colors. This transformation reproduces Gaia photometry reasonably well for stars which are not too red. For a -comparison, we have seleted all PS1 stars with Gaia measurements +comparison, we have selected all PS1 stars with Gaia measurements meeting the following criteria: $14 < i < 19$, with at least 10 total measurements, within a modest color range $0.2 < g - r < 0.9$. We @@ -2210,5 +2217,5 @@ % set Gr = -0.090 + gr*gi*0.229 + gi*(-0.207+gi*(gi*0.015 - 0.250)) + gr*(0.491+gr*(-0.021*gr - 0.052)) -%\[ +%\begin{equation} %G - r = -0.09 + 0.229(g-r)(g-r) + (g-i)(( @@ -2247,4 +2254,8 @@ median differences are ($\sigma_\alpha, \sigma_\delta) = (4, 3)$ milliarcseconds. + +For a future data release, we will recalibrate the Pan-STARRS $3\pi$ +astrometry using the Gaia DR2 release. The addition of Gaia-measured +proper motions will obviate the need to correct for the Galactic rotation. \subsection{Calculation of Object Astrometry} @@ -2376,6 +2387,6 @@ \bibliographystyle{apj} -\bibliography{lib}{} -% \input{calibration.bbl} +% \bibliography{lib}{} +\input{calibration.bbl} \end{document}