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\include{preface} \standalonefalse \renewcommand{\okinfinal}[1]{{#1}} % Version 2.0: The BGPS Outer Galaxy extension \title{The Bolocam Galactic Plane Survey VIII: Data Release 2 and Outer Galaxy Extension} \include{authors} \keywords{ISM: all of it --- stars: formation} \include{abstract} \include{introduction} % move to top? \include{calibration} % v2 calibration + v1 error description [nothing to be added] \include{expansion} \include{reduction} % only delta-v1 or things left out \include{pointing} % done [reviewed by group] \include{stf} % done [reviewed by group] \include{source_extraction} % \include{conclusion} % \include{appendix} % Begin appendices (only for thesis?) % \include{simulations} % move before stf... or just cut it out (describe simulations in STF section) % % only include relevant parts for source extraction / stf sections % \include{reduction_part2} % \include{cal_appendix} %\clearpage \bibliographystyle{apj_w_etal} \bibliography{v2} \end{document}
\input{preface} \section{The Angular Transfer Function of the BGPS} \subsection{Atmosphere Tests} \label{sec:atmotests} In order to determine the angular response of the Bolocam array and BGPS pipeline in realistic observing conditions, we performed simulations of a plausible synthetic astrophysical sky with synthetic atmospheric signal added to the timestream. To generate the simulated atmosphere, we fit a piecewise power law to a power spectrum of a raw observed timestream. The power spectrum varies in amplitude significantly depending on weather conditions and observation length, but the shape is generally well-represented by $P\propto \nu^{-2}$ for $\nu < 2 $ Hz and $P \propto \nu^{-1} $ for $\nu \geq 2$ Hz where $\nu$ is the frequency. We show a fitted timestream power spectrum in Figure \verb|\ref{fig:powerspecfit}|. %\optional{ %At low frequencies, the power spectrum turns over because of the AC sampler %(offset from the DC value, not the total power, is the measured value). %Despite the break, we use the low-frequency power fit to represent the AC %sampling. %} \Figure{{figures/050706_o53_raw_ds2.nc_indiv13pca_PowerSpectrumFit}.png} {Fit to the power spectrum of a $\sim30$ minute observation. Three independent power laws are fit to the data, with a fixed break at 0.02 Hz (below which the AC sampler removes signal) and a fitted break at higher frequency, near 2 Hz, where the power spectrum flattens towards white noise. %The Y-axis indicates the spectral power in units of Jy$^2$ for a single beam; the %power spectra were taken on the calibrated data } {fig:powerspecfit}{0.5}{0} %Variations %upon these atmospheric parameters were not investigated in detail, but in the %limit that the atmosphere is perfectly correlated across the array, the details %of the atmospheric behavior should not affect the pipeline's performance. The Fourier transform of the atmosphere timestream is generated by applying noise to the fitted power spectrum. The power at each frequency is multiplied by a random number sampled from a gaussian distribution with width 1.2, determined to be a reasonable match to the data, and mean 1.0. The resulting Fourier-transformed timestream is $FT(ts) = (r_{\nu1} P_f)^{1/2} + i (r_{\nu2} P_f)^{1/2}$, where $r_1$ and $r_2$ are the normally distributed random variables and $P_f$ is the fitted power-law power spectrum. The atmosphere timestream is then created by inverse Fourier transforming this signal. % I don't know why this is right, but I think it is: see % PowerSpectrumStuff.ipynb Gaussian noise is added to the atmospheric timestream of each bolometer independently, which renders the correlation between timestreams imperfect. The noise level set in the individual timestreams sets the noise level in the output map. \subsubsection{Simulated Map Parameters} We simulated the astrophysical sky by randomly sampling signal from a circularly symmetric 2D power-law distribution in Fourier space. We modeled this signal using power spectrum power-law indices ranging from -3 to +0.5; in the HiGal $\ell=30$ SDP field, the power-law index measured from the 500 \um\ map is $\alpha\sim-2$ (see Section \verb|\ref{sec:otherdata}|). The data were smoothed with a model of the instrument PSF to simulate the telescope's aperture and illumination pattern. For each power-law index, four realizations of the map using different random seeds were created. The signal map was then sampled into timestreams with the Bolocam array using a standard pair of perpendicular boustrophedonic scan patterns. Examples of one of these realizations with identical random numbers and different power laws are shown in Figure \verb|\ref{fig:exp10gridin}|. \FigureTwo{figures/exp10_input_grid}{figures/exp10_recovered_grid} {Examples of input (left) and output (right) maps for different power law $\alpha$ values. For very steep power laws, most of the power is on the largest scales. $\alpha=0$ is white noise. The axis scales are in pixels, where each pixel is 7.2\arcsec, so each field is approximately 1\arcdeg\ on a side. The Bolocam footprint is plotted in the lower-right panel of the left figure as an indication of the largest possible recovered angular scales. The input images are normalized to have the same \emph{peak} flux density. The pipeline recovers no emission from the simulation with $\alpha=3$, but this value of $\alpha$ is not representative of the real astrophysical sky - Herschel sees structure with $\alpha\lesssim2$, and the BGPS detected a great deal of astrophysical signal (see Section \verb|\ref{sec:otherdata}| and Figure \verb|\ref{fig:higalpowerlaw}|). } {fig:exp10gridin}{1} % We found that all power-law indices returned broadly consistent results, but % the steeper indices had no signal recovery at small spatial scales because of % low signal-to-noise ratio (i.e., the selected normalization put all recoverable % structure below the observational noise level). Example recovered images as a function of $\alpha$ % are shown in figure \verb|\ref{fig:exp10gridout}|. We therefore only used the % simulations with moderate power-law indices ($-2 < \alpha < -1$) for % quantitative analysis. % \Figure{figures/exp10_recovered_grid} % {Examples of the recovered maps for different power law $\alpha$ values. % For the steepest power-law, most of the flux above the noise level is lost. } %