esac PACS Spectrometer: forward model tool for science use

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1 esac European Space Astronomy Centre (ESAC) P.O. Box, Villanueva de la Cañada, Madrid Spain PACS Spectrometer: forward model tool for science use Prepared by Elena Puga Reference HERSCHEL-HSC-TN-2131 Issue 1 Revision 0 Date of Issue 25 Jan 2017 Status For review Document Type Technical note Distribution PACS-ICC, HSC

2 Title Document template for HPDP release notes Issue 1 Revision 0 Author E. Puga Date 27 January 2017 Approved by: Date Reason for change Draft Issue Revision Date First version of document January 2017

3 1 Table of Contents 2 INTRODUCTION RELEVANT CONNECTED DOCUMENTS FORWARD MODEL TOOL... 4 HIPE task description... 5 Science validation strategy Input HSA products Source model Projection algorithm consistency Final product for raster-mode observations Appendix material Appendix A... 12

4 2 INTRODUCTION The uneven illumination of the PACS IFU field-of-view is produced by the non-perfectly uniform detector s response at all PACS-S wavelengths. The reduction of the spaxel s active area (~8 x8, instead of the idealized detector with a nominal size 9.4 x9.4 and a uniform response) leads to a flux loss comparable to that observed in reality. This flux loss is accounted for in the calibration schemes for well-centred point and fully-extended sources, via the central (or central 3x3) spaxels calibration in total flux density and surface brightness, respectively. However, the specific correction is science-case dependent. In particular, the level2 pacsrebinnedcubes and spectral mosaic cubes may render imperfect extracted spectra (via aperture extraction on spectral mosaic cubes in the latter) for: Off-centred point sources Crowded fields Semi-extended structures In the case of single-pointed observations of sources centred in the IFU field-of-view, the E2P HIPE task can be applied for semi-extended sources, as an additional correction step to the total flux density calibration of the central or central 3x3 spaxels from the pacsrebinnedcubes,. Provided that an analytical model is representative of the source flux distribution, the following document details the use of a forward model tool, to simulate a PACS observation, in order to estimate the proper calibration correction on the surface brightness. 3 RELEVANT CONNECTED DOCUMENTS PACS Spectrometer Simulation and the Extended to Point Correction, Jeroen de Jong, Feb 11, 2016 (no TN number) Technical Note on Cube Interpolation Validation, Elena Puga, Nov (no TN number) 4 FORWARD MODEL TOOL Chapter 5 of the PACS Spectrometer Handbook explains the surface brightness calibration

5 performed by the Standard Generation Processing (SPG) pipeline. f!"#$%& Jy beam = x! f!"#"$%&'" Jy beam The pipeline includes an additional extended-source correction (ESCF) to account for losses between the beams in the case of a fully extended source, which corresponds to the solid angle ratio between the beam efficiency of the central spaxel and the nominal size of 9.4 x9.4. This effectively changes the units of surface brightness from [Jy/beam] to [Jy/spaxel] in the following way f!"#$%& Jy spaxel = x! f!"#"$%&'" Jy beam ESCF spaxel beam The Forward Model Tool (FMT) is available in HIPE 15.0, it generalizes the calculation of the coupling factor for each detector (s) Jy f!"# beam = ξ! = S!,! B!,!;!!,! with S!,! being the source model surface brightness distribution in units of [Jy/pixel], and B!,!;! the synthetic beam efficiency. The point- and extended-source corrections are recovered when considering a very small spatially extended source (delta function), as ξ!" = PSCF, and a fully extended source of S!,! = 1 Jy/pixel, for which ξ!" = ESCF (9.4)!. HIPE task description The task pacsspecfrommodel simulates PACS cubes according to user- provided source flux distribution model (spatially and spectrally) folding in the imperfect response via the multiplication by the beam efficiencies of each detector on every pointing (mapping) pattern. ξ! Jy beam = S!,!!,! Jy arcsec! 0.5! arcsec! pixel B!,!;! pixel beam The task requires a reference observation to obtain the raster pattern information. Reference products can be either a pacsrebinnedcubes or a pacscubes (and their sliced versions). It also needs a source model, which extends the class ExtendedSpectralSource via the ExtendedSpectralSourceAdaptor. The task utilizes the task BeamsProjector, shared with E2P. 5

6 Correspondent tests are also provided within HIPE. Science validation strategy Two usefult scripts are provided, with an end-to-end comparisons of a point source spectrum extraction. The example observation is of RDor in a 5x5 oversampled raster of the H2O line, obsid number The selection of the slices mimics observations in the different observing modes applicable to the task (single pointing, undersampled rasters using specproject, and oversampled rasters using drizzle): ForwardModelToolSinglePointingUnderRasters.py ForwardModelToolOverRasters_drizzle.py Using a centred point-like source simplifies the source-modelling effort and constitutes a good sanity check as can be easily compared with the PSCF (see result in Figure 1). Additionally, the total observed source flux can be estimated from the central spaxel s spectrum (in the central raster position, for rastered cases) corrected to the total source flux, via the PSCF, as it is done by the task extractcentralspectrum. For non point-like sources, this estimate of the total flux may come from photometry maps Input HSA products ESCF removal In order to compare the simulations with the observed cube pipeline product, the latter must be transformed back to units of [Jy/beam]. The removal of the ESCF involves application two different functions depending on the input products: pacsrebinnedcubes or slicedpacsrebinnedcubes: undoextendedsourcecorrection (needs to be imported from herschel.pacs.spg.spec.extractcentralspectrumtask) slicedpacscubes: undoextendedsourcecorrectionslicedcube. This function is at the same location in HIPE 16.0, but it is not available in HIPE 15.0 and therefore its definition must be run in the useful script for oversampled rasters. See Appendix A. The ESCF correction is of the order of 30% in the blue and 5% in the red Pointing effects pacsspecfrommodel calculates the simulated observation using the pointing information at 6

7 every rebinned wavelength slice (pacsrebinnedcube) or at every sample in the dot-cloud (pacscubes). This means that any average pointing offset, or even the pointing jitter throughout the observation is accounted for in the simulated data. The global offset can be estimated from the distance between ranominal,decnominal and the averaged a-posteriorireconstructed pointing product in ra,dec metadata. In the case of , it corresponds to 2.27 (HSA javascript). As a first approach, we compare a centred point source with a perfectly pointed reference observation. For that purpose, we create a function removeoffset, that subtracts from the reference product (datasets ra,dec) the global offset of the central spaxel (in the central raster position) and the jitter. Figure 1 PSCF Recovery check using the simulated central spaxel of the pacsrebinnedcube for the central raster position in RDor. Here, the assumption is that the source is perfectly centred and we have removed the global pointing offset and jitter Source model 7

8 Figure 2 Total flux density conservation with respect to Gaussian FWHM computed using the FMT algorithm (open squares) and the jython function visualization methods (filled circles). Jython function definition in Appendix A, input flux density is 144 Jy. The source model in units of [Jy/arcsecs 2 ] can be input via: an existing HIPE task SmallExtendedSpectralSource that models spatially a centred symmetric Gaussian function and spectrally a continuum with a first order polynomial and a line with a Gaussian profile, whose amplitude is scaled to the continuum. a user-provided jython class that extends the class ExtendedSpectralSourceAdapter. It must contain a method named getflux. An example of such a function is provided in Appendix XX, including the necessary methods to ensure proper visualization of the input model. The model is constructed within the task pacsspecfrommodel (BeamsProjector) in a twostep fashion: first on a finer grid (5 times smaller than the beam grid) and then rebinned into the final 0.5 grid of the synthetic beams with a dedicated averaging function. The algorithm, being flux conservative by a scaling factor (0.1)! (0.5)!, imposes a minimum size FWHM for a Gaussian equivalent to 0.2 (see Figure 2). The surface brightness is normalized to the source s total flux density using the integral of the 2D-Gaussian (2π σ! ). WARNING: the source diameter can only be estimated from the PACS observation ifself only in the case of an oversampled map on a large-enough field-of-view that comprises the source. In the case of undersampled rasters or single pointings, the source size cannot the measured on the PACS observations, as the PSF is convolved with the squared 9.4 x9.4 spaxel size. 8

9 4.1.3 Projection algorithm consistency Figure 3 Central spaxel comparison for RDor undersampled raster (central raster position rpos=4) As stated in Sect. 4, the simulated PACS observations at the pacsrebinnedcubes or pacscubes level are in units of [Jy/beam] (see Figure 3). However, all three projection algorithms available to construct PACS spectral mosaic cubes have a flux-conserving scaling factor, in order to allow for aperture extraction in the final spectral mosaic cube. In all three cases this factor corresponds to the ratio between the nominal size of the idealized detector 9.4 x9.4 and the grid pixel size of the mosaic cube: s = 9.4! pixsize! Hence, it is necessary to modify this scaling factor and remove the dependency on the spaxel nominal size. This is precisely ESCF, which is the ratio between the beam s solid angle and the spaxel nominal size. The result of the simulation is depicted in Figure 4. 9

10 Figure 4 Aperture extracted line spectrum of RDor. C1 is the extracted central spaxel spectrum from the central raster position (source model). The spectra extracted from the observed cube (blue) shows a line flux 20% lower than C1. The simulated spectrum, once corrected from flux scaling, recovers the initial flux density of the continuum and line flux Final product for raster-mode observations In the case of raster maps, we can construct the ratio of the observed and the simulated spectral mosaic cubes. The resulting simulation efficiency map provides a coverage map to aid the user to identify areas in which the spectral aperture extraction is feasible with respect to the source s flux distribution. The simulation efficiency provides a pixel-to-pixel correction that must be applied to the observed mosaic cube (see Figure 5). However, the task does not model the wavelength shift and skew effects in the line emission that the IFU has (see Calibration and Performance document PICCKLTN041 ), and thus the ratio values at the wings of the lines should not be over-interpreted. This effect is averaged out when considering spatially symmetric apertures on the spectral mosaic cube. 10

11 Figure 5 Simulation Efficiecy at um for the RDor undersampled raster rasterline=[1,3,5], rastercol=[1,3,5]. Produced by useful script ForwardModelToolSinglePointingUnderRasters.py. 5 Appendix material 11

12 Appendix A Remove ESCF correction function for pacscubes (used as input for drizzle in oversampled mosaic cubes) caltree=getcaltree() def undoextendedsourcecorrectionslicedcubes(slicedcubes,caltree=caltree,verbose=1): verbose=verbose) slicedcubesout = slicedcubes.copy() for slice in range(len(slicedcubes.refs)): if verbose: print 'slice',slice cubout = undoextendedsourcecorrectioncube(slicedcubes.get(slice), caltree=caltree, slicedcubesout.replace(slice,cubout) slicedcubesout.meta["extendedsourcecorrected"].value = False return slicedcubesout def undoextendedsourcecorrectioncube(cube, caltree=none, verbose=0): """undoextendedsourcecorrection(cube, caltree=none, verbose=0) At Level 2 (Final rebinned cubes), PACS abs. flux calibration is established for a perfectly extended point source (flat surface brightness). This calibration contains a specific "Extended Source Correction" step to account for the spatial beam inefficiency, i.e. to account for the fact that the spaxels don't have a perfect and flat response over 9.4"x9.4", but that some flux is 'lost between the spaxels' """ if (("extendedsourcecorrected" in cube.meta.keyset()) and (cube.meta["extendedsourcecorrected"].value == 1)): cube=cube.copy() if not caltree: caltree= getcaltree() if caltree.version < 70: print "Please update your calibration tree version "+str(caltree.version) +" to version >= 70" extloss = caltree.spectrometer.extendedsourceloss extipol = LinearInterpolator(extLoss.getWavelength(), extloss.getsignalfraction(), True) wave, flux = cube.getwave(), cube.getflux() # else: for x in range(5): for y in range(5): interpolatedfractions = extipol(wave[:,x,y]) flux[:,x,y] *= interpolatedfractions cube.setflux(flux) cube.setfluxdescription("flux") cube.meta["extendedsourcecorrected"].value = False print "The extended source correction was not applied to these data," print "It will hence not be undone here!" return cube 12

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