Frecuencias de respuestas según el grado de satisfacción

During an observation scan, the photons reflected by Herschel ’s mirror onto the bolomet- ers are absorbed and increase the temperature as the telescope scans the sky. The data obtained from the bolometers is referred to as “time-ordered data” or TOD as it exists as a one dimensional stream of data separated by scan and detector number. This data needs to be turned into an image of the sky (map) to work with HerMES source detection algorithms. HerMES uses the standard HIPE (Herschel Interactive Processing Environ- ment, Ott (2010), Valtchanov (2014)) pipeline for part of the map reconstruction then uses an algorithm developed by the SMAP team to create the final maps (Viero et al.,

2013;Levenson et al.,2010)).

2.2.1 HIPE

HerMES maps are constructed from two different pipelines. The first processing from level 0.5 to 1 product was done using HIPE, the Herschel Interactive Processing Environment. Whilst this timeline processing was not explored in this thesis, the main algorithms are summarised below for context and completeness.

The first step is to remove electrical crosstalk. Electrical crosstalk is interference with signals from individual detectors, for example a signal in one detector inducing a signal in another. A cross-talk removal matrix is recorded for each SPIRE photometer array, noting the relative induction introduced by each bolometer and thus providing a linear decomposition of each data stream from each bolometer as a function of the signal from all bolometers. From there the signals can be decoupled and the signal from each bolometer understood independently.

Deglitching is performed. Glitches are caused by cosmic rays hitting a detector, in- creasing the temperature rapidly and spiking the signal. If propagated through the map they appear as a very bright streak that dims in the direction of the scan. The timelines are first analysed for these sharp peaks through a kappa-sigma function. Kappa-sigma clipping is a way of identifying data in the timeline that is drawn from a different pop- ulation distribution as the background. In this case, it is a method of finding signals in the timeline that are much higher or lower than expected, many standard deviations away from the mean. First, the mean and standard deviation of all values of the data are found.

The mean is subtracted off and pixels within a range of κσ are found. κ = 5 as standard within the pipeline. Then the mean and standard deviation of the new sample are found again and the criteria reapplied. This is iterated 100 times or until the mean changes by a fraction of < 1.0 × 10−10. Then all pixels outside that value are flagged to be masked or replaced with white-noise representative of the mean and sigma derived from the last iteration. Cosmic ray glitches typically only effect one bolometer at a time.

Other glitches can be removed, these include cooler-burps which are longer lasting deviations from the signal than cosmic rays. The temperature of the bolometer array constantly increases as the focal plane is exposed to the sky, this is known as temperature drift. Thermistors on the focal plane act to monitor this increase in temperature which can be used to subtract off the temperature drift from the timeline. Cooler-burps and are an atypical increase in temperature of the focal plane (i.e. all the bolometers) that cannot be taken into account with a standard temperature drift correction. The resultant is a paler then darker stripe across the map as the gradient of the temperature drift correction is far steeper or shallower than required, an example is shown in figure2.2.

The electrical response of the signal is filtered with a low-pass filter to remove small scale fluctuations in the signal not caused by an in-sky signal. As filtering can cause aberrations, an electrical filter correction is applied by dividing by the corresponding transfer function. Units of the detector are then converted into flux density; the response of each detector is slightly different and non-linear and further discussed byGriffin et al.

(2013).

The SMAP team have their own filter to remove the low frequency noise of less than 1Hz associated with temperature drifts and a stricter glitch detector. Therefore during the above pipeline the TOD is not corrected for temperature drifts.

2.2.2 SMAP Algorithm

The second stage is to make the level-one data into maps. HIPE has its own map making process, the Na¨ıve mapper. In this algorithm, the TODs from each obsID are stitched together to form a continuous data stream and a temperature drift correction is applied. The median value is subtracted from the timelines to speed up the convergence of the iterative mapmaker described below. Whilst the instruments are kept at an extremely steady temperature by the liquid helium coolant system, small fluctuations in temperature are introduced exposing the detectors to light. There are two thermistors on the focal plane, exposed to the same light as the bolometers. These thermistors (and any masked

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Figure 2.2: An image of the 250µm GAMA15 field (a H-ATLAS collaboration field, see chapter 6) in mJy/beam showing an unaccounted for temperature drift. The flux associ- ated with the temperature drift has been incorrectly subtracted towards the edge of the map, showing the surface brightness increasing due to the erroneous temperature rise. The white region on the bottom-right is a foreground barred spiral galaxy NGC 5746. bolometers) can track the µK fluctuations in temperature. Averaging the thermistors, (or, in cases where a cosmic ray has hit a thermistor and this has been noted, just using one value) allows a subtraction to be made to the bolometer response. The specifics of this algorithm ensure all the scans are mean subtracted. NB, as of writing, no absolute calibration has been calculated for the Herschel maps that would add a true background to these maps, so mean subtraction is a reasonable way to present the data. These temperature drifts are responsible for 1/f noise in the data. 1/f noise is noise with a power inversely proportional to the frequency of the noise and can be correlated across detectors. Removing these temperature drifts accounts for the majority of 1/f noise in the map. (Levenson et al.,2010).

Binning in the SMAP pipeline is performed differently. A weighted mean is constructed instead. The signal on the sky, S can be described as

Sdsj = gdM (xdxj, ydxj) + Pdsn + Ndsj (2.1)

where d is an individual detector, s a scan and j a time sample. This signal can be described as the gain on a detector g, M (xdsj, ydsj) the sky brightness at a detector at a

particular scan and time sample. P_dsn is an order-n polynomial baseline offset that will be calculated iteratively, N is the noise.

The initial sky map M0(xdsj, ydsj) is set to zero with gains set to 1.0. In each step

of the iteration, either the gains are held constant or P_dsn, with each alternate step in the iteration switching between either the gains or polynomial fit to the scans and detectors allowed to vary. Both g and P are determined by minimising the residual variance between the model and map between steps.

Then a weighted mean is constructed Mi(x, y) = P dsjwids(Sdsj− Pdsni)/gdi P dsjwids (2.2) In other words, the value of the flux at a time sample that has been binned into a pixel is the weighted sum of the signal minus the background subtraction divided by the gain for each detector and scan. At this point the polynomial P_dsn is chosen to minimise the residual value between the current and previous iteration of the map such that the residual map R is given as

Ri_dsj = Sdsj− gid[Mi−1(xdsj, ydsj) + Psdni] (2.3)

The weights w_dsj are the inverse variance of the residual of the timeline w_dsi = 1/1 N N X j=1 (Ri_dsj)2 (2.4)

where N is the number of samples in scan S, and the weights are normalised to sum to 1. Thus scans that have a low variance in the residual are weighted more highly.

From this a noise map can be calculated using these residual variances and expressed in terms of the weight of each sample as

σj(x, y) = (X

dsj

wj_ds)−1/2 (2.5)

In other words, the noise represents the standard propagation of errors as calculated from the variances of of samples on individual pixels in the residual map.

The order of polynomial Pnto fit will depend on the size of the map. This polynomial will be calculated and subtracted off for each scan and detector. Therefore the best fit polynomial will depend on the length of a scan. Smaller fields with be n = 2 up to n = 3 for the widest HerMES fields. The level 7 field HeLMS’s map was an exception and was created using SANEPIC (Patanchon et al.,2008).

From the sky map M and baseline fit Pn fits, a model for what each detector sees can be constructed. This is set to occur after ten iterations to ensure values are close to their final value. Any detector that varies 10σ from this model (i.e. is glitched) is removed from subsequent iterations and therefore the final map-making process.

Also occurring after ten iterations is a calculation of map offset. Each AOR is stacked with Spitzer MIPS 24µm sources. Sources within these catalogues are known to an ac- curacy of < 1 arcsec by checking against 2MASS sources in the same fields so are a valid measure of offset. The centre of a 2D Gaussian fit is recorded and each offset and glitched detector is noted for the remaining iterations.

Each map is produced with an image map in units of Jy/beam, an error map again in units of Jy/beam, a coverage map in units of seconds and for some datasets a flag extension that flags regions in the map with a binary mask, 0 for no coverage, 1 for coverage in scans in one direction, and 2 for “central” scans. This final flag extension will be removed from all maps for the final data release.

Jackknife maps are also constructed by dividing the data into two sets after the para- meters for equation 2.1 have been determined. They are labelled “ang” for data divided by scan orientation, “bolo” for division by bolometer number, and “half” by dividing the data by time. Some maps will not have enough data per pixel to do division by time or bolometer. Further, dividing by scan direction means only the overlapping regions can be examined. Nested maps do not have jackknife maps released. Jackknife maps are useful for noise estimation, as a way of estimating errors during data extraction on maps, and for map validation - glitches or cosmic rays that pass through detection algorithms can be caught by eye and scans or detectors removed in further reruns of the maps-making software.

2.2.3 SMAP Simulation Pipeline

Simulations are an integral part of testing astrophysical models. Models that produce galaxy catalogues must be able to recreate the observations they were derived on when run through simulations of telescope pipelines. Simulated images and catalogues provide a controlled way to test the performance of data reduction pipelines by giving a known input to measure outputs against. The process of creating simulated Herschel SPIRE images is given below when a simulated catalogue of fluxes and possible positions is given.

The input catalogue or truth catalogue is given as a series of fluxes at different wavelengths spanning the SPIRE bands. The fluxes are converted to Jy and are put into an array rep- resenting the sky at a size equivalent of 2 arcsec2 length per pixel, far smaller than the final SPIRE product maps. Any fluxes found to be in the same pixel are summed. The array is then convolved with a Gaussian representation of the telescope beam (discussed below) which produces a sky, a true representation of the simulated catalogue on the sky

given the PSF.

The SMAP team have developed an algorithm to transform a simulated sky into a SPIRE photometer timeline, and then allow the entire SMAP data reduction to be per- formed. The timeline simulator is given a HerMES field to mimic, so the same depth, scan masking and scan pattern can be used. 1/f noise to represent temperature fluctuations and Gaussian noise can be optionally applied. The full iterated pipeline is run again, find- ing the baseline subtraction to remove the 1/f noise. This simulation pipeline was able to show SMAP’s 1/f noise removal worked very well (Levenson et al., 2010). Jackknife maps are also produced either by scan orientation, scan number or bolometer number. The resultant products are referred to as simulated maps, and any catalogues generated are output catalogues.