Propuesta e ideas del Dibujo

All our targets are selected from the SDSS spectroscopic survey, so we accurately know both their positions on the sky and their redshifts. To extract a spectrum for a given galaxy, we first select the ALFALFA data-cube that contains the target and then: (a)

integrate over the sky to extract the raw spectrum;(b) evaluate the noise level of the spec- trum to establish its quality;(c) perform a final quality check. Here we discuss these steps.

a. Spectrum extraction

The signal from each target is integrated over the whole frequency range of the corre- sponding data-cube and over a sky region centered on the object position. Because noise increases with the square root of the integration area, integrating over too large a region lowers the quality of the spectrum without increasing the signal. Our targets are always smaller than the ALFA beam (the mean R90 for sample A is 1000), so we simply integrate

over a sky region of 40×40. In Figure 2.3, we illustrate examples of spectra extracted at two different positions of the sky inside the same data-cube. The coloured regions indicate where the spectra would be evaluated (but their size is not scaled).

The H_i spectrum is an histogram of flux density S as a function of velocity. For each velocity channel v, the corresponding flux density Sv is obtained by integrating the signal

3.2 ALFALFA stacking tool 39 sv(x, y) over the spatial pixels centered at the target galaxy position, as observed by a

radio telescope of beam response pattern B:

Sv[Jy] =

ΣxΣysv(x, y) ΣxΣyB(x, y)

,

wherex,y are the sky coordinates (the two polarizations are kept separated). The expres- sion above means that the spatially integrated profile is obtained by summing the signals over all the spatial pixels of interest and dividing by the sum of the normalized beam

B(x, y) over the same pixels (for a detailed discussion see Shostak & Allen 1980). The ALFALFA beam pattern can be approximated by:

B(x, y) = exp −1 2 x σx 2 −1 2 y σy 2! , with σx = (2 √ 2 ln 2)−1_×3.30_{, and σ} y = (2 √ 2 ln 2)−1_×3.80 _{(Giovanelli et al. 2005).}

We note that we discard a spectrum if more than 40% of the pixels of the integrated region have a quality weight w less than 10. We also keep track of the three strongest continuum sources in an area covering 400×400 around each source, since they can affect our spectra by creating standing waves. Standing waves are periodic fluctuations in the background, which occur when radiation from a source located near the target is multi- ply reflected and scattered by the telescope structure before reaching the receiver. These multiple reflections, which happen in telescopes with blocked aperture like Arecibo, can degrade the data and increase the noise. In the following we do not discard blindly any spectrum because of standing waves, but we record the strongest continuum sources for a possible subsequent inspection. Moreover, this information would be useful if an automatic quality threshold had to be implemented.

b. Rms evaluation

For each spectrum we need to measure the noise level, which is an indicator of the quality of the spectrum and which will later be used as a weighting factor when we stack spectra. Ideally the signal is zero in any channel outside the galaxy emission region; in practice there are fluctuations of the signal measured in the different channels. As noise estimate we use the standard deviation of the measured baseline from the expected zero line, hereafter identified as rms (root mean square). The rms has to be evaluated in regions of the spectrum where there is no emission from the target galaxy and where there are no spurious signals, such as H_i emission from companion galaxies. In Figure 3.2, for example, some of these features are visible in the first two rows in the velocity range [-1500;-1000] km s−1_.

These strong RFI “absorption features” must not be included in the rms evaluation; since they are far from the galaxy signal we anyway do not need to discard the spectrum.

In order to define the spectral region that might contain galaxy emission, we estimate its expected observed H_i width. The measured width of the H_i line depends on the rotational velocity of the galaxy, which can be estimated from its luminosity using the well-known Tully-Fisher relation (Tully & Fisher 1977), and on the galaxy inclination since we actually measure the velocity component along the line-of-sight. For each target we estimate the expected observed velocity wT F;o from the SDSS data, following Giovanelli et al. (1997a).

We use the i-band magnitude, k-corrected and corrected for Galactic and internal extinc- tion (according to equations 11 and 12 in Giovanelli et al. 1997b) to estimate wT F, and

then project this value on the line-of-sight using the estimated inclination in order to ob- tainwT F;o. We are aware that the Tully-Fisher relation does not hold for all morphological

types and environments, but we think this is not a major issue since these velocities are only used to estimate the region of the spectrum that should contain a significant sig- nal from the galaxy. In any case, the mean observed velocity that we estimate, of about

300km s−1_{, is compatible with the one measured by the GASS survey for the same stellar}

mass range (Catinella et al. 2010).

Once we know where the signal from the target should be located, we apply a robust linear fit to the baseline excluding these channels and regions of the spectrum with a qual- ity factor w < 10 (half the maximum value). This step allows us to eliminate possible gradients in the background, as for example seen in the top right panel in Figure 2.3, where the spectrum has a tilted baseline. We do not try to eliminate possible residual wavy baselines at this stage, as we will perform a manual reduction of the final stacked spectrum. We underline that the ALFALFA baselines are already almost flat and all with similar noises, and both characteristics are essential for the stacking. The quality of the baselines and their homogeneity is confirmed by the rms that we measure over the same regions of the spectrum just fitted. The average rms for the whole sample is 3.6±0.5 mJy for each polarization. After averaging the two polarizations, armsof∼2.5 mJy is obtained, which is comparable to the average rms of 2.2 mJy evaluated for published, individually reduced ALFALFA spectra of detections.

c. Final quality check

After we have extracted the spectra, we visually inspect each of them. We check the extraction process, and we discard spectra with bad baselines caused by continuum sources and those with possible spurious signals close to the galaxy. For example, if one polarization has a significantly stronger signal than the other, we discard the spectrum because it is

3.2 ALFALFA stacking tool 41

contaminated by RFI, as the 21 cm emission is not polarized. These cuts eliminate 624 objects (out of 5350) from the initial sample.