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5.8 Expected Telemetry Rate

As it was mentioned at various times, the amount of data one would ideally like the GAIA satellite to transmit to the ground is far larger than the available telemetry rate. Any observing proposal must therefore provide an estimate of the necessary effort in terms of telemetry rate which is implied by the suggested observations.

Generally speaking, we would like to observe galaxies in all sky areas that trigger the detection and from a suitable surrounding area, and to send the corresponding data to the ground. Such a surrounding area could be defined as composed by all the square areas of a given side that are adjacent to the areas where an excess surface brightness has been detected, as it is shown in Figure 5.3, where a side of 2 arcsec was chosen for illustrative purposes.

Figure 5.3: Galaxy Data Transmission. The solid squares indicate the sky areas where an excess surface brightness has been detected, while the dashed line delimits the sky area from which galaxy data are trasmitted to the ground. Right arrows indicate the satellite scan direction. The GAIA Astro Airy Disk is also shown to illustrate the high resolution achievable in galaxy observations.

The outlined observation strategy appears to satisfactorily cover the galaxy regions whose surface brightness is just below the detection limit, thus allowing to study the galaxy morphology in greater detail. In the following, however, in order to estimate the telemetry rate required for galaxy observations, a few simplifying assumptions will be made. It is assumed that data are transmitted from circular areas centered on the galaxy center, and that the radius $ r_t$ of this areas can be written as

$\displaystyle r_t=r_e+\Delta\,r~,$ (5.7)

where $ \Delta\,r$ is a positive constant. The overall sky area $ \Omega_t$ within a radius $ r_t$ for all galaxies brighter than $ I$ could then be used as a rough estimate of the overall sky area from which data should be transmitted to the ground in order to observe all galaxies down to this magnitude. Neglecting the possible superposition on the sky between different galaxies, which is correct as far as the sky area in consideration is reasonably small, $ \Omega_t$ can be written as

...{d}I'+ \pi\,(\Delta\,r)^2\,\,\Omega_{sky}\,N_c(I)~, \end{split}\end{displaymath} (5.8)

Table 5.7: Fraction of sky $ \Omega _t/\Omega _{sky}$ within a radius $ r_t=r_e+\Delta\,r$ for all galaxies brighter than $ I$ for some values of $ I$ and $ \Delta\,r$. $ \Omega _t/\Omega _{sky}$ in $ 10^{-6}$ sky, $ \Delta\,r$ in arcsec and $ I$ in magnitudes. Values calculated via Newton integration (see Section 9.7 in [Press et al. 1996]) of Equation 5.8.
$ \frac{\Omega_t}{\Omega_{sky}}$   $ \Delta\,r$
    2 4 6 8 10
$ I$ 10 5.9559699 6.4369017 6.9178336 7.3987655 7.8796973
  11 13.015628 14.507042 15.998455 17.489869 18.981282
  12 28.234900 32.617360 36.999820 41.382281 45.764741
  13 62.711973 74.930181 87.148388 99.366598 111.58480
  14 147.90940 180.29082 212.67225 245.05368 277.43510
  15 379.93125 461.71573 543.50020 625.28469 707.06916
  16 1059.6399 1257.0964 1454.5528 1652.0093 1849.4657
  17 3118.8339 3576.2198 4033.6057 4490.9917 4948.3775
  18 9354.6744 10375.459 11396.243 12417.028 13437.812
  19 27814.818 30020.274 32225.728 34431.184 36636.639
  20 80550.210 85187.870 89825.529 94463.189 99100.849

Numerical values of $ \Omega _t/\Omega _{sky}$ for different values of $ I$ and $ \Delta\,r$ are given in Table 5.7. From these it can be concluded that, with $ \Delta\,r=6$ arcsec, all galaxies brighter than the detection limit $ I_{det}=17$ would cover about $ 0.4\%$ of the sky. The telemetry rate required to cover such a sky area can be derived as function of the adopted sample size under the assumptions that each sample value is coded into 16 bits and that a loss-less compression factor of 16/5 can be applied before transmission. The assumption of such a relatively high compression factor is deemed realistic, since most sample values will be low, thus allowing a very efficient compression.

Under these assumptions, the required telemetry rate after compression $ TR$ for galaxy observations can be estimated as

$\displaystyle TR=\sin\phi_{lim}\,B\,\frac{\Omega_t}{\Omega_{sky}}\,\frac{v_s\,h_{fov}}{A_{sam}}\,BPS~,$ (5.9)

where $ \phi_{lim}$ is the chosen lower limit in Galactic latitude for galaxy observation ( $ \sin \phi_{lim}$ is the fraction of sky where the absolute value of the Galactic latitude $ b$ is greater than $ \phi$), $ B$ the number of photometric bands in which observations will be carried out, $ v_s$ the scan velocity of the satellite, $ h_{fov}$ the height of the field of view, $ A_{sam}$ the sample size and $ BPS$ indicated the number of bits per sample after compression. Values of $ TR$ are given in Table 5.8 for the presently assumed values of the relevant parameters.

Table 5.8: Telemetry rate after compression required for galaxy observations as function of the sample size. Values calculated from Equation 5.9, where $ \phi_{lim}=15~\textrm{deg}$, $ B=5$, $ \Omega_t/\Omega_{sky}=0.004$ and 5 bits/sample after compression have been assumed. Sample size expressed in pixels, telemetry rate in kbits/s.
$ 6\times8$ $ 6\times4$ $ 6\times2$ $ 1\times8$
108 217 433 650

As mentioned in Section 2.6, a total telemetry rate of about 1 Mbit/s after compression is presently foreseen for GAIA. From Table 5.8, it appears that the observation of galaxies, carried out with $ 6\times8$ or $ 6\times4$ pixels/sample, as suggested in Section 5.7, would require a significant, but probably not unreasonable, part of the total telemetry. On the other hand, observing the assumed fraction of the sky with a smaller sample size would require a prohibitively high telemetry rate.

next up previous contents
Next: 6. Simulation and Stacking Up: 5. Detection and Observation Previous: 5.7 Expected Accuracy in   Contents
Mattia Vaccari 2000-12-05