Quick detection of NEOs with GAIA
=================================

GAIA-CUO-103   E. Hoeg                    5 Feb. 2002

Full text on http://www.astro.ku.dk/~erik/gaia/A103.neo.obs (7 pp.)


ABSTRACT: 
A new method is proposed for quick onboard detection of
NEOs with GAIA. The alert and the information can be available on
the ground within hours.  The detection may reach V=21 mag, and
perhaps 22 mag. Broad-band multi-colour photometry of the NEO is
included. 



NOTE:
The method of NEO detection is described especially for GAIA-2, the new
version of GAIA with 6 hours rotation, but it is in principle valid
also for the baseline version of GAIA with 3 hours rotation.  The 
technical requirement is a modified sampling of ASM3 and AF17 in 
the two Astro telescopes.  A summary of proposed sampling for the 
Astro telescopes with superposed fields and 6 hours rotation 
period is given for GAIA-2.

The assumed 6 hours rotation is a preliminary value, and it should be
noted that the previous value of 3 hours may still be selected.
The question of superposed fields for Astro-1 and -2 is not settled. 
For these reasons the following description is fairly complicated, 
and may contain inconsistencies. But the report is distributed now 
so that the new possibility for NEO detection may be taken into 
account in the new GAIA design.

The detection of NEOs with GAIA has been discussed by Perryman (2000)
and Mignard (2002) where e.g. a comparison with detection by other 
methods is given. Hoeg (2000) and Hoeg & Knude (2001) discuss an 
enhanced detection with GAIA, and the possibility for ground-based 
follow-up.

GST = GAIA Science Team
GSR = GAIA Study report (=white report=ESA-SCI(2000)4)



1. Sampling in GAIA-2 for the Astro telescope

A new version of GAIA, here called GAIA-2, is being studied by 
industry in collaboration with the GAIA Science Team (GST). At 
the meeting of GST on 17 Jan I proposed the sampling for GAIA-2
on a viewgraph, hence the schematic form of this section:

** Basic assumptions:

The spin axis moves at constant angular velocity at a constant angle
from the sun:
- Precession rate 170 mas/s at 55 deg sun angle.
(the rate is only 5 % higher at 45 deg sun angle)

The fields of Astro-1 and -2 will probably be superposed on one
focal plane assembly in GAIA-2. But it is considered to provide separate
ASM1s for the two fields, see Section 4.

Maximum vertical motion (i.e. in the cross scan direction) of all stars
in the field of view, in case of 6 hours revolution of the satellite :

   2s ~ 0.34" ~ 3.1 pixel during integration in Astro
   40s ~ 6.8" ~ 60.0 pixel during Astro field crossing
   6s ~ 1.0" ~ 2.0 pixel during integration in Spectro

Typical asteroid velocities are according to GSR Fig.1.32:
NEO 40 mas/s, <100mas/s
Trojan 10 "/hr=3 mas/s.

** Proposed sampling, modified from that in  CUO-100.3:

ASM1 and 3, Detection and windowing :

   ASM1 at V=20, G2V, sigma : sg_y= 8 mas across scan, p.161 in GSR
     The 2 s integration time in GAIA-2 would mean 5.6 mas,
     which we do not here take into account.
     Along scan sigma : sg_x= 3 mas

   ASM3 comes 4 sec later, sigma=8 mas 
   across scan velocity sigma=11 mas/4s=2.8 mas/s
   along scan velocity sigma=3x1.4 mas/4s=1.1 mas/s

   From the cros-scan velocity measured by ASM1, 3 decide whether the 
     star is in Astro-1 or -2. Use then the known attitude velocity 
     of the telescope to allocate the following windows.
       Direct use of measured velocity is not good because of the
       too large cross scan 3xsigma offset of 3.0 pixels:
         After ~40 s field crossing: 
         cross scan position: 3*sigma=3*110 mas=330 mas=3.0 pixels

AF17 for stars in superposed fields if NEO detection is *not* required:
   Read area as in GAIA-1 of 60x12 pixels:
     12 samples, 2x12 pixels/sample
     6x4 samples, 2x3 pixels/sample
     12 samples, 2x12 pixels/sample
   The 6x4 samples are used to determine the cross-scan position
     to confirm the choice of Astro field for the star.
   Transmit these 48 samples, 
     instead of 30 in GAIA-1 where fields are not superposed

AF17 if NEO detection *is* required is discussed in the following
   sections.

BBP, implement resolutions as in Astro-1 and 2 :
     like Astro-1 in the middle half of CCDs (mBBP) 
     as Astro-2 in remaining outer rows of CCDs (oBBP) 
       for stars and galaxies

AF1-16 and mBBP : 9 or 10 pixels/sample


2. Detection of NEOs with the Astro telescopes

I assume here the newly proposed 6 hours revolution period. The
proposed method works also with superposed ASM1 fields as discussed in
Section 4, but the present discussion is for separate ASM1 fields.

A NEO can have a maximum speed of 100 mas/s and can thus move by 400
mas during the 4 s from ASM1 to ASM3. Therefore a window of 12x6
samples = 888x1332 mas =~1 sq.arcsec should be taken in ASM3 instead
of the present 5x5 window if such a NEO shall be within. It is
proposed to read such windows unless the star density is high. At the
average density of 25000 stars/sq.deg brighter than V=20 there is
0.0019 star/sq.arcsec. The larger windows could therefore be read at
up to 10 times average star density without getting too many 'false'
stars.

A detection process is run on the ASM3 window. If an object is
detected which is consistent with the object detected in ASM1 it is
assumed to be a normal star for which a 5x5 sample window of ASM3 is
transmitted, and the star shall be observed on all following
CCDs as hitherto. 

If no consistent object is detected at the centre,
but an object with consistent magnitude is detected at an offset
position it is supposed to be a NEO, provided the offset exceeds 3
sigma. This means a cross-scan velocity difference of 3x2.8=8.4 mas/s at
V=20 mag which gives a quite good distinction of NEOs since the 
typical speed of a NEO is 40 mas/s.

We have here considered the excess velocity only in cross scan
direction to distinguish a NEO from a star. But the along scan
position is measured much more accurately, sigma =3 mas instead of 8 mas
at V=20, and still with 1 second integration assumed (see Section 1). 
Our estimate is therefore very conservative. We believe
that V=21 or 22 may be a realistic limit (see Section 5). 
It is noted that G and V are identical within 0.1 mag for 
-0.4<V-I<1.4 (GSR, p.239).

Certain criteria of M times sigma in either or both coordinates to
distinguish a NEO from a star should be chosen with care. If M=3
probably only about 1 per cent of stars will mistakenly be taken for a
NEO in ASM3.  This seems acceptable. If however M=2 is chosen several
per cent of the stars will be taken for NEOs and thus be measured with
windows in AF and BBP which are offset in position and therefore
giving inferior measurements.  This problem must be studied separately
for the main GAIA stars brighter than 20 mag, and for the fainter ones
which are observed differently, cf.  Section 5.

It was shown above that the number of false NEOs due to a random star 
within the 1 sq.arcsec window in ASM3 will be about 1 per cent at 
20 mag in case of a 10 times higher than normal star density. 
According to GSR Fig.6.4b, 98 per cent of the sky
contains less than 110 stars/8 arcmin down to the limit counted in the
A1.0 catalogue. The text on p.244 says that 200 stars/8 arcmin in the
catalogue corresponds to N_20=200 000 star/sq.deg (N_nn = the number of
stars brighter than nn mag.) This means quite safely that NEOs may be
efficiently detected in 98 per cent of the sky, and this statement is
fairly independent of the reliability of the A1.0.

With superposed fields, however, the average star density is twice as
high, but NEOs can still be detected on a large fraction of the sky.

In addition to random stars may come possibly consistent objects 
due to cosmic events.  Such false NEOs will be safely rejected 
by means of the AF17 data so that no data will be transmitted for them.

If a NEO is detected  12x6=72 samples of the ASM3 window are 
kept for transmission. 

No readings need be taken in AF for the sake of NEO discovery, but AF
measurements are of interest for accurate orbit determination.

Modified readings are taken in AF17, cf. Table 2.  
A window with 12x4 samples, 2x3 pixels/sample, and with 9x1 samples,
2x12 pixels/sample before and after, is  taken in AF17 for 
a NEO, in total 9+48+9=66 samples, 
instead of the usual 30 samples of 2x12 pixels/sample in GAIA-1
for a star. Detection is made in the window, and for all 
consistent detections the positions, elongation and magnitude values 
may be transmitted. For the most probable position, the usual windows 
in BBP are allocated and transmitted.

The detection software must be able to detect elongated images having
a length up to 200 mas during the 2 s integration. The
elongation and its direction should be measured in ASM1, ASM3 and AF17
and be used for the check of consistency, and be transmitted.

An elongated image will obtain a less precise position than a
point-like image, and consequently a less precise velocity, but the
object can still be well distinguished as a NEO just because of the
large velocity causing the elongation.


3. Detection of NEOs with Spectro and Astro

The detection of all objects in Spectro down to V=20 is required.
With such a detection and that in Astro it is ensured that most NEOs
will be detected in at least two GAIA telescopes if it is detected in
one. It can be shown that even a NEO with the extreme velocity of 100
mas/s in direction perpendicular to the scanning circle would rarely
escape detection in two telescopes, not even when this circle moves
with maximum velocity.

Any NEO detected and measured in one of the Astro telescopes can
safely be identified in the Spectro if it is detected there. The
vector resulting from positions observed in two telescopes, i.e. two
Astro telescopes or an Astro and the Spectro, is so accurate that the
NEO can be retrieved from the ground within a few days as described
in CUO-84.

The detection limit in G-magnitude should be set a little fainter in
ASM3, AF17 and SSM than in ASM1 in order that nearly all objects
detected in ASM1 are also detected in the three other places.
Otherwise objects near the limit would too often be missed because of
photon noise.  One could even set the detection limits for NEO
treatment somewhat fainter, also for ASM1 detection, say at G=21 mag 
without significant increase of telemetry because so much less data 
are transmitted for a NEO than for a star. Perhaps G=22 mag could be 
reached considering the longer integration time of 2 s per CCD and 
the resulting doubling of number of photons and lower readnoise per 
sample, cf Section 5.


4. Superposed fields

One of the optical designs being considered for GAIA-2 contains
superposed fields of AF and BBP, but separate CCDs for the ASM1. This
is possible because the optical system contains an intermediate focus
where a stop may be placed to cover part of the field for one
telescope.  The above considerations show however that no decisive
disadvantage is encountered for V<20 mag when both fields are entirely
superposed, neither for stars nor for NEOs, but separate field are
of course advantageuous.

In case of superposed fields in the ASM1 sky mapper we cannot decide
which field a moving object like a NEO is in, if only the observations
from ASM1 and ASM3 are available. In case a NEO is suspected both
Astro-1 and -2 must be taken as possibilities, i.e. two windows must be
read in AF17 corresponding to the two telescopes. The AF17 measurement
will be used to decide whether the NEO is in Astro-1 and 2.
Therefore BBP windows need only be allocated for one of the Astro 
telescopes. Thus superposed fields are acceptable for the detection 
of NEOs but will give somewhat inferior performance.

The advantage of separate fields in ASM1 is greater for NEOs fainter
than 20 mag because the higher uncertainty in the ASMs and AF17 for
faint objects makes the simultaneous distinction of fields and
star/NEO more difficult.  With separate ASM1 fields only the star/NEO
distinction is required. This is then possible already with the
ASM1/3 data, and again, much more accurately, with the ASM/AF17 data.


5. NEOs fainter than 20 mag

The previous discussion was concerned with detection of NEOs among
objects brighter than the general limit of GAIA at 20 mag. Detection
of fainter NEOs should be considered, it requires additional
modification of the sampling and onboard processing.
We here assume separate ASM1 fields except in paragraphs where noted.

The detection in ASM1 shall go to a fainter limit, say 22 mag. The
detection in ASM3 shall be based on the same window of 12x6=72 samples
and go to the same limit of 22 mag. The resulting standard errors as
function of V (or G) are given in Table 1, assuming for simplicity
that the errors are multiplied by a factor 2.0 per magnitude. sg_x is
the along scan error and sg_y is across scan. A3 is the area
corresponding to +-3 sigma in both coordinates, N is the average
number of stars in the sky per sq.deg brighter than V; n3 is the
average number of stars brighter than V in the area A3.


---------------------------------------------------------------------
Table 1. Standard errors in GAIA detection in Astro and the resulting
average number of stars brighter than V within a +- 3 sigma area A3.
Assumption is that the Astro fields are separate.

 V    sg_x   sg_y     A3          N         n3
mag   mas    mas   sq.arcsec   st/sq.deg   stars
20     3      8      .86         25000    0.00166
21     6     16     3.5          50000    0.0133
22    12     32    13.8         100000    0.106
---------------------------------------------------------------------

A realistic limit of detection in ASM1 is G=22.0 with the newly
proposed 2 s integration.  This follows from Table 8.1 in GSR which
gives a detection probability of 0.41 at G=21.0 based on simulation
with a real detection algorithm. Since the simulation assumed 0.86 s
integration time per CCD it may be possible to reach 22.0 mag with 2 s
integration and the lower readnoise per sample. In Table 1 we still
assume a conservative 1 s integration for the standard errors which
may become smaller by a factor 1.4 with 2 s integration.

It follows from Table 1 that the velocities determined from the ASM1
and 3 measurements will have 4 times larger errors at 22 mag than at
20, thus 4x(1.1, 2.8) mas/s=(4.4, 14.4) mas/s in x and y respectively. 
A 3 sigma detection in y will only catch fast NEOs, but in x also  
the slow ones may be caught. A limit of 2 sigma could be considered 
since the resulting several per cent false NEOs will be recognized 
as such when compared with the AF17 observation.

The window in AF17 is centred on the position predicted by the ASM1
and 3 detections. When the object arrives at AF17 34 s after the ASM3 
measurement the position has an uncertainty of (150, 490)mas=
(4.0, 4.4) pixel. The window in AF17 should therefore contain  
about 15x10=150 samples with 2x3 pixel/sample rather than the 
12x4=48 samples required above at 20 mag.

If an object detected in AF17 is consistent in position and magnitude
with the ASM detections, and if perhaps also the image elongations are
consistent, the object is a suspected NEO for which data should be
transmitted to ground. Otherwise no data need be transmitted.

It seems from the value of n3 in Table 1 that it is possible to reach
22 mag on the part of the sky having average star density or less, if
about 1 per cent of the stars is allowed to generate a false NEO. This
may be allowed without a severe penalty on telemetry since the AF1-16
and the BBP need not be transmitted for the sake of NEO discovery for
stars fainter than 20 mag.

It is seen from Fig.6.4b that about 70 percent of the sky has less
than average star density, which corresponds to 25 stars/8 arcmin^2 in
the A1.0 catalogue. For each CCD in the ASM a running mean of the
number of detected stars should be kept all the time, and this density
value should be used to decide about the transmission of NEO data. It
should also be used to decide about the window sizes to be read in
ASM3 and AF17 since the reading of many large windows at high stars
densities for the sake of NEOs would have a penalty on the measurement
of ordinary stars.

If the ASM1 fields are superposed there is a penalty.  For the faint
objects the higher star density of superposed fields will give
significantly more confusion.

It is proposed to transmit the AF data from a few CCDs midway between
ASM3 and AF17, say from AF6 and AF12. Any false NEO from the above
proposed data would very rarely be confirmed by some random star in
these CCDs. This should be decided by on-ground analysis before a
science alert is given.

These considerations are of course quite preliminary. Investigations
with a realistic design of GAIA, the readnoise, the sampling, the star
densities and with simulations are required in order to decide what is
feasible.


---------------------------------------------------------------------
Table 2. Samples per window in Astro and the transmission, assuming
two separate telescope fields. BBP windows are always transmitted for
V<20 mag, but it is TBD for V>20.

                    ASM3                      AF17
         Sample  Read    Transmit   Sample  Read   Transmit
mag       pixel  sample  sample      pixel  sample  sample

V<20 star  2x2   12x6     5x5        2x3    12x4    12x4  cf. Section 2
                                     2x12  9+9x1    18x1
V<20 NEO   2x2   12x6     5x5        2x3    12x4    12x4 
                                     2x12  9+9x1    18x1

V>20 star  2x2   12x6       0        2x3    15x10     0  cf. Section 5
V>20 NEO   2x2   12x6     5x5        2x3    15x10    5x5 
For a NEO transmit also AF17 position, mag, elongation, AF6, AF12 
---------------------------------------------------------------------

The detection of NEOs fainter than 20 mag in the Spectro telescope by
means of only one sky mapper, SSM1, faces a penalty on telemetry since
the positions of all detected stars must be transmitted to ground
where a comparison with suspected NEOs from a closely preceding or
following Astro telescope is made. The required complete transmission
of positions and magnitudes of all 4 billion stars brighter than 22
mag may result in an interesting complete survey, so this should be
considered.

A significant reduction of the required telemetry could be achieved
with a second sky mapper, SSM2, right after, or at a short distance
from the first, SSM1. Only in case of an inconsistency in the two
positions should the data be transmitted for stars fainter than 20
mag.

This new SSM2 has a function very different from the SSM2 proposed in
previous CUO reports, where it was placed as far as possible from
SSM1, at the very end of the field in order to provide an accurate
velocity vector by analysis entirely on the ground, based on
transmitted data for all detected objects from both SSMs. This "old"
SSM2 is not required anymore since the vector is supplied by the Astro
fields.


6. Conclusions

NEOs or other fast moving asteroids with velocities above certain limits
may be detected in the Astro telescopes. The 3 sigma limits at V=20 mag
are about 9 mas/s in the cross scan direction and 3.2 mas/s along scan.

Detection and measurement of a NEO in an Astro telescope gives a
position and a velocity vector with a precision of 0.3 mas/s across
scan. This comes from +-8 mas per position at each end of a 34 s 
interval. The position uncertainty after one day is then about 
30 arcsec across scan and much smaller along scan which may be 
sufficient for recovery by ground-based observations within a few hours.

A NEO detected in an Astro telescope can be easily recognised if it
is detected in a Spectro or Astro telescope two hours before or
after.  This combined data will then give a much improved velocity
vector, about 100 times more accurate.

The NEO detection down to 20 mag will be efficient at star densities 
up to ten times the average density, i.e. in about 98 per cent of 
the sky.  NEOs as faint as 22 mag may be detected in about 70 per cent 
of the sky having less than average star density.

The NEO detection possibilities could be fully esploited if GAIA
data were transmitted to ground almost continuously, not only during
the presently foreseen 8 hours out of 24. The advantage of having two 
ground stations should be investigated further.

All estimates of performance given in this report are preliminary and
should be revised in due course. The estimates are on the
conservative side when the GSR baseline size of mirrors is assumed,
and they may therefore still hold with the smaller mirrors now
foreseen for GAIA-2. It is especially important for the detection of
NEOs fainter than 20 mag to have separate fields for ASM1 in GAIA-2.


7. References

SAG-MP-002    M. A. C. Perryman   2000
Near-Earth Objects Observable with GAIA

SAG_CUO_77    E. Hoeg               23 June 2000
NEO measurement with GAIA

GAIA-CUO-84   E. Hoeg, J. Knude          12 Feb. 2001
Detection of NEOs with GAIA and ground-based follow-up

F. Mignard  5 Jan 2002    Submitted to A&A
Observations of solar system objects with GAIA, I- Detection of NEOs
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