El teorema de Stone-Weierstrass

RECONS has been using SuperCOSMOS as our primary sky catalog utilizing a special output catalog produced by Nigel Hambly to get around the fact that the generic catalog processing (as with many compiled sky catalogs) generally assumed stars have zero proper motion, and only looked within 6′′

for matches (Hambly et al. 2001a) across plates. Stars with proper motions larger than 0.2′′ _yr−1 _{on a set of plates with an epoch spread of ∼30}

years will move more than 6′′_{, and won’t get crossmatched to their other appearances. The}

main SuperCOSMOS catalog thus contains multiple disconnected entries for high proper motion objects, a small price to pay – perhaps a hundred thousand badly-matched objects out of nearly two billion.

to sources identified on all four plates. The variable epoch spreads between the plates result in a variable upper limit for proper motions that is above 0.18′′

yr−1_{, except in regions}

northward of -18 DEC, where far older POSS-I E red plates were used. In those areas, the reliable upper limit is at least 0.12′′ _yr−1_.

The TINYMO survey was done in two pieces, the first (between 20h and 08h) by Dr. Henry in October 2007; the second (between 08h and 20h) by myself in May 2009. In both cases, the SuperCOSMOS Science Archive1 was searched via SQL query for objects in the southern sky that:

Appeared on all four plates. This sets an upper proper motion limit as described above, as well as limits on color – the star could not be so red it did not appear in the BJ

plate. This cuts out a number of cool and faint stars. This also cut out a small region of sky (roughly RA 16:00 to 16:20, DEC ₋10 to ₋15) where there is no R1 plate.

Appeared to be single stellar sources by ellipticity and other quality param- eters. This cut out a large number of extragalactic and spurious sources.

Are brighter than R2 = 16.5. The R2 magnitude limit allows for detection of stars

withBJ=21 andBJ−R2 colors as red as 6 (a brown dwarf), and matches the Giclas surveys

(Giclas et al. 1979) as well as previous RECONS proper motion surveys.

Were detected in 2MASS within 5′′ _{of the weighted mean plate position. The}

mean plate position recorded by SuperCOSMOS is weighted by the positional accuracy of each of the detections; the epoch of this effective plate position is usually around 1985 (Hambly, N.C. private communication, 2010), while the mean epoch of 2MASS is around

2000. Thus, any star moving less than 5′′ _{in 15 years (µ <0.333}′′_yr−1_{) will be matched to its}

2MASS entry. The more stringent limit is thus the 4-plate-detection requirement, although requiring 2MASS entries does limit us to the 470 million targets in the 2MASS point source catalog Cutri et al. (2003).

Are in the southern hemisphere, more than 10 degrees from the Galactic plane and 20 degrees from the Galactic center. This removes the enormously reddened and crowded fields in the center of the Galaxy. In the second half of the TINYMO search we had to go back and eliminate three other small areas (RA 15:00 to 16:00, DEC +00 to ₋30; RA 15:00 to 16:00, DEC ₋30 to ₋60; RA 17:00 to 18:00, DEC +00 to ₋30) around the North Galactic Spur just outside the bulge that contained as many potential nearby stars as the rest of the sample combined (see Figure 4.1 and Figure 4.2). We did not, however, remove the Large and Small Magellanic clouds. Cutting out these areas of the sky (and the one removed by the missing R1 plate) reduces the area covered by TINYMO to 16214 square

degrees, or 39.3% of the sky.

The limit of 2MASS is effectively JHK _≈15. SuperCOSMOS goes to BJ = 21, and we

have set our magnitude cutoff at R2 = 16.5, which roughly means our faintest V (assuming

the average of BJ and R2 is v) is v=18.75. The limiting magnitudes for M dwarfs are

all set by the R2 filter. For an M0V star (see Appendix A) (MBJ = 10, BJ −R2 = 2.3, BJ −K = 4.5) corresponding to our cutoff at R2 = 16.5 are BJ = 18.8, R2 = 16.5, and

K = 14.3. This implies a limiting distance of 630 pc. For an M9.0V star (MBJ = 20.4,

Figure 4.1: Molleweide equal-area projection of the TINYMO survey extraction centered on RA=0h,DEC=0d, with a 10◦

band around the Galactic equator and a 20◦

region around the Galactic Center removed. The colored points (green, yellow, orange, and red) are stars selected by later phases of the survey processing, demonstrating the crowded areas around the Galactic bulge that were later removed. Also visible is the 25 square degree area without R1 plate data.

which implies a limiting distance of 6.6 pc. Within 25 pc (distance modulus 1.99) we should be able to detect every M dwarf bluer than BJ −R2 = 2.6 (M7V).

Ultimately, the search picked up just short of 14 million stars in the covered 16000 square degree region seen in Figure 4.2.

SELECT

s.objID,t.pts_key,s.ra,s.dec,muacosd,sigmuacosd,mud,sigmud,scormagB,scorma gR1,scormagR2,scormagI,j_m,j_msigcom,h_m,h_msigcom,k_m,k_msigcom

FROM Source AS s WITH (INDEX(0)),

CrossNeighbours2MASSPSC AS x, TWOMASS..twomass_psc AS t WHERE

s.ra BETWEEN 0.0 AND 2.0 AND s.dec BETWEEN 0 AND -30.0 and Nplates=4 AND sCorMagR2 < 16.5 AND chi2 < 3.0 AND prfstatB BETWEEN -3.0 AND +3.0 AND

prfstatR1 BETWEEN -3.0 AND +3.0 AND prfstatR2 BETWEEN -3.0 AND +3.0 AND prfstatI BETWEEN -3.0 AND +3.0 AND ellipB < 0.2 AND ellipR1 < 0.2 AND ellipR2 < 0.2 AND ellipI < 0.2 AND qualB < 128 AND qualR1 < 128 AND qualR2 < 128 AND qualI < 128 AND

s.objID=x.ssaID AND t.pts_key=x.pscID AND distanceMins < 5.0/60.0 order by s.objID

Code 1: The SQL query. Carried out in chunks 2h RA by 30◦ _DEC.

Table 4.1: The TINYMO Search Cuts

Step Sift Number

0 Stars in SuperCOSMOS 1.9 billion

1 Stars meeting quality, plate detection, and sky coverage criteria 14 million

2 . . . within 25 pc by plate distance 88586

3 . . . within color regions 1077

4 . . . and remnants of the original color regions 1154

5 . . . plus by-eye companion detections 1215