6666( 3) - 02/22/96 10:48 - [ 1] PROPOSAL FOR HUBBLE SPACE TELESCOPE OBSERVATIONS ST ScI Use Only ID: 6666 Version: 3 Check-in Date: 22-Feb-1996 10:38:07 1.Proposal Title: The Mass Function and Binary Star Fraction of the Trapezium Cluster ------------------------------------------------------------------------------------ 2. Scientific Category 3. Proposal For 4. Cycle BINARIES AND STAR FOR GO 6 ------------------------------------------------------------------------------------ 5. Investigators Contact? PI: John Stauffer Center for Astrophysics CoI: Lynne Hillenbrand University of California at Berkeley N CoI: Mark McCaughrean Max-Planck Institut fur Astronomie N CoI: Lee Hartmann Center for Astrophysics N CoI: Burton Jones University of California at Santa Cruz N CoI: Andrea Ghez University of California at Los Angeles N ------------------------------------------------------------------------------------ 6. Abstract We propose deep WFPC2 images of the Trapezium cluster to determine the low-mass end of the initial mass function, to search for brown dwarfs, and to explore the close binary population in the cluster. The Trapezium is not only the best open cluster in terms of distance and compactness to study with HST; it is the only nearby representative of dense star formation regions where the extinction is sufficiently low that extensive optical studies are feasible. The V and I-band photometry derived from our WFPC-2 images will be combined with ground-based data, including existing and proposed JHK photometry, optical imaging, and optical spectroscopy. These data will enable us to determine the effects of environment - star/gas densities and the presence of massive stars - on the form of the initial mass function and binary distribution, and to search for brown dwarfs in this extremely young cluster down to masses ~ 0.02 M(sun). The proposed two-color images of the entire Trapezium cluster with WFPC2 will greatly improve upon our AO1 PC imaging of ~ 1/3 of the cluster, which had been seriously limited by spherical aberration effects. ------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 2] Observations Description ------------------------ Our goal is to obtain V band photometry for the entire Trapezium cluster region to a limit corresponding to the hydrogen mass-burning limit, and to obtain I band data for this region that extends as faint as possible (our goal was 0.01 M(sun); we have settled for 0.02 M(sun)). We have used the D'Antona and Mazzitelli (1993) PMS models (Alexander opacities, CM convection theory) and the Kirkpatrick Etal (1993) temperature scale for low mass stars. For A_V = 2.4, the extinction derived by HT for the Trapezium cluster, these models predict a V magnitude for a 0.08 M(sun), 1 Myr old star of V = 22.9. The same model calculations predict that a 0.02 M(sun)\\ Trapezium member would have I = 21.7. Because of the very bright nebulosity in the Trapezium (surface brightnesses at v and i of about 16.5 and 15.5 magnitudes per sq. arcsec, respectively), it is best to use filters which avoid the major nebular emission lines. The F547M filter does this reasonably well as a V replacement. There is no appropriate medium-band filter located near the I-band, and we have chosen to use the F791W filter instead of the `standard' WFPC2 I filter (F814W), as the former excludes the bright HII region emission lines of SII at 9069 and 9532A, and therefore gives us an increased sensitivity to stars in this region. By adopting 10 carefully chosen field centers (the positions given are for the center of PC1), we can tile a region of 6 x 6 arcminutes almost completely with two extensions to the NE and SW to sample the r ~ 5 arcmin stellar density at V and I. The two extensions to larger radii will be used to tie the HST imaging photometry to ground-based photometry from the NTT in order to insure the calibration of the reddest, faintest stars is well-calibrated on a standard system and as a further test of mass segregation. For each field, we will obtain short and long exposures in each of the two filters (60 sec and 19 minutes, with a CR-SPLIT for F547M; and 60 seconds and 10 minutes for F791W). With standard overheads these exposures fit within the 53 minutes available for one orbit. We estimate that the long-exposures should reach our desired magnitude limits with the average nebular surface brightness with S/N ~ 10 in the central pixel using both the formulae provided in the WFPC2 manual and from scaling derived directly from O'Dell's 1 minute ERO F547M image of one Trapezium field. Real Time Justification ----------------------- Calibration Justification ------------------------- Additional Comments ------------------- ------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 3] Data Distribution Media: 8MM Blocking Factor: 10 Ship To: *Center for Astrophysics*60 Garden St.*Cambridge, MA*02138 Ship Via: UPS Email: , ------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 4] TARGET LIST a) Fixed Targets ------------------------------------------------------------------------------------------------------------------------------------ Tar| Target | Target | Target |Coord | Radial | Flux data No | Name | Description | Position |Eqnx | Vel. | ------------------------------------------------------------------------------------------------------------------------------------ 1 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 22.00S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS1 Cluster -05D 22' 00.0" +/- 1" B-V = 2.0+/-0.5 2 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 22.00S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS2 Cluster -05D 24' 40.0" +/- 1" B-V = 2.0+/-0.5 3 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 16.45S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS3 Cluster -05D 20' 40.0" +/- 1" B-V = 2.0+/-0.5 4 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 16.45S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS4 Cluster -05D 23' 16.0" +/- 1" B-V = 2.0+/-0.5 5 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 11.12S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS5 Cluster -05D 21' 56.0" +/- 1" B-V = 2.0+/-0.5 6 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 11.12S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS6 Cluster -05D 24' 40.0" +/- 1" B-V = 2.0+/-0.5 7 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 05.79S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS7 Cluster -05D 23' 16.0" +/- 1" B-V = 2.0+/-0.5 8 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 05.79S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS8 Cluster -05D 20' 40.0" +/- 1" B-V = 2.0+/-0.5 9 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 00.46S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS9 Cluster -05D 24' 40.0" +/- 1" B-V = 2.0+/-0.5 10 TRAPEZIUM- STELLAR CLUSTER, Open RA=5H 35M 27.33S +/- 0.1S, DEC= J2000 V = 22.0+/-0.5 POS10 Cluster -05D 19' 19.0" +/- 1" B-V = 2.0+/-0.5 6666( 3) - 02/22/96 10:48 - [ 5] Visit: 01 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 1 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS1 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 2 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS1 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 3 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS1 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 4 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS1 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 5 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS1 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 6] Visit: 02 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 21 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS2 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 22 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS2 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 23 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS2 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 24 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS2 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 25 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS2 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 7] Visit: 03 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 31 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS3 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 32 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS3 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 33 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS3 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 34 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS3 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 35 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS3 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 8] Visit: 04 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 41 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS4 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 42 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS4 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 43 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS4 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 44 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS4 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 45 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS4 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 9] Visit: 05 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 51 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS5 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 52 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS5 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 53 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS5 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 54 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS5 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 55 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS5 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 10] Visit: 06 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 61 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS6 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 62 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS6 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 63 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS6 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 64 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS6 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 65 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS6 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 11] Visit: 07 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 71 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS7 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 72 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS7 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 73 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS7 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 74 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS7 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 75 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS7 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 12] Visit: 08 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 81 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS8 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 82 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS8 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 83 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS8 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 84 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS8 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 85 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS8 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 13] Visit: 09 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 91 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS9 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 92 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS9 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 93 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS9 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 94 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS9 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 95 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS9 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 14] Visit: 10 Visit Requirements: ORIENTation 303.0D TO 320.0D On Hold Comments: Additional Comments: Exposures ------------------------------------------------------------------------------------------------------------------------------------ Exposure| Target |Instr | Oper. | Aper |Spectral|Central| Optional |Num| Time | Special Number | Name |Config| Mode |or FOV |Element |Waveln.| Parameters |Exp| | Requirements ------------------------------------------------------------------------------------------------------------------------------------ 101 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 60.0S POS10 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 102 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 60.0S POS10 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 103 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS10 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 104 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F791W CLOCKS=YES,ATD- 1 300.0S POS10 GAIN=15 ------------------------------------------------------------------------------------------------------------------------------------ 105 TRAPEZIUM- WFPC2 IMAGE PC1-FIX F547M CLOCKS=YES,ATD- 1 1120.0S POS10 GAIN=15,CR- TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ 6666( 3) - 02/22/96 10:48 - [ 15] Summary Form for Proposal 6666 Item Used in this proposal ------------------------------------------------------------------------------------------------------------------------------------ Configurations WFPC2 ------------------------------------------------------------------------------------------------------------------------------------ Opmodes IMAGE ------------------------------------------------------------------------------------------------------------------------------------ Optional Parameters CLOCKS=YES ATD-GAIN=15 CR-TOLERANCE=0.1 ------------------------------------------------------------------------------------------------------------------------------------ Proposal Category GO ------------------------------------------------------------------------------------------------------------------------------------ Scientific Category BINARIES AND STAR FORMATION ------------------------------------------------------------------------------------------------------------------------------------ Special Requirements ORIENTation 303.0D TO 320.0D ------------------------------------------------------------------------------------------------------------------------------------ Spectral Elements F547M F791W ------------------------------------------------------------------------------------------------------------------------------------ Target Names TRAPEZIUM-POS1 TRAPEZIUM-POS2 TRAPEZIUM-POS3 TRAPEZIUM-POS4 TRAPEZIUM-POS5 TRAPEZIUM-POS6 TRAPEZIUM-POS7 TRAPEZIUM-POS8 TRAPEZIUM-POS9 TRAPEZIUM-POS10 ------------------------------------------------------------------------------------------------------------------------------------