Citation
On Dust, Carbon Monoxide, and Molecular Hydrogen in the Census of High and Medium-Mass Protostars

Material Information

Title:
On Dust, Carbon Monoxide, and Molecular Hydrogen in the Census of High and Medium-Mass Protostars
Creator:
Pitts, Rebecca L
Publisher:
University of Florida
Publication Date:
Language:
English

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Astronomy
Committee Chair:
Barnes,Peter
Committee Co-Chair:
Lada,Elizabeth Anne
Committee Members:
Sarajedini,Ata
Deumens,Erik
Graduation Date:
8/9/2019

Subjects

Subjects / Keywords:
astronomy
astrophysics
dust
infrared
stars
Genre:
Unknown ( sobekcm )

Notes

General Note:
I used FIR and sub-millimeter continuum data from Herschel and APEX to fit pixel-by-pixel modified Planck SEDs to prestellar and protostellar clumps in the Census of High- and Medium-mass Protostars (CHaMP). I present maps of dust temperature and molecular column density for molecular clumps throughout the CHaMP survey, with detailed study of the Carina Nebula complex (Regions 9 through 11) and surrounding RCW 64 (Region 26). I find that temperature minima coincide with column density maxima 86% of the time, implying that cooling and density enhancement must be simultaneous steps in prestellar clump evolution. I compared the column densities of CO and H$_2$ to chart local variations in their correspondence, and derive maps of CO abundance. The CO abundance varies by an order of magnitude or more across each region, and the distribution across each clump correlates in both form and magnitude with environmental conditions, especially dust temperature. The CO abundance has a temperature dependence that is parabolic in the log for the aggregated CHaMP data. Combined with the power law of Barnes et al. 2018, however, this temperature-abundance relation is unsuitable for low-column gas. Molecular hydrogen column densities from SED-fitting of dust, which is optically thin, allowed me to compute the X-factor directly for the entire CHaMP sample (>80,000 pixels). It is not constant: the X-factor is a broken power law with a broad transition, and exponents of -0.49 and 1.3 for low and high values of CO line intensity respectively. These values agree well with simulations. For the greatest and smallest CO line intensities, a constant X-factor underpredicts the molecular gas column density by up to 60%. Finally, I present multi-wavelength data on the globally collapsing molecular cloud/protostellar cluster BYF 73, revealing eight protostellar objects, of which only two had detectable far-infrared counterparts. MIR 2 is the most massive at about 240 solar masses, more massive than all the others combined by up to tenfold, and may have a dynamical age as small as 7000 years. Altogether, a portrait emerges of molecular gas clumps as physically and chemically distinct entities with long latency periods spent cooling and contracting before star-formation can begin. Despite the sensitivity of gas-phase CO abundance to local conditions, comparison with dust emission reveals surprisingly simple methods of compensation, with broad implications for measured molecular hydrogen mass budgets in the Milky Way and beyond.

Record Information

Source Institution:
University of Florida
Holding Location:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Embargo Date:
8/31/2020

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PAGE 5

X

PAGE 6

2

PAGE 8

TTTI N2T N2T 10 L=MT 10N2L=M TN2 TN2 (870m)T I12NN=N2

PAGE 9

T10N=N2 N=N2T N=N2 N=N2T N2I12X N2X^XCOI12 XN2I12 N2T N=N2 N2N2 TT N2N2 TT

PAGE 10

N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT N2N2 TT TN2 TN2 TN2 TN2 TN2

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TN2 TN2 TN2 TN2 TN2 TN2 TN2 TN2

PAGE 12

280<`<300)]TJ /F6 11.9552 Tf 9.299 0 Td[(480;000XI12

PAGE 13

I12XN22402

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+

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212IW2N2X 24)]TJ /F5 7.9701 Tf 6.586 0 Td[(2)]TJ /F5 7.9701 Tf 6.587 0 Td[(1)]TJ /F5 7.9701 Tf 6.586 0 Td[(1 1318NI12 XAV X2)]TJ /F5 7.9701 Tf 6.587 0 Td[(42 )]TJ /F5 7.9701 Tf 6.586 0 Td[(42

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AV 910)]TJ /F5 7.9701 Tf 6.587 0 Td[(3 X 1318NIXN2 XIX2 X2

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2XN2I12< .M 22 2

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2 22XN2N2 2 +2

PAGE 19

X

PAGE 20

280<`<300)]TJ /F6 11.9552 Tf 9.298 0 Td[(4
PAGE 21

12 )]TJ /F6 11.9552 Tf 9.299 0 Td[(24v)]TJ /F6 11.9552 Tf 24.205 0 Td[(21)]TJ /F5 7.9701 Tf 6.586 0 Td[(1 )]TJ /F6 11.9552 Tf 9.298 0 Td[(26v)]TJ /F6 11.9552 Tf 23.063 0 Td[(18)]TJ /F5 7.9701 Tf 6.587 0 Td[(1 0

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v)]TJ /F1 11.9552 Tf 9.299 0 Td[<00650058006a>-325<00690051>]TJ /F9 11.9552 Tf -408.327 -23.908 Td[()]TJ /F1 11.9552 Tf 9.299 0 Td[<006a005200580038>-325<0046004b>-493<0062>]TJ /F11 7.9701 Tf 50.028 4.339 Td[()]TJ /F5 7.9701 Tf 6.587 0 Td[(1 )]TJ /F6 11.9552 Tf 9.299 0 Td[(11:6v)]TJ /F6 11.9552 Tf 23.089 0 Td[(30)]TJ /F5 7.9701 Tf 6.586 0 Td[(118 vv)]TJ /F1 11.9552 Tf 9.298 0 Td[<006b006400580052>-326<00690051>]TJ /F9 11.9552 Tf 38.711 0 Td[()]TJ /F1 11.9552 Tf 9.299 0 Td[<0039003900580079>-325<0046004b>-493<0062>]TJ /F11 7.9701 Tf 50.029 4.338 Td[()]TJ /F5 7.9701 Tf 6.586 0 Td[(1 + +20.v.+40 )]TJ /F1 11.9552 Tf 9.298 0 Td[<0079007900580039>]TJ -439.764 -23.908 Td[<001c004d002f>-326<006b004e003300580033>]TJ /F9 11.9552 Tf 48.191 0 Td[()]TJ /F1 11.9552 Tf 9.299 0 Td[<007900790058006a>-325<0055>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 86.768 -585.743 Td[<00710042004800620051004d>-326<00320069>-326<001c00480058>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 148.433 -585.743 Td[<002d>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 155.582 -585.743 Td[<0052004e00640079>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 179.014 -585.743 Td[<0056002d>-326<001c00540054>-27<0032001c>26<0060>-325<0054>26<00600051004b0042004d0032004d006900480076>-325<0042004d>-326<0069003f0032>-326<00480051>26<0072>27<00320060>-325<00600042003b003f0069>-326<002b0051>26<0060004d00320060>-325<00510037>-326<00360042003b006d00600032>]TJ -179.014 -23.908 Td[<0055>]TJ ET 0 0 1 RG 0 0 1 rg BT /F1 11.9552 Tf 4.555 -609.651 Td[<006b00400039>]TJ ET 0 G 0 g BT /F1 11.9552 Tf 20.168 -609.651 Td[<00560058>-434<002200510069003f>-326<005f0032003b00420051004d0062>-326<006b006a>-326<001c004d002f>-326<006b0065>-326<004800420032>-326<0023>-27<00320069>26<0072>27<00320032004d>-325<0069003f0032>-326<00600042004b0062>-326<00510037>-326<0069003f0032>-326<0042004d004d00320060>-326<001c004d002f>-326<0051006d006900320060>-326<002b001c007000420069004200320062002d>-326<001c004d002f>-326<003b004200700032004d>]TJ -20.168 -23.908 Td[<0069003f001c0069>-326<0023001c002b0046003b00600051006d004d002f>-326<002b0051004d0069001c004b0042004d001c006900420051004d>-326<002b001c004d>-326<00620042003b004d0042007d002b001c004d006900480076>-326<0042004d007e001c00690032>-326<0032006200690042004b001c006900320062>-326<00510037>]TJ /F2 11.9552 Tf 335.761 0 Td[(N2

PAGE 23

)]TJ /F1 11.9552 Tf 9.298 0 Td[<00650079>]TJ /F11 7.9701 Tf 11.716 4.338 Td[(.`.)]TJ /F1 11.9552 Tf 9.298 0 Td[<0052>]TJ /F11 7.9701 Tf 5.858 4.338 Td[(.b. 000012

PAGE 24

?00 zyyyy z y? 0000s00s

PAGE 25

2 IB(T)[1)]TJ /F2 11.9552 Tf 11.955 0 Td[(e)]TJ /F7 7.9701 Tf 6.587 0 Td[(] = 0N2m0 ;B(T)T00N2 m

PAGE 26

10N2N2TN2T0N20 =N)]TJ /F5 7.9701 Tf 6.587 0 Td[(302 N= 0m0 ;0 02)]TJ /F5 7.9701 Tf 6.587 0 Td[(10TN2 Td

PAGE 27

TTN2 2N2

PAGE 28

N2N2 T2 N2N2N2

PAGE 29

70870<250 10N2)]TJ /F1 11.9552 Tf 9.299 0 Td[<007900580079003300560058>-434<0068>81<0051>-325<0032006200690042004b001c00690032>-326<003f0051>26<0072>-325<004b006d002b003f>]TJ /F2 11.9552 Tf 149.196 0 Td[(T

PAGE 30

TTTTT TTTTTTTT.T.TTITTTTTN2..

PAGE 31

12

PAGE 36

TTTITTI

PAGE 37

22 4L)]TJ /F5 7.9701 Tf 6.587 0 Td[(2Myr)]TJ /F5 7.9701 Tf 6.587 0 Td[(1 227)]TJ /F5 7.9701 Tf 6.586 0 Td[(227)]TJ /F5 7.9701 Tf 6.587 0 Td[(2 2 H2

PAGE 38

N22527)]TJ /F5 7.9701 Tf 6.587 0 Td[(22 02 227)]TJ /F5 7.9701 Tf 6.587 0 Td[(2 00

PAGE 39

v)]TJ /F1 11.9552 Tf 9.299 0 Td[<00520033>-325<001c004d002f>]TJ /F9 11.9552 Tf 37.12 0 Td[()]TJ /F1 11.9552 Tf 9.299 0 Td[<006b0079>-325<0046004b>-326<0062>]TJ /F11 7.9701 Tf 38.926 4.338 Td[()]TJ /F5 7.9701 Tf 6.586 0 Td[(1vv 26)]TJ /F5 7.9701 Tf 6.587 0 Td[(2226)]TJ /F5 7.9701 Tf 6.587 0 Td[(2v2

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26)]TJ /F5 7.9701 Tf 6.586 0 Td[(2 Av226)]TJ /F5 7.9701 Tf 6.586 0 Td[(2TN2 N2TN22 N2

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2 2

PAGE 42

2 p()d=1 p 22)]TJ /F6 11.9552 Tf 13.151 8.088 Td[(()]TJ /F6 11.9552 Tf 12.781 0 Td[()2 22dN2 2=ln(1+b2M2):M 0:3.b.1

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2=2jj(N=N)(N=eN)NeNNN p()=pcs c=pcN Ncsscpc=p(c) N2>25)]TJ /F5 7.9701 Tf 6.586 0 Td[(2

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p() N2

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N2 p()10%% 10%0:71:110N230% 102 n&100

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N2&10 Ncpc10 b

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b1=3Mb1 N225:7

PAGE 48

% L=ML=M 32L=ML=M.L=ML=M&L=MTL=M32 L=MT 0TN21)]TJ /F2 11.9552 Tf 10.443 0 Td[(e)]TJ /F7 7.9701 Tf 6.586 0 Td[( 32n1011)]TJ /F5 7.9701 Tf 6.586 0 Td[(3

PAGE 49

L=MN2L=M L=M L=M4 XXXXXN2mZ10XXXXXN2m0 0B(T)d=40h c20kT h+4\(+4)(+4))]TJ /F1 11.9552 Tf 11.212 0 Td[<00420062>-325<0069003f0032>-326<0042004d00690032003b0060001c0048>-326<00370051>26<0060004b>-325<00510037>-326<0069003f0032>-326<003b001c004b004b001c>-326<0037006d>-1<004d002b006900420051004d002d>-326<001c004d002f>]TJ /F2 11.9552 Tf 237.393 0 Td[(00L=M/T4+ TL=MLML=ML=ML=M/T4N)]TJ /F5 7.9701 Tf 6.587 0 Td[(12L=MN2N)]TJ /F5 7.9701 Tf 6.587 0 Td[(12L=M/N'2<'< TN2L=MT TN2

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L=M/8>><>>:T4+0)]TJ /F5 7.9701 Tf 6.586 0 Td[(11T4N)]TJ /F5 7.9701 Tf 6.587 0 Td[(121 N2/T)]TJ /F7 7.9701 Tf 6.587 0 Td[()]TJ /F5 7.9701 Tf 6.587 0 Td[(10: TN2N2T TTN2

PAGE 51

TNTN2 TN2TN2N2 TN2>+0:25 N2T

PAGE 52

10:1 N2T(850m)(850m)4 TN2 N2

PAGE 53

N2T2)]TJ /F5 7.9701 Tf 6.586 0 Td[(2

PAGE 57

N2T2)]TJ /F5 7.9701 Tf 6.586 0 Td[(2

PAGE 59

10N2

PAGE 60

L=MT=1:8L=M

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10N2L=MTL=M

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TN2rs

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TN2TN2

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TN2TN2T (870m)T

PAGE 65

I12 Ndust2Ndust2I12)]TJ /F5 7.9701 Tf 6.587 0 Td[(1)]TJ /F5 7.9701 Tf 6.587 0 Td[(112Ndust2I12Ndust2Ndust2I12Ndust2I12NNdust2NNNdust2Ndust2

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Ndust2Ndust2Ndust2NNdust2Ndust2Ndust2Ndust2NNdust2I12 NNdust2N

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Ndust2NN2I12 NNdust2)]TJ /F5 7.9701 Tf 6.587 0 Td[(42 N=N2N=N2Ndust2 Ndust2N=N2)]TJ /F5 7.9701 Tf 6.586 0 Td[(52N=N210)]TJ /F5 7.9701 Tf 6.586 0 Td[(4NN=N2N=N2Ndust2Ndust2N=N2

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Ndust22 N=N2&10)]TJ /F5 7.9701 Tf 6.586 0 Td[(42Ndust2N=N2Ndust2 N=N2Ndust2N=N2.10)]TJ /F5 7.9701 Tf 6.587 0 Td[(52Ndust2N=N2Ndust2.Ndust2Ndust2 T2 T2 20.T.25

PAGE 69

hTihTi hTihTi 20.T.25T T.80 TN=N2

PAGE 70

T.25T.20N=N2)]TJ /F5 7.9701 Tf 6.587 0 Td[(52)]TJ /F5 7.9701 Tf 6.587 0 Td[(52TNdust2)]TJ /F5 7.9701 Tf 6.586 0 Td[(52>N=N2 N=N2)]TJ /F5 7.9701 Tf 6.586 0 Td[(5N=N2TNdust2N=N2)]TJ /F5 7.9701 Tf 6.586 0 Td[(52

PAGE 71

T.15N22627)]TJ /F5 7.9701 Tf 6.586 0 Td[(2 20 0T0Ndust20 )]TJ /F5 7.9701 Tf 6.587 0 Td[(52Ndust2Ndust2N=N2Ndust2N=N2.2)]TJ /F5 7.9701 Tf 6.587 0 Td[(5

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0+N=N2N=N2 8.n.1010)]TJ /F5 7.9701 Tf 6.587 0 Td[(3N=N2G0G04G0 2G0N=N20 G0G02n1010)]TJ /F5 7.9701 Tf 6.586 0 Td[(3n109)]TJ /F5 7.9701 Tf 6.586 0 Td[(3n108)]TJ /F5 7.9701 Tf 6.587 0 Td[(32G02

PAGE 73

N=N2N=N2.10)]TJ /F5 7.9701 Tf 6.586 0 Td[(5T>T<
PAGE 74

Ndust2 T TNdust22

PAGE 75

TTN2

PAGE 76

N2 TN2

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TN=N2 T%N=N2T log10%=log10NCO NdustH2=0:25f)]TJ /F5 7.9701 Tf 6.586 0 Td[(1log210Td Td;0+log10%0f10Td;010%0TN=N2N=N2f+0:002)]TJ /F5 7.9701 Tf 6.586 0 Td[(0:00610Td;0+0:01)]TJ /F5 7.9701 Tf 6.586 0 Td[(0:02+0:4)]TJ /F5 7.9701 Tf 6.587 0 Td[(1:010%0+0:01)]TJ /F5 7.9701 Tf 6.587 0 Td[(0:02+0:2)]TJ /F5 7.9701 Tf 6.587 0 Td[(0:310)]TJ /F5 7.9701 Tf 6.586 0 Td[(52 f10Td;010%0
PAGE 78

T 104 % N=N2TL=M =2:165

PAGE 79

+0:4)]TJ /F5 7.9701 Tf 6.587 0 Td[(0:9 2 2

PAGE 80

T 10%0N2 I12N2 N2.31025)]TJ /F5 7.9701 Tf 6.586 0 Td[(2 X X 121318+ 121213182X12 N2N2N2

PAGE 81

%I12 ^XCO(I012CO) NH2=N0H2Is1?"1 2+I1=? 2#(s2)]TJ /F7 7.9701 Tf 6.587 0 Td[(s1) I?=I12CO I012COI12N022I012s1s2xy0:5log10(x2)]TJ /F2 11.9552 Tf 12.484 0 Td[(x1)y(x.x1)/xs1y(x&x1)/xs2 sigmad2n2=5en XXI12s1s2N2I12s2

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N=N2T N0H2=(1:3+0:3)]TJ /F5 7.9701 Tf 6.586 0 Td[(0:2)1026)]TJ /F5 7.9701 Tf 6.587 0 Td[(2I012CO=8010)]TJ /F5 7.9701 Tf 6.587 0 Td[(1s1=0:510:03s2=2:30:4=0:23+0:05)]TJ /F5 7.9701 Tf 6.587 0 Td[(0:04N=N2T I12N2I12N2X N2X N2 I12X%2I12X%I12XN2%N2X%s=0:51X

PAGE 83

2 Tex%% I12s2I12N2I12N2 I12N1212.1.N.21020)]TJ /F5 7.9701 Tf 6.587 0 Td[(212 %N1318NNI1212TT<10T12NI12N2/Xss

PAGE 84

TexNI122 NI12 X 26)]TJ /F5 7.9701 Tf 6.587 0 Td[(2N2AV 2n3106)]TJ /F5 7.9701 Tf 6.587 0 Td[(3N2&1026)]TJ /F5 7.9701 Tf 6.587 0 Td[(2 N0H2=I012CO^XCOI12X I12^XCOI12^XCOI12 n3106)]TJ /F5 7.9701 Tf 6.587 0 Td[(3 X

PAGE 85

N2&31026)]TJ /F5 7.9701 Tf 6.587 0 Td[(2XN=N2N231026)]TJ /F5 7.9701 Tf 6.586 0 Td[(2N=N2)]TJ /F5 7.9701 Tf 6.587 0 Td[(4)]TJ /F5 7.9701 Tf 6.587 0 Td[(5XN2N2&31025)]TJ /F5 7.9701 Tf 6.586 0 Td[(2AV3ms2 N2/I12212s1X AVXN2N2^XCOI12 10m
PAGE 86

G0 XI12 )]TJ /F5 7.9701 Tf 6.586 0 Td[(110)]TJ /F5 7.9701 Tf 6.586 0 Td[(1I12I12 N2I12X N2I12AVmm AVI12)]TJ /F5 7.9701 Tf 6.587 0 Td[(1AVmmN21026)]TJ /F5 7.9701 Tf 6.586 0 Td[(2I12)]TJ /F5 7.9701 Tf 6.587 0 Td[(1AVI12

PAGE 87

XN2I12N2 2m
PAGE 88

I12NN=N212)]TJ /F5 7.9701 Tf 6.586 0 Td[(1 N2N2N

PAGE 94

T10N=N2

PAGE 95

N=N2T

PAGE 96

N=N2

PAGE 97

N=N2TTd%Td1)]TJ /F2 11.9552 Tf 11.955 0 Td[(

PAGE 99

N2I12XX X^XCOI12

PAGE 101

N2X^XCOI12I12I12N2XI12^XCOI12XN2

PAGE 102

XN2I12XI12^XCOI12I12X

PAGE 103

M)]TJ /F5 7.9701 Tf 6.587 0 Td[(1 4M4L.

PAGE 104

:00 5)]TJ /F6 11.9552 Tf 13.39 0 Td[(600000 0000

PAGE 105

:00 6388145158 6""<<12"0<<)]TJ /F5 7.9701 Tf 6.586 0 Td[(1)]TJ /F5 7.9701 Tf 6.587 0 Td[(1)]TJ /F5 7.9701 Tf 6.586 0 Td[(1)]TJ /F5 7.9701 Tf 6.586 0 Td[(11581458863

PAGE 106

+13+J!:0 +< :00:00

PAGE 107

:00:000=10;6007400 nG=G0 nG=G0158145886314515863145158158nG=G0 G=G0n10)]TJ /F5 7.9701 Tf 6.586 0 Td[(11)]TJ /F5 7.9701 Tf 6.586 0 Td[(3AV10mG=G0n158145158nG=G0n

PAGE 108

63145nG=G010:7)]TJ /F5 7.9701 Tf 6.586 0 Td[(3n n=9:54:25)]TJ /F5 7.9701 Tf 6.587 0 Td[(1 n=(mH)813)]TJ /F5 7.9701 Tf 6.586 0 Td[(3 nG=G0 )]TJ /F5 7.9701 Tf 6.587 0 Td[(3L158)]TJ /F5 7.9701 Tf 6.587 .001 Td[(3L145 JHKJK>00

PAGE 109

TbolLsubmm=Lboltinf=M=_M7000>1031AV9:7 mmAV NH25)]TJ /F5 7.9701 Tf 6.587 0 Td[(2AVNH2 =1:88M)]TJ /F5 7.9701 Tf 6.586 0 Td[(2(N2=1024m)]TJ /F5 7.9701 Tf 6.587 0 Td[(2) 1950650M)]TJ /F5 7.9701 Tf 6.587 0 Td[(2650190M)]TJ /F5 7.9701 Tf 6.586 0 Td[(24 11040M4010M

PAGE 110

63:00 >160I=F=B(T)[1)]TJ /F2 11.9552 Tf 12.136 0 Td[(e)]TJ /F7 7.9701 Tf 6.586 0 Td[(]=(=0)N2m0=B(T)T00N22mTN2 0=(3502)]TJ /F5 7.9701 Tf 6.586 0 Td[(1

PAGE 111

2 D2=2:0910)]TJ /F5 7.9701 Tf 6.586 0 Td[(32D=2:5:0091:00D2=5:110)]TJ /F5 7.9701 Tf 6.586 0 Td[(42 NH2+3:6)]TJ /F5 7.9701 Tf 6.587 0 Td[(1:728)]TJ /F5 7.9701 Tf 6.586 0 Td[(2TdNH2+1:3)]TJ /F5 7.9701 Tf 6.586 0 Td[(0:528)]TJ /F5 7.9701 Tf 6.587 0 Td[(2Td N2 MIR2(70m)14AV7000m2+0:3)]TJ /F5 7.9701 Tf 6.587 0 Td[(0:4105M)]TJ /F5 7.9701 Tf 6.587 0 Td[(2+80)]TJ /F5 7.9701 Tf 6.587 0 Td[(50M+100)]TJ /F5 7.9701 Tf 6.587 0 Td[(500LLTd=45_M=0:0340:017M)]TJ /F5 7.9701 Tf 6.586 0 Td[(1 R4500Lg=GM_MR)]TJ /F5 7.9701 Tf 6.587 0 Td[(1260LMIR1(70m)5MIR1+3)]TJ /F5 7.9701 Tf 6.586 0 Td[(2104M)]TJ /F5 7.9701 Tf 6.587 0 Td[(2+20)]TJ /F5 7.9701 Tf 6.586 0 Td[(10M

PAGE 112

1100100L1900LML30 00.001 310&

PAGE 113

K 10

PAGE 115

14563nG=G014563nG=G0158)]TJ /F5 7.9701 Tf 6.586 0 Td[(7)]TJ /F5 7.9701 Tf 6.586 0 Td[(2)]TJ /F5 7.9701 Tf 6.586 0 Td[(1145)]TJ /F5 7.9701 Tf 6.586 0 Td[(8)]TJ /F5 7.9701 Tf 6.586 0 Td[(2)]TJ /F5 7.9701 Tf 6.586 0 Td[(163)]TJ /F5 7.9701 Tf 6.587 0 Td[(11)]TJ /F5 7.9701 Tf 6.587 0 Td[(2)]TJ /F5 7.9701 Tf 6.587 0 Td[(1n)]TJ /F5 7.9701 Tf 6.587 0 Td[(3G=G0G0 )]TJ /F5 7.9701 Tf 6.587 0 Td[(6)]TJ /F5 7.9701 Tf 6.587 0 Td[(2

PAGE 116

N2 NN2TN2XL=MTTN222N2TN2TN2T90%L=MN2<>TN2

PAGE 117

L=MT&10N210%2)]TJ /F5 7.9701 Tf 6.586 0 Td[(52N2&10)]TJ /F5 7.9701 Tf 6.587 0 Td[(42N=N2N2N=N2N2T

PAGE 118

%N231025XXN2/I120:51I12.70)]TJ /F5 7.9701 Tf 6.587 0 Td[(1N2/I122:3I12&90)]TJ /F5 7.9701 Tf 6.586 0 Td[(1 I12X^XCOI12N2%37
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220:5k

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N2T2)]TJ /F5 7.9701 Tf 6.587 0 Td[(2

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2)]TJ /F5 7.9701 Tf 6.587 0 Td[(2

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N2N2N2T < IB(T)[1)]TJ /F2 11.9552 Tf 11.955 0 Td[(e)]TJ /F7 7.9701 Tf 6.587 0 Td[(]+B(T)[e)]TJ /F7 7.9701 Tf 6.586 0 Td[(]:

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N2N2N2N2 NN2

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10N2)]TJ /F5 7.9701 Tf 6.587 .001 Td[(2T

PAGE 127

N=N2

PAGE 129

N2N2

PAGE 130

TT

PAGE 131

N2N2

PAGE 132

TT

PAGE 133

N2N2

PAGE 134

TT

PAGE 135

N2N2

PAGE 136

TT

PAGE 137

N2N2 TT

PAGE 138

N2N2

PAGE 139

TT

PAGE 140

N2N2

PAGE 141

TT

PAGE 142

N2N2

PAGE 143

TT

PAGE 144

N2N2

PAGE 145

TT

PAGE 146

N2N2

PAGE 147

TT

PAGE 148

N2N2

PAGE 149

TT

PAGE 150

N2N2

PAGE 151

TT

PAGE 152

10N2)]TJ /F5 7.9701 Tf 6.586 0 Td[(2T

PAGE 154

2TN2

PAGE 155

TN2

PAGE 156

TN2

PAGE 157

TN2

PAGE 158

TN2

PAGE 159

TN2

PAGE 160

TN2

PAGE 161

TN2

PAGE 162

TN2

PAGE 163

TN2

PAGE 164

TN2

PAGE 165

TN2

PAGE 166

TN2

PAGE 167

TN2