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The Evolution of the Warm Absorber Reveals a Shocked Outflow in the Narrow Line Seyfert 1 Galaxy IRAS 17020+4544

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2018

Publication Year

2021-01-07T10:44:33Z

Acceptance in OA@INAF

The Evolution of the Warm Absorber Reveals a Shocked Outflow in the Narrow

Line Seyfert 1 Galaxy IRAS 17020+4544

Title

Sanfrutos, Mario; Longinotti, Anna Lia; Krongold, Yair; GUAINAZZI, MATTEO;

PANESSA, Francesca

Authors

10.3847/1538-4357/aae923

DOI

http://hdl.handle.net/20.500.12386/29519

Handle

THE ASTROPHYSICAL JOURNAL

Journal

868

Number

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RF w yBBUNEfi OwRAGNE yBVCBANAG “UBP T − ≥1>4fi UBP Mt−1/>8(fi BHG˚BJRAP wG − 12// TV F 0–

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mN ABJ zNFyERxN GQN VBzNU zNINUBCNz GB +G GQN HUGEw OwFG JRAz RA GQN CENFNAG JBET– jQN kre QNEN RF FGRUU FGEHyGHENz wF w VHUGRflCQwFNfi VHUGRflyBVCBANAG JRAz JRGQ GJB zRffiNENAG INUByfl RGRNF yUBFN GB − />0L– jQN +EFG yBVCBANAG RF BHGfl ˚BJRAP wG 1Ω8// ≤ 1// TV F 0fi wAz RF OBEVNz

xL wG UNwFG GJB zRffiNENAG FQNUUFfi AwVNz kre 0 wAz kre 1 RA jwxUN 0– mQNA JN UNG GQN INfl UByRGRNF BO GQNFN GJB FQNUUF OENN GB IwEL RAzNCNAfl zNAGULfi JN FGRUU PNG GQN FwVN BHG˚BJ INUByRGL OBE xBGQ BO GQNV– kre 0 GEwyNF w yBBU wAz FQwUfl UBJ yBVCBANAG BO GQN JRAz “UBP T & ≥1>W6Λ+M04

+M08fi

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+IN BEzNEF BO VwPARGHzN VBEN RBARMNz “UBP T & 1>Ω2Λ+M+f+M02( wAz GQENN BEzNEF BO VwPARGHzN zNAFNE

“UBP Mt& 12>6/ ≤ />04(–

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≥/>24Λ+M01

+M08fi UBP Mt & 1/>WΛ+M1+Mf(fi wAz kre W RF

yBBUNE wAz FURPQGUL GQRyTNE “UBP T − ≥0>11Λ+M0+

+M+4fi

UBP Mt−1/>74Λ+M+2+M+5(–

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VBzNU–

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2–1– 1--m nccfldNvsXA zwsw

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wG 128// ≤ 0// TV F 0fi ENFCNyGRINUL “FNN ERPQG

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zwGw OEBV 1//W– mN yBVCHGN w ˚HK UNINU BO 0>/2Λ+M+0+M+7 0/ 00NEP yV 1F 0 RA GQN /–2fl1 TNl

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m yBVCBANAGF AB– 0 wAz 1 wEN yBAFRFGNAG RA 1//W wAz 1/0Wfi FB GQwG RG RF yBAyNRIwxUN GQwG xBGQ BO GQNV ENVwRA wG ENFG “BE TNNC RA˚BJRAP wG ONJ QHAzENzF TV F 0( wOGNE w zNywzN– mRAz

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F OBE m Wfi JN BxFNEIN VwEPRAwU yBAFRFGNAyL xNGJNNA RGF yBUHVA zNAFRGRNF RA 1//W wAz 1/0Wfi GQBHPQ RGF RBARMwGRBA RA 1/0W RF xNGJNNA BAN wAz GJB BEzNEF BO VwPARGHzN UwEPNE GQwA RA 1//W` wUFBfi GQRF yBVCBANAG RF FGRUU RA˚BJRAPfi xHG wG w UBJNE INUByRGL RA 1/0W “≥064/ ≤ 14/ TV F 0fi GB

xN yBVCwENz JRGQ ≥18// ≤1// TV F 0GNA LNwEF

NwEURNE(–

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mN BffiNE w zNGwRUNz RAGNECENGwGRBA BO GQN ENfl FHUGF OEBV GQN FCNyGEwU wAwULFRF RA iNyGRBAW–

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Ω i v A O D t G n F N G v T ,

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—/0W —//W

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blNUByRGL yBVCBANAG wUBAP GQN URAN BO FRPQG RA TV F 0¸ dNPwGRIN . CBFRGRIN IwUHNF ENFCNyGRINUL ENONE GB RA˚BJRAP . BHG˚BJRAP VwGNERwU¸

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13 14 15 16 17 1 0 − 2 0 5 × 1 0 − 2 1 2 × 1 0 − 2 0 5 × 1 0 − 2 0 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) NeX(WA2) NeVIII(UFO3+4) NeVII(UFO3+4) NeIX(WA2) FeXIX(WA4) FeXVIII(WA4) OVIII(UFO2) OVIII(UFO3+4)

FeXVII(WA2) OVIII(WA2) OVII(UFO3+4) OVIII(WA4) 2014 13 14 15 16 17 1 0 − 2 0 5 × 1 0 − 2 1 2 × 1 0 − 2 0 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) NeIX(WA2) OVIII(UFO3) FeXVII(UFO3) NeII(WA3) 2004 18 19 20 21 22 23 1 0 − 2 0 1 0 − 1 9 2 × 1 0 − 2 0 5 × 1 0 − 2 0 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) OVII(UFO3+4) OVIII(UFO2) OVIII(UFO3+4) OVII(WA2)

OVII(WA1)OVII(WA2)

OVIII(WA2) OVIII(WA4) Instr. feature OVII(UFO3+4) . OVI(UFO3+4) (UFO1) OVI(UFO3+4) OV(UFO1) OIV(UFO1) OIII(UFO1)

OVII(WA1)OVII(WA2)

OVI(WA1) OVI(WA1) OV(WA3) 18 19 20 21 22 23 1 0 − 2 0 1 0 − 1 9 2 × 1 0 − 2 0 5 × 1 0 − 2 0 2 × 1 0 − 19 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) OVIII(UFO3) OVII(WA4) OVII(WA2)

OVIII(WA2) OVII(UFO3)

OVI(UFO1) OV(UFO1) OIV(UFO1) OVII(WA2) OVII(WA1) OVII(WA4) OVI(WA1) OVI(WA1) . Instr. feature 24 25 26 27 28 29 1 0 − 1 9 2 × 1 0 − 2 0 5 × 1 0 − 2 0 2 × 1 0 − 1 9 D a ta /A re a ( C ts s − 1 H z −1 c m − 2) Observed wavelength (Å) OV(WA1) OIV(WA3) OIV(WA1) . OIII(WA3) OII(WA3) CVI(UFO3+4) NVII(WA2) NVI(WA1) CVI(UFO3+4) NVI(UFO3+4) . NV(UFO1)CVI(WA2) NIV(UFO1) . 24 25 26 27 28 29 1 0 − 2 0 1 0 − 19 2 × 1 0 − 2 0 5 × 1 0 − 2 0 2 × 1 0 − 1 9 D a ta /A re a ( C ts s − 1 H z −1 c m − 2) Observed wavelength (Å) OV(WA1) OIV(WA1)

OII(WA3)OIII(WA1)

NVII(WA4) CVI(UFO3) NIV(UFO1)

30 31 32 33 34 35 1 0 − 1 9 5 × 1 0 − 2 0 2 × 1 0 − 1 9 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) CVI(WA1) NVI(WA1) NV(WA1) NIV(WA1)

NIII(WA3) NII(WA3)

CVI(UFO3+4) CV(UFO1) CV(UFO3+4) CV(WA1) 30 31 32 33 34 35 1 0 − 2 0 1 0 − 1 9 2 × 1 0 − 2 0 5 × 1 0 − 2 0 2 × 1 0 − 1 9 D a ta /A re a ( C ts s − 1 H z − 1 c m − 2) Observed wavelength (Å) NVI(WA1) NVI(WA4) NV(WA1) NIV(WA1) CVI(UFO3) CV(WA1) .

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RA PENNAfi m — RA xUHNfi m 2 RA VwPNAGwfi m W RA ENzfi wAz GQN kreF RA xUwyT¸ qINEL URAN VwETNz RA GQRF

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0/f TV F 0 FQByTF JRGQ GQN wVxRNAG VNzRHV

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(11)

0/ ivAODtGnF NG vT, GBEFfi GQN FUBJ RA˚BJ INUByRGL VNwFHENz OBE m

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ABGQNE CBFFRxUN RAGNECENGwGRBA RF CEBIRzNz xL GQN yBAzNAFNz yUBHzF FyNAwERBfi JQRyQ RAIBUINF AB FQByT– uAFGNwzfi GQN RA˚BJ ByyHEF IRw yQwBGRy yBUz wyyENGRBA∆ yBUz yUBHzF ’EwRA5 OEBV GQN VwGNERwU GQwG yBBUF wF RG ˚BJF wJwL OEBV GQN

(12)

UwHAyQRAP ENPRBA “FNN N–P– swFCwER Γ i-wzBJFTR 1/06(– YBVCBANAGF GQwG zB ABG ENwyQ GQN NFfl ywCN INUByRGL OBE GQRF FLFGNV FRVCUL OwUU zBJA wPwRA–

tBJNINEfi GQN yBAzNAFNz yUBHzF FyNAwERB ywAfl ABG NKCUwRA GQN RBARMwGRBA BO FBVN BO GQN yBVfl CBANAGF RA GQRF FLFGNV– uA OwyGfi JN zB ABG zNfl GNyG yBUz PwF wG wUUfi xHG JwEV RAFGNwz “R < 0/fa(– rRAwUULfi yBAFRzNERAP GQwG OENNflOwUU INUByfl

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GJB wUGNEAwGRIN FyNAwERBF ywA NKCUwRA RA˚BJ INfl UByRGRNF BO GQN BEzNE BO 1 ≥ 2 0/2 TV F 0 URTN

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hqrqhqdYqi

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q¸fi NG wU¸ —//2fi Γ fi W/2fi W70

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XEwAzHwEzRflhwLVBAGfi s¸fi Γ FQGBAfi Y¸ q¸

—//4fi Γ fi W20fi 000

YwFQfi m¸ 0868fi Cvfi ——7fi 828

zN sERSCfi c¸ t¸ a¸fi aNNUfi m¸ Y¸fi cRUNLfi s¸ a¸fi

sBHzOEBBRSfi f¸fi Γ bHxfi v¸ 088—fi Γ ifi 8”fi 278

zN lERNFfi Y¸ f¸fi zNA tNEzNEfi v¸ m¸fi swxERNUfi Y¸fi NG

wU¸ —/04fi Γ fi 462fi 0—7

zNA tNEzNEfi v¸ m¸fi XERATVwAfi ¸ Y¸fi awQAfi i¸ c¸fi

NG wU¸ —//0fi Γ fi 2”4fi b6

qURGMHEfi c¸fi Γ iQUBFVwAfi u¸ —//”fi Cv bNGGNEFfi

”W7fi b0/0

qUIRFfi c¸ —/06fi Cvfi 7W6fi 4”

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rNEHPURBfi Y¸fi rRBENfi r¸fi YwEARwARfi i¸fi NG wU¸ —/04fi

Γ fi 472fi 88

swFCwERfi c¸fi Γ i-wzBJFTRfi ¸ —/06fi Cvfi 726fi 0W8

sNBEPNfi u¸ c¸fi jHEANEfi j¸ v¸fi dNGMNEfi t¸fi NG wU¸

0887fi Cvifi 00Wfi 62

sREBUNGGRfi c¸fi fwANFFwfi r¸fi bBAPRABGGRfi ¸ b¸fi NG wU¸

—/06fi Γ fi ”//fi 76

sB3BEzfi v¸fi hNNINFfi v¸ d¸fi jBVxNFRfi r¸fi NG wU¸ —/02fi cdh ifi W2/fi ”/

twUCNEAfi v¸ f¸ 087Wfi Cvfi —70fi 8/

awwFGEwfi v¸ i¸fi cNJNfi h¸fi bRNzwQUfi Z¸ ¸fi aBVBFFwfi

i¸fi Γ XERATVwAfi ¸ Y¸ —///fi Γ fi 24Wfi b72

awwFGEwfi v¸ i¸fi ZNGVNEFfi h¸ s¸fi cNQzRCBHEfi c¸fi NG

wU¸ —/0—fi Γ fi 428fi 006

awwFGEwfi v¸ i¸fi aERFFfi s¸ ¸fi YwCCRfi c¸fi NG wU¸

—/0Wfi iyRNAyNfi 2W4fi ”W

awUxNEUwfi f¸ c¸ m¸fi XHEGBAfi m¸ X¸fi twEGVwAAfi

Z¸fi NG wU¸ —//4fi Γ fi WW/fi 664

awUUVwAfi j¸fi Γ XwHGRFGwfi c¸ —//0fi Cvifi 022fi ——0

awFCRfi i¸fi XEwAzGfi m¸ d¸fi dNGMNEfi t¸fi NG wU¸ —///fi Cv bNGGNEFfi 424fi b06

awFCRfi i¸fi XEwAzGfi m¸ d¸fi sNBEPNfi u¸ c¸fi NG wU¸

—//—fi Cvfi 46Wfi ”W2

aRAPfi ¸ h¸ —/0/fi cdh ifi W/—fi 040”

aRAPfi ¸fi Γ fBHAzFfi a¸ —/04fi h Γ fi 42fi 004

(13)

01 ivAODtGnF NG vT,

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iZ jNwV —/07fi duij GBVRy iCNyGEw

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aEBURTfi v¸ t¸fi Γ aERFFfi s¸ ¸ —//0fi Cvfi 4”0fi ”7W

aEBAPBUzfi o¸fi dRywFGEBfi r¸fi XERyTQBHFNfi d¸ i¸fi NG

wU¸ —//2fi Cvfi 486fi 72—

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aEBAPBUzfi o¸fi dRywFGEBfi r¸fi XERyTQBHFNfi d¸ i¸fi

qUIRFfi c¸fi Γ cwGQHEfi i¸ —//4fi Cvfi ”——fi 7W—

aEBAPBUzfi o¸fi dRywFGEBfi r¸fi qUIRFfi c¸fi NG wU¸ —//6fi Cvfi ”48fi 0/——

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ZNJwAPwAfi s¸ Y¸fi Γ aNVxQwIRfi ¸ a¸ —/0”fi

cdh ifi W46fi 278”

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wU¸ —/02fi Cvfi 6””fi 0/W

bBAPRABGGRfi ¸ b¸fi aEBAPBUzfi o¸fi sHwRAwMMRfi c¸fi NG

wU¸ —/04fi Cvfi 702fi 28

bBAPRABGGRfi ¸ b¸ —/07fi wEnRIı07/7¸/0/W2

cwEyBARfi ¸fi hRFwURGRfi s¸fi sRUURfi h¸fi NG wU¸ —//Wfi

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cBEwAfi q¸ Y¸fi twUCNEAfi v¸ f¸fi Γ tNUOwAzfi Z¸ v¸

088”fi Cvifi 0/”fi 2W0

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W/4

dNGMNEfi t¸ 0876fi cdh ifi ——4fi 44

dNGMNEfi t¸ —//7fi dNJ FGEBA¸ hNI¸fi 4—fi —46

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fBHAzFfi a¸ ¸fi Γ lwHPQwAfi i¸ —/00fi cdh ifi

W02fi 0—40

hNLABUzFfi Y¸ i¸ 0886fi cdh ifi —7”fi 402 iwAOEHGBFfi c¸fi cRARHGGRfi s¸fi aEBAPBUzfi o¸fi

P;∆FflsBAM;wUNMfi X¸fi Γ bBAPRABGGRfi ¸ b¸ —/0”fi

cdh ifi W46fi 40/

iVRGQfi h¸ a¸fi XERyTQBHFNfi d¸ i¸fi bRNzwQUfi Z¸ ¸fi Γ

hwLVBAzfi v¸ Y¸ —//0fi Cv bNGGNEFfi 44”fi b80

jBVxNFRfi r¸fi YwCCRfi c¸fi hNNINFfi v¸ d¸fi Γ XEwRGBfi l¸ —/0—fi cdh ifi W——fi b0

jBVxNFRfi r¸fi YwCCRfi c¸fi hNNINFfi v¸ d¸fi NG wU¸ —/02fi cdh ifi W2/fi 00/—

jBVxNFRfi r¸fi cNU;NAzNMfi c¸fi lNRUUNHKfi i¸fi NG wU¸ —/04fi dwGHENfi 408fi W2”

lNUwMDHNMfi f¸ r¸fi sBVNMfi Z¸ e¸fi ZHxANEfi s¸ c¸fi

zN YwFGEBfi s¸ s¸fi Γ YBFGwfi ¸ 0887fi Γ fi 22Wfi

0/”/

mwAPfi j¸fi Γ bHfi o¸ —//0fi Γ fi 266fi 4—

mRFBGMTRfi b¸fi Γ XwzNfi d¸ 0886fi Γ fi 2—/fi 284

pwTwVFTwfi d¸ b¸fi Γ sENNANfi v¸ q¸ —/0Wfi cdh ifi WW—fi 67W

pHxBIwFfi a¸fi Γ aRAPfi ¸ —/0—fi Cv bNGGNEFfi 6W4fi

(14)

iuaTb 1¸ xFBECGRBA URANF CEBzHyNz xL GQN wxFBExRAP yBVCBANAGF wF RzNAGR+Nz JRGQ GQN ft iq VBzNU RA GQN —/0W wAz —//W ncc,dNvsXA hsi FCNyGEw¸

—/0W —//W

uBA jEwAFRGRBA / ’,(9u( xF¸ exF¸ / ’,(9a( qm ’,( exF¸ / ’,(9a( qm ’,(

dNK 0p0×—C0’a<( 0—β02W m — 0—β77— ≤ /β//0 W ≤ 0

dNRK 0p1×0p0—C0’a<( 02βWW6 m — 0Wβ—6” ≤ /β//0 04 ≤ 0 0Wβ—22 ≤ /β//0 06Λ0

1

dNIRRR 0p1—p0×0p0—p0—C0’a<( 02β”W” kre 2 02β2”8 ≤ /β//0 7 ≤ 0

dNIRRR 5 02β”W” kre W 02β26/ ≤ /β//0 6 ≤ 0

rNKRK —Cf×—C22c0’b<( 02β684 m W 0Wβ6/WΛ+M++0

+M++7 — ≤ 0

dNIRR —p1×0p0—p1—C0’a<( 02β70W kre 2 02β42W ≤ /β//0 02 ≤ 2

dNIRR 5 02β70W kre W 02β42W ≤ /β//0 0— ≤ 2 rNKIRRR —C4×—Cf2c0’b<( 0Wβ047 m W 04β/8— ≤ /β//0 — ≤ 0 rNKIRRR 5 0Wβ—/7 m W 04β0WWΛ+M++0+M++7 W ≤ 0 rNKIRRR 5 0Wβ—/7 m W 04β0WWΛ+M++0+M++7 W ≤ 0 rNKIRRR 5 0Wβ—4” m W 04β08”Λ+M++0 +M++8 — ≤ 0 dNRR —C4×0p0—p1—C5’a<( 0Wβ”// m 2 04β—7— ≤ /β//W 6Λ0 1 eIRRR 0p0×”C0 0Wβ”2W kre 2 0Wβ24 ≤ /β/0 4 ≤ 2 rNKIRR —C5×—C42c0’b<( 04β/0W kre 2 0Wβ62 ≤ /β/0 04 ≤ 0/ rNKIRR 5 04β/0W m — 04β828 ≤ /β//0 ”Λ21 eIRRR 0p0×WC0 04β06” kre 2 0Wβ78 ≤ /β/0 7 ≤ 4

eIRRR 0p0×2C0’aα( 0”β//” kre — 04β424 ≤ /β//— 2Λ51

eIRRR 5 0”β//” kre 2 04β”70 ≤ /β//0 6Λ02 eIRRR 5 0”β//” kre W 04β”7— ≤ /β//0 6 ≤ 0 eIRRR 5 0”β//” m — 0”β88— ≤ /β//0 4 ≤ 0 eIRRR 5 0”β//” m W 06β/”0Λ+M++0 +M+0+ 2 ≤ 0 eIRR 0p1×0p04C0 06β28” kre 2 06β/W2 ≤ /β//0 7 ≤ 4 eIRR 5 06β28” kre W 06β/WW ≤ /β//0 7 ≤ 0 eIRR 0p1×0p0WC0 06β6”7 m — 07β7”2 ≤ /β//0 2 ≤ 0 eIRR 5 06β6”7 m W 08β/0 ≤ /β/— 00 ≤ 4

eIRR 0p1×0p02C0’aα( 07β”—6 kre 2 07β—W8 ≤ /β//0 8Λ5

6

eIRR 5 07β”—6 kre W 07β—4/ ≤ /β//0 0W ≤ 0

eIRR 5 07β”—6 m 0 08β6”8 ≤ /β//0 2— ≤ 0

eIRR 5 07β”—6 m — 08β664 ≤ /β//0 6 ≤ 0 08β60” ≤ /β//0 8 ≤ 0

eIRRR 0p0×—C0’a<( 07β8”8 kre — 07βW00 ≤ /β//— 06 ≤ 4

(15)

0W ivAODtGnF NG vT,

iuaTb 1´yXAsRAtNz(

—/0W —//W

uBA jEwAFRGRBA / ’,(9u( xF¸ exF¸ / ’,(9a( qm ’,( exF¸ / ’,(9a( qm ’,(

eIRRR 5 07β8”8 kre 2 07β47W ≤ /β//0 06Λ14 07β”0 ≤ /β/— —/ ≤ 02

eIRRR 5 07β8”8 kre W 07β474 ≤ /β//0 06 ≤ 0

eIRRR 5 07β8”8 m — —/β027 ≤ /β//0 —” ≤ 0 —/β/67 ≤ /β//0 —7 ≤ —

eIRRR 5 07β8”8 m W —/β——/Λ+M++0+M+01 8 ≤ 0

eIRR 0p1×0p0—C0’a<( —0β”/0 kre 2 —0β0”2 ≤ /β//0 ——Λ1f

0f —0β08 ≤ /β/— 07 ≤ 0— eIRR 5 —0β”/0 kre W —0β0”2 ≤ /β//0 W”Λ12 eIRR 5 —0β”/0 m 0 ——β8—4 ≤ /β//0 ”/ ≤ — ——β8—7Λ+M++0+M++6 ”/Λ705 eIRR 5 —0β”/0 m — ——β82— ≤ /β//0 2— ≤ 2 ——β7”W ≤ /β//0 26Λ46 eIRR 5 —0β”/0 m W —2β00— ≤ /β//0 —— ≤ 04 eIR 5 —0β7// kre 2 —0β247 ≤ /β//0 6 ≤ — eIR 5 —0β7// kre W —0β247 ≤ /β//0 6Λ10 eIR 5 —0β7// m 0 —2β02” ≤ /β//0 20 ≤ 0 —2β0W/Λ+M++0 +M++7 2—Λ18

eIR 0p1—p0×0p0—p0—C0’a<( ——β/08 kre 0 —0β260 ≤ /β//0 8Λ2

4 —0β—6 ≤ /β/0 0/ ≤ 7 eIR 5 ——β/08 kre 2 —0β462 ≤ /β//W —/ ≤ 2 eIR 5 ——β/08 kre W —0β462 ≤ /β//0 08Λ2 1 eIR 5 ——β/08 m 0 —2β2”8 ≤ /β//0 48 ≤ 0 —2β26—Λ+M++0+M++6 ”/Λ57 eI —p1×0p0—p1—C0’a<( ——β26W kre 0 —0β60” ≤ /β//0 0”Λ0 2 —0β”0 ≤ /β/0 02 ≤ 8 eI 5 ——β26W m 0 —2β6W4 ≤ /β//0 48 ≤ 0 —2β6W8Λ+M++0 +M++7 ”0Λf1 eI 5 ——β26W m 2 —2β446 ≤ /β//W 06 ≤ 0

eRI —C0×0p0—p1—C1’a<( ——β””/ kre 0 —0β882 ≤ /β//0 7 ≤ 0

eRI 5 ——β””/ m 0 —Wβ/W8 ≤ /β//0 —6Λ02 eRI 5 ——β””/ m 2 —2β748 ≤ /β//W 0/ ≤ 0 eRI 5 ——β6W/ kre 0 ——β/60 ≤ /β//0 06 ≤ 0 —0β86 ≤ /β/0 0— ≤ 6 eRI 5 ——β6W/ m 0 —Wβ02W ≤ /β//0 W6 ≤ 0 —Wβ026Λ+M++0+M++6 40Λ41 eRI 5 ——β6W/ m 2 —2β8W2 ≤ /β//W —— ≤ 0 eRI 5 ——β66/ kre 0 ——β0// ≤ /β//0 04 ≤ 0 ——β// ≤ /β/0 0/ ≤ 6 eRI 5 ——β66/ m 0 —Wβ0”” ≤ /β//0 W4 ≤ 0 —Wβ0”8Λ+M++0+M++7 W7Λf0 eRI 5 ——β66/ m 2 —2β86W ≤ /β//W 07Λ4 0 eRRR —C1×0p0—p1—C2’a<( —2β/2/ m 2 —Wβ—W7 ≤ /β//W 6 ≤ 0 eRRR 5 —2β/6/ kre 0 ——β280 ≤ /β//0 6Λ2f eRRR 5 —2β/6/ m 0 —WβW77Λ+M++0 +M++7 —6 ≤ 6 eRRR 5 —2β/6/ m 2 —Wβ—8/ ≤ /β//W 7 ≤ 0 eRRR 5 —2β/8/ kre 0 ——βW00 ≤ /β//0 7 ≤ W jwxUN 1 yXAsRAtNz

(16)

iuaTb 1´yXAsRAtNz(

—/0W —//W

uBA jEwAFRGRBA / ’,(9u( xF¸ exF¸ / ’,(9a( qm ’,( exF¸ / ’,(9a( qm ’,(

eRRR 5 —2β/8/ m 0 —Wβ4/8Λ+M++0+M++7 —2 ≤ 6 eRRR 5 —2β/8/ m 2 —Wβ200 ≤ /β//W 0W ≤ 0 eRR —C2×0p0—p1—Cf’a<( —2β—4/ m 2 —WβW7/ ≤ /β//W 8 ≤ 0 —Wβ22—Λ+M++f +M++2 0/ ≤ 0 eRR —p0—Cf×0p0—p0—C4’a<( —2β—8— m 2 —Wβ4—W ≤ /β//W —0 ≤ 0 —Wβ26” ≤ /β//2 —2Λ5 1 eRR —C2×0p0—p1—Cf’a<( —2β2W4 m 2 —Wβ47/ ≤ /β//W —2 ≤ 0 —WβW20Λ+M++f +M++2 —”Λ42 dIRR 0p0×—C0’a<( —Wβ670 m — —”β2/7 ≤ /β//0 0— ≤ 0 dIRR 5 —Wβ670 m W —”β4” ≤ /β/4 6 ≤ 4 dIR 0p1×0p02C0’aα( —Wβ787 m 0 —”βW—W ≤ /β//0 —” ≤ 0 YIR 0p0×4C0 —”β246 kre 2 —4β7—2 ≤ /β//0 7Λ0 5 YIR 5 —”β246 kre W —4β7—2 ≤ /β//0 6 ≤ 0 YIR 0p0×WC0 —”β88/ m — —7β”42 ≤ /β//0 W ≤ 0

YIR 0p0×2C0’aα( —7βW”” kre 2 —6β778 ≤ /β//0 0”Λ0

7 —6β8— ≤ /β/2 7 ≤ 4 YIR 5 —7βW”” kre W —6β778 ≤ /β//0 0” ≤ 0 YIR 5 —7βW”” m 0 2/β—00 ≤ /β//0 2WΛ10 dIR 0p1×0p0—C0’a<( —7β676 m W 2/β7/ ≤ /β/— —” ≤ 0— dIR 5 —7β676 kre 2 —7β—/2 ≤ /β//0 —W ≤ — dIR 5 —7β676 kre W —7β—/W ≤ /β//0 —WΛ01 dIR 5 —7β676 m 0 2/β440 ≤ /β//0 46Λ1 0 2/β44”Λ+M++0+M+0+ 47Λ701 dI —p0×0p0—p0—C0 —8βW47 kre 0 —7β480Λ+M++1 +M++0 ”Λ02 dI 5 —8βW47 m 0 20β—”2 ≤ /β//0 W2 ≤ 0 20β—”7Λ+M++0+M+0+ W4Λ0f

dRI —p1×0p0—p1—C0’a<( —8β8—7 kre 0 —8β/W7 ≤ /β//0 0/ ≤ 0 —7β80 ≤ /β/0 8 ≤ 4

dRI 5 —8β8—7 m 0 20β6”— ≤ /β//— W0Λ02 20β6”6Λ+M++0+M+0+ W—Λ50 dRRR —p0—C1×0p0—p0—C2’a<( 2/βW72 m 2 2—β/84 ≤ /β//4 ” ≤ 0 dRRR 5 2/βW74 m 2 2—β/87 ≤ /β//” 8 ≤ 0 dRRR —C0×0p0—p1—C1’a<( 2/β4/0 m 2 2—β00W ≤ /β//4 7 ≤ 0 dRR —p0—C2×0p0—p0—Cf’a<( 2/β72” m 2 2—βW”6 ≤ /β//” 6 ≤ 0 dRR 5 2/β768 m 2 2—β40— ≤ /β//4 7 ≤ 0 dRR —C1×0p0—p1—C2’a<( 2/β8—W m 2 2—β4”/ ≤ /β//” 8 ≤ 0 YI 0p1×0p04C0 2—β64W m 0 2Wβ6”0 ≤ /β//0 24 ≤ 0 2Wβ6”6Λ+M++0 +M+00 2”Λ14

YIR 0p0×—C0’a<( 22β62” kre 2 22β/42 ≤ /β//0 2—Λ1

1f 22β/8 ≤ /β/2 0” ≤ 00 YIR 5 22β62” kre W 22β/42 ≤ /β//0 2WΛ 1 YI 0p1×0p02C0’aα( 2Wβ862 kre 0 22β8WWΛ+M++1 +M++0 0—Λ02 YI 5 2Wβ862 kre 2 2Wβ—”W ≤ /β//— 07 ≤ — jwxUN 1 yXAsRAtNz

(17)

0Ω ivAODtGnF NG vT,

iuaTb 1´yXAsRAtNz(

—/0W —//W

uBA jEwAFRGRBA / ’,(9u( xF¸ exF¸ / ’,(9a( qm ’,( exF¸ / ’,(9a( qm ’,(

YI 5 2Wβ862 kre W 2Wβ—”WΛ+M++1+M++0 06 ≤ —

dnGN1 UU GQN wGBVRy GEwAFRGRBAF zwGw wEN PwGQNENz OEBV GQN GBVZX zwGwxwFN I¸2¸/¸8 ’iVRGQ NG wU¸ —//0(fi

GQN duij zwGwxwFN I¸4¸4¸” ’aEwVRzw NG wU¸ —/07(fi wAz GQN nij h zwGwxwFN I¸—¸28 ’awUUVwA Γ XwHGRFGw

—//0(¸ qINEL wxFBECGRBA URAN RAyUHzNz RA GQRF GwxUN RF zNCRyGNz RA rRP¸0¸

v/ ENONEF GB GQN GQNBENGRywU JwINUNAPGQ BO GQN wxFBECGRBA URAN RA GQN FBHEyN=F ENFGOEwVN¸ ajQN VNwFHENz / IwUHNF ENONE GB GQN BxFNEINE=F ENFGOEwVN¸

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