STUDY OF FLUX EMITTED FROM THE OUTER
SURFACE OF STAR SIRIUS OBSERVED FROM
NATIONAL OBSERVATORY NAGARKOT, NEPAL
B.P. Pant*, P.R. Dhungel*, U. Khanal** and S.R. Shahi***
6W[DYLHU¶V&ROOHJH0DLWLJKDU.DWKPDQGX1HSDO
&HQWUDO'HSDUWPHQWRI3K\VLFV7ULEKXYDQXQLYHUVLW\.LUWLSXU.DWKPDQGX1HSDO
***%3.RLUDO0HPRULDO3ODQHWDULXP2EVHUYDWDUR\DQG6FLHQFH0XVHXP'HYHORSPHQW%RDUG6LQJKD'XEDU
.DWKPDQGX1HSDO
Abstract: :HSUHVHQWWKH
6WXG\RIÀX[HPLWWHGIURPWKHRXWHUVXUIDFHRIVWDU6LULXV
7KH),76LPDJHVZHUHFROOHFWHG
E\0HDGHLQFK/;*366FKPLGW&DVVHJUDLQ7HOHVFRSHGXULQJWKHSHULRGIURP'HFHPEHUWR1RYHPEHU
IURPWKH1DWLRQDO2EVHUYDWRU\1DJDUNRW1HSDO7KHLPDJHVFDSWXUHGLQ),76)OH[LEOH,PDJH7UDQVSRUW6\VWHP
IRUPDWXVLQJ$87267$568,7(VRIWZDUHDQGZDVSURFHVVHGLQWKHVRIWZDUH$/$',17KHGDWDVRREWDLQHG
ZHUHDQDO\]HGLQ25,*,17KHREVHUYHGWZRGLPHQVLRQDOLPDJHRIVWDUZDVGLYLGHGLQWRGLUHFWLRQDQGYDULDWLRQ
RIUHODWLYHGHQVLW\DORQJHDFKGLUHFWLRQZDVPHDVXUHG,WZDVIRXQGWKDWWKHUHZDVFRQVLVWHQWGHFUHDVHLQUHODWLYHÀX[
GHQVLW\IURPLQQHUWRRXWHUUHJLRQ7KHUHODWLYHÀX[GHQVLW\SHUSL[HOZDVIRXQGLQWKHUDQJHRIWR,Q
DGGLWLRQZHVWXGLHGWKHRXWHUFRQWRXURIDOOUHJLRQVLHIRXUTXDGUDQWV7KHYDOXHRIUHODWLYHÀX[GHQVLW\IRU¿UVW
VHFRQGWKLUGDQGIRXUWKUHJLRQZHUHIRXQGWREHDQGUHVSHFWLYHO\7KLVVXJJHVWWKDWWKH
VWUXFWXUHRI6LULXVZDVV\PPHWULFDODQGQRVLJQL¿FDQWÀDWWLQJRIGLVNZDVREVHUYHGIURPRXUDQDO\VLV
Keywords: 6LULXV2EVHUYDWLRQ6FKPLGW&DVVHJUDLQ7HOHVFRSH)OX[GHQVLW\
7KHVWDUKDVWKH%D\HUGHVLJQDWLRQ$OSKD&DLQV0DMRULV
Į &0D 6LULXV DSSHDUV EULJKW EHFDXVH RI ERWK LWV
LQWULQVLF OXPLQRVLW\ DQG LWV SUR[LPLW\ WR (DUWK $W D
GLVWDQFHRISDUVHFVO\DVGHWHUPLQHGE\WKH
Hipparcos astrometry satellite [1], the Sirius system is
RQHRI(DUWK
VQHDUQHLJKERUVIRU1RUWKHUQKHPLVSKHUH
REVHUYHUVEHWZHHQGHJUHHVDQGGHJUHHVRIODWLWXGH
it is the closest star (after the Sun) that can be seen with a
QDNHGH\H6LULXVLVJUDGXDOO\PRYLQJFORVHUWRWKH6RODU
System, so it will slightly increase in brightness over
WKHQH[W \HDUV$IWHU WKDWWLPHLWV GLVWDQFHZLOO
begin to recede, but it will continue to be the brightest
VWDU LQ WKH (DUWK
V VN\ IRU WKH QH[W \HDUV [2 ] 7KHV\VWHPLVEHWZHHQDQGPLOOLRQ\HDUVROG,W
ZDVRULJLQDOO\FRPSRVHGRIWZREULJKWEOXLVKVWDUV7KH
distance separating Sirius A from its companion varies
EHWZHHQDQG$8[3]7KHPRUHPDVVLYHRIWKHVH
6LULXV%FRQVXPHGLWVUHVRXUFHVDQGEHFDPHDUHGJLDQW
before shedding its outer layers and collapsing into its
FXUUHQWVWDWHDVDZKLWHGZDUIDURXQGPLOOLRQ\HDUV
DJR 7KH SURMHFWHG URWDWLRQDO YHORFLW\ LV D UHODWLYHO\
ORZNPV [4]ZKLFKGRHVQRWSURGXFHDQ\VLJQL¿FDQW
ÀDWWLQJ RI LWV GLVN [5]7KXV ZH WRRN LW DV DQ REMHFW RI
interest and decided to study its symmetrical feature
E\ SURFHVVLQJ ),76 LPDJH REWDLQHG IURP WKH 1DWLRQDO
2EVHUYDWRU\ WKURXJK WKH GDWD UHGXFWLRQ VRIWZDUH
$/$',1
INTRODUCTION
Sirius (HD 48915, HIP 32349, G 66) is white mainsequence star of spectral type A1V, termed Sirius A,
:LWK D YLVXDO DSSDUHQW PDJQLWXGH RI í 8í%!
FRORU LQGH[ í DQG %í9! FRORU LQGH[ LW LV
almost twice as bright as Canopus, the next brightest
star and a faint white dwarf companion of spectral type
'$FDOOHG6LULXV%
Fig 1: FITS image of Sirius taken on November 09,2012
Author for Correspondence: %33DQW6W[DYLHU¶V&ROOHJH0DLWLJKDU.DWKPDQGX1HSDO(PDLOSWELUHQ#JPDLOFRP
1
Scientific World, Vol. 11, No. 11, July 2013
OBSERVATION
line 3
6LULXVZDVREVHUYHGWKURXJK0HDGHLQFK/;*36
WHOHVFRSHLQVWDOOHGDWWKH1DWLRQDO2EVHUYDWRU\1DJDUNRW
GXULQJ WKH SHULRG IURP 'HFHPEHU WR 1RYHPEHU
line 4
line 2
line 5
line 1
line 6
OBSERVATION TECHNIQUES
line 12
$ *RRJOH 6N\ 0DS DQG VWDU FKDUW LV XVHG WR LGHQWLI\
WKHKHDYHQO\ERGLHVDQGWKHUHDFWXDOSRVLWLRQLQWKHVN\
ZLWKQDNHGH\HV%HIRUHREVHUYLQJDSDUWLFXODUKHDYHQO\
ERG\ RQH RI WKH EULJKWHVW VWDU 6LULXV ZH LGHQWL¿HG
'HQHERI&\JQXVFRQVWHOODWLRQDQGLWLVGH¿QHGDVWKH
reference frame with the telescope at its center while
WKH $OWDLU LV WDNHQ DV DQRWKHU UHIHUHQFH IUDPH :H
manually set the telescope so that the Altair was at the
FHQWHURIWKH¿HOGRIYLHZ$IWHUWKLVVWDUZDVVHWLQWKH
memory of the telescope, we set it again to focus on
WKH 'HQHE:KHQ WKLV VWDU ZDV VHW LQ WKH PHPRU\ ZH
JRWWKHPHVVDJH$OLJQPHQW6XFFHVVIXO7KLVPHVVDJH
ensured that the reference frame was set and we were
UHDG\ WR XVH WKH WHOHVFRSHWR YLHZ DQ\ SRVVLEOH REMHFW
LQWKHVN\2QFHDUHIHUHQFHIUDPHLVVHWWKHWHOHVFRSH
ZRUNV DXWRPDWLFDOO\ DV SHU WKH FRPPDQGV JLYHQ WR LW
WKURXJKWKH$87267$5,,KDQGER[:KHQZHJLYHWKH
command to go to the Sirius star, the telescope would
URWDWHLWVHOIWRIRFXVRQLW7KHVWDUZRXOGDSSHDULQRU
QHDUWKH¿HOGRIYLHZGHSHQGLQJRQWKHDFFXUDF\ZLWK
ZKLFK ZH ¿[ D UHIHUHQFH IUDPH 2QFH WKH WHOHVFRSH
DOLJQV LWVHOI WR IRFXV RQ WKH GHVLUHG REMHFW WKH RQO\
HIIRUW ZH KDYH WR PDNH LV WR EULQJ LW LQ WKH FHQWHU RI
WKH¿HOGRIYLHZ:KHQWKHEULJKWHVWVWDU6LULXVLVLQWKH
¿HOGRIYLHZRIH\HSLHFHZHUHPRYHGWKHH\HSLHFHDQG
used cable which allows to show image on screen, from
ZKHUHZHDUHDEOHWRFDSWXUH),76DQG-3(-LPDJHRI
6LULXVVWDU
line 7
line 11
line 10
line 8
line 9
Fig 2: image of the Sirius showing contours, axes and clicks, i.e.,
clicks along twelve lines in the software ALADIN 2.5
RESULT AND DISCUSSION
Relative Flux Density
We give the results concerning the variation of relative
ÀX[ GHQVLW\ LQ DQG DURXQG WKH VWDU 6LULXV )RU WKLV ZH
XVHG WKH LPDJH FDSWXUHG E\ XV XVLQJ 0HDGH LQFK
/;*36 6FKPLGW&DVVHJUDLQ WHOHVFRSH DW 1DJDUNRW
2EVHUYDWRU\GXULQJ1RYHPEHU2XUSULPHLQWHUHVW
LVWRVWXG\WKHYDULDWLRQRIUHODWLYHÀX[GHQVLW\DURXQG
the star Sirius.
Relative Flux Density Variation from the Inner to the
Outer Region
In this section we are going to discuss the variation of
UHODWLYHÀX[GHQVLW\DORQJWKHOLQHVIURPWKHLQQHUWR
WKHRXWHUUHJLRQ7KHYDOXHVRIWKHUHODWLYHÀX[GHQVLW\
Graphical Analysis and Data Reduction
IRU WKHVH OLQHV KDYH EHHQ REWDLQHG IURP $/$',1
Sirius's photographic images obtained by telescope
LV D WZR GLPHQVLRQDO SURMHFWLRQ RI WKH GLVWDQW WKUHH
GLPHQVLRQDO VWUXFWXUH ),76 LPDJH LV SURFHHG ZLWK
WKH GDWD UHGXFWLRQ VRIWZDUH $/$',1 WR JHQHUDWH
LQIRUPDWLRQ DERXW WKH YDOXH RI UHODWLYH ÀX[ GHQVLW\
ÀX[ DW HDFK SL[HO:H GHFLGHG WR VWXG\ WKH YDULDWLRQ
RI UHODWLYH ÀX[ GHQVLW\ DORQJ GLIIHUHQW GLUHFWLRQV DQG
LQ GLIIHUHQW UHJLRQV :H GUHZ OLQHV WKDW PHHW DW
WKH FHQWHU VXFK WKDW DQJOH EHWZHHQ DQ\ WZR DGMDFHQW
OLQHVLVDOPRVWƕ:HFOLFNHGRQHDFKSL[HOIURPWKH
LQQHU WR WKH RXWHU UHJLRQ WKDW WKH OLQHV SDVV WKURXJK
:H UHFRUGHG WKH SRVLWLRQ DQG UHODWLYH ÀX[ GHQVLW\
DVVRFLDWHG ZLWK HDFK RI WKH FOLFNHG SL[HO 7KH IXUWKHU
SURFHVVLQJ ZDV GRQH LQ 25,*,1 25,*,1 LV DQ
HDV\WRXVHVRIWZDUHDSSOLFDWLRQGHYHORSHGE\0LFURFDO
6RIWZDUH,QF,WSURYLGHVSRZHUIXOGDWDDQDO\VLVFXUYH
¿WWLQJ FDSDELOLWLHV DQG SXEOLFDWLRQTXDOLW\ JUDSKLQJ
FDSDELOLWLHV 8VLQJ WKLV VRIWZDUH ZH SORWWHG JUDSKV
IRU UHODWLYH ÀX[ GHQVLW\ DJDLQVW QXPEHU RI SL[HO DQG
REWDLQHGWKHLUSRO\QRPLDO¿WV
while the associated graphs have been derived from
Scientific World, Vol. 11, No. 11, July 2013
25,*,1VRIWZDUH
Variation of Relative Flux density along line One
1RZ ZH DUH JRLQJ WR GLVFXVV WKH YDOXHV RI UHODWLYH
ÀX[ GHQVLW\ IRU OLQH ZKLFK OLHV WRZDUGV HDVW LQ WKH
1stTXDGUDQWLHDWDQDQJOHRIƕ with the horizontal
D[LV7KHYDOXHVDUHOLVWHGRQWKHWDEOH
7KH¿UVWFROXPQJLYHVWKHVHULDOQXPEHUIRUWKHFOLFNV
LH SL[HOV VKRZLQJ WKDW WKH FOLFNV DUH IURP LQQHU WR
outer region, the second and third columns give the
pixel coordinates, the fourth column gives the value of
UHODWLYHÀX[GHQVLW\IRUHDFKSL[HODQGWKHODVWFROXPQ
JLYHVVWDQGDUGHUURULQÀX[GHQVLW\LH)'(U±)
2
P1
[
<
)D
)'(U“
2
3
4
5
6
Relative Flux Density
Table 1: The values of relative flux density along line one
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
3
6
9
12
15
18
21
24
27
30
33
36
39
Pixel Number
8
9
11
12
13
14
15
16
18
19
21
22
23
24
25
26
28
ı IRU WKH VHFRQG RUGHU SRO\QRPLDO PRGHO LV 29
While comparing standard error with standard deviation
REWDLQHG IURP VHFRQG RUGHU SRO\QRPLDO ¿W VWDQGDUG
31
error is less than standard deviation which shows that
32
WKH UHODWLYH ÀX[ GHQVLW\ GLVWULEXWLRQ KDV QR VLJQL¿FDQW
33
GHYLDWLRQIURPWKHSRO\QRPLDO¿W
34
35
36
7DEOH6XPPDU\RIWKHUHODWLYHÀX[GHQVLW\DORQJDOO
OLQHV7KH¿UVWWZRFROXPQVOLVWWKHOLQHVDQGWKHWRWDO
)LJ9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHRQH
:HWRRNWKH¿UVWFROXPQRI7DEOHWR25,*,1DQG
ODEHOHG ZLWK SL[HO QXPEHU LH µU¶ :H WRRN WKH IRXUWK
FROXPQWR25,*,1DQGODEHOHGLWZLWKUHODWLYHÀX[
GHQVLW\ )D :H FDOFXODWHG WKH VWDQGDUG HUURU IRU WKH
FROXPQ RI UHODWLYH ÀX[ GHQVLW\ )D LH IRU FROXPQ
IRXU DQG SORWWHG WKH JUDSK RI UHODWLYH ÀX[ GHQVLW\
DJDLQVWU$VWKHYDOXHRIULQFUHDVHVWKHYDOXHRIUHODWLYH
ÀX[ GHQVLW\ JRHV RQ GHFUHDVLQJ VR WKDW WKH VORSH JRHV
RQ FKDQJLQJ ,Q HDFK RI WKH JUDSKV VTXDUH UHSUHVHQWV
YDOXHVRIUHODWLYHÀX[GHQVLWLHVFRUUHVSRQGLQJWRYDOXHV
RI U (DFK RI WKH VTXDUHV LV DWWDFKHG WR WZR EDUV RQH
RQLWVXSSHUVLGHDQGWKHRWKHURQLWVORZHUVLGH7KHVH
EDUVDUHFDOOHGHUURUEDUV7KHHUURULVDFWXDOO\VWDQGDUG
HUURUIRUWKHYDOXHVRIUHODWLYHÀX[GHQVLW\DVREWDLQHG
WKURXJK VWDQGDUG DQDO\VLV 7KH QDWXUH RI UHODWLRQVKLS
EHWZHHQ UHODWLYH ÀX[ GHQVLW\ DQG SL[HO QXPEHU LV
GHWHUPLQHG E\ XVLQJ SDUDEROLF ¿W PRGHO \ D1x2+b1x
+c1 7KH FXUYH ¿WWLQJ RI UHODWLYH ÀX[ GHQVLW\ DJDLQVW
SL[HO QXPEHU IRU OLQH RQH LV VKRZQ LQ )LJ ZKHUH D
VROLGFXUYHUHSUHVHQWVVHFRQGRUGHUSRO\QRPLDO¿W)RU
WKH¿UVWOLQHWKHVHFRQGRUGHUSRO\QRPLDOLVIRXQGWREH
\ [2[ZLWKHUURULQWKHFRHI¿FLHQWV
UHVSHFWLYHO\ 7KH VWDQGDUG GHYLDWLRQ
Flux Variation on all twelve lines
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
QXPEHURIFOLFNVLHSL[HOVDORQJHDFKOLQH7KHWKLUG
RQH LV VKRZQ LQ ¿JXUH 7KH JUDSKV DUH SORWWHG SL[HO
FROXPQ JLYHV WKH WRWDO UHODWLYH ÀX[ GHQVLW\ 7KH ODVW
QXPEHU YHUVXV UHODWLYH ÀX[ GHQVLW\ 7KH JUDSKV VKRZ
FROXPQUHSUHVHQWVWKHYDOXHRIUHODWLYHÀX[GHQVLW\SHU
WKDW UHODWLYH ÀX[ GHQVLW\ FRQWLQXRXVO\ GHFUHDVHV IURP
SL[HO:HFDQVHHWKDWWKHYDOXHRIUHODWLYHÀX[GHQVLW\
LQQHUWRRXWHUUHJLRQV
per pixel is maximum for line three and minimum for
OLQHVL[
3
Scientific World, Vol. 11, No. 11, July 2013
7DEOH6XPPDU\RIWKHUHODWLYHÀX[GHQVLW\Dlong all
12 lines
VKRZQLQ)LJZKHUHDVROLGFXUYHUHSUHVHQWVVHFRQG
RUGHU SRO\QRPLDO ¿W )RU WKH VHFRQG OLQH WKH VHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2 [ ZLWK HUURU LQ WKH FRHI¿FLHQW UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
RUGHUSRO\QRPLDOPRGHOLV
/LQHV
1 ™)D
)DP
2
3
4
5
6
8
9
11
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHWKUHH
12
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ OLQH WKUHH DUH
VKRZQ LQ ¿J 7KLV JUDSK GLIIHUV VOLJKWO\ IURP JUDSK RI
OLQHRQHDQGOLQHWZR7KHJUDSKVKRZVVOLJKWO\YDULDWLRQRI
ÀX[ GHQVLW\ LQ WKH UHJLRQ DURXQG SL[HO U 7KH QDWXUH RI
UHODWLRQVKLS EHWZHHQ UHODWLYH ÀX[ GHQVLW\ DQG SL[HO QXPEHU
LVGHWHUPLQHGE\XVLQJSDUDEROLF¿WPRGHO\ D1x2+b1x +c1
7KHFXUYH¿WWLQJRIUHODWLYHÀX[GHQVLW\DJDLQVWSL[HOQXPEHU
IRUOLQHWKUHHLVVKRZQLQ)LJZKHUHDVROLGFXUYHUHSUHVHQWV
VHFRQGRUGHUSRO\QRPLDO¿W)RUWKHVHFRQGOLQHWKHVHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2[ ZLWKHUURULQWKHFRHI¿FLHQWUHVSHFWLYHO\7KH
VWDQGDUGGHYLDWLRQıIRUWKHVHFRQGRUGHUSRO\QRPLDOPRGHO
LV
Relative Flux Density
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
285
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
3
6
9
12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
Pixel Number
DISCUSSION
We have already discussed the nature of the graph for
OLQH :LWK UHJDUGV WR WKLV JUDSK DQG WKH LQIRUPDWLRQ
SURYLGHGE\WKHSUHFHGLQJWDEOHVWDEOHZHFDQPDNH
a comparative analysis of the graphs for all other 11
OLQHV
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
285
270
255
Pixel
240
Polynomial Fit
225
Relative Flux Density
Relative Flux Density
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
0
3
6
9
12
15
18
21
24
27
30
33
36
39
Pixel
Polynomial Fit
0
42
3
6
9
12
15
18
21
24
27
30
33
36
39 42
Pixel Number
Pixel Number
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHWZR
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHIRXU
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
IRXUZKLFKOLHVLQVHFRQGTXDGUDQWVDUHVKRZQLQ¿J
6\PEROVDVLQ)LJ7KHJUDSKVVKRZWKDWUHODWLYH
ÀX[ GHQVLW\ FRQWLQXDOO\ GHFUHDVHV IURP LQQHU WR RXWHU
UHJLRQV)RUWKHIRXUWKOLQHWKHVHFRQGRUGHUSRO\QRPLDO
LV IRXQG WR EH \ [2 [ ZLWK HUURU
LQ WKH FRHI¿FLHQW UHVSHFWLYHO\ 7KH
VWDQGDUGGHYLDWLRQıIRUWKHVHFRQGRUGHUSRO\QRPLDO
PRGHOLV
7KHYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJWKHOLQHWZR
ZKLFK OLHV DQ DQJOH RI ƕ from the horizontal axis)
DUHVKRZQLQ¿J7KHJUDSKVDUHSORWWHGSL[HOQXPEHU
LHUYHUVXVUHODWLYHÀX[GHQVLW\7KHJUDSKVVKRZWKDW
UHODWLYHÀX[GHQVLW\FRQWLQXDOO\GHFUHDVHVIURPLQQHUWR
RXWHUUHJLRQV7KHQDWXUHRIUHODWLRQVKLSEHWZHHQUHODWLYH
ÀX[ GHQVLW\ DQG SL[HO QXPEHU LV GHWHUPLQHG E\ XVLQJ
SDUDEROLF¿WPRGHO\ D1x2+b1x +c17KHFXUYH¿WWLQJRI
UHODWLYHÀX[GHQVLW\DJDLQVWSL[HOQXPEHUIRUOLQHWZRLV
Scientific World, Vol. 11, No. 11, July 2013
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
4
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
Relative Flux Density
Relative Flux Density
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
0
3
6
9
12
15
18
21
24
27
30
33
36
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
39
3
6
9
12
15
18
21
24
27
30
33
36
39
Pixel Number
Pixel Number
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH¿YH
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHVHYHQ
7KHYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJWKHOLQH¿YH
LVVKRZQLQ¿JXUH6\PEROVDVLQ)LJ7KHJUDSK
VKRZVWKDWUHODWLYHÀX[GHQVLW\FRQWLQXRXVO\GHFUHDVHV
IURPLQQHUWRRXWHUUHJLRQV)RUWKH¿IWKOLQHWKHVHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2 [ ZLWK HUURU LQ WKH FRHI¿FLHQW UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
RUGHUSRO\QRPLDOPRGHOLV
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
VHYHQLVVKRZQLQ¿JXUH6\PEROVDVLQ)LJ7KH
JUDSK VKRZV VLPLODU QDWXUH DV JUDSK RI OLQH VL[ 7KH
JUDSK VKRZV WKDW UHODWLYH ÀX[ GHQVLW\ FRQWLQXRXVO\
GHFUHDVHV IURP LQQHU WR RXWHU UHJLRQV 7KH VHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2 [ ZLWK HUURU LQ WKH FRHI¿FLHQW UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
RUGHUSRO\QRPLDOPRGHOLV
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
Relative Flux Density
Relative Flux Density
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
0
3
6
9
12
15
18
21
24
27
30
3
6
9
12
15
18
21
24
27
30
33
36
39 42
33
Pixel Number
Pixel Number
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHVL[
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHHLJKW
WKHYDULDWLRQRI UHODWLYHÀX[ GHQVLW\DORQJWKHOLQHVL[
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
LVVKRZQLQ¿JXUH6\PEROVDVLQ)LJ7KHJUDSK
HLJKWZKLFKOLHVLQWKLUGTXDGUDQWLVVKRZQLQ¿JXUH
VKRZV VLPLODU QDWXUH DV JUDSK RI OLQH ¿YH 7KH JUDSK
6\PEROVDVLQ)LJ7KHJUDSKVKRZVVLPLODUQDWXUH
VKRZVWKDWUHODWLYHÀX[GHQVLW\FRQWLQXRXVO\GHFUHDVHV
DV JUDSK RI OLQH VHYHQ 7KH JUDSK VKRZV WKDW UHODWLYH
IURPLQQHUWRRXWHUUHJLRQV)RUWKHVL[WKOLQHWKHVHFRQG
ÀX[GHQVLW\FRQWLQXRXVO\GHFUHDVHVIURPLQQHUWRRXWHU
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [ [ UHJLRQV7KHVHFRQGRUGHUSRO\QRPLDOLVIRXQGWREH\
ZLWK HUURU LQ WKH FRHI¿FLHQW [2 [ZLWKHUURULQWKHFRHI¿FLHQW
UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
UHVSHFWLYHO\ 7KH VWDQGDUG GHYLDWLRQ
RUGHUSRO\QRPLDOPRGHOLV
ıIRUWKHVHFRQGRUGHUSRO\QRPLDOPRGHOLV
2
5
Scientific World, Vol. 11, No. 11, July 2013
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
Relative Flux Density
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
45
Pixel
Polynomial Fit
48
Pixel Number
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHQLQH
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHHOHYHQ
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
1LQH ZKLFK OLHV LQ WKLUG TXDGUDQW LV VKRZQ LQ ¿JXUH
6\PEROVDVLQ)LJ7KLVJUDSKLVVOLJKWO\GLIIHUV
IURPWKHRWKHUJUDSKVLWVKRZVDVOLJKWYDULDWLRQRIÀX[
GHQVLW\LQWKHUHJLRQDURXQGSL[HO DQG6RPHLQ
homogeneity is found in these region, The graph shows
WKDW UHODWLYH ÀX[ GHQVLW\ FRQWLQXRXVO\ GHFUHDVHV IURP
LQQHUWRRXWHUUHJLRQV7KHQDWXUHRIUHODWLRQVKLSEHWZHHQ
UHODWLYHÀX[GHQVLW\DQGSL[HOQXPEHULVGHWHUPLQHGE\
XVLQJSDUDEROLF¿WPRGHO\ D1x2+b1x +c17KHVHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2 [ ZLWK HUURU LQ WKH FRHI¿FLHQW UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
RUGHUSRO\QRPLDOPRGHOLV
7KH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
eleven (which lies in fourth quadrant) is shown in
¿JXUH6\PEROVDVLQ)LJ7KHJUDSKVKRZVWKDW
UHODWLYHÀX[GHQVLW\FRQWLQXRXVO\GHFUHDVHVIURPLQQHU
WR RXWHU UHJLRQV 7KH QDWXUH RI UHODWLRQVKLS EHWZHHQ
UHODWLYHÀX[GHQVLW\DQGSL[HOQXPEHULVGHWHUPLQHGE\
XVLQJSDUDEROLF¿WPRGHO\ D1x2+b1x +c17KHVHFRQG
RUGHU SRO\QRPLDO LV IRXQG WR EH \ [2 [ ZLWK HUURU LQ WKH FRHI¿FLHQW UHVSHFWLYHO\7KHVWDQGDUGGHYLDWLRQıIRUWKHVHFRQG
RUGHUSRO\QRPLDOPRGHOLV
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
Pixel
Polynomial Fit
Relative Flux Density
Relative Flux Density
9DULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQH
0
3
6
9
12
15
18
21
24
27
30
33
36
39
42
270
255
240
225
210
195
180
165
150
135
120
105
90
75
60
45
30
15
0
Pixel
Polynomial Fit
0
3
6
9
12
15
18
21
24
27
30
33
36
39
Pixel Number
Pixel Number
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHVL[
)LJYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJOLQHWZHOYH
7KHYDULDWLRQRIUHODWLYHÀX[GHQVLW\DORQJWKHOLQH7HQ
ZKLFK OLHV LQ IRXUWK TXDGUDQW LV VKRZQ LQ ¿JXUH 6\PEROV DV LQ )LJ 7KH JUDSK VKRZV WKDW UHODWLYH
ÀX[GHQVLW\FRQWLQXRXVO\GHFUHDVHVIURPLQQHUWRRXWHU
UHJLRQV 7KH QDWXUH RI UHODWLRQVKLS EHWZHHQ UHODWLYH
ÀX[ GHQVLW\ DQG SL[HO QXPEHU LV GHWHUPLQHG E\ XVLQJ
SDUDEROLF¿WPRGHO\ D1x2+b1x +c The second order
SRO\QRPLDOLVIRXQGWREH\ [2[
ZLWKHUURULQWKHFRHI¿FLHQWUHVSHFWLYHO\
7KH VWDQGDUG GHYLDWLRQ ı IRU WKH VHFRQG RUGHU
SRO\QRPLDOPRGHOLV
TKH YDULDWLRQ RI UHODWLYH ÀX[ GHQVLW\ DORQJ WKH OLQH
WZHOYH DUH VKRZQ LQ ¿JXUH 7KH JUDSK DUH SORWWHG
Scientific World, Vol. 11, No. 11, July 2013
QXPEHURUSL[HOYHUVXVUHODWLYHÀX[GHQVLW\7KHJUDSK
VKRZ WKDW UHODWLYH ÀX[ GHQVLW\ FRQWLQXRXVO\ GHFUHDVHV
IURPLQQHUWRRXWHUUHJLRQV7KHQDWXUHRIUHODWLRQVKLS
EHWZHHQ UHODWLYH ÀX[ GHQVLW\ DQG SL[HO QXPEHU LV
GHWHUPLQHG E\ XVLQJ SDUDEROLF ¿W PRGHO \ D1x2+b1x
+c1 7KH FXUYH ¿WWLQJ RI UHODWLYH ÀX[ GHQVLW\ DJDLQVW
6
SHULRG RI 'HFHPEHU WR 1RYHPEHU WKURXJK
LQFK /;*36 6FKPLGW &DVVHJUDLQ 7HOHVFRSH
XVLQJ$87267$568,7VRIWZDUHDQGLPDJHZDV
SURFHVVHGLQVRIWZDUH$/$',12XUFRQFOXVLRQRI
GLVVHUWDWLRQZRUNDUHDVIROORZV
SL[HOQXPEHUIRUOLQHWZHOYHLVVKRZQLQ)LJZKHUH
D VROLG FXUYH UHSUHVHQWV VHFRQG RUGHU SRO\QRPLDO ¿W
)RU WKH OLQH WZHOYH WKH VHFRQG RUGHU SRO\QRPLDO LV
IRXQGWREH\ [2[ZLWKHUURULQWKH
FRHI¿FLHQW UHVSHFWLYHO\ 7KH VWDQGDUG
GHYLDWLRQıIRUWKHVHFRQGRUGHUSRO\QRPLDOPRGHOLV
:KLOH FRPSDULQJ VWDQGDUG HUURU ZLWK VWDQGDUG
GHYLDWLRQ REWDLQHG IURP VHFRQG RUGHU SRO\QRPLDO ¿W
standard error is less than standard deviation which
VKRZVWKDWWKHUHODWLYHÀX[GHQVLW\IROORZVWKHVHFRQG
RUGHUSRO\QRPLDO¿W
‡7KHLQQHUVXUIDFHRIVWDUVKRZVKRPRJHQHRXVUHODWLYH
ÀX[ GHQVLW\ 7KH YDOXHV RI UHODWLYH ÀX[ GHQVLW\ LQ WKH
UHJLRQ RI LQWHUHVW UDQJHV IURP WR DQG
UHODWLYH ÀX[ GHQVLW\ SHU SL[HO UDQJHV IURP WR
7KHUH ZDV FRQVLVWHQW GHFUHDVH LQ UHODWLYH ÀX[
density from inner to outer regions of interest of surface
RIWKHVWDU6LULXV7KHYDULDWLRQRIUHODWLYHÀX[GHQVLW\
from inner to outer region may be ongoing process of
K\GURJHQEXUQLQJLQWKHFRUH
9DULDWLRQRI)OX['HQVLW\LQWKH2XWHU5HJLRQV
‡7KHUHZHUHQRREVHUYHGDV\PPHWU\LQWKHVWDULQRXU
DQDO\VLVRILPDJH
Region 1
Region 2
‡1RVLJQL¿FDQWÀDWWLQJZDVREVHUYHGIURPRXUDQDO\VLV
ZKLFK PDWFKHG ZLWK ZRUNV RI 5R\HU ) HW DO And
.HUYHOOD3HWDO [4], [5]
‡7KHVWDQGDUGHUURULQ5HODWLYH)OX['HQVLW\)'(U±) was
OHVV WKDQ VWDQGDUG GHYLDWLRQ ı REWDLQHG IURP VHFRQG
RUGHU SRO\QRPLDO ¿W 7KH YDULDWLRQ RI UHODWLYH ÀX[
density from inner to outer region follows the second
order polynomial, implying that it was the best method
WROHDNWKHUDGLDWLRQSURGXFHGLQWKHFRUHRIWKHVWDUDV
IDUDVSRVVLEOH
Region 4
Region 3
)LJYDULDWLRQRIÀX[GHQVLW\LQWKHRXWHUUHJLRQRI6LULXV
ACKNOWLEDGEMENT
:H KDYH VWXGLHG WKH UHODWLYH ÀX[ GHQVLW\ LQ RXWHU
regions, for this we have divided the image into four
TXDGUDQWV)LUVWFROXPQRI7DEOHVKRZVTXDGUDQWLH
region second and third column represents number of
SL[HODQGWRWDOÀX[GHQVLW\DQGODVWFROXPQUHSUHVHQWV
ÀX[GHQVLW\SHUSL[HO
:H DFNQRZOHGJH %3 .RLUDOD 0HPRULDO 3ODQHWDULXP
2EVHUYDWRU\DQG6FLHQFH0XVHXP'HYHORSPHQW%RDUG
0LQLVWU\ RI 6FLHQFH 7HFKQRORJ\ (QYLURQPHQW
*RYHUQPHQWRI1HSDOIRUDOORWWLQJVHYHUDOQLJKWVIRUWKH
REVHUYDWLRQ2QHRIWKHDXWKRUV%LUHQGUD3UDVDG3DQW
DFNQRZOHGJHV WKH ERDUG IRU ¿QDQFLDO VXSSRUW WR FDUU\
RXWWKHGLVVHUWDWLRQZRUN
4XDGUDQW
1
™)D
)DP
)LUVW
Second
REFRENCES
Third
>@ YDQ/HHXZHQ)1RYHPEHU³9DOLGDWLRQRIWKHQHZ
+LSSDUFRVUHGXFWLRQ´$$474 (2): 653–664
)RXUWK
>@ 6N\DQG7HOHVFRSH$SULO%DVHGRQFRPSXWDWLRQVIURP
+LSSDUFRVGDWDS
>@ 6FKDDI)UHG7KH%ULJKWHVW6WDUV+RERNHQ1HZ-HUVH\
-RKQ:LOH\6RQVS
7KHYDULDWLRQRIÀX[GHQVLW\SHUSL[HOLVIRXQGDOPRVW
FRQVWDQW IRU HDFK TXDGUDQW KRZHYHU ÀX[ GHQVLW\ SHU
pixel is found slightly more in second quadrant with
FRPSDUHWRRWKHUTXDGUDQWV
>@ 5R\HU)HWDO³5RWDWLRQDOYHORFLWLHVRI$W\SHVWDUV,
0HDVXUHPHQWRIYVLQLLQWKHVRXWKHUQKHPLVSKHUH´$$ 381±
>@ .HUYHOOD3HWDO³7KHLQWHUIHURPHWULFGLDPHWHUDQG
LQWHUQDOVWUXFWXUHRI6LULXV$´$$407 (2): 681–688
The nature of image of Sirius is found to be symmetric
LQ RXWHU UHJLRQV VR QR ÀDWWLQJ GLVN LV REVHUYHG LQ RXU
LPDJHDQDO\VLV
CONCLUSION
The main sequence star Sirius was observed from
1DWLRQDO 2EVHUYDWRU\ 1DJDUNRW 1HSDO GXULQJ WKH
7
Scientific World, Vol. 11, No. 11, July 2013