Download AST 207 7 Homew

AST 207
7
Homew
work 5
Due 18 Octoober 2010
at beginningg of class.
No laate papers.
H
mod
del of a star. Imagine that you have maade “stars” ouut of hot platees and you aree
1. Hot-plate
pllotting them on
o a Hertzsprrung-Russell diagram
d
a. (3 pts.) How can yo
ou make two hot
h plates witth the same sppectral class aand differing
absolu
ute magnitudee?
Chang
ge the hot plattes size. For all
a parts, the kkey idea is thaat the H-R diaagram is a ploot of
absolu
ute magnitudee or luminosity
aand temperatuure.
b. (3 pts.) If you moveed the hot plaate to a greaterr distance, hoow would its pplace on the H
HR
diagram change?
It wou
uld not, the HR
R diagram deepends on the absolute maggnitude, not oon the apparennt
magnitude or the stars distance from
f
us.
c. (3 pts.) If you turneed the setting on the hot plaate from “higgh” to “mediuum,” how wouuld its
i the HR diagram change??
place in
It wou
uld move to th
he right and down. Doing this would firrst, decrease tthe temperatuure,
thus reeddening the star
s and moviing it to the riight, and secoond, decrease its luminositty.
Movin
ng it down.
2. Life
L on Deneb
b. Here you will
w find out wh
hat it means tto live near a ggiant like Denneb. Recall thhat the
lu
uminosity of a star
, where T is its temperaature and R iss its radius.
Abs. mag. Diistance (pc)
Appp. Mag. A
Star
a. In classs we found th
hat a star 10 Sun
-2 6.74
4.83
1/2200,000
times fainter
f
has a magnitude
m
Deneb 1.225
-77.3
5000
+2.5 greater.
g
This relationship
betweeen the flux fA and fB of
two staars A and B and
a their magn
nitudes can bbe expressed m
mathematicallly as mA–mB= –2.5
log(fA/ fB). (3 pts.) How much brrighter is Denneb than the suun if both aree placed at thee same
distancce? (2 pts.) What
W quantity
y makes this ccomparison inn the most dirrect manner?
mA–mB= –2.5 log(ffA/ fB), where mA will be Deeneb, and mB will be the sun, solving foor the
ratio of
o their fluxes, we get
fA
 10
fB
( m A  mB )
 2 .5
 10
( 7.3 4.83)
2 .5
 71000
Deneb
b is 71000 tim
mes as bright at
a the sun.
Absolu
ute magnitudee makes this comparison
c
inn the most dirrect way. If yyou used appaarent
magnitude, you wou
uld have to acccount for disstance.
00K, and the ttemperature oof Deneb is 98800K. (2 pts.)) How
b. The temperature of the sun is 570
l
is Deneeb than the su
un? (3 pts.) Exxplain the prinnciple(s) that you use and w
where
much larger
you go
ot the values.
We kn
now
. Use the raatio of the lum
minosity of Deeneb to that oof the sun.
2
Thereffore: 71000 
R Deneb TDeeneb
2
RSun TSunn
Solvin
ng for the radiii ratio we gett:
4
2
4

R Denebb (9800) 4
2
RSun (5700) 4
AST 207
7
Homew
work 5
Due 18 Octoober 2010
at beginningg of class.
No laate papers.
2
2
 TSun 
RDenebb
 57000 
 71000 
  71000 
  90
RSun
 98000 
 TDeneb 
Deneb
b is 90 times the radius of the
t sun.
To ansswer this we needed
n
to kno
ow the ratio oof luminosities from part a,, and luminossity’s
relationship to the radius
r
and tem
mperature of a star. The tem
mperatures caame from the data
given.
btends ½ degree in the sky. If Deneb repplaced the sunn, what angle w
would
c. (2 pts.)) The sun sub
our rep
placement sub
btend? (2 pts..) Explain thee principle(s) that you use aand where yoou got
the vallues.
The haalf-angle of th
he sun is
/ , where R is its radiuus and D is its distance. If D
Deneb
replaceed the sun, thee radius is larger by a factoor of 90. Thereefore the anglle subtended bby the
replaceement sun is 90 0.5° 45°.
The raadius was from
m part b.
M
Figure 1 is the Hertzssprung-Russelll diagram off the star clustter M15.
3. M15.
gnitude of thee hottest mainn-sequence staars?
a. (2 pts.) What is the absolute mag
t HR diagraam, the hottesst main sequeence stars are about 3.5
From the
b. (3 pts.) Why are theere no hotter main-sequenc
m
ce stars?
m sequencce because theey all already used up theirr
There are no hotter stars on the main
gen cores and
d left the main
n sequence. H
Hotter stars usse up their fuel faster.
hydrog
c. Stars with
w a color B-V=0.6 span a range of 5 m
magnitudes. (22 pts.) What pproperty of thee stars
accoun
nts for this ob
bservation? (3
3 pts.) What iss the range off this propertyy?
Their size
s (or radius) accounts fo
or this range iin observationn.
Since color is relateed to
temperrature, the
temperratures are thee
same.
nitudes is two
o steps
5 magn
of 2.5 mag, which is
i two
factorss of 10 in
lumino
osity, or 102, or
o 100.
So if lu
uminosity (L))
increasses by a facto
or of
100, an
nd temperaturre (T)
stays constant,
c
then
n using
, 100 = R2, or
R=10.
Thereffore the radius
coverss a factor of 10. The
radius of the giants is ten
times that
t of the dw
warfs.
Fig
gure 1 Hertzsprrung-Russell ddiagram of the sstar cluster M115. B-V is a
meeasure of color.. The vertical sscale on the lefft is apparent m
magnitude, and the
scaale on the rightt is absolute maagnitude.