Transcript Star - Uplift Education

ASTROPHYSICS
SUMMARY
Constellation is a group of stars that form a pattern
as seen from the Earth, but not bound by gravitation
Stellar cluster is a group of stars held together by gravitation
in same region of space, created roughly at the same time.
Galaxy is a huge group of stars, dust, and gas held together by gravity,
often containing billions of stars, measuring many light years across.
Star is a massive body of gas held together by gravity, with fusion going
on at its center, giving off electromagnetic radiation. There is an
equilibrium between radiation/gas pressure and gravitational pressure
Stars’ and planets’ radiation spectrum is approximately the same as
black-body radiation/ Plank’s law.
Intensity as a function of wavelength depends upon its temperature
Wien’s law: Wavelength at which the intensity
of the radiation is a maximum λmax, is:
2.9×10-3
max (m) 
T(K)
Luminosity (of a star) is the total power (total energy per second) radiated
by an object (star). If we regard stars as black body, then luminosity is
L = A σT4 = 4πR2σT4
(Watts)
Stefan-Boltzmann’s law
A is surface area of the star, R is the radius of the star,
T surface temperature (K), σ is Stefan-Boltzmann constant.
(Apparent) brightness (b) is the power from the star received per
square meter of the Earth’s surface
L
b = 4π𝑑2
(W/m2)
L is luminosity of the star; d its distance from the Earth
Suppose I observe with my telescope two red stars A and B that are part of a binary
star system. Star A is 9 times brighter than star B.
What can we say about their relative sizes and temperatures?
Since both are red (the same color), the spectra peak at the same wavelength.
By Wien's law
 peak
3
2.9

10

T
L = 4π R2 σ T4
 peak in m
T in K
then they both have the
same temperature.
(W)
It must be that star A is bigger in size (since it is the same temperature
but 9 times more luminous). How much?
Star A is 9 times brighter and as they are the same distance away from Earth
star A is 9 times more luminous:
LA 4RA2TA4

LB 4RB2TB4
RA2
 9 2
RB
 RA  3 RB
So, Star A is three times
bigger than star B.
Suppose I observe with my telescope two stars, C and D, that form a
binary star pair.
▪ Star C has a spectral peak at 350 nm - deep violet
▪ Star D has a spectral peak at 700 nm - deep red
What are the temperatures of the stars?
By Wien's law
 peak
3
2.9

10

T
 peak in m
T in K
Thus we have for star C,
3
3
2.9

10
2.9

10
TC 

 8300 K
 peak
350 10 9
and for star D
3
3
2.9

10
2.9

10
TD 

 4150 K
9
 peak
350 10
If both stars are equally bright (which means in this case they
have equal luminosities since the stars are part of a pair the
same distance away), what are the relative sizes of stars C and D?
LC 4RC2 TC4

LD 4RD2 TD4
RC2 83004
RC2
4
 1  2
 2  2
4
RD 4150
RD
RD2  16 RC2  RD  4 RC
So that stars C is 4 times smaller than star D.
Magnitude Scale • Magnitudes are a way of assigning a
number to a star so we know how bright it is
Apparent magnitude (m) of a celestial body is a measure of its brightness as
seen from Earth. The brighter the object appears the lower its apparent
magnitude. Greeks ordered the stars in the sky from brightest to faintest…
Later, astronomers accepted and quantified this system.
• Every one step in magnitude corresponds to a factor of 2.51 change in
brightness. Ex: m1 = 6 and m2 = 9, then b1 = (2.51)3 b2
Absolute magnitude (M) of a star is the apparent magnitude that a
star would have if it were at distance of 10 pc from Earth.
It is the true measurement of a star’s brightness seen from a set distance.
m – M = 5 log
d
10
m – apparent magnitude
M – absolute magnitude of the star
d – its distance from the Earth measured in parsecs.
• If two stars have the same absolute magnitude but different apparent
magnitude they would have the same brightness if they were both
at distance of 10 pc from Earth, so we conclude they have the same
luminosity, but are at different distances from Earth !!!!!!!!!!!!!!
• Every one step in absolute magnitude corresponds to a factor of 2.51
change in luminosity. Ex: M1 = – 2 and M2 = 5, then L1 / L2 = (2.51)7
Binary star is a stellar system consisting of two stars
orbiting around their common center of mass.
The ONLY way to find mass of the stars is when they are the part of binary
stars. Knowing the period of the binary and the separation of the stars
the total mass of the binary system can be calculated (not here).
Visual binary: a system of stars that can be
seen as two separate stars with a telescope
and sometimes with the unaided eye
They are sufficiently close to Earth and the stars are well
enough separated.
Sirius A, brightest star in the night sky and its companion first
white dwarf star to be discovered Sirius B.
Spectroscopic binary: A binary-star system which from Earth
appears as a single star, but whose light spectrum (spectral
lines) shows periodic splitting and shifting of spectral lines due
to Doppler effect as two stars orbit one another.
Eclipsing binary: (Rare) binary-star system in
which the two stars are too close to be seen
separately but is aligned in such a way that
from Earth we periodically observe changes in
brightness as each star successively passes in
front of the other, that is, eclipses the other
The Hertzsprung–Russell (H – R) diagram(family portrait) is a scatter graph of stars
showing the relationship between the stars' absolute magnitudes / luminosities versus
their spectral types(color) /classifications or surface temperature. It shows stars of
different ages and in different stages, all at the same time.
main sequence stars:
fusing hydrogen into helium, the
difference between them is in mass
left upper corner more massive than right
lower corner.
white dwarf compared to a main sequence
star: • has smaller radius • more dense
• higher surface temperature
• energy not produced by nuclear fusion
LQ = sun luminosity = 3.839 × 1026 W
Techniques for determining stellar distances:
stellar parallax, spectroscopic parallax and Cepheid variables.
Stellar parallax
• two apparent positions of a close star with respect to position of distant stars as seen by
an observer from two widely separated points are compared and recorded;
• the maximum angular variation from the mean, p, is recorded;
• the distance (in parsecs) can be calculated using geometry
tan p =
Sun−earth distance
1 AU
=
Sun−star distance
d
for small angles: tan θ ≈ sin θ ≈ θ (in radians)
d=
1 AU
p
if p = 1 sec of arc, d = 3.08x1016 m defined as 1 pc
d (parsecs) =
1
p(arcseconds)
limit because of small parallaxes: d ≤ 100 pc
Spectroscopic parallax: no parallax at all!!!! (a lot of uncertainty in calculations)
• light from star analyzed (relative amplitudes of the absorption spectrum lines) to
give indication of stellar class/temperature
• HR diagram used to estimate the luminosity
• distance away calculated from apparent brightness
limit: d ≤ 10 Mpc
Spectroscopic parallax is only accurate enough to measure stellar distances of up to
about 10 Mpc. This is because a star has to be sufficiently bright to be able to
measure the spectrum, which can be obscured by matter between the star and the
observer. Even once the spectrum is measured and the star is classified according to
its spectral type there can still be uncertainty in determining its luminosity, and this
uncertainty increases as the stellar distance increases. This is because one spectral
type can correspond to different types of stars and these will have different
luminosities.
1 - Spica
• Apparent magnitude, m = 0.98
• Spectral type is B1
• From H-R diagram this indicates an absolute magnitude, M, in the range: -3.2 to -5.0
m – M = 5 log
M= -3.2,
M= -5.0,
d
10
d = 10 (m-M+5)/5
d = 10 (0.98 - (-3.2) +5)/5 = 68.54 pc
d = 10 (0.98 - (-5.0) +5)/5 = 157.05 pc
The Hipparcos measurements give d = 80.38 pc
2 - Tau Ceti
• Apparent magnitude, m = 3.49
• Spectral type is G2
• From H-R diagram this indicates an absolute magnitude, M, in the range: +5.0 to +6.5
m – M = 5 log
M= +5.0,
M= +6.5,
d
10
d = 10 (m-M+5)/5
d = 10 (3.49 -5.0 +5)/5 = 5.00 pc
d = 10 (3.49 -6.5 +5)/5 = 2.50 pc
The Hipparcos measurements give d = 3.64 pc
Cepheid variables are stars with regular variation in absolute magnitude (luminosity)
(rapid brightening, gradual dimming) which is caused by periodic expansion and
contraction of outer surface (brighter as it expands). This is to do with the balance
between the nuclear and gravitational forces within the star. In most stars these forces are
balanced over long periods but in Cepheid variables they seem to take turns, a bit like a
mass bouncing up and down on a spring.
Left: graph shows how the apparent
magnitude (the brightness) changes,
getting brighter and dimmer again
with a fixed, measurable period for a
particular Cepheid variable.
There is a clear relationship between the period of a Cepheid variable and its
absolute magnitude. The greater the period then the greater the maximum
luminosity of the star. Cepheids typically vary in brightness over a period of about
7 days. Left is general luminosity – period graph.
So, to find out how far away Cepheid is:
•
•
•
•
•
Measure brightness to get period
Use graph absolute magnitude M vs. period to find absolute magnitude M
Measure maximum brightness
Calculate d from b = L/4πd2
Distances to galaxies are then known if the Cepheid can be ascertained to be within a specific galaxy.
Thank you Francis
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