exploring the stars Flashcards
number
~100b
Unable to see a star evolve from
birth to death.
Stars are not born at the same time – > elaborate
each at different life stage
We can see only brief moments of;
a star’s life
Luminosity
= TOTAL ( all wavelengths)power (energy per second!)radiated by a star into space (in
watts [W]).
Brightness of stars as we see them in the sky is referred to as the
Apparent brightness = Amount of power reaching us per unit area (luminous flux)
The farther away the
star, the fainter it appears
Apparent brightness obeys the inverse square law:
Apparent brightness =Luminosity/4πd2
A light source of very well known luminosity is called
‘standard candle’
Apparent brightness can be measured:
Use a photodetector, e.g. CCD, CMOS sensors
The detector has to be properly calibrated
Measure a ‘standard candle’ first
Account for absorption & scattering in the atmosphere/space
How do we measure distance of stars?
Small annual shifts in star’s apparent position as Earth orbits the Sun
Analogous to triangulation used by surveyors:
Measure angle by looking at C w.r.t. some fixed background objects at A & B
Measure distance between A & B
Parallax angle is the angle
subtended by 1 AU.
sin p (talking about parallax angle here)
1 AU/d
If p «_space;1, sinp ≈ p–> d = 1 AU/p
The distance to an object with a parallax angle of 1
arcsecond (1”) is called what
1 parsec
what is the formula for parsec
d[pc] = 1/(a[arc sec])
60’’
1 arc minute (1’)
60’
1 degree (1*)
360*
1 full circle
Classification of stars based on their brightness
& position in the sky says what
very little about their true (physical) nature.
A star could be very bright because it is very close to us
In the 20th century,
astronomers developed a
more appropriate
classification system based on
Luminosity Surface Temperature Stellar life cycles can be reconstructed since these properties depend on mass & age of star
The luminosity of a star is
(Apparent brightness) × 4πd^2
Stellar luminosities are usually stated in comparison
with that of
the Sun, LSun
Stars have a wide range of luminosities —>
Our Sun is somewhere in the middle
(when using a LOGARITHMIC scale for the luminosity).
Dimmest star luminosity = 10^‒4 * LSun
Brightest star luminosity = 10^6 * LSun
Dim stars are far more common than bright ones.
Our Sun is brighter than most stars in our galaxy!
Stars can be classified based on their
brightness and location in the sky
Astronomers still use an ancient method to measure
brightness
Magnitude System
Magnitude System:
Apparent magnitude
= −2.5 log(Apparent Brightness)
Star brightness
measured as it appears from Earth
Magnitude of 5 difference
factor of 100× in brightness
Each magnitude step
2.5 × variation (↑ or↓) in brightness
However, to properly characterize a star, it is more
practical and reliable to
define an absolute magnitude
absolute magnitude:
A star’s absolute magnitude M is the apparent
magnitude it would have IF it were located at a
distance of 10 parsecs (32.6 light-years) from Earth
A star’s absolute magnitude M for the Sun
4.8
how to calculate the ratio of luminosity of the studied star can be obtained
From the difference between the measured magnitude of a studied star and that of a “reference” star of known magnitude and luminosity (e.g. the Sun), the ratio of luminosities can be calculated
Stars behave like a blackbody meaning?
Blackbody = a theoretical object:
• It is a perfect absorber for all incident radiation.
• It also is an ideal diffuse (isotropic) emitter
Spectra of stars
Very hot inner region emits continuous radiation-->Actually the star’s core is the blackbody! Cooler outer layers absorb certain wavelengths. Reveal chemical composition of the star!
The stellar spectrum reveals the
temperature
&
chemical composition of a star.
Spectral type is defined by
absorption lines, and
their relative strengths due to various elements (atoms, ions &
molecules)
But spectral type is NOT determined by composition
ALL stars are made primarily of H & He.
spectral type is determined by
surface temperature
Spectral type is determined by surface temperature,
which is dictated by the
core temperature, which
Dictates the energy states of electrons in atoms/molecules/ions
Dictates the types of ions or atoms/molecules
This, in turn, determines the number & relative strengths of
absorption lines in the star’s spectrum
o
> 30,000
B
10,000 ~ 30,000
A
7,500 ~ 10,000
F
6,000 ~ 7,500
G
5,000 ~ 6,000
K
> 3500 ~5000
M
2,000 ~ 3,500
(L)
1,500 ~ 2,000
blue
0
“white”
A
“yellow”
F
“red”
M
Each spectral class is divided into 10 parts:
the lower the number, the hotter the temperature: A0 is hotter than A1, etc.
Spectral class O is an exception
(sub-divided into O4 - O9)!
the last part of the classification indicates the
luminosity class
1a
bright supergiants
1b
less brights supergiants
11
bright giants
111
giants
1v
subgiants
v
dwarfs
sd
subdwarfs
wd
white dwarfs
The luminosity class describes the region of the
H-R diagram
in which the star falls.
A star’s luminosity class is more closely related to its size
than to its actual luminosity.
whats needed to fully classify a star
Both spectral type
& luminosity class
Other important parameters added to completely characterize
a star are the
color indices
single most important property of a star.
Mass
At each stage of a star’s life, mass determines
luminosity and spectral tyle, or surface temperature
Stellar mass is generally more difficult to measure than
surface temperature or luminosity.
Mass can only be measured directly by
observing the
effect which gravity from another object has on the star.
Kepler’s third law
Most easily done for two stars which orbit one another —–> binary star systems
Visual binary
Pair of stars which is visually distinct
eclipsing binary
Pair of stars orbiting in the plane of our line of sight
When one eclipses the other, the apparent brightness drops
Light curve (apparent brightness vs. time) reveals the eclipse
pattern
Spectroscopic binary
Neither visual or eclipsing
Small distance between the stars
Existence of two stars inferred from the Doppler shift of the
spectral lines
doppler effect
frequency shift when source ad observer move relatively to each other
Star size can be found from the
Stefan-Boltzmann law
Luminosity =
= (surface area)×(power emitted per unit area)
L =
(4πR^2)×σT^4
σ
Stefan-Boltzmann constant
Results for main-sequence stars:
R∝M^¾
A very
luminous
star is either
very large, OR has a very high surface temperature, or both. If 2 stars have same temp., one can be more luminous only if it is larger in SIZE.
Main sequence stars
They differ in temperature & luminosity because the H fusion rate depends strongly on mass. A main-sequence star’s mass can be estimated from just knowing its spectral type. Notice that stellar masses decrease downward along the main sequence
Luminosity is also dictated by a star’s mass
L∝M^a, with a = 3…4.
In practice, the relation is used to deduce a main sequence star’s mass from its measured luminosity
Luminosity–mass relation implies that
massive stars have shorter lives -> more fuel but burn out very fast!
—> → Only applicable for main-sequence stars!
More detailed eqn.s show that the main-sequence lifetime τ of a star depends on both its
mass & luminosity
Why/How does a star’s mass determine its luminosity?
A more massive star needs more expansive internal pressure to be in gravitational equilibrium.
This is provided by the inherently much higher core temperature which boosts tremendously the fusion rate, leading to a significantly larger luminosity
To summarize why/How does a star’s mass determine its luminosity?
M ↑ -> pcore ↑↑ -> Tcore ↑↑↑ -> fusion rate ↑↑↑↑↑↑ ->L ↑↑↑↑↑↑↑
What are giants & supergiants?
Stars near the ends of their lives. Very bright: can be seen even if not especially close to us. Identified by their reddish colors. Giants & supergiants are considerably rarer than main sequence stars
What are white dwarfs?
White dwarfs are the remaining cores of stars that ran out of fuel.
Outer layer ejected
All nuclear fusion ceased
Example: Sirius B
Some unstable stars vary significantly in brightness with time, why?
Upper layers are too opaque Energy & pressure builds up Expands in size Outer layer become transparent Energy escapes & pressure drops Contracts in size Oscillate in size in a futile quest to achieve equilibrium Brightness varies in a regular pattern
Most pulsating variable
stars occupy the
instability strip on the H-R diagram.
A special category of very
luminous stars in the upper
portion of the strip is
known as
Cepheid variable stars = their pulsation periods are closely to their luminosities -> can be used to measure distances to many galaxies
All stars are born from giant
=interstellar gas clouds.
One cloud can have enough material to form
many stars. Stars almost inevitably form in groups. These groups are known as star clusters
Stars in a cluster lie at about the same distance
from Earth
All stars have roughly the
same age & initial chemical composition
their study provides“evolutionary snapshots” at different moments in their evolution and that of the Universe
Open Cluster
Always found in the galactic disk of the galaxy.
Young in age, 1m…1b years old.
Typically 30 l.y. across & sparsely packed.
Contain from 10s to 1,000s stars, typical 100s.
Globular Clusters
Found mostly in the spherical halo of the galaxy.
Consists of old stars, 8~13
b years old.
10,000~100,000s of stars.
Typically 60~150 l.y. in diameter.
Densely packed & concentrated in a ball shape.
Stars can be separated by only a fraction of a light year in the core.
How do we determine the age of a star cluster?
Stars in a cluster have the same age, distance & the same
initial composition -> but mass differs!
Massive stars on the main sequence have shorter lives.
How do we determine the age of a star cluster?
O type stars→1m years.
Our Sun→ 10b years.
M stars→> 100b years.
Plot all stars in the cluster on
the H-R diagram->the
precise point at which the stars diverge from the mainsequence is called its mainsequence turnoff point
The age of the cluster is equal to the lifetime of stars
at its main sequence turnoff point.
M4 globular cluster age how sia
Main sequence turnoff point is near to our Sun
Age of cluster = 13b years!
