Download BV Color Index and Temperature - The University of Texas at Dallas

B-V Color Index and Temperature
Hot stars appear bluer than cooler stars - cooler stars are redder than hotter stars.
• B-V color index way of quantifying this - determining spectral class using two different filters
Ø one a blue (B) filter that only lets a narrow range of colors or
wavelengths through centered on the blue colors,
Ø and a “visual” (V) filter that only lets the wavelengths close to the
green-yellow band through.
Hot star has a B-V color index close to 0 or negative,
Cool star has a B-V color index close to 2.0. Other stars are somewhere in
between.
⇒ 1. Measure the apparent brightness (flux) with two different filters (B, V).
⇒ 2. The flux of energy passing through the filter tells you the magnitude
(brightness) at the wavelength of the filter.
⇒ 3. Compute the magnitude difference of the two filters, B - V.
Hipparcos satellite measured
105 bright stars with
δp>0.001" ⇒ confident
distances for stars with d<100
pc
Hertzsprung-Russell diagram
for the 41704 single stars
from the Hipparcos Catalogue
with relative distance
precision better than 20% and
σ (B-V) less than or equal to
0.05 mag. Colors indicate
number of stars in a cell of
0.01 mag in (B-V) and 0.05
mag in absolute magnitude
(MV).
Notice the spread in stars on main sequence.
First H-R diagram from the Gaia mission
A model atmospheric transmission for the mean
conditions at Mt. Hopkins - ~8500 ft (location of one of the
PHYS-3380
2MASS telescopes)
Gaia asteroid detections
Ecliptic
Gaia asteroid detections compared with the positions on the sky
of a sample of 50,000 known asteroids. The color indicates
accuracy of the detection - the separation on the sky between the
observed position of Gaia's detection and the expected position of
PHYS-3380
each asteroid.The regions showing lower accuracy (red) of
Milky Way
Ecliptic
PHYS-3380
The Milky Way on the Celestial Sphere
Yes, the ecliptic plane (and earth’s) equator are tilted with
respect to each other – about 60 degrees.
PHYS-3380
Mass–Luminosity Relation
All main sequence stars fuse H into He in their cores.
Luminosity depends directly on mass because:
- more mass means more weight from the star’s outer layers
- nuclear fusion rates must be higher in order to maintain gravitational
equilibrium
L ∝ m3.5
So mass is the single most important property of any star.
- at each stage of a star’s life, mass determines…
- what its luminosity will be
- what its spectral type will be
Its lifetime on the main sequence is dependent on its mass
PHYS 3380
Lifetime on the Main Sequence
How long will it be before MS stars run out of fuel? i.e.
Hydrogen?
How much fuel is there?
How fast is it consumed?
M (solar mass)
L ∝ M3.5
How long before it is used up?
M/L = M/M3.5 = M-2.5
MS Lifetime τ = 1010 yrs / M2.5
Our Sun will last 1010 years on the Main Sequence
PHYS 3380
Masses of Stars in the Hertzsprung-Russell Diagram
The higher a star’s mass,
the more luminous
(brighter) it is:
L ~ M3.5
High-mass stars have
much shorter lives than
low-mass stars:
tlife ~ M-2.5
Sun: ~ 10 billion yr.
10 Msun: ~ 30 million yr.
0.1 Msun: ~ 3 trillion yr.
Masses in units of
solar masses
40
18
6
3
1.7
1.0
0.8
0.5
PHYS 3380
Lifetime on the Main Sequence
So for example:
B2 (10 M¤) lasts
3.2 x 107 yr
F0 (2 M¤) lasts
1.8 x 109 yr
M0 dwarf (.5 M¤) lasts
5.6 x 1010 yr
But the Universe is 1.37 x 1010 yr old!
Every M dwarf that was ever created is still on the main sequence!!
PHYS 3380
Spectroscopic Parallax
1. Determine star’s spectral class/color index.
2. Determine luminosity class from spectral line width.
3. Use photometry to measure the apparent magnitude of the star.
4. Knowing spectral class/color index allows placement of the star on a
vertical line or band along a Hertzsprung-Russell Diagram.
5. Knowing its luminosity class further constrains its position along this line,
i.e. we can distinguish between a red supergiant, giant or main sequence
6. Once we know its position on the HR diagram we can infer what its
absolute magnitude should be by either reading off across to the vertical scale
of the HR diagram or looking it up from a reference table. A main sequence
(luminosity class V) star with a color index of 0.0 (i.e. A0 V) has an absolute
magnitude of +0.9 for example.
7. Now knowing mV from measurement and inferring MV we can use the
distance modulus equation to find the distance to the star, d, in parsecs:
mV – MV = -5 + 5 log10(d [pc])
PHYS 3380
Spectroscopic Parallax
In practice not very precise
Uncertainties in absolute magnitude of stars of specific spectral and
luminosity class range from about 0.7 up to 1.25 magnitudes.
• give a factor of 1.4 to 1.8 × variation in the resultant distance.
• increases as the stellar distance increases
only accurate enough to measure stellar distances of up to about 10
Mpc.
• star has to be sufficiently bright to be able to measure the
spectrum
• can be obscured by matter between the star and the observer.
PHYS 3380
Binary Stars
About 1/3 of all stars in
our Milky Way are not
single stars, but belong
to binaries:
Pairs or multiple
systems of stars which
orbit their common
center of mass.
If we can measure and
understand their orbital
motion, we can
estimate the stellar
masses.
The Center of Mass
Newton showed that two
objects attracted to each
other by gravity actually
orbit about their center of
mass = balance point of the
system.
Both masses equal =>
center of mass is in the
middle, rA = rB.
The more unequal the
masses are, the more it
shifts toward the more
massive star.
Using this formulation, we can determine the total mass of a binary
star system if we can determine the orbital characteristics of the
system.
Examples: Estimating Mass
a) Binary system with period of P = 32 years and
separation of a = 16 AU:
MA + MB =
163
____
= 4 solar masses.
2
32
b) Any binary system with a combination of period P=1
year and separation a=1 AU that obeys Kepler’s 3rd Law
must have a total mass of 1 solar mass.
Binary Star Systems
Three types:
- Visual - stars separately visible in telescope
- Spectrographic - not separately visible - evidence of
binary system determined spectroscopically
- Eclipsing - orbital plane nearly edge on from Earth - one
star periodically eclipses other.
Visual Binaries
The ideal case:
Both stars can be seen
directly, and their separation
and relative motion can be
followed directly. Can take
years or decades to work out
- depends on period.
- Orbital period of
is 50 years
- Top photo taken in
1960
Sirius
Spectroscopic Binaries
Usually, binary separation a can not be measured directly because the
stars are too close to each other.
A limit on the separation and thus the masses can be inferred in the
most common case: Spectroscopic Binaries
In a spectroscopic binary system, the
approaching star produces blue
shifted lines; the receding star
produces red shifted lines in the
spectrum.
Spectral lines shifting apart and then
merging sign of spectroscopic binary
Doppler shift → Measurement of radial
velocities
→Estimate of separation a
→→ Estimate of masses
Spectroscopic Binaries
Typical sequence of spectra from a
spectroscopic binary system
Time
Problems With a Spectroscopic Binary
Cannot see the two stars separately:
• Distance/semimajor axes must be guessed from the orbit
motions.
• Can't tell how the orbit is tilted on the sky
Eclipsing Binaries
Usually, inclination angle
of binary systems is
unknown → uncertainty in
mass estimates.
Special case:
Eclipsing Binaries
In the case of an
eclipsing binary, we
know that we are
looking at the system
edge-on.
Eclipsing Binary
In this case, a small hot star orbits a
large, cool star.
- we see total light when no
eclipse occurs
- as the hot star passes in front
of the of the cool star, there is a
decrease in the brightness.
- when the hot star is
eclipsed behind the cool
start,
the brightness again
drops.
The depth of the eclipses depends on
the surface temperatures of the stars
Eclipsing Binaries
Example:
Algol in the constellation of
Perseus
From the light curve of Algol,
we can infer that the system
contains two stars of very
different surface
temperature, orbiting in a
slightly inclined plane.
VW Cephei
- an eclipsing binary star system in constellation Cepheus.
- contains a red supergiant (A) which fills its Roche lobe when closest to
its companion blue star, which appears to be on the main sequence
Peculiar “double-dip” light curve of
VW Cephei
- lower curve shows
observations - indicate so close
together that gravity
distorts their
shape
- evidence of dark spots on
surface - upper curve shows
what light curve would look like if
there were no spots
VV Cephei A's mass estimated from
orbital motion - about 100 solar
masses.
Mass estimated from its luminosity is
about 25-40 solar masses.
Problems With Eclipsing Binaries
Eclipsing Binary stars are very rare.
Measurement of the light curves is complicated by details:
• Partial eclipses yield less accurate numbers.
• The atmospheres of the stars soften the edges.
• Close binaries can be tidally distorted.
However, the best masses are from eclipsing binaries.
From a combination of visual and eclipsing binaries, masses are known
for about 150 stars.
Maximum Masses of Main-Sequence Stars
Mmax ~ 50 - 100 solar masses
a) More massive clouds fragment into
smaller pieces during star formation.
b) Very massive stars lose mass
in strong stellar winds
Eta Carinae
Example: Eta Carinae: Estimated to be over 100 Msun. Dramatic mass
loss; major eruption in 1843 created double lobes.
Minimum Mass of Main-Sequence Stars
Mmin = 0.08 Msun
Gliese 229B
At masses below 0.08
Msun, stellar progenitors
do not get hot enough to
ignite thermonuclear
fusion.
→ Brown Dwarfs
The Life Cycle of Stars
Aging
supergiant
Young stars, still
in their birth
nebulae
Dense, dark
clouds,
possibly
forming stars
in the future
Stars are produced in dense nebulae in which much of
the hydrogen is in the molecular (H2) form, so these
nebulae are called molecular clouds. The largest such
formations are called giant molecular clouds.
Giant Molecular Clouds
Barnard 68
Infrared
Visible
Star formation collapse of the cores of giant molecular clouds:
Dark, cold, dense clouds obscuring the light of stars behind them.
←
(More transparent in infrared light.)
Parameters of Giant Molecular Clouds
Size: r ~ 50 pc
Mass: > 100,000 Msun
Temp.: a few 0K
Dense cores:
R ~ 0.1 pc
M ~ 1 Msun
Much too cold and too low density to
ignite thermonuclear processes
Clouds need to contract and heat up
in order to form stars.
Contraction of Giant Molecular Cloud Cores
Horse
Head
Nebula
• Thermal Energy (pressure)
• Magnetic Fields
• Rotation (angular momentum)
• Turbulence
→ External trigger required to initiate
the collapse of clouds to form stars.
Three Kinds of Such Nebulae
1) Emission Nebulae
Hot star illuminates
a gas cloud;
excites and/or
ionizes the gas
(electrons kicked
into higher energy
states);
electrons
recombining, falling
back to ground
state produce
emission lines.
The Trifid
The Fox Fur Nebula NGC 2246
Nebula
Three Kinds of Nebulae
Star illuminates a gas and
dust cloud;
star light is reflected by the
dust;
reflection nebulae appear blue
because blue light is scattered
by larger angles than red light;
the same phenomenon makes
the day sky appear blue (if it’s
not cloudy).
2) Reflection Nebulae
Three Kinds of Nebulae
Dense clouds of gas and dust absorb the light from the stars
behind;
3) Dark Nebulae
appear dark
in front of the
brighter
background;
Barnard 86
Horsehead Nebula