Stars !
Common Name Scientific Name Distance (light years) Apparent Magnitude Absolute Magnitude Spectral Type
Sun - -26.72 4.8 G2V
Proxima Centauri V645 Cen 4.2 11.05 (var.) 15.5 M5.5Vc
Rigil Kentaurus Alpha Cen A 4.3 -0.01 4.4 G2V
Alpha Cen B 4.3 1.33 5.7 K1V
Barnard's Star 6.0 9.54 13.2 M3.8V
Wolf 359 CN Leo 7.7 13.53 (var.) 16.7 M5.8Vc
BD +36 2147 8.2 7.50 10.5 M2.1Vc
Luyten 726-8A UV Cet A 8.4 12.52 (var.) 15.5 M5.6Vc
Luyten 726-8B UV Cet B 8.4 13.02 (var.) 16.0 M5.6Vc
Sirius A Alpha CMa A 8.6 -1.46 1.4 A1Vm
Sirius B Alpha CMa B 8.6 8.3 11.2 DA
Ross 154 9.4 10.45 13.1 M3.6Vc
Ross 248 10.4 12.29 14.8 M4.9Vc
Epsilon Eri 10.8 3.73 6.1 K2Vc
Ross 128 10.9 11.10 13.5 M4.1V
61 Cyg A (V1803 Cyg) 11.1 5.2 (var.) 7.6 K3.5Vc
61 Cyg B 11.1 6.03 8.4 K4.7Vc
Epsilon Ind 11.2 4.68 7.0 K3Vc
BD +43 44 A 11.2 8.08 10.4 M1.3Vc
BD +43 44 B 11.2 11.06 13.4 M3.8Vc
Luyten 789-6 11.2 12.18 14.5
Procyon A Alpha CMi A 11.4 0.38 2.6 F5IV-V
Procyon B Alpha CMi B 11.4 10.7 13.0 DF
BD +59 1915 A 11.6 8.90 11.2 M3.0V
BD +59 1915 B 11.6 9.69 11.9 M3.5V
CoD -36 15693 11.7 7.35 9.6 M1.3Vc
Measurement of Distances to Nearby Stars
Parallax Revisited
R Parallax Angle
d
Tan =R
d
Measurement of Distances to Nearby Stars
Parallax Revisited
R Parallax Angle
d
For small angles (valid for stellar measurements):
Tan where is measured in radians
R
d
Measurement of Distances to Nearby Stars
Parallax Revisited
R Parallax Angle
d
(radians) = R
d
For astronomical measurements R and d are measured in A.U.
Measurement of Distances to Nearby Stars
Parallax Revisited
(radians)
R (in A.U.)d (in A.U.) =
A convenient variation: 1 radian = 206265 arc seconds
(radians)
R (in A.U.)d (in A.U.) =
(arc seconds)
R (in A.U.)=
206265
(arc seconds)
R (in A.U.)206265=
Measurement of Distances to Nearby Stars
Parallax Revisited
One parsec is defined to be 206265 A.U.
(arc seconds)
1d (in parsecs) =
Measurement of Speeds of Nearby Stars
Radial Speed – Doppler Shift Revisited
Blue Shift toward Earth
Red Shift away from Earth
Doppler shifts are caused by line of sight velocities (called radial velocity) of the source.
Sources moving away from the earth are red shifter.
Sources moving toward the earth are blue shifted.
Measurement of Speeds of Nearby Stars
Radial Speed – Doppler Shift Revisited
Astrophysics and Cosmology
Longer , lower f
Shorter , higher f
In general
Apparent Wavelength
True Wavelength Apparent Frequency
True Frequency Velocity of Source
Wave Speed= = 1 +
Note: If the source and detector are moving apart, the Velocity of the Source is POSITIVE. If the source and detector are toward one another, the Velocity
of the Source is NEGATIVE.
Measurement of Speeds of Nearby Stars
Radial Speed – Doppler Shift Revisited
Measurement of Speeds of Nearby Stars
Transverse (sideways) Speeds
Motion of Barnards Star captured: left 1997 (Jack Schmidling), right 1950 (POSS)
Proper motion is defined to be the transverse motion of the star across the sky
Measurement of Speeds of Nearby Stars
Transverse (sideways) Speeds
(radians) = w
d
Measurement made same time during the year
w
d
d x (radians) w =
If the time interval between measurements is measured, then v = w/ t
Measurement of Speeds of Nearby Stars
vt
vR
Pythagorian Theorem:
v2 = vR2 + vt
2
v
A very recent animation of the historical motion of thousands of currently nearby stars
http://www.spacedaily.com/news/milkyway-04b.html
Measurement of Speeds of Nearby Stars
Luminosity (brightness) of a Star
Luminosity is the amount of energy per second (Watts) emitted by the star
Recall:
The luminosity of the sun is about 4 x 1026 W
Absolute Brightness: The luminosity per square meter emitted by the star at it’s surface. This is an intrinsic property of the star.
Apparent Brightness: The power per square meter as measured at the location of the earth.
Luminosity (brightness) of a Star
Note:
Absolute Brightness =Power (or Luminosity)
Surface Area of star
Also Note: Because of conservation of energy, the energy per second radiated through the area of a sphere of any radius must be a constant. Therefore
Apparent Brightness =Power (or Luminosity)
Surface Area of sphere of radius equal to the distance between the star and the earth
Luminosity (brightness) of a Star
Apparent Brightness Power (or Luminosity)
d2
Apparent brightness can be measured at the earth with instruments. d is measured using parallax. These pieces of information can be used to measure the luminosity of the star.
Temperature of a Star
Photometry Revisited
Photometer – An instrument which measure the brightness of an object
Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object
Photometer – An instrument which measure the brightness of an object
Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object
X
Intensity
Wavelength
Temperature of a Star
Photometry Revisited
X
Intensity
Wavelength
Photometer – An instrument which measure the brightness of an object
Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object
Temperature of a Star
Photometry Revisited
X
Intensity
Wavelength
Temperature of object is 7000 K
Photometer – An instrument which measure the brightness of an object
Will measure the TOTAL brightness of an object, which might be difficult to interpret. However, when combined with filters, can be used to measure the amount of light produced over a narrow range of frequencies. This can be compared with standard Blackbody radiation curves to determine the temperature of the object
Temperature of a Star
Photometry Revisited
Temperature of a Star
Photometry Revisited
Different typical filters used:
B (blue) Filter: 380 – 480 nm
V (visual) filter: 490 – 590 nm (range of highest sensitivity of the eye)
U (ultraviolet) filter: near ultraviolet
Stellar Magnitude (brightness)
Magnitude is the degree of brightness of a star. In 1856, British astronomer Norman Pogson proposed a quantitative scale of stellar magnitudes, which was adopted by the astronomical community.
Each increment in magnitude corresponds to an increase in the amount of energy by 2.512, approximately. A fifth magnitude star is 2.512 times as bright as a sixth, and a fourth magnitude star is 6.310 times as bright as a sixth, and so on.
Originally, Hipparchus defined the magnitude scale of stars by ranking stars on a scale of 1 through 6, with 1 being the brightest and six the dimmest. Using modern tools, it was determined that the range of brightness spanned a range of 100, that is, the magnitude 1 stars were 100 times brighter than magnitude 6. Therefore, each change in magnitude corresponds to a factor of 2.512 change in brightness, since
(2.512)5 = 100 (to within roundoff)
Stellar Magnitude (brightness)The naked eye, upon optimum conditions, can see down to around the sixth magnitude, that is +6.
Under Pogson's system, a few of the brighter stars now have negative magnitudes. For example, Sirius is –1.5. The lower the magnitude number, the brighter the object. The full moon has a magnitude of about –12.5, and the sun is a bright –26.51!
Stellar Magnitude (brightness)
Star Magnitude
How Much Brighterthan a Sixth Magnitude
Star
Logarithmic scale of2.512 X between magnitude
levels Starting at Sixth Magnitude
1 100 Times 2.51 x 2.51 x 2.51 x 2.51 x 2.51
2 39.8 Times 2.51 x 2.51 x 2.51 x 2.51
3 15.8 Times 2.51 x 2.51 x 2.51
4 6.3 Times 2.51 x 2.51
5 2.51 Times 2.51 x
6
Stellar Magnitude (brightness)Star Magnitude Table Showing How Much DimmerOther Magnitudes are as Compared to a -1 Magnitude Star
Star MagnitudeHow Much Dimmer
than a -1 Magnitude StarHow Much Dimmer
than a -1 Magnitude Star
-1
0 1/2.51 0.398
1 1/6.31 0.158
2 1/15 0.063
3 1/39 0.0251
4 1/100 0.0100
5 1/251 0.00398
6 1/630 0.00158
7 1/1,584 0.000630
8 1/3,981 0.000251
9 1/10,000 0.000100
10 1/25,118 0.0000398
11 1/63,095 0.0000158
12 1/158,489 0.00000631
13 1/398,107 0.00000251
14 1/1,000,000 0.00000100
15 1/2,511,886 0.000000398
16 1/6,309,573 0.000000158
17 1/15,848,931 0.000000063
18 1/39,810,717 0.000000025
19 1/100,000,000 0.000000010
Stellar Radii
Stefan’s Law
Power Emitted per unit Area = T4
= 5.67 x 10-8 W / m2 – K4 (Stefan-Boltzmann constant)
Note: The power in this expression is the star’s luminosity
Stellar Radii
Stefan’s Law
Power Emitted per unit Area = T4
Once the absolute luminosity and temperature is measured, the star’s radius can be calculated.
Spectral ClassesStar Type
ColorApproximate Surface Temperature
Average Mass (The Sun = 1)
Average Radius (The Sun = 1)
Average Luminosity (The Sun = 1) Main Characteristics Examples
O Blue over 25,000 K 60 15 1,400,000Singly ionized helium lines (H I) either in emission or absorption. Strong UV
continuum.
10 Lacertra
B Blue 11,000 - 25,000 K 18 7 20,000Neutral helium lines (H II) in
absorption.RigelSpica
A Blue 7,500 - 11,000 K 3.2 2.5 80Hydrogen (H) lines strongest for A0
stars, decreasing for other A's.Sirius, Vega
FBlue to White
6,000 - 7,500 K 1.7 1.3 6Ca II absorption. Metallic lines
become noticeable.Canopus, Procyon
GWhite to Yellow
5,000 - 6,000 K 1.1 1.1 1.2Absorption lines of neutral metallic atoms and ions (e.g. once-ionized
calcium).
Sun, Capella
KOrange to Red
3,500 - 5,000 K 0.8 0.9 0.4 Metallic lines, some blue continuum.Arcturus, Aldebara
n
M Red under 3,500 K 0.3 0.40.04
(very faint)Some molecular bands of titanium
oxide.Betelgeuse, Antares
Stellar Classifications
Stellar Spectral Types Stars can be classified by their surface temperatures as determined from Wien's Displacement Law, but this poses practical difficulties for distant stars. Spectral characteristics offer a way to classify stars which gives information about temperature in a different way - particular absorption lines can be observed only for a certain range of temperatures because only in that range are the involved atomic energy levels populated. The standard classes are:
Type Temperature
O 30,000 - 60,000 K Blue starsB 10,000 - 30,000 K Blue-white starsA 7,500 - 10,000 K White starsF 6,000 - 7,500 K Yellow-white starsG 5,000 - 6,000 K Yellow stars (like the Sun)K 3,500 - 5,000K Yellow-orange starsM < 3,500 K Red stars
The commonly used mnemonic for the sequence of these classifications is"Oh Be A Fine Girl, Kiss Me".
Stellar Classifications
O-Type Stars The spectra of O-Type stars shows the presence of hydrogen and helium. At these temperatures most of the hydrogen is ionized, so the hydrogen lines are weak. Both HeI and HeII (singly ionized helium) are seen in the higher temperature examples. The radiation from O5 stars is so intense that it can ionize hydrogen over a volume of space 1000 light years across. One example is the luminous H II region surrounding star cluster M16. O-Type stars are very massive and evolve more rapidly than low-mass stars because they develop the necessary central pressures and temperatures for hydrogen fusion sooner. Because of their early development, the O-Type stars are already luminous in the huge hydrogen and helium clouds in which lower mass stars are forming. They light the stellar nurseries with ultraviolet light and cause the clouds to glow in some of the dramatic nebulae associated with the H II region
CLASS O DARK BLUE
TEMPERATURE 28,000 - 50,000°K
COMPOSITION Ionized atoms, especially helium
EXAMPLE Mintaka (01-3III)
CLASS B BLUE
TEMPERATURE 10,000 - 28,000°K
COMPOSITION Neutral helium, some hydrogen
EXAMPLE Alpha Eridani A (B3V-IV)
CLASS A LIGHT BLUE
TEMPERATURE 7,500 - 10,000°K
COMPOSITION Strong hydrogen, some ionized metals
EXAMPLE Sirius A (A0-1V)
CLASS F WHITE
TEMPERATURE 6,000 - 7,500°K
COMPOSITION
Hydrogen and ionized metals, calcium and iron
EXAMPLE Procyon A (F5V-IV)
CLASS G YELLOW
TEMPERATURE 5,000 - 6,000°K
COMPOSITION Ionized Calcium, both neutral and ionized metals
EXAMPLE Sol (G2V)
CLASS K ORANGE
TEMPERATURE 3,000 - 5,000°K
COMPOSITION Neutral Metals
EXAMPLE Alpha Centauri (K0-3V)
CLASS M RED
TEMPERATURE 2,500 - 3,500°K
COMPOSITION Ionized atoms, especially helium
EXAMPLE Wolf 359 (M5-8V)
Each Spectral class is divided into 10 subclasses, ranging from 0 (hottest) to 9 (coolest). Stars are also divided into six categories according to luminosity: 1a (most luminous supergiants), 1b (less luminous supergiants), II (luminous giants), III (normal giants, IV (subgiants), and V (main sequence and dwarfs). For instance, Sol is classified as a G2V, which means that it is a relatively hot G-classed main sequence star.