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.