1. Edward Murphy RARE CATS Summer 2001
Stars
Edward Murphy
RARE CATS
Summer 2001
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2. Stellar Luminosity
The luminosity of a star is the rate at which it is giving off energy.
Not all stars have the same luminosity.
They range from 1/20 to 700,000 times the luminosity of the Sun.
Luminosity varies with temperature.
E = s T4 (energy per square meter).
Luminosity depends on size.
A = 4 p R2 (number of square meters).
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3. Apparent Brightness
The apparent brightness depends on the luminosity of the star and its distance from Earth.
Apparent brightness drops as square of distance (Inverse Square Law of Light).
The apparent brightness is measured in apparent magnitudes.
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4. Magnitude System
Around 150 B.C. the Greek astronomer Hipparchus compiled a catalog of nearly 1000 stars listing their positions and apparent brightness.
The brightest stars were first magnitude stars.
The next brightest were second magnitude stars.
The faintest stars he could see were sixth magnitude stars.
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5. Magnitude System
Today, the magnitude system is defined such that a difference of 5 magnitudes is exactly a factor of 100 times in brightness.
One magnitude is a difference in brightness of about 2.5 times.
Two magnitudes are 2.5x2.5=6.3 times.
Three magnitudes are 2.5x2.5x2.5=15.9 times.
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6. Magnitude Differences
Brightness Difference 1
2.5 times 2
6.3 3 16 4 40 5
100 6
250 10
10,000 = 104 15
1,000,000 = 106
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7. Magnitude System
Unfortunately, it turns out that many objects are brighter than first magnitude.
These have been assigned magnitudes smaller than 1, including negative numbers.
Sirius, the brightest star in the sky, has an apparent magnitude of –1.5.
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8. Magnitude System
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9. Fainter objects have larger apparent magnitudes.
Magnitude System
Fainter objects have larger apparent magnitudes.
Brighter objects have smaller apparent magnitudes.
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10. Magnitude System The Sun has a magnitude of –26.2.
Your eye can easily see the full moon (magnitude about –13) and the faintest stars (magnitude 6). This is a difference of nearly 20 magnitudes or a range of 108.
The magnitude system is only used in visual astronomy. All other areas of astronomy define brightness in terms of energy per second per area received here on Earth.
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11. Colors of Stars
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12. Blackbody Curves
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13. Spectrum of the Sun
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14. Formation of Stellar Spectra
Stars do not have identical absorption line spectra.
Astronomers thought this was due to the fact that the chemical composition of stars varied.
However, most stars have the same composition as the Sun (74% H, 25% He, 1% everything else).
Today we know that stellar spectra look different because different stars have different temperatures.
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15. Classification of Stellar Spectra
Originally, the spectra of stars were classified based on their complexity:
A was the simplest, B was next…
Annie J. Cannon was the first to realize that there was a better classification scheme.
In order from hottest to coolest the order is: OBAFGKML
Oh Be a Fine Girl (Guy) Kiss My Lips
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16. 12/26/2018
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17. Classification of Stellar Spectra
Class L is new.
The 8 classes have been divided into 10 subclasses designated by number:
A B0 is the hottest B star, a B9 is the coolest and is slightly hotter than an A0 star.
The Sun is a G2 star.
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18. 12/26/2018
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19. 12/26/2018
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20. 12/26/2018
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21. 12/26/2018
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22. 12/26/2018
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23. Absorption Lines
The strengths of the absorption lines in a stellar spectrum depend not only on the amount of a given element (its abundance), but also the temperature of the star.
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24. Hydrogen Absorption Lines
For example, let’s consider hydrogen, the most abundant element in stars.
In very hot stars, hydrogen is completely ionized. Without any electrons, the hydrogen cannot absorb any light hence we see no hydrogen lines.
In moderately hot stars, we see both the Lyman (UV) and Balmer (visible) series.
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25. Line Series
n=6
n=5
n=4
n=3
n=2
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n=1

26. Formation of Stellar Spectra
In cool stars, we see only the Lyman series and not the Balmer series. Why?
The Balmer series is absorption from the n=2 orbit. The electron must be excited (either through collisions or through UV light) to be in n=2.
In cool stars, there is not enough UV light and the temperature is not high enough to keep the electrons excited, so very few are in n=2.
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27. Stellar Absorption Lines
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28. Spectral Classification
Violet
>28000
Relatively few absorption lines. Lines of N++, Si+++, and lines of other highly ionized atoms. B
Blue
Lines of neutral He, Si++, Si+, O+.
H lines more pronounced. A
Strong lines of H. Lines of Mg+, Si+, Fe+, Ti+, Ca+, and others. Weak lines from neutral metals. F
Blue to white
H lines weaker than in A stars, but still strong. Lines of Ca+, Fe+ and neutral Fe. More neutral metals.
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29. Spectral ClassificationG
White to yellow
Lines of Ca+ are strongest. Many ionized and neutral metals. H lines weaker still, CH present. K
Orange to Red
Lines of neutral metals dominate. CH bands still present. M
Red
Strong lines of neutral metals and molecular bands of TiO dominate. L
<2000
Molecular lines dominate spectrum.
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30. Astronomical Distances
The astronomical unit (AU) is defined as the average distance from the Earth to the Sun.
1 AU = x 1011 m
The light year (LY) is defined as the distance light travels in one year
1 LY = x 1015 m
1 AU = 8.3 light minutes
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31. Appendix 11: The Brightest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Sirius (a CMa) 24 9
A1V
Canopus (a Car)
12,000
316
F0I
Alpha Centauri 4
G2V
Arcturus (a Boo)
187 37
K2III
Vega (a Lyr) 50 25
A0V
Capella (a Aur)
145 42
G8III
Rigel (b Ori)
60,000
773
B8Ia
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32. Appendix 11: The Brightest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Procyon (a CMi) 7 11
F5IV-V
Betelgeuse (a Ori)
700,000
427
M2Iab
Achernar (a Eri)
2,800
144
B3V
b Centauri (Hadar)
65,000
525
B1III
Altair (a Aql) 10 17
A7IV-V
Aldebaran (a Tau)
450 65
K5III
Spica (a Vir)
12,000
262
B1V
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33. Appendix 11: The Brightest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Antares (a Sco)
850,000
604
M1Ib
Pollux (b Gem) 40 34
K0III
Fomalhaut (a PsA) 16 25
A3V
Deneb (a Cyg)
240,000
3,228
A2Ia
b Crucis
160,000
352
B0.5IV
Regulus (a Leo)
230 77
B7V
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34. Bright Stars
The Sun would appear as a magnitude 6.0 star (barely visible to the naked eye) at a distance of 56 LY
A star with a luminosity 10,000 times that of the Sun will be visible with the naked eye up to 100 times farther, 5600 LY (the inverse square law says that if we move it 100 times farther, it gets 1002=10,000 times fainter).
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35. Appendix 10: The Nearest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Sun 1 -
G2V
Proxima Centauri
6x10-6
4.2
M5V
Alpha Centauri A
1.5
4.4
Alpha Centauri B
0.5
K0V
Barnard’s Star
4x10-4
6.0
M4V
Wolf 359
2x10-5
7.8
M6V
Lalande 21185
5x10-3
8.3
M2V
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36. Appendix 10: The Nearest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Sirius A 24
8.6
A1V
Sirius B
3x10-3
w.d.
Luyten A
6x10-5
8.7
M5V
Luyten B
4x10-5
M6V
Ross 154
5x10-4
9.7
M4V
Ross 248
1x10-4
10.3
Epsilon Eridani
0.3
10.5
K2V
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37. Appendix 10: The Nearest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
Lacaille 9352
1x10-2
10.7
M1V
Ross 128
3x10-4
10.9
M4V
Luyten A
1x10-4
11.3
M5V
Luyten B -
Luyten C
Procyon A
7.7
11.4
F5IV
Procyon B
6x10-4
w.d.
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38. Appendix 10: The Nearest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
61 Cygni A
8x10-2
11.4
K5V
61 Cygni B
4x10-2
K7V
Gleise 725 A
3x10-3
11.5
M3V
Gleise 725 B
2x10-3
M4V
Gleise 15 A
6x10-3
11.6
M1V
Gleise 15 B
4x10-4
Epsilon Indi
0.14
11.8
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39. Appendix 10: The Nearest Stars
Name
Luminosity
Sun=1
Distance
(LY)
Spectral Type
DX Cancri
1x10-5
11.8
M7V
Tau Ceti
0.45
G8V
GJ 1061
8x10-5
11.9
M5V
Luyten
3x10-4
12.1
Luyten’s Star
1x10-3
12.4
M4V
Kapteyn’s Star
4x10-3
12.8
M1V
AX Microscopium
0.03
12.9
M0V
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40. Faint Stars
The Sun would appear as a magnitude 6.0 star (barely visible to the naked eye) at a distance of 56 LY.
A star with a luminosity 1/100 of the Sun must be 10 times closer to have the same apparent magnitude (inverse square law). That is, it must be within 5.6 LY of the Sun to be visible with the naked eye.
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41. Density of Stars in the Solar Neighborhood
There are 59 stars within 16 LY of the Sun.
This is a volume of 17,157 cubic LY.
There is 1 star for every 290 cubic LY.
The average distance between stars is 6.6 LY (cube root of 290).
The closest star to the Sun is Alpha Centauri system (4.4 LY).
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42. Density of Matter in the Solar Neighborhood
Density of matter is expressed in g/cm3.
Water has a density of 1 g/cm3, rocks g/cm3, and gold 19.3 g/cm3.
If a typical star has a mass of 0.4 Msun, the average density in the solar neighborhood is 3x10-24 g/cm3.
This is about 1-2 hydrogen atoms per cubic centimeter (compare that to the 2.4x1019 molecules per cm3 in the air in this room).
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43. Binary Stars
Roughly half of all stars are in binary systems (some triple and quadruple).
Visual binaries are binary star systems where each star can be seen with a telescope.
Spectroscopic binaries are those in which the stars are too close to see individually, but the spectral lines show the Doppler shift due to the orbital motion of the stars.
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44. Orbit of Kruger 60
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45. Orbit of a Binary Star
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46. Spectroscopic Binary
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47. Ursa Major, The Big Bear (Big Dipper)
From Heavens Above Web page
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48. Mizar Mizar is an example of a complicated system.
If you have good eyesight, you can see a faint companion to Mizar called Alcor. These stars are an optical double, that is, they appear close together but do not orbit one another.
In a telescope, Mizar does have a close companion. Thus, Mizar is a visual binary. The two visible components are Mizar A and Mizar B.
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49. Mizar
In fact, Mizar was the first binary star, noticed in 1650 by Riccioli.
With a spectroscope, it can be seen that both Mizar A and Mizar B are spectroscopic binaries.
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50. Mass of Sirius
When we are dealing with binary stars, the masses of the two stars are often similar, and we cannot simply ignore the mass of the lighter object like we can with planets, moons or satellites.
For example, consider the star Sirius and its companion (a white dwarf). The period of the orbit is 50 years and the distance between the stars is 20 AU.
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51. Mass of Sirius Therefore, the total mass of the system is: 12/26/2018
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52. 12/26/2018
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53. Wobble of Sirius
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54. Orbits of Sirius A and B
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55. Binary Stars Total Mass
Kepler’s Law gives us the total mass of the system, not the mass of each star individually.
However, the larger star is closer to the center of mass and has a smaller orbit.
Therefore, it moves more slowly than the lighter star.
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56. Binary Star Masses
If we can measure the speed with which each star orbits the center of mass, we can determine the relative masses of the two stars.
By watching the changing Doppler shifts of the two stars, we can determine the speed of each star and then the mass of one star compared to the other.
If we know the total mass of the two stars from Kepler’s Law, then we can compute the mass of each star individually.
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57. Stellar Masses
From the studies of masses of binary stars, astronomers have learned that:
Stars more massive than the Sun are rare.
No nearby stars (within 33 LY) are more massive than 4 solar masses.
There are a handful of stars with masses over 50 solar masses.
There may be a few stars with masses up to 100 solar masses.
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58. Stellar Masses Stars smaller than the Sun are the most common.
The smallest stars that can still burn H into He have a mass 1/12 of the Sun.
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59. Failed Stars
Stars between 1/100 and 1/12 the mass of the Sun may be able to burn deuterium into helium for a short time, but cannot sustain nuclear reactions.
Such “failed” stars are called brown dwarfs. They are similar in size to Jupiter with masses of times that of Jupiter.
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60. Gliese 229B
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61. Failed Stars
Objects below 1/100 the mass of the Sun are called planets.
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62. Diameters of Stars
Even in the largest telescopes, stars appear as tiny points of light.
The size of a star on a photograph of the sky is typically caused by the blurring effects of the Earth’s atmosphere.
In only a very few cases (e.g. Betelgeuse) has the diameter of the star been measured directly by imaging.
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63. Betelgeuse
This is the first direct image of a star other than the Sun and was made with the Hubble Space Telescope. The image reveals a huge UV atmosphere with a mysterious hotspot that is more than 10 times the diameter of the Earth and 2000 K hotter than the rest of the surface of the star.
For more information on this HST image, check out the web page
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64. Diameters of Stars
In a few cases, the diameter can be measured by noting how long it takes the light to dim as the Moon passes in front of the star.
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65. Diameters of Stars
Today, astronomers can use special telescopes called optical interferometers to directly measure the diameters of some stars.
An optical interferometer is a series of small telescopes linked together which have the resolving power of a much larger telescope.
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66. Eclipsing Binary Stars
The majority of stellar diameters have been measured using eclipsing binary stars.
An eclipsing binary is a system in which one star passes behind the other during every revolution.
When one stars blocks the light of the other, the blocked star is said to be eclipsed.
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67. Eclipsing Binary Light Curve
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68. Eclipsing Binary Stars
The diameters of the stars can be measured from the time it takes for the eclipse to begin or end, and by measuring the duration of the eclipses.
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69. Measuring the Diameters of Eclipsing Binary Stars
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70. The Diameters of Stars
Most stars have a diameter roughly the size of the Sun.
A few of the very luminous stars that are red in color are giants or supergiants.
Betelgeuse has a diameter of nearly 10 AU. If placed in our solar system, it would extend almost all the way to Jupiter.
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71. H-R Diagram
In 1911 and 1913, two Ejnar Hertzsprung and Henry Norris Russell discovered that the temperature of a star is related to its luminosity.
The Hertzsprung-Russell Diagram (H-R Diagram) is a plot of temperature (spectral class) vs. luminosity.
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72. H-R Diagram
In an H-R Diagram, temperature increases to the left and luminosity toward the top.
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73. 12/26/2018
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74. H-R Diagram
The great majority of stars are found in a band running from the upper left (hot, blue and luminous) to lower right (red, cool and dim) on the diagram. This band is called the Main Sequence.
Stars in the upper right corner (red, cool and luminous) are Giants or Supergiants.
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75. 12/26/2018
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76. H-R Diagram
Stars in the lower left corner (blue, hot and dim) are called white dwarfs.
Overall, about 89% of stars are on the main sequence, about 10% are white dwarfs, and about 1% are giants or supergiants.
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77. Main Sequence
Stars on the main sequence are producing energy by fusing H to He.
Stars spend about 90% of their lives on the main sequence.
For stars on the main sequence, their size, luminosity, and temperature are determined by two parameters: mass and composition.
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78. Main Sequence
Stars with the largest masses are the hottest and most luminous. They are located in the upper left portion of the H-R Diagram.
The least massive stars are the coolest and least luminous. They are in lower right.
The main sequence is a sequence of stellar masses.
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79. Main-Sequence Stars Spectral Type Mass (Sun =1) Luminosity (Sun=1)
Temperature
(K)
Radius O5 40
700,000
40,000 18 B0 16
270,000
28,000 7 A0
3.3 55
10,000
2.5 F0
1.7 5
7,500
1.4 G0
1.1
6,000 K0
0.8
0.35
5,000 M0
0.4
0.05
3,500
0.6
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80. White Dwarfs White dwarfs have a very small size:
White dwarfs are very hot (typically 10,000 to 50,000 K).
White dwarfs are very faint.
The typical white dwarf has a mass close to the mass of the Sun but a size about the same as the Earth.
The density of a white dwarf is around 200,000 g/cm3. One teaspoonful would weigh 50 tons.
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81. Sirius B Again consider the companion to Sirius, Sirius B.
Mass = MSun
Radius = 5846 km
Temperature = 24,790 K
Luminosity = 1/425 LSun
Surface gravity = 3x108 gSun
Numbers from Holberg, J. B., Barstow, M. A., Bruhweiler, F. C., Cruise, A. M. and Penny, A. J. 1998, Astrophysical Journal, 497,
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82. Sirius Optical Image 12/26/2018 RARE CATS
From McDonald Observatory on
Sirius A is the brighter source while Sirius B is the small star to the lower left. The elongated streaks are instrumental artifacts.
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83. Sirius B X-ray image 12/26/2018 RARE CATS
Chandra Cycle 1 X-ray image of Sirius A and B in October Sirius B is the brighter object. The image of Sirius A is likely due to ultraviolet light leaking through the filter.
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