2. PULSATING VARIABLE STARS
Cepheids and RR Lyrae
PULSATING VARIABLE STARS
Types of Intrinsic Variables:
Long-period variables
Cepheid variables
RR Lyrae variables
Flare stars
Cepheid variables are type F to type K supergiants - yellow in color, pulsating stars, and relatively rare.
Average Temperature = 4000 to 8000 Kelvin
Average Luminosity = 300 to 40,000 Lsun

3. Some Information About Stars
On the Main Sequence

4. Cepheid & RR Lyrae Variables

6. Distances Using Cepheid Variables
These variable stars show intrinsic brightness variations.
d Cephei

7. RR Lyrae
Cepheid
From the `light curve', you can tell that it is a Cepheid or RR Lyrae variable.
The period is simple to measure, as is the apparent maximum brightness.

8. A complicating factor: There are two types of Cepheids.
In addition to the standard Type I Cepheids, there is also a Type II Cepheids
Classical

9. m – M = 5 log(d)-5 To find the distance to a Cepheid Variable:
(1) Determine that the star is a Cepheid Variable
(2) Measure period of pulsation of the star.
(3) Magnitude (Mv) from the Period.
(4) Measure the apparent magnitude m
(5) Calculate the distance to the star using:
m – M = 5 log(d)-5

10. Why are Cepheid variable stars important?
The period of a cepheid variable is directly linked to its average brightness: the longer the period, the brighter the star.
RR Lyrae Stars
Similar to Cepheids, only smaller and fainter.
Period = 4 hours to 1 day

11. Variable stars are named by constellation and in the order that they are identified.
The first variable star in a constellation is called R (e.g. , R Orionus), the second S and so on through Z. After that, the next set uses double letters, beginning with RR, then RS , and on to RZ. Repeat to ZZ.
Then we next start with AA to QZ and after that V followed by a number.An example is V335 Tau. There are over 2000 known variable stars in Sagittarius alone.

16. The Milky Way COBE image of the Milky Way:
The Milky Way is a gravitationally bound collection of roughly a hundred billion stars. Our Sun is one of these stars and is located roughly 24,000 light years (or 8000 parsecs) from the center of our the Milky Way.
COBE image of the Milky Way:
                                                                                                                                                                                        

17. The Great Debate Harlow Shapley Heber Curtis
April 26, 1920
April 1920 a discussion that became known as the Shapley - Curtis Debate was held.

18. Shapley believed the spiral nebulae to be relatively small , nearby objects scattered around in our galaxy.
Curtis believed that each spiral nebulae is a separate rotating system of stars much like our own galaxy.
The debate was heated but little light was shed.
The problem being how to measure the distances to these objects .

19. This showed that it was definitely outside our galaxy.
The Answer
Hubble found cepheid variables in other spiral nebulae and determined that that the spiral nebula Andromeda was about 2,000,000 ly away.
This showed that it was definitely outside our galaxy.

21. Finding Our Place Early view Sun at center
Globular Clusters evenly distributed
Early view
Sun at center
Sun
Globular Clusters unevenly distributed
Harlow Shapley

23. Schematic of the Milky Way
Number of Stars in M.W.
1 X 10 ^ 22
Total Mass of Milky Way
1012MSUN

24. DISK - POPULATION I STARS
Thin Disk is 120,000 LY wide, x ~ 2,000 LY thick, and surrounds nuclear bulge
Most new star formation goes on here, so stars are much younger
Much free-floating gas & dust.
Also contains
Galactic Clusters (open clusters)
Disk has Young, Rich (in metals) Population I

25. GALACTIC HALO
A halo of stars and globular clusters surrounds the entire galaxy.
Old Stars
Little Interstellar Gas
Metal Poor
Also contains
Globular Clusters
No star formation
Contains ~200 globular clusters
Perhaps 300,000 light year diameter
Also contains large amounts of dark matter

26. Nuclear Galactic Bulge in center
Contains most of the visible mass in the galaxy.
12,000 LY wide x 10,000 LY thick
Made of old stars
Contains galaxy’s nucleus, at center a black hole with mass of 4,000,000 suns.
Very little gas & dust
Little star formation
Metal poor stars (Pop II)
Stars on random orbits

27. has been around the Milky Way 20 times.
Spiral Arms
The Milky Way appears to have 4 major arms.
Arms fade away in about 10,000,000 years and new arms form.
The sun is near the inner edge of a short
arm or spur called the Orion Arm.
It takes 225,000,000 years for the Sun to circle the Milky Way . The age of sun is about 4,500,000,000 years This means the sun
has been around the Milky Way 20 times.
Our galaxy is also moving through space in the direction of the constellation Hydra at a speed over 600 km/sec.

30. Mapping the Galaxy Visible Light Radio Light
Strong interstellar absorption
We can see only pcs
Radio Light
Can observe entire galaxy
In infrared and far-infrared structure , the structure of the disk and bulge start to show

32. H I 21-cm Line The energy state of an electron spinning
Anti –parallel (Poles Opposite) is slightly lower than the energy state of a parallel-spin(Poles Aligned) electron. Remember that the atom always wants to be in the lowest energy state possible, so the electron will eventually flip to the anti-parallel spin direction.

33. As the atom flips from the parallel to the anti- parallel state, it emits a radio-wave
photon with a wavelength of 21.1 cm, equivalent to a frequency of
1,420 MHz.
Most of what is known about the distribution of cold gas and the mapping of the nearby spiral arms, has come from studies of the variation of 21-cm emission.

34. Mapping the Galaxy
H clouds in different spiral arms will have different Doppler Shifts
Sun
Wavelength

36. Galactic Rotation Galactic year = 250,000 years
Stars in the Sun's vicinity move in Keplarian orbits
The motions of the stars around the center of mass of the Galaxy can be used to determine the mass of the Galaxy, using Newton's version of Kepler's 3rd law.
M = a3/P2
Stars in the inner part of the Galaxy appear to move like a rigid body.

37. Mass of the galaxy

38. Mass of the Galaxy

39. What’s the center of our galaxy like?
 The center of the galaxy is a very busy place.  It’s obscured by dust and hard to see, but we do know there’s a 4 million solar mass black hole inside! This intense X-ray and radio source is called Sagittarius A.

40. Formation of a Galaxy PREGALACTIC CLOUD
Slowly rotating, roughly spherical cloud.
Composed of hydrogen and helium.
Very low amount of heavy elements.

41. Polulation II stars form first and retain their spherical distribution.
Galactic halo forms.
Remain gas concentrates in the galactic disk.

43. Interstellar Medium (ISM)
Though the space between the stars is not completely empty.
There is some material between the stars composed of gas and dust. This material is called the interstellar medium, and it affects star light, and is needed for star formation.
About 99% of the material is gas and the rest is ``dust''.
Interstellar gas :
traces of C, N, O, Ca, Na, etc...
about 90% hydrogen (by no. of atoms)
about 10% helium

44. Interstellar dust: Small bits of solid material size< 1 micron
like cigarette smoke C, N, silicates
Effects of dust:
obscures our view of stars behind a dust cloud
makes stars look dimmer, and redder
reflects light & shines brightly
The interstellar medium is clearly evident as it blocks the light from many stars in the Milky Way.

46. The End

47. True
Space
Motion

48. Actual Motion from Radial Motion & Proper Motion
(vr)
Doppler Motion
(Radial Motion) v
Actual Motion
(vt).
Line of Sight
Proper Motion
(Tangential Motion)

49. Stellar Motion (True Space Motion)
Astronomers must measure two speeds, in order to determine the true movement of a star through space.
1. Radial Velocity
2. Tangential Velocity
The speed of a star at right angles to the line of sight, or how fast a star is moving across the sky. We also need :
The distance to the star, and its angular motion across the sky.

50. Star moving towards Earth: Blueshift
Radial Velocity
The radial velocity of a star is how fast it is moving directly towards or away from us. (Doppler Effect)
                                                                          
Radial velocities are measured using the Doppler Shift of the star's spectrum:
Star moving towards Earth: Blueshift
Star moving away from Earth: Redshift
Star moving across our line of sight: No Shift
In all cases, the Radial Velocity is Independent of Distance.
Earth

51. The formula above gives vt in km/sec.
Tangential Velocity
Over a period of time, a star will have moved across the sky a distance. Divide that distance by the time and get the
Velocity and also measure the Proper Motion Angle..
Tangential Velocity (vt).
where:
m = Proper Motion in arcsec/yr
d = Distance in parsecs
The formula above gives vt in km/sec.

53. The End