1446 Introductory Astronomy II

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1446 Introductory Astronomy II

• Chapter 16B
• Hubbles Law Distance Measurements
• R. S. Rubins
  Fall, 2009

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Hubbles Law
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Hubbles Law Calculation

• Galaxies which are not bound to the Milky Way by
  gravity, are receding from us according to
  Hubbles Law i.e.
• v Hod,
• where v is the recessional speed (in km/s), d
  is the distance of the galaxy (in Mpc), and Ho
  74 km/s/Mpc is the most recent determination of
  Hubbles constant (2008).
• Example
• From its measured redshift, a distant galaxy
  is found to be receding from us at 1850 km/s. How
  far away is that galaxy?
• Answer
• d v/Ho 1850 km/s /74 km/s/Mpc 25
  Mpc.
• Hubbles Law works for distances of beyond
  about 10 Mpc.

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Distance Measurements 1

• 1. Radar ranging
• (up to about 1 AU)
• A radar pulse is reflected off a planet or
  satellite.
• The total travel time is
• t 2d/c.
• 2. Parallax
• (up to about 400 ly)
• Parallax is the apparent change in position
  of an object (relative to a more distant object)
  caused by viewing it from a different location.

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Distance Measurements 2

• While radar ranging and parallax are direct
  methods of measuring distances to stars, since
  they do not depend on our understanding of the
  nature of stars.
• The remaining types of measurement, which cover
  much larger distances, may be found from the
  equation
• M m 5 log(d/10),
• where m, the apparent magnitude, is determined
  from an Earth-based measurement of brightness,
  and M, the absolute magnitude, is deduced from
  some physical property of the star or galaxy.
• The remaining measurements are based on
  methods of measuring M.

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Distance Measurements 3

• 3. Spectroscopic parallax
• (200 ly to 40,000 ly)
• A distant stars apparent magnitude and
  temperature (spectral type) are measured, and its
  luminosity class is determined from its spectrum.
• M is well-defined for stars of given spectral
  type and luminosity class.

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Distance Measurements 4

• 4. Variable stars
• (3000 ly to 100 million ly)
• A Cepheid variable star pulsates with a
  period which depends on the mean values of its
  luminosity L, which in turn is related to M.

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Distance Measurements 5

• 5. Tully-Fisher relation (3 million ly to 300
  million ly)
• The Tully-Fisher relation connects the mass of a
  spiral galaxy and its rotational velocity, by the
  relationship
• mass ? v4.
• The rotational velocity is obtained from the
  Doppler effect, which causes an increase in the
  width of the 21 cm emission line of atomic H,
  thus allowing the absolute magnitude of the
  galaxy to be calculated from the Tully-Fisher
  relationship.
• In 2007, it was realized that the relationship
  between mass and rotational velocity extends to
  all galaxy shapes, combining the Tully-Fisher
  relationship with a similar relationship which
  was found to exist for elliptical galaxies.

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Distance Measurements 6

• 6. Type 1a supernovae (beyond 3 million ly)
• A Type 1a supernova explosion acts as a standard
  candle, since it occurs precisely when a white
  dwarf in a binary star system, which is stealing
  matter from its companion, reaches the
  Chandrasekhar Limit of 1.4 solar masses.
• The absolute magnitude reaches a maximum value of
  17.
• The apparent magnitude of the galaxy is obtained
  from measurements of the brightness of the
  supernova as viewed from the Earth.

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Hubbles Law Revisited

• Hubbles Law
• (beyond 100 million ly)
• The recessional velocities of galaxies beyond
  the Local supercluster are given by
• v Hod,
• where Ho 71 km/s/Mpc.
• When disagreements have been found between
  measurements of d by Hubbles Law and by Type Ia
  supernovae, the latter has been considered to be
  the better method.

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Distance Measurements 7