Download Lecture 11

Stellar distances and velocities
ASTR320
Wednesday October 5, 2016
Why are stellar distances important?
• Distances are necessary for estimating:
– Total energy emitted by an object (Luminosity)
• Testing models of stellar evolution
– Masses of objects from their orbital motions
– True motions through space of stars
• The problem is that distances are very hard to
measure...
Parallax angle
• Stellar (trigonometric)
parallax is the apparent
shift in the position of a
nearby star, with
respect to background
stars, due to the orbital
motion of the Earth
around the Sun.
• The parallax angle, π,
is the difference
between the geocentric
and heliocentric
positions of the star.
Parallax decreases with distance
• In the upper figure,
the star is about 2.5
times nearer than the
star in the lower
figure, and has a
parallax angle which
is 2.5 times larger.
Image credit: Rick Pogge, Ohio State
Parallax
• R=1 a.u.
• d is very large
• Small angle approximation says
𝑅
tan 𝜋 ~ 𝜋 =
𝑑
• Measured parallaxes are small: π < 1" for all stars
Distance unit: parsec
• Define 1 parsec (“parallax arcsecond,” pc):
• A star with a parallax of 1 arcsecond has a distance of 1
Parsec.
• This is a fundamental unit of distance in astronomy:
• 1 parsec (pc) is equivalent to:
– 206,265 AU
– 3.26 Light Years
– 3.086x1013 km
Distance unit: light year
• An alternative unit of astronomical distance is the Light Year
(ly).
• 1 Light Year is the distance traveled by light in one year.
• 1 light year (ly) is equivalent to:
– 0.31 pc
– 63,270 AU
• The light year is used primarily by writers of popular science
books and science fiction writers—rarely used in astrophysical
research .
• This is because the parsec is directly derived from the
quantity that is being measured (the stellar parallax angle),
whereas the light-year must be derived from having previously
measured the distance in parsecs. The parsec is a more
"natural" unit to use than the light year, particularly for nearby
objects.
Nearest neighbor
• Nearest star: Proxima Centauri
– 1.31 pc = 4 ly
– π = 0.76" = the size of dime at d = 6 km.
Nearest stars
Parallax
• Parallaxes are hard to
measure
– Not seen until 1838 by F.W.
Bessel, who determined the
parallax of 61 Cygni to be 0.29
arcsec
– (Final proof of the heliocentric
solar system)
• Best π from ground: π ~ 0.002"
– Most distant stars that can be
measured from the ground are
at d ~ 100 pc (with 20% errors)
– This is not a very large radius
around the Sun!
– Not many stars
– Not many stellar types
represented
Astrometric accuracy has
improved over time. Image: ESA
Space astrometry
Advantages:
• No atmospheric
distortion.
• Improved image
quality.
• Low gravity: reduced
mechanical flexure.
ESA’s GAIA mission
From: sci.esa.int
Space astrometry
• Until 13 September 2016, the best space π came from
the High Precision Parallax Collecting Satellite
(HIPPARCOS)
– π ~ 0.001" for 120,000 stars
– Reached a distance of ~200 pc for most stars with 20% errors
(limited by brightness of the stars)
– Not very far!
HIPPARCOS:
ESA, 1989-1993
Space astrometry
• ESA’s new GAIA mission is way better:
• π ~ 10-5 arcsec for 1 billion stars
– 100x better parallaxes
– 10,000x more stars
– Stars that are ~100 times fainter than Hipparcos
The position of a
billion stars will
precisely (and
hopefully accurately!)
be measured by
GAIA; this image
shows the first
preliminary data
release.
From sci.esa.int/gaia
GAIA has three instruments:
•
The Astrometric instrument (ASTRO) is devoted to star angular
position measurements, providing the five astrometric parameters:
–
–
–
–
•
•
Star position (2 angles)
Proper motion (2 time derivatives of position)
Parallax (distance)
ASTRO is functionally equivalent to the main instrument used on the Hipparcos
mission.
The Photometric instrument provides very low resolution (30 to 270
Angstroms/pixel) star spectra (sufficient to judge the spectral energy
distribution, "SED") to derive estimates of stellar parameters (like
temperature, metallicity) in the band 320-1000 nm and the ASTRO
chromaticity calibration.
The Radial Velocity Spectrometer (RVS) provides radial velocity and
medium resolution (R ~ 11,500) spectral data in the narrow band 847874 nm, for stars to about 16th magnitude (~150 million stars) and
astrophysical information (reddening, atmospheric parameters,
rotational velocities) for stars to 12th mag (~5 million stars), and
elemental abundances to about 11th mag (~2 million stars).
GAIA’s mission objectives:
• “measure the positions of ~1 billion stars both in our
Galaxy and other members of the Local Group, with an
accuracy of 24 microarcseconds for stars to V = 15 and
to 0.5 milliarcsec for stars to V = 20;
• perform spectral and photometric measurements of
these objects;
• derive space velocities of the Galaxy's constituent stars
using the stellar distances and motions;
• create a three-dimensional structural map of the Galaxy.”
Why are stellar velocities important?
• Most useful when measured for many stars.
• Use the statistics of the motions to learn many things,
including:
– Whether a group of stars is gravitationally bound.
– Masses of groups of stars
• Are they dark matter-dominated?
• Important tool for studying the structure of the Milky Way
galaxy.
Space velocity
where:
• Vs = space velocity (total velocity of a star)
• Vt = transverse velocity (velocity perpendicular to line of
sight, obtained by knowing proper motion, μ, and
distance, d)
• Vr = radial velocity (velocity parallel to line of sight =
Doppler velocity)
Radial velocity
• Line-of-sight (radial) velocity for stars can be obtained by
the Doppler shift:
𝜆 − 𝜆0
𝑉𝑟 = 𝑐
𝜆0
• where λ is the observed wavelength of a particular
spectral line and λ0 is the rest frame wavelength of the
line.
• Actually it’s more complicated because we measure
geocentric RVs but want to report heliocentric RVs
• Need to account for other motions:
– Earth’s orbital velocity (maximum 30 km/s correction)
– Earth’s rotational velocity (maximum 0.5 km/s correction)
Proper motion
• Transverse velocities, Vt, cannot be measured directly.
• Only the angular change, the proper motion, can be observed.
• To convert from the proper motion to the transverse velocity, one
needs to know the distance, d, to the star.
Proper motion
• If you work out the math:
• The proper motion, μ, has units of angle change per unit time.
• Common units for proper motions (which are typically very
small) are milliarcseconds/year (mas/yr)
• By the above equation, we see that a proper motion can be
large if:
– the star has small distance, d
– the star has a large transverse velocity with respect to the Sun
• Typical star velocities with respect to the Sun are 10s of km/s.
Proper motion
• Typical star velocities
with respect to the Sun
are 10s of km/s.
• But typical stars are far,
so proper motions
are small!
• For naked eye stars,
typically < 0.1" per year
• But over time this
amount of motion adds
up:
Proper motion
• The largest known
proper motion is that
of nearby Barnard's
star:
– μ = 10.25”/yr
• Barnard's Star has a
large motion because
it is the 4th closest
star to us
– d~1.8 pc.
Proper motion
• Proper motion is a motion in both right ascension and
declination (see homework #1).
– Provide both the size and the direction of the proper motion
– Proper motions are given as the pair of values (µα, µδ) or (μ, θ).
• The direction of motion is called the position angle, θ, of the
motion, and it is the angle between the direction of the NCP
and the direction of motion of the star.
– Define θ = 0° as motion due North and θ = 90° as motion due East.
(The cosδ term is needed to account for the
convergence of meridians toward the NCP
and SCP. (The cosδ is small when δ is large.)
Proper motion
• Derive PMs by measuring accurate locations of stars
(astrometry) over a long baseline
– Measure locations of stars at two epochs
• Increase accuracy of PMs by increasing time baseline Δt
or improving positional accuracy ΔΘ
Proper motion
• Knowing whether a target has a sizable proper motion is
important because outdated coordinates will point
telescope to the wrong place.
• In addition to giving the equinox of the coordinates,
which tells you what precessional year your coordinate
system corresponds to, for high proper motion stars you
have also to give the epoch of the coordinates of the
star, which tells in what year the star was at any specific
coordinates.
– For example, what would it mean to give the position of a star at
epoch 1975 in equinox 2000 coordinates?
• If you know the proper motion of the star for one year,
you can correct the coordinates to the position the star
has in any other year.