Stellar distances and velocities. ASTR320 Wednesday January 24, 2018

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1 Stellar distances and velocities ASTR320 Wednesday January 24, 2018

2 Special public talk this week: Mike Brown, Pluto Killer Wednesday at 7:30pm in MPHY204

3 Why are stellar distances important? Distances are necessary for studying many things, including: Total energy emitted by an object (Luminosity) Testing models of stellar evolution Studying properties of distant galaxies Masses of objects from their orbital motions True motions through space of stars Cosmological parameters Locations of high redshift galaxies in order to map out the mass distribution of the Universe and learn more about Dark Energy The problem is that distances are very hard to measure...

4 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.

5 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

6 Parallax π R=1 a.u. d is very large Small angle approximation says tan π ~ π = R d Measured parallaxes are small: π < 1" for all stars

7 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 a.u. (astronomical units) 3.26 light years 3.086x10 13 km

8 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.

9 Distances are important! The cosmic distance ladder is anchored by parallax measurements

10 Nearest neighbor Nearest star: Proxima Centauri 1.31 pc = 4 ly π = 0.76" = the size of dime at d = 6 km.

11 Nearest stars

12 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

13 Space astrometry Advantages: No atmospheric distortion Improved image quality Low gravity: reduced mechanical flexure ESA s GAIA mission From: sci.esa.int

14 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,

15 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

16 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 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 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).

17 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.

18 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

19 Space velocity where: V s = space velocity (total velocity of a star) V t = transverse velocity (velocity perpendicular to line of sight, obtained by knowing proper motion, μ, and distance, d) V r = radial velocity (velocity parallel to line of sight = Doppler velocity)

20 Radial velocity Line-of-sight (radial) velocity for stars can be obtained by the Doppler shift: V r = c λ λ 0 λ 0 where λ is the observed wavelength of a particular spectral line and λ 0 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)

21 Proper motion Transverse velocities, V t, 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.

22 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.

23 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 Over time this amount of motion adds up:

24 Proper motion The largest known proper motion is that of nearby Barnard's star: μ = /yr Barnard's Star has a large motion because it is the 4th closest star to us d~1.8 pc.

25 Proper motion Proper motion is a motion in both right ascension and declination. Provide both the size and the direction of the proper motion Proper motions are given as the pair of values (µ α, µ δ ) 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.)

26 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

27 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.

28 A note on measurements of time Astronomers don t really care about leap years, rather we measure absolute time elapsed since some zeropoint Julian Date (JD) is defined as the amount of time elapsed since noon on January 1, 4714 BC (specified by the Julian calendar) JD of J is JD Today s Julian date (at noon) is JD Modified Julian Date (MJD) is more commonly used MJD JD Begins at midnight, more useful to astronomers Tonight s MJD is Universal Time (UT) is the time in Greenwich, England Location of Prime Meridian on Earth