BASIC PROPERTIES of STARS - 2BASIC PROPERTIES of STARS - 2BASIC PROPERTIES of STARS - 2BASIC PROPERTIES of STARS - 2

Distances to the starsDistances to the stars

Stellar motionsStellar motions

Sections 3.1 & 3.2, poorlySections 3.1 & 3.2, poorly covered in the text covered in the text

DISTANCES to the STARSDISTANCES to the STARSDISTANCES to the STARSDISTANCES to the STARS Wide variety techniques to measure Wide variety techniques to measure

distances.distances.

With increasing distance, each technique With increasing distance, each technique relies on measurements of nearer relies on measurements of nearer objects.objects.

An error at one step translates through all An error at one step translates through all subsequent steps.subsequent steps.

““Nearby” objects Nearby” objects “Most distant” is a “Most distant” is a sequence of decreasing accuracysequence of decreasing accuracy..

Astronomical Distance PyramidAstronomical Distance PyramidAstronomical Distance PyramidAstronomical Distance Pyramid

Distances inside Solar SystemDistances inside Solar SystemDistances inside Solar SystemDistances inside Solar System

Laser distance to Moon, radar distance to Venus.

Radar timing to Venus gives accurate distance to Sun.

Accuracy of a few cm (10-8 % for Moon).

Some Laser Ranging FactsSome Laser Ranging FactsSome Laser Ranging FactsSome Laser Ranging Facts

US Apollo manned missions to Moon left arrays of mirrors on Moon (late ‘60s - ‘70s)

Like highway signposts

Aiming to hit one of these like hitting dimeWith rifle from distance ~1 km

Echo signal weak - only 1 in 1018 photons sent is detected

Distances inside Solar System: Distance to the SunDistances inside Solar System: Distance to the Sun Distances inside Solar System: Distance to the SunDistances inside Solar System: Distance to the Sun

Time radar returnsTime radar returns

(T(Tdistantdistant + T + Tnearestnearest) x c / 4 = E-) x c / 4 = E-

S distanceS distance

1 Astronomical Unit (AU) 1 Astronomical Unit (AU) = 1.49597870 x 10= 1.49597870 x 108 8 km km accuracy of about 100accuracy of about 100 m

Orbit of Earth

Orbit of Venus

Closest approach of E Closest approach of E and Vand V

Most distant E and VMost distant E and V

Sun

FlashcardsFlashcardsFlashcardsFlashcardsVenus is about 105,000,000 km from the Sun.

(1) What is approximate time to get the return signal from Venus when it is at its closest to Earth? C = 3 x 105 km/s (A 150; B 200; C 300; D 400 seconds)

(2) What is the approximate time to get a return signal from Venus when Venus is at its most distant position? (A 850; B 1700; C 2550; D 3400 seconds)

If (1) is 300 seconds and (2) is 1700 seconds, what is 1 AU in km?

Stellar Aberration & AU Stellar Aberration & AU Stellar Aberration & AU Stellar Aberration & AU Because of Earth’s Because of Earth’s motion, light from stars motion, light from stars appearsappears to come from a to come from a direction different from direction different from that if Earth were that if Earth were stationary.stationary.

v<<c v<<c displacement displacement smallsmall

tantan = v/c, = v/c, is the angle is the angle between direction motion between direction motion and starand star

Measure maximum Measure maximum (20.5”) get v = 29.8 km/s(20.5”) get v = 29.8 km/s

Get AU = (29.8x3.2x10Get AU = (29.8x3.2x1077)/2)/2= 1.5 x 10= 1.5 x 1088 km km

First measured in 1725 by Bradley

PARALLAX §3.1PARALLAX §3.1PARALLAX §3.1PARALLAX §3.1

PARALLAXPARALLAXPARALLAXPARALLAXWith a Sun-centered Solar Systemand a moving Earth, objects outsidethe Solar System can potentiallyexhibit parallax. Whether we can measure it will depend on theirdistance.

Tycho Brahe looked for parallax ofthe stars in the 1570’s as proof ofthe Copernican Theory. Did notsee it - concluded that Earth did notmove. Measurement accuracy 1’whereas the parallax of nearest star< 1”.

STELLAR PARALLAXSTELLAR PARALLAXSTELLAR PARALLAXSTELLAR PARALLAX

STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1OnlyOnly direct way of getting distances to stars direct way of getting distances to stars

Smaller the parallax, farther is starSmaller the parallax, farther is star

Over year star, describes ellipse on sky (special Over year star, describes ellipse on sky (special cases: circle at pole, line if in ecliptic) - semi cases: circle at pole, line if in ecliptic) - semi major axis is parallax (major axis is parallax ())

Unit of distance is parsec (pc) defined so that at 1 Unit of distance is parsec (pc) defined so that at 1 pc star subtends angle 1” on E-S baselinepc star subtends angle 1” on E-S baseline

From small angle formula: From small angle formula: 1” = 1 AU / 1 pc 1” = 1 AU / 1 pc 1/206265 = 1AU / 1parsec 1/206265 = 1AU / 1parsec 1 pc = 206265 AU = 3 x 10 1 pc = 206265 AU = 3 x 1013 13 kmkm

D = 1/D = 1/, , in “, D in pc; in “, D in pc; nearest star: nearest star: = 0.762”, 1.31 pc = 0.762”, 1.31 pc (limit 100 pc)(limit 100 pc)

STELLAR PARALLAXSTELLAR PARALLAXSTELLAR PARALLAXSTELLAR PARALLAX

Distance measurements possible with various baselines

Parallax and positionParallax and positionParallax and positionParallax and position

Position of star Position of star determines the determines the parallax effectparallax effect

Bessel Measures Stellar Bessel Measures Stellar Parallax 1838!Parallax 1838!

Bessel Measures Stellar Bessel Measures Stellar Parallax 1838!Parallax 1838!

61 Cygni61 Cygni

Parallax 0.314”Parallax 0.314”

Manhattan taxi Manhattan taxi

as viewed fromas viewed from

Mexico CityMexico City

STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1STELLAR PARALLAX §3.1OnlyOnly direct way of getting distances to stars direct way of getting distances to stars

Smaller the parallax, farther is starSmaller the parallax, farther is star

Over year star, describes ellipse on sky (special Over year star, describes ellipse on sky (special cases: circle at pole, line if in ecliptic) - semi cases: circle at pole, line if in ecliptic) - semi major axis is parallax (major axis is parallax ())

Unit of distance is parsec (pc) defined so that at 1 Unit of distance is parsec (pc) defined so that at 1 pc star subtends angle 1” on E-S baselinepc star subtends angle 1” on E-S baseline

From small angle formula: From small angle formula: 1” = 1 AU / 1 pc 1” = 1 AU / 1 pc 1/206265 = 1AU / 1parsec 1/206265 = 1AU / 1parsec 1 pc = 206265 AU = 3 x 10 1 pc = 206265 AU = 3 x 1013 13 kmkm

D = 1/D = 1/, , in “, D in pc; in “, D in pc; nearest star: nearest star: = 0.762”, 1.31 pc = 0.762”, 1.31 pc limit 2-300 pclimit 2-300 pc

Aside: Stellar Motions p.16-17Aside: Stellar Motions p.16-17Aside: Stellar Motions p.16-17Aside: Stellar Motions p.16-17 Before continuing with distances we must have Before continuing with distances we must have

a small diversion and discuss stellar motions.a small diversion and discuss stellar motions.

Beyond apparent motion due to parallax, many Beyond apparent motion due to parallax, many stars exhibit motion in a constant direction - stars exhibit motion in a constant direction - proper motion.proper motion.

Velocity of a star can be divided into 2 Velocity of a star can be divided into 2 components.components.

VVtt is tangential velocity is tangential velocity

VVrr is the radial velocity is the radial velocity

RADIAL VELOCITIESRADIAL VELOCITIESRADIAL VELOCITIESRADIAL VELOCITIES

Data obtained with spectrographData obtained with spectrograph

//oo = v/c = v/c

Velocities of stars in our Galaxy range up Velocities of stars in our Galaxy range up to +/- 300 km/sec. A few up to 600 km/s to +/- 300 km/sec. A few up to 600 km/s (escape velocity from Galaxy). Typical (escape velocity from Galaxy). Typical for stars in disk is 30 km/sec.for stars in disk is 30 km/sec.

PROPER MOTIONS p.17PROPER MOTIONS p.17PROPER MOTIONS p.17PROPER MOTIONS p.17

Measured over a period of years from direct Measured over a period of years from direct images. Unit is “/year. images. Unit is “/year. Largest measured Barnard’s star 10.25”/year. Largest measured Barnard’s star 10.25”/year. Few 100 stars with PM > 1”/year. Note that PM Few 100 stars with PM > 1”/year. Note that PM will depend on distance.will depend on distance.

Effect of proper motionsEffect of proper motionsEffect of proper motionsEffect of proper motions

Parallax and positionParallax and positionParallax and positionParallax and positionThis shows howparallax and proper motionare distingushed.Parallax repeatsItself yearly whileproper motiondoes not. Solvefor bothsimultaneously.

Back to distancesBack to distances Star Clusters Star Clusters Back to distancesBack to distances Star Clusters Star Clusters

Clusters are groups stars formed at same time in sameregion space - gravitationallybound. More later.

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination §16.2§16.2

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination §16.2§16.2

Taurus and the Hyades: Pleiades at top, Saturn Taurus and the Hyades: Pleiades at top, Saturn to left, Aldebaran is not a memberto left, Aldebaran is not a member.

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination

Raphael Santi’s “The School of Athens” 1511

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination

True space velocity = vTrue space velocity = vRadial velocity = vRadial velocity = vradrad

Tangential velocity = vTangential velocity = vtt

vvtt = 4.74 = 4.74 rr

vvradrad = v cos = v cos vvtt = v sin = v sin vvtt/v/vradrad = tan = tan

Thus:Thus:r = vr = vradrad tan tan / 4.74 / 4.74Do this for every star in cluster

average r values to get distance

Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination Moving Cluster Method Distance DeterminationMoving Cluster Method Distance Determination

By measuring PMs, radial velocities, and By measuring PMs, radial velocities, and the best position of the convergent point the best position of the convergent point of stars in the Hyades, we derive the of stars in the Hyades, we derive the distance to the cluster.distance to the cluster.

ddhyadeshyades = 47 +/- 4 pc (8% precision cf Venus) = 47 +/- 4 pc (8% precision cf Venus)

Limit of technique ~100 pcLimit of technique ~100 pc

Hyades cluster is one of fundamental Hyades cluster is one of fundamental calibrators of stellar distances - do with calibrators of stellar distances - do with parallax and moving cluster.parallax and moving cluster.

A ProblemA ProblemA ProblemA Problem

The proper motion of Aldebaran is The proper motion of Aldebaran is = = 0.20”/year0.20”/year

The parallax of Aldebaran is The parallax of Aldebaran is = 0.048” = 0.048”

A spectral line of iron at A spectral line of iron at = 440.5 nm is = 440.5 nm is displaced 0.079 nm towards the red.displaced 0.079 nm towards the red.

What are radial, tangential and total velocities?What are radial, tangential and total velocities?