Modern Astronomy: Lives of the Stars

University of SydneyCentre for Continuing Education

Spring 2013

Lecture 10

The distances to the stars

Outline

The distances to the stars triangulation and parallax

Hipparcos Historys greatest star map

Gaia the Billion Star Surveyor

Course end the outstanding questions in stellar astrophysics

Parallax

Knowing the distances to the stars is vital to any kind of understanding of how they work, how much light they emit, how big they are etc.

The problem is that measuring distances is hard.

To measure the distance to stars, we use exactly the same methods that surveyors use determine the distance to a remote object: triangulation.

Suppose we want to measure the distance across a river.

Suppose we want to measure the distance across a river. We lay out a baseline and measure its length.

b

Suppose we want to measure the distance across a river. We lay out a baseline and measure its length. We measure the angle between one end of the baseline and a fixed marker (a house)

b

and then the angle from the other end of the baseline.

Simple trigonometry gives us the lengths of the sides of the triangle. The angle at the apex p is the difference in the houses apparent position when seen from the ends of the baseline: this is the parallax (actually, half this angle).

parallax angle p

The size of the apparent shift is proportional to the length of the baseline: the longer the baseline, the larger the shift. So the longer the baseline, the further the distance to which you can measure.

Hipparchus of Rhodes (190120 BC) used the distance between Alexandria and Syene to determine the distance to the moon.

In order to measure distances to stars, the only baseline long enough is the size of the Earths orbit.

If we observe a star from opposite sides of the Earths orbit (say, in January and June), we should be able to detect a very small shift in a nearby stars position compared to distant stars.

p

In order to measure distances to stars, the only baseline long enough is the size of the Earths orbit.

If we observe a star from opposite sides of the Earths orbit (say, in January and June), we should be able to detect a very small shift in a nearby stars position compared to distant stars.

p

In fact, the wobble of a star due to parallax is in an ellipse, whose size depends on the distance to the star, and whose shape depends on the angle from the ecliptic plane.

A star directly above the ecliptic will move in a circle.

In fact, the wobble of a star due to parallax is in an ellipse, whose size depends on the distance to the star, and whose shape depends on the angle from the ecliptic plane.

A star in the ecliptic plane will move in a straight line.

A star in between will move in an ellipse: the closer the stars position to the ecliptic, the flatter the ellipse.

This annual shift turns out to be tiny: even the nearest star, Alpha Centauri, has a parallax of only 0.74 arcseconds.

Here are two images of a nearby star, showing the motion due to parallax.

[A parsec is the distance at which a star has a parallax of 1 arc second; 1 pc = 3.26 light years].

This tiny shift makes it extremely difficult to detect.

The typical size of a stars image (because of seeing, the blurring due to the Earths atmosphere) is about 1 arcsecond, so the shift due to parallax is always smaller than this.

This explains why it so long for stellar parallax to be discovered: it was not until 1838, when Friedrich Wilhelm Bessel announced that 61 Cygni had a parallax of 0.314 arcseconds, indicating a distance of 11 light years.

The measurement of parallax is a subset of the science of astrometry: the measurement of the stars.

All position measurements are relative: a position is defined only with respect to something. Astrometric measurements fall into two major classes:

wide-field measurements, where the positions of objects all over the sky can be tied together to a common reference frame.

small-field measurements, where the position of an object is measured relative to nearby stars

Ideally, we would like to measure positions relative to objects which are truly stationary. Such objects do not exist; however, really distant objects such as quasars are so distant that any transverse velocity they have results in an angular motion so small as to unobservable.

The International Celestial Reference Frame is a collection of 212 quasars whose positions define the astronomical coordinate system.

The defining and candidate sources which make up the International Celestial Reference Frame.

For example, instruments such as transit circles, which are telescopes which rotate on only one axis, are used to time very precisely when a star crosses the meridian. This effectively converts the measurement of position, which is difficult, into a measurement of time, which is much more accurate.

Airys transit circle at the Royal Greenwich Observatory.

Thats the theory: now we have to actually do it. The measurement of large angles is extremely difficult, and several solutions have been found.

Transit measurements are measurements relative to the Earths own rotation. However, this is not fixed in space, as the gravitational pull of the Moon causes the Earths axis to wobble in space with a period of 25,800 years.

There are a large number of effects which complicate the measurement of parallaxes from the ground:

Instrumental effects: stability, precision, ...

Atmospheric effects: seeing atmospheric refraction: the atmosphere bends the

light from stars, and bends blue light more than red light (size: a few arc seconds, minimised at zenith)

Effects due to the Earths motion: precession nutation: a small 19-year wobble in the Earths axis

on top of the 26,000-year precession (up to 9 arcseconds)

stellar aberration: the velocity of the Earth, and the finite velocity of the speed of light, cause the position of a star to be displaced in the direction of the Earths motion by an amount vorb/c = 20 arcseconds

All of these factors combine to restrict the measurement of parallax from the ground to an accuracy of, at best, about 0.01 arcseconds. This restricts the number of stars whose distances can be determined severely:

stars with distances of up to 12pc with 20% errors (250300 stars)

stars with distances of up to 30pc with 50% errors (4000 stars)

Furthermore, errors in the global coordinate system are very hard to eliminate. A telescope at a single site cannot cover the whole sky, so observations from different observatories and instruments have to be combined. Despite best efforts, global errors of several tenths of an arcsecond remained, particularly in the south.

This size of uncertainty is unacceptable, particularly for comparisons between different wavelengths (optical, radio, X-ray etc.) where positional overlays are vital for understanding sources.

Error circle for the X-ray pulsar SAX J2103.5+4545 (From Reig et al. 2004)

and was designed and operated by the European Space Agency.

Enter Hipparcos, the first and (so far) only satellite dedicated to astrometry.

Hipparcos stands for

HIgh Precision PARallax COllecting Satellite

By observing from space, Hipparcos eliminated many of the problems associated with ground-based measurements.

Its design was revolutionary: it aimed to determine positions, parallaxes and proper motions for over 100,000 stars distributed all around the sky in a single, global solution.

The Hipparcos design centred around a split mirror to simultaneously observe two fields 58o apart. This results in a very rigid positional frame, eliminating the errors associated with building up the whole sky from small patches next to each other.

The satellite spun about its axis, rotating in 2 hours and 8 minutes. The rotation axis moved slowly on a circle of 43o radius centred on the Sun, making a revolution in 57 days. This gave each star a 50% chance of being observed on successive scans. This pattern is repeated every two months.

This scanning pattern required active attitude control of the satellite using six thrusters.

Coverage of the sky by Hipparcos over 6 months. Almost the entire sky was covered in at least two directions every half-year: two small areas near the ecliptic were not covered.

The Hipparcos flight model undergoing thermal vacuum testing at a spin rate of 5 rpm

As the satellite spins, stars drift across a finely-spaced grid of slits. There are typically 45 programme stars in the field at once, so the detector switches between them. A star takes ~20s to cross the field.

It was vital to know in advance when the stars were going to come across the field: an input catalogue was required, giving the positions of all the stars to be observed with an accuracy

Effectively, the angular distance between stars was measured along great circles in the sky, with about 2000 stars per orbit, and 2768 orbits.

When many such orbits were combined together, the locations and motions of all the stars could be determined with high precision.

The positions are fit with a five parameter curve: x, y position x, y velocity parallax

Because the location of each star was very well determined in the direction of rotation, but not so well determined in the other direction, each observation of a star constrained its position to be on one of the straight lines in the following picture. A star was observed between 30 and 150 times, depending on where in the sky it was.

More examples of the apparent paths of stars across the sky, and the astrometric fits to them.

There are many more observations than unknown variables, so the astrometric variables can be measured very precisely. In the first solution, for instance, using only the 40,000 best observed stars, there were

106 simultaneous equations with 200,000 astrometric parameters (5 per star) 2000 parameters describing orientation of satellite

(reference great circles)

Hipparcos was launched on an Ariane 4 rocket on 8 August 1989, destined for a geostationary orbit.

However, the apogee boost motor failed, leaving Hipparcos in a highly elliptical orbit (perigee 500 km, apogee 36,500 km)

There were fears that this had ruined the entire mission. However, with a lot of hard work, Hipparcos operated successfully for 3.5 years and achieved results even better than the original aims. Radiation damage to the computer and gyros resulted in the termination of observations in March 1993; the mission was terminated in August 1993.

In all, it completed 2768 orbits, corresponding to 1230 days.

The final results, after reductions by two independent teams, were released in 1997.

These consisted of:

astrometry for 118,000 stars, with 90,000 having distances determined to better than 20%

photometric data for 11500 variable stars, 8200 of them new, including 273 Cepheid variables

24,000 solved or suspected binary/multiple star systems, including doubling the number of eclipsing binaries.

Did you know:

the angles that have been measured by the Hipparcos satellite are about one thousandth of a second of arc (0.001 arcsec)

This accuracy corresponds to the angular size of a golf ball viewed from the other side of the Atlantic Ocean; to the size of a person standing on the Moon as seen from the Earth; and to the growth of a human hair in 10 seconds viewed from a distance of about 10 metres.

In 2007, a new reduction of the Hipparcos data (from scratch) was released. New work has identified and modelled some peculiarities of the spacecraft dynamics, which had limited the accuracy of the parallaxes.

Scan-phase jumps were caused by minute (~ few m) movements of one of the solar panels, especially when coming in or out of eclipse.

Dust particles hitting the spacecraft could change the spin-rate by tiny amounts (equivalent to one rotation of the satellite in a few years) but this was enough to affect the astrometry.

When these effects were taken into account, parallaxes improved by up to a factor of 5, and distances of open clusters are 23 times more accurate.

The formal errors on the parallaxes as a function of stellar magnitude, in the old solution (left) and the new solution (right).

Gaia

ESA has built a successor to Hipparcos. Named Gaia, it aims to measure parallaxes with an accuracy of 4 arcseconds for a billion stars down to 20th magnitude. This will give distances accurate to 10% for stars at distances up to 25 kpc.

The prime contractor to build the spacecraft was selected in May 2006, and construction was completed this year. Gaia is scheduled for launch in late 2013.

Gaia will orbit around the Sun-Earth L2 point, and instead of needing an input catalogue, will measure the positions of stars as they drift across more than 100 CCDs.

Animation of a sky patch being swept by GAIA

47

Data Reduction Principles

Sky scans(highest accuracy

along scan)

Scan width: 0.7

1. Object matching in successive scans2. Attitude and calibrations are updated

3. Objects positions etc. are solved4. Higher terms are solved5. More scans are added

6. System is iteratedFigure courtesy Michael Perryman

Animation illustrating how Gaia will scan the sky during its all-sky survey.

Light bending in microarcsec, after subtraction of the much larger effect by the Sun

50

Schedule

ProposalConcept & Technology Study

Mission Selection

Re-Assessment StudyPhase B1

Scientific operation

Launch spring 2012

Final

Studies

Mission Data Processing

Implementation

Data Processing

Definition

Operation

Mission Products Intermediate

Selection of Prime Contractor (EADS Astrium)

Phase B2Phase C/D

Software Development

1995

2000

2005

2010

2015

2020

1994

1993

1997

1998

1999

2019

2018

2017

2016

2014

2013

2012

2011

2009

2008

2007

2006

2004

2003

2002

2001

1996

2021

NowFigure courtesy Michael Perryman and Franois Mignard

Imagine you are asked to build:

a 4-m machine with a foldable 10-m sunshield that needs to be launched into space,

that spins at a rate of 60 degrees per hour with deviations smaller than 0.01%,

that has about 100 cameras

that can measure stars differing in brightness by 1 million times

measure simultaneously their colour,

and if they are not too faint: take their spectrum.

Oh, and please do that for 1 billion objects!

Berry Holl, member of the Gaia Data Processing and Analysis Consortium, from the Gaia blog

A time lapse sequence, at 7 times actual speed, showing the deployment of Gaia's sunshield during testing in the S1B integration building at Europe's Spaceport in Kourou, French Guiana, on 10 October 2013.

Gaia arrived in French Guiana in August 2013 for launch on a Soyuz-STB launch vehicle.

On 22 October, it was announced that, due to technical issues with two of the spacecrafts transponders, the launch would be postponed.

Gaia is now scheduled for launch on20 December.

That completes our in-depth tour of the lives of stars.

I hope Ive shown you, not only what we know, but also how much we dont, and how we aim to address that.

What follows is my personal list of the outstanding questions in stellar astrophysics, in no particular order.

1. Why are stars born with the masses they have?

Why do some regions form only low-mass stars, and some form all types? What determines how many of each type of star you get? Why is this so constant over our galaxy and others?

Pillars of star formation in the Carina Nebula

Planetary nebula Hubble 5, with two lobes inflated by fast winds.

2. How much mass do stars lose?

How much mass do different types of stars lose during their lifetime, and what does that do to their evolution? How much does stellar rotation matter? What does that do the structure and evolution of the star, and what remnant it leaves behind?

Coronal loops

3. Magnetic fields!

There is so much we dont understand about magnetic fields. How do jets form? How is a stars magnetic field created? How does it heat the corona? How we can we predict space weather?

4. How do supernovae explode?

How exactly does the shock wave get out of the collapsing star? What are the progenitors of Type Ia supernovae?

(And can we please have another one?!)

Supernova 1998bu in M96

And while were dreaming, heres my personal wish-list for new astronomical discoveries:

A pulsar-black hole binary. Edge-on, please.

Detection of gravity waves

A non-hierarchical multiple star system

A SN 1a progenitor system

A nearby supernova

IceCube Telescope Finds High-Energy Neutrinos, Opens Up New Era in Astronomy

http://www.wired.com/wiredscience/2013/11/icecube-neutrinos-detected/

Late breaking news

Next year, Ill be giving more courses

Modern Astronomy: Voyage to the Planets

where we look at the wonderful results coming from Cassini, the Mars missions, the Dawn mission to the asteroids...

and maybe a new course.

Anyone interested in being informed of future Mt Wilson star-viewing trips should contact John at

j.obyrne@physics.usyd.edu.au

The history of the quest to find the distances to the stars, up to Bessells measurement of the first parallax, is described in Parallax: The Race to Measure the Cosmos by Alan. W. Hirshfeld (WH Freeman, 2001). A wonderful read.

Michael Perryman, the Project Scientist for Hipparcos, has written a popular account of the mission called The Making of Historys Greatest Star Map (Springer, 2010).

The official Hipparcos website is at http://www.rssd.esa.int/Hipparcos/. The Gaia website is at http://www.esa.int/science/gaia.

Another nice description of what GAIA will be able to achieve is in Lecture 10 of Chris Flynns Galactic Dynamics course, http://www.astro.utu.fi/~cflynn/galdyn/lecture10.html

The press release describing the re-reduction of the Hipparcos data is at http://smart.esa.int/science-e/www/object/index.cfm?fobjectid=41375

The Gaia blog is at http://blogs.esa.int/gaia/. It already has some nice articles, like why the launch time is so constrained.

Further reading

Sources for images used: Triangulation: from The Great Trigonometrical Survey http://www.bluesci.org/?p=2028 Parallax: from from http://courses.learn60.ca/mod/book/tool/print/index.php?id=18325 Hipparchus measurement of the distance to the moon: http://astrosun2.astro.cornell.edu/academics/courses//astro201/hipparchus.htm Motion due to parallax: from Distances to nearby stars and their motions: An Introductory Astronomy Lab,

http://www.astro.washington.edu/labs/parallax/parallax_distance.html Distribution of sources in the ICRF: from http://hpiers.obspm.fr/icrs-pc/icrf/Icrf.html Airys transit circle: from Portcities London, http://www.portcities.org.uk/london/server/show/conMediaFile.1245/Airys-transit-circle.html Precession: from NASA JPL http://www2.jpl.nasa.gov/basics/bsf2-1.html and Wikipedia: Precession of the equinoxes http://en.wikipedia.org/wiki/Precession_of_the_equinoxes Refraction: from from "Explorations: An Introduction to Astronomy" by Thomas Arny, Fig. 5.6 http://www.mhhe.com/physsci/astronomy/arny/instructor/graphics/ch05/0506.html Stellar aberration: from Courtney Seligman, Bradley's Discovery of Stellar Aberration, http://cseligman.com/text/history/bradley.htm Hipparcos: from Dutch Space http://www.dutchspace.nl/pages/about/content.asp?id=219&PID=147 Hipparcos layout: from Perryman et al., In-orbit performance of the HIPPARCOS astrometry satellite, A&A 258, 1 (1992), available at http://adsabs.harvard.edu/abs/1992A%26A...258....1P Hipparcos testing: from Hipparcos photographs http://www.rssd.esa.int/Hipparcos/vis_pics.html Scanning pattern: from van Leeuwen, The HIPPARCOS Mission, Space Science Reviews 81, 201 (1997), Fig. 129, available at http://adsabs.harvard.edu/abs/1997SSRv...81..201V Hipparcos observed stars: from Hipparcos statistics, http://www.rssd.esa.int/Hipparcos/vis_stat.html Fitted curve for parallax: from Perryman et al. Parallaxes and the Hertzsprung-Russell diagram for the preliminary HIPPARCOS solution H30, A&A 304, 69 (1995), available at http://adsabs.harvard.edu/abs/1995A%26A...304...69P

Sources for images used: Hipparcos launch: from Hipparcos photographs http://www.rssd.esa.int/Hipparcos/vis_pics.html Hipparcos orbit: from Perryman, HIPPARCOS - Revised mission overview, Advances in Space Research 11, 15 (1991), available at http://adsabs.harvard.edu/abs/1991AdSpR..11Q..15P Gaia mission: from Gaia Image Gallery http://www.rssd.esa.int/index.php?project=GAIA&page=IG_Accuracy_1 Gaia animation and orbit: from University of Leicester http://www.star.le.ac.uk/xra/facilities/gaia.shtml GAIA performance from GAIA presentations http://www.rssd.esa.int/index.php?project=GAIA&page=presentations Star formation in Carina: from http://www.nasa.gov/multimedia/imagegallery/image_feature_1647.html Planetary nebula Hubble 5: from Hubble release STScI-1997-38 http://hubblesite.org/newscenter/archive/releases/1997/38/ Supernova 1998bu in M96: from http://messier.seds.org/more/m096_sn_more.html Coronal loops: from http://zeus.nascom.nasa.gov/~dmueller/loop_intro.htm