option e - astrophysics e3 stellar distances parallax method

OPTION E - ASTROPHYSICS

E3 Stellar distancesParallax method


E3 Stellar distancesParallax method

Astronomical distances – recap Astronomical distances – recap

The SI unit for length, the metre, is a very small unit to measure astronomical distances. There units usually used is astronomy:

The Astronomical Unit (AU) – this is the average distance between the Earth and the Sun. This unit is more used within the Solar System.

The SI unit for length, the metre, is a very small unit to measure astronomical distances. There units usually used is astronomy:

The Astronomical Unit (AU) – this is the average distance between the Earth and the Sun. This unit is more used within the Solar System.

1 AU = 150 000 000 kmor

1 AU = 1.5x1011m

Astronomical distances – recapAstronomical distances – recapThe light year (ly) – this is the distance travelled by the light in one year. The light year (ly) – this is the distance travelled by the light in one year.

1 ly = 9.46x1015 m

c = 3x108 m/st = 1 year = 365.25 x 24 x 60 x 60= 3.16 x 107 s

Speed =Distance / Time

Distance = Speed x Time = 3x108 x 3.16 x 107 = 9.46 x 1015 m

The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.

The parsec (pc) – this is the distance at which 1 AU subtends an angle of 1 arcsencond.

1 pc = 3.086x1016 m or

1 pc = 3.26 ly

“Parsec” is short forparallax arcsecond

E.3.1 Define the parsec.

http://upload.wikimedia.org/wikipedia/commons/f/fd/Parsec-fr.svg

1 parsec = 3.086 X 1016 metres1 parsec = 3.086 X 1016 metres

Nearest Star 1.3 pc

(206,000 times further than the Earth is from the

Sun)

Angle star/ball appears to shift

“Baseline”

Distance to star/ball

Where star/ball appears relative to

background

Bjork’s Eyes Space

E.3.2 Describe the stellar parallax method of determining the distance to a star.

Parallax, more accurately motion parallax, is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer.

Simply put, it is the apparent shift of an object against the background that is caused by a change in the observer's position over a period of 6 months.

Parallax, more accurately motion parallax, is the change of angular position of two observations of a single object relative to each other as seen by an observer, caused by the motion of the observer.

Simply put, it is the apparent shift of an object against the background that is caused by a change in the observer's position over a period of 6 months.


Baseline – R(Earth’s orbit)

Dist

ance

to

Star

- d

Parallax - p(Angle)

We know how big the Earth’s orbit is, we measure the shift (parallax), and then we get the distance…


For very small angles tan p ≈ p

(Distance) d(Baseline) R

(Parallax) tan p

d

R p

In conventional units it means that

m 10 x 3.986 m

3600

1

360

2 10 x 1.5

pc 1 1611


arcsecond) ( p

1 (parsec) d

m 10 x 3.986 m

3600

1

360

2 10 x 1.5

pc 1 1611

d

R p

p

R d


360 degrees (360o) in a circle

60 arcminutes (60’) in a degree

60 arcseconds (60”) in an arcminute

Angular sizesAngular sizes

The farther away an object gets, the smaller its shift.

Eventually, the shift is too small to see.

E.3.3 Explain why the method of stellar parallax is limited to measuring stellar distances less than several hundred parsecs.

Measurements from Earth only allow distances up to 300ly, or roughly 100pc, to be determined with the parallax method.With satellites, distances of around 500 pc can be determined.

How Do We Measure the Distance to Stars? - Instant Egghead #46https://www.youtube.com/watch?v=vyiauRjJBNQ

https://www.youtube.com/watch?v=vyiauRjJBNQ



E.3.4 Solve problems involving stellar parallax.

Go to Option E – Astrophysics SL worksheet


E3 Stellar distancesAbsolute and apparent magnitudes


E3 Stellar distancesAbsolute and apparent magnitudes

Another thing we can figure out about stars is their colours…

Another thing we can figure out about stars is their colours…

We’ve figured out brightness, but stars don’t put out an equal amount of all light…

…some put out more blue light, while others put out more red light!

E.3.5 Describe the apparent magnitude scale.

Usually, what we know is how bright the star looks to us here on Earth…Usually, what we know is how bright the star looks to us here on Earth…

We call this its Apparent Magnitude

“What you see is what you get…”


Magnitudes are a way of assigning a number to a star so we know how bright it is

Similar to how the Richter scale assigns a number to the strength of an earthquake

Magnitudes are a way of assigning a number to a star so we know how bright it is

Similar to how the Richter scale assigns a number to the strength of an earthquake

This is the “8.9” earthquake off of

Sumatra

Betelgeuse and Rigel, stars in Orion with apparent

magnitudes 0.3 and 0.9


The historical magnitude scale…The historical magnitude scale…

Greeks ordered the stars in the sky from brightest to faintest…

…so brighter stars have smaller magnitudes.

Greeks ordered the stars in the sky from brightest to faintest…

…so brighter stars have smaller magnitudes.

Magnitude Description

1st The 20 brightest stars

2nd stars less bright than the 20 brightest

3rd and so on...4th getting dimmer each time

5th and more in each group, until

6th the dimmest stars (depending on your eyesight)

Later, astronomers quantified this system.

Later, astronomers quantified this system.

Because stars have such a wide range in brightness, magnitudes are on a “log scale”

Every one magnitude corresponds to a factor of 2.5 change in brightness

Every 5 magnitudes is a factor of 100 change in brightness

(because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)

Because stars have such a wide range in brightness, magnitudes are on a “log scale”

Every one magnitude corresponds to a factor of 2.5 change in brightness

Every 5 magnitudes is a factor of 100 change in brightness

(because (2.5)5 = 2.5 x 2.5 x 2.5 x 2.5 x 2.5 = 100)

Brighter = Smaller magnitudesFainter = Bigger magnitudesBrighter = Smaller magnitudesFainter = Bigger magnitudes

Magnitudes can even be negative for really bright objects! Magnitudes can even be negative for really bright objects!

Object Apparent Magnitude

The Sun -26.8

Full Moon -12.6

Venus (at brightest) -4.4

Sirius (brightest star) -1.5

Faintest naked eye stars 6 to 7

Faintest star visible from Earth telescopes

~25


• Given a star of apparent brightness b, we assign that start and apparent magnitude m defined by:

Where is taken as the reference value for apparent brightness

• Or:

𝑏𝑏0

=2.512−𝑚• The first equation can also be re-written as:

𝑚=−52𝑙𝑜𝑔 ( 𝑏𝑏0

)

However: knowing how bright a star looks doesn’t really tell us anything about the star itself!

However: knowing how bright a star looks doesn’t really tell us anything about the star itself!

We’d really like to know things that are intrinsic properties of the star like:

Luminosity (energy output)and

Temperature

We’d really like to know things that are intrinsic properties of the star like:

Luminosity (energy output)and

Temperature

E.3.6 Define absolute magnitude.

…we need to know its distance!…we need to know its distance!

In order to get from how bright something looks…

to how much energy it’s putting out…


The whole point of knowing the distance using the parallax method is to figure out luminosity…The whole point of knowing the distance using the parallax method is to figure out luminosity…

It is often helpful to put luminosity on the magnitude scale…

Absolute Magnitude (M):

The magnitude an object would have if we put it 10 parsecs away from Earth

Once we have both brightness and

distance, we can do that!


The Sun is -26.5 in apparent magnitude, but would be 4.4 if we moved it far away

Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitude

The Sun is -26.5 in apparent magnitude, but would be 4.4 if we moved it far away

Aldebaran is farther than 10pc, so it’s absolute magnitude is brighter than its apparent magnitude

Remember magnitude scale is “backwards”

removes the effect of distanceand

puts stars on a common scale

Absolute Magnitude (M)Absolute Magnitude (M)


Absolute Magnitude (M)Absolute Magnitude (M)

Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation:

Knowing the apparent magnitude (m) and the distance in pc (d) of a star its absolute magnitude (M) can be found using the following equation:

5log5 dMm

Example: Find the absolute magnitude of the Sun.The apparent magnitude is -26.7

The distance of the Sun from the Earth is 1 AU = 4.9x10-6 pc

Therefore, M= -26.7 – log (4.9x10-6) + 5 =

= +4.8

So we have three ways of talking about brightness:So we have three ways of talking about brightness:

Apparent Magnitude - How bright a star looks from Earth

Luminosity - How much energy a star puts out per second

Absolute Magnitude - How bright a star would look if it was 10 parsecs away

Apparent Magnitude - How bright a star looks from Earth

Luminosity - How much energy a star puts out per second

Absolute Magnitude - How bright a star would look if it was 10 parsecs away

E.3.7 Solve problems involving apparent magnitude, absolute magnitude and distance.

E.3.8 Solve problems involving apparent brightness and apparent magnitude.


E3 Stellar distancesSpectroscopic parallax


E3 Stellar distancesSpectroscopic parallax

Spectroscopic parallax is an astronomical method for measuring the distances to stars.

Despite its name, it does not rely on the apparent change in the position of the star.

This technique can be applied to any main sequence star for which a spectrum can be recorded.

Spectroscopic parallax is an astronomical method for measuring the distances to stars.

Despite its name, it does not rely on the apparent change in the position of the star.

This technique can be applied to any main sequence star for which a spectrum can be recorded.

E.3.9 State that the luminosity of a star may be estimated from its spectrum.

The Luminosity of a star can be found using an absorption spectrum.

Using its spectrum a star can be placed in a spectral class.

Also the star’s surface temperature can determined from its spectrum (Wien’s law)

Using the H-R diagram and knowing both temperature and spectral class of the star, its luminosity can be found.

E.3.10 Explain how stellar distance may be determined using apparent brightness and luminosity.

E.3.11 State that the method of spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc.

E.3.12 Solve problems involving stellar distances, apparent brightness and luminosity.

Distance measurement

by parallax

d = 1 / p Luminosity

L = 4πd2 b

apparent brightness

spectrum

Wien’s Law (surface

temperature T)

Chemical composition

of corona

L = 4πR2 σT4

Stefan-Boltzmann

Radius

Distance measured by parallax:


E3 Stellar distancesCepheid variables


E3 Stellar distancesCepheid variables

Cepheid variablesCepheid variables are stars of variable luminosity.The luminosity increases sharply and falls of gently with a well-defined period.The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star.

Cepheid variablesCepheid variables are stars of variable luminosity.The luminosity increases sharply and falls of gently with a well-defined period.The period is related to the absolute luminosity of the star and so can be used to estimate the distance to the star.

A Cepheid is usually a giant yellow star, pulsing regularly by expanding and contracting, resulting in a regular oscillation of its luminosity.The luminosity of Cepheid stars range from 103 to 104 times that of the Sun.

E.3.13 Outline the nature of a Cepheid variable.

The relationship between a Cepheid variable's luminosity and variability period is quite precise, and has been used as a standard candle (astronomical object that has a known luminosity) for almost a century.

This connection was discovered in 1912 by Henrietta Swan Leavitt. She measured the brightness of hundreds of Cepheid variables and discovered a distinct period-luminosity relationship.

E.3.14 State the relationship between period and absolute magnitude for Cepheid variables.

http://en.wikipedia.org/wiki/Image:Leavitt_aavso.jpg

The scale has been calibrated using nearby Cepheid stars, for which the distance was already known.This high luminosity, and the precision with which their distance can be estimated, makes Cepheid stars the ideal standard candle to measure the distance of clusters and external galaxies.

E.3.14 State the relationship between period and absolute magnitude for Cepheid variables.A three-day period Cepheid has a luminosity of about 800 times that of the Sun.A thirty-day period Cepheid is 10,000 times as bright as the Sun.

E.3.14 State the relationship between period and absolute magnitude for Cepheid variables.

E.3.15 Explain how Cepheid variables may be used as “standard candles”.

• The luminosity of a Cepheid variable can be determined from its period.

• The brightness of the Cepheid (b) can be determined from its apparent magnitude.

• Then, from the relationship

the distance to the Cepheid can be determined.

• If a Cepheid variable is located in a particular galaxy, then the distance to the galaxy may be determined.

• The Cepheids method can be used to find distances up to a few Mpc.

𝒃=𝑳

𝟒𝝅𝒅𝟐

Apparent brightness

Distance (d)

b = L / 4πd2

Luminosity class

spectrum

Surface temperature (T)

Wien’s Law

Chemical composition

Stefan-Boltzmann

L = 4πR2 σT4

Radius

Distance measured by spectroscopic parallax / Cepheid variables:

H-R diagram

Spectral type

Luminosity (L)

Period

Cepheid variable

E.3.16 Determine the distance to a Cepheid variable using the luminosity–period relationship.

option e - astrophysics e3 stellar distances parallax method

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