Physical Astronomy

7/25/2019 Physical Astronomy

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1/3/2016 Introduction to Physical Astronomy - The Sun

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The Sun

The home page for the Solar Data Analysis Center at NASA Goddard Space Flight Center includes current solar images in a variety of wavelengths. Since

wavelengthis inversely proportional to temperature, visible light images show the Sun's photosphere("surface"), ultraviolet images show the chromosphere and the

transition region(20,000 to 1,000,000 K) to the corona, which is seen in x-ray images (and during eclipses):

The solar corona has very low density (less than a billion particles per cubic centimeter), but very high temperatures (up to 4 million K). (source)

(View Cosmos DVD 5, episode 9, on solar activity)

Here are a number of movies of the Sun. Look for granules(convection cells with dark edges where cooler gases sink), spicules(vertical "spikes"), coronal holes

(large areas of low density where the Sun's magnetic field opens outward, allowing outflow of the solar wind) and filaments ("curves" following magnetic field lines

above the surface):

a movie of the solar surface(10.59 MB) (source);

a Hinode movie of the same(15.86 MB) (source);

a STEREO movie of solar prominence on 4/13/10(8.57 MB) (source);

an SDO (Solar Dynamics Observatory) closeup of an eruption on 12/31/12(1.08 MB) (source);

an SDO movie of coronal rainfollowing a coronal mass ejectionon 7/19/12 (15.38 MB, centered on 304 Angstroms, covering 21.5 hours; source);

a SOHO movie of sunspots from the week starting 3/27/01 (1.06 MB) (source);

a SOHO movie of solar activity, in UV, from 10/21/03 to 11/06/03(24.61 MB) (source);

Hinode magnetic field images(4.46 MB) from a 12/13/06 flare(2.81 MB) (source);

a Hinode movie of solar X-ray jets(26.14 MB) (source).

a STEREO movie of a coronal mass ejection washing over Earth(40.52 MB) (source).

The magnetic fields of astronomical bodies are thought to be generated by the movement of conducting fluids. In the case of the Earth, this is the liquid Iron in the

outer core, and results in the reasonably regular dipole field we observe, with its North and South magnetic poles.

The case of the Sun, however, is much more complicated. In addition to the Sun's differential rotation, in which the rotation speeds vary with latitude, the conducting

plasma responsible for the Sun's magnetic field undergoes radial as well as polar convection in the outer 30% of the Sun's radius. The result is much more chaotic,

where field lines are warped and often reconnect with violent results:

A snapshot of the solar magnetic field. (source)
http://sdo.gsfc.nasa.gov/gallery/potw.php?v=item&id=28http://sdo.gsfc.nasa.gov/gallery/potw.php?v=item&id=28http://science.nasa.gov/science-news/science-at-nasa/2011/18aug_cmemovie/http://kias.dyndns.org/astrophys/movies/Stereo.CME.121308.movhttp://science.nasa.gov/headlines/y2007/06dec_xrayjets.htm?list721068http://kias.dyndns.org/astrophys/movies/Hinode.XrayJets.011007.movhttp://solarb.msfc.nasa.gov/http://kias.dyndns.org/astrophys/movies/HinodeSOT.121306.flare.mpeghttp://kias.dyndns.org/astrophys/images/HinodeSOT.121306.Bfields.gifhttp://sohowww.nascom.nasa.gov/gallery/Movies/flares.htmlhttp://kias.dyndns.org/astrophys/movies/SOHO.EUIT.110403.flare.movhttp://sohowww.nascom.nasa.gov/hotshots/2001_03_29/http://kias.dyndns.org/astrophys/movies/soho.032901.sunspot.movhttp://www.nasa.gov/mission_pages/sdo/news/coronal-rain.htmlhttp://kias.dyndns.org/astrophys/movies/coronal.rain.avihttp://www.nasa.gov/multimedia/videogallery/index.html?collection_id=15505&media_id=158014611http://kias.dyndns.org/astrophys/movies/eruption.121231.mp4http://stereo.gsfc.nasa.gov/gallery/item.php?id=stereoimages&iid=122http://kias.dyndns.org/astrophys/movies/prominence.100413.movhttp://kias.dyndns.org/astrophys/movies/prominence.100413.movhttp://antwrp.gsfc.nasa.gov/apod/ap061204.htmlhttp://kias.dyndns.org/astrophys/movies/sunaction_hinode.mpeghttp://www.astro.physik.uni-goettingen.de/~bruno/APOD/apod.htmlhttp://kias.dyndns.org/astrophys/movies/sunsurface.movhttp://umbra.nascom.nasa.gov/eclipse/images/eclipse_images.htmlhttp://kias.dyndns.org/astrophys/waves.htmlhttp://umbra.nascom.nasa.gov/


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Especially strong magnetic fields inhibit convection, and so their poles on the solar surface are cooler and appear darker (although the regions surrounding them are

usually much brighter in ultraviolet). These are the familiar sunspots.

Sunspots come and go in 11 year cycles:

The most recent complete solar cycle (seen here in 284 Angstroms) began in 1996. (source)
http://sohowww.nascom.nasa.gov/hotshots/2007_12_02/


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Note the Maunder Minimumbetween 1645 and 1715:

Sunspot cycles since 1610. (source)

At the start of each new cycle, the polarity of sunspot "pairs" reverse. For instance, during the cycle which is beginning in 2008, active regions in the

northern hemisphere are oriented so that their south poles are west of their north poles (the opposite occurs in the southern hemisphere). In the previous

cycle, the order was reversed. Here is a SOHO movie of magnetic fields from May 1998(8.37 MB) (source).

The solar wind, particles streaming from the surface of the Sun, gives us auroras and comet tails. It is a ubiquitous phenomenon, especially in hot young stars like LL

Orionis:

Bow shock around LL Orionis. (source)
http://hubblesite.org/newscenter/archive/releases/2002/05/image/a/http://antwrp.gsfc.nasa.gov/apod/ap051107.htmlhttp://sohowww.nascom.nasa.gov/gallery/Movies/sunspots.htmlhttp://kias.dyndns.org/astrophys/movies/soho.0598.bfield.movhttp://solarscience.msfc.nasa.gov/SunspotCycle.shtml


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The solar wind speed is around 400 km/s, which is about 2/3 of the escape velocity at the surface of the Sun. The wind, however, starts from the

corona, which extends several solar radii; the escape velocity at 2.4 solar radii is 400 km/s. The current solar wind velocity is available from SOHO.

The solar wind carries away about 10-14solar masses annually. This is about 634 million kg per second. If the wind was entirely made up of protons,

the outgoing flux would be 3.79 * 1035protons per second. Assuming that they are emitted isotropically, we should detect an average of about 3.37 per

cubic centimeter at the Earth. The measured value is actually about twice that.

Even radiation pressure sculpts the interstellar medium:

Cloud IC 349, shaped by radiation pressure from the star Merope, above upper right. (source)

Solar flaresare classified using the following scheme of letters and numbers (n):

class Peak Intensity comments

An n * 10-8W/m2 A-class flares are approximately at background levels.

Bn n * 10-7W/m2 B- and

Cn n * 10-6W/m2 C-class flares are not strong enough to have much of an effect on the Earth.

Mn n * 10-5W/m2 M-class flares can cause polar radio blackouts, and can pose a health risk to astronauts.

Xn n * 10-4

W/m2

X-class flares cause intense auroras and can damage electromagnetic equipment.

Intensities are measured at wavelengths between 1 and 8 Angstroms.

Table of Contents

References
http://kias.dyndns.org/astrophys/refs.htmlhttp://kias.dyndns.org/astrophys/toc.htmlhttp://www.nasa.gov/mission_pages/sunearth/news/classify-flares.htmlhttp://heritage.stsci.edu/2000/36/big.htmlhttp://sohowww.nascom.nasa.gov/home.html


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Index

2013, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

Please send comments or suggestions to the author.
mailto:[email protected]://kias.dyndns.org/astrophys/index.html


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1/3/2016 Introduction to Physical Astronomy - Distance vs. Direction

file:///E:/NSEA/Introduction%20to%20Physical%20Astronomy%20-%20Distance%20vs.%20Direction.html 1/5

Distance vs. Direction

Because the universe is so vast, many of the distance units we use are based on the travel time of the fastest thing there is: light. The speed of lightin vacuum is

c = 299,792,458 meters per second

= 2.998 * 108m/s.

(Scientific notation, using exponents, are ubiquitous in physics; the scope of our inquiry demands their use.)

The distance in meters can then be computed using

distance = velocity * time.

So, for example, one lightsecond is 2.998 * 108m. We will find the following distance units useful:

One Astronomical Unit (AU)is the average radius of Earth's orbit, equal to 1.496 * 10 11meters (m).

One lightyear (ly)is the distance light travels in a vacuum in one year, equal to 9.461 * 10 15m.

One parsec (pc)is the distance to a star whoseparallax angleis one arcsecond; 1 pc = 3.086 * 1016m = 3.262 ly.

Here are some images which might help you appreciate the orders of magnitude involved in our study:

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the Java VM (Virtual Machine)for your

version of Windows at the download section at java.sun.com.

"NGC" stands for New Galactic Catalog, and objects designed by "M" followed by a number from 1 to 110 are Messier Objects, cataloged by Charles Messier

in the latter part of the 18thcentury.

(View Cosmos DVD 6, episode 10, Milky Way Simulation and Large Scale Structure Images.)

Parallax

The parallax of the red star is larger than the parallax of the gold star.

The two blue-green circles represent the Earth at opposing points in its orbit. The large yellow circle between them of course represents Sol (our Sun). Suppose we

want to measure the distances to the red and gold stars. As the Earth moves over half its orbit, each star appears to change position. This is called parallax and the

change in position is twice the parallax angle. The parallax angle for the red star is and that for the gold star is . is less than because the gold star is farther

away.

If we know the radius r of the Earth's orbit we can compute the distances Rito the stars:

Rred= r cot () and Rgold= r cot ()

Since for large distances cot() is very close to 1/ (if is measured in radians!), we have

Rred= r / and Rgold= r /
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A parallax angle of 1 arcsecondyields a distance of 1 parsec (there are 360 degrees around a circle, 60 minutes of arc in a degree and 60 seconds of arc in a

minute). Therefore to find the distance in parsecs of a star whose parallax is measured in milliarcseconds (mas), simply divide 1000 by the parallax.

The Partial Perspective Viewer

will help you find your place in the universe (with a very fond wink at the shade of Douglas Adams) :

This applet knows wheresomethings in the universe are, and will display their locations in 3D. You may change the orientation by dragging on the image: horizontal

dragging rotates about the z axis, verticle dragging tilts the z axis. You may change the distance scales using the "Zoom In" and "Zoom Out" buttons below. The Milky

Way Galaxy is identified at its center. Earth (representing the entire solar system) is drawn in green. Even though there is no "center" of the universe, Earth is drawn

for convenience at the origin of the graph.



As you zoom out into the furthest reaches of the universe, you will notice a "dust" of unlabeled dots. Each dot is a cluster of galaxies, from the Abell

Catalog. Some Abell clusters have been labeled, but most are not for the sake of clarity.

2MASS, the 2 Micron All Sky Survey, permits us to see the nearest million and a half galaxies all at once. (source)

Portfolio Exercise:If we adopt a scale of 1 cm to represent 1 lightsecond, then 1 foot would represent 30.5 lightseconds and 1 mile would represent160934 lightseconds, or 1.86 lightdays.

If we imagine the Sun to lie at mile marker zero on I-75 in Florida, how far from that point would the Earth lie? The midpoint between Jupiter and

Saturn? Pluto?

I-75 is 467 miles long in Florida; 353 miles long in Georgia; 160 miles long in Tennessee; 192 miles long in Kentucky; 210 miles long in Ohio; and 394

miles long in Michigan. Where along I-75 would you locate Alpha Centauri?

To deal with the rest of the universe, we obviously need a different scale. Let us now use 1 inch to represent 1 parsec. Then 1 mile would represent

63360 parsecs. Where along I-75 (using this new scale) is Betelgeuse? The Crab Nebula? The center of the Milky Way? Supernova 1987A? M31?

M104? Stephen's Quintet? Place these seven objects as accurately as possible on this map of I-75and include it in your portfolio.

The Changing Cosmos

We rarely see change as we observe the distant cosmos, supernovaebeing the obvious exceptions.

This time lapse of M3 over a single night shows one of the few phenomena that are observable on human time scales: variable stars of the RR Lyrae type. (source)
https://www.cfa.harvard.edu/~jhartman/M3_movies.htmlhttp://kias.dyndns.org/astrophys/evolution.html#neutronhttp://kias.dyndns.org/astrophys/images/i75.jpghttp://spider.ipac.caltech.edu/staff/jarrett/papers/LSS/http://adc.gsfc.nasa.gov/adc-cgi/cat.pl?/catalogs/7/7110A/http://java.com/en/download/index.jsp


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RR Lyraeis a star in the constellation Lyra. It is a variable star, whose luminositychanges regularly with time as it fuses Helium in its core. Its distance is known

because it belongs to a cluster whose parallax is known. Since stars of its type have a well-defined relationship between their luminosity and the period of their

variability, they are useful standard candles: objects whose behavior dictates their luminosity. This, as we will see, can be compared to their apparent brightness to

determine their distance.

This sequence of the Cat's Eye Nebula shows the expansion of the nebula over a 3 year period. (source)

Orion - What you see and where things really are

The constellation Orion; the red line represents the celestial equator, and the white line represents 6 hours Right Ascension.
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The stars are labeled with Greek letters (in order, "alpha", "beta", "gamma", "delta", "epsilon", "kappa" and "zeta") indicating their relative brightnesswithin the constellation; their common names, celestial coordinates, visual magnitude, parallax, distance and spectral classes are given here:

Name Common Name RA dec mag Parallax (mas) distance (ly) Spectral Class

Orionis Betelgeuse 05 55 10.29 +07 24 25.3 0.45 7.63 427.3 M2Ib

Orionis Rigel 05 14 32.27 -08 12 05.9 0.18 4.22 772.5 B8Ia

Orionis Bellatrix 05 25 07.87 +06 20 59.0 1.64 13.42 242.9 B2III

Orionis Mintaka 05 32 00.40 -00 17 56.7 2.25 3.56 915.7 O9.5II+

Orionis Alnilam 05 36 12.81 -01 12 06.9 1.69 2.43 1341.6 B0Ia

Orionis Saiph 05 47 45.39 -09 40 10.6 2.07 4.52 721.2 B0.5Iavar

Orionis Alnitak 05 40 45.52 -01 56 33.3 1.74 3.99 817.0 O9.5Ib SB

This data comes from the Hipparcos Catalog. Note that the common names are all of Arabic origin. Alpha Orionis is a semi-regular pulsating star,

gamma and kappa Orionis are variable stars, delta Orionis is an eclipsing binary and zeta Orionis is a double star.

This photograph of the Eastern horizon was taken in the early hours of a mid-October morning in 2002. It is a composite of several 8 second exposures taken with a

Canon G1 (in Cincinnati, it takes a little over 10 seconds for the Earth to rotate enough to cause a star to start to become a streak).

Note the tilt of the celestial equator, which is the projection of the Earth's equatorial plane into the sky: 23.45 degrees because of the tilt of the Earth's axis of

rotation. The declination (dec)measures "celestial latitude" relative to the celestial equator and is measured in degrees. Comparing the labeled image with the table

below, we can see that positive declinations are above the equator, and negative declinations are below it.

Also note that the Right Ascension (RA)increases from right to left; this is because angles increase in counterclockwise rotation, which when looking toward the

South is from West to East. The Right Ascension is measured in hours (24 hours is a circle, so there are 15 degrees per hour).

We will discuss magnitudeand spectral classlater, but there is one very important thing to notice about the table: the distances in lightyears. The constellation Orion

looks like it does to us only in a small neighborhood of the Earth. Since the stars are at widely varying distances, any significant shift in position will change the anglesbetween them, and the constellation will appear much different. You can use the Partial Perspective Viewerto get an idea of how this works: try zooming out to 10 2.5

parsecs and tilting the z axis. From that perspective, Rigel, Mintaka, Saiph and Alnitak form a trapezoid obviously disconnected from the others.

Here is a deeper view of Orion(and check out this image of Barnard's Loop).

Portfolio Exercise:Use SIMBADto find the celestial coordinates of the five brightest stars in the constellation Cassiopeia ( through Cas). On a

piece of graph paper, set up a coordinate system where the horizontal axis runs from 0 to 2 hours of Right Ascension, and the vertical axis runs from 55

to 65 degrees of declination. Plot the locations of the five stars. Find the constellation in the night sky and use your graph to identify the stars. How do

you have to orient your graph so that it looks correct? Why did you have to orient it that way?

Astronomical Distances

Light transit time and parallax are just two of a number of methods for measuring astronomical distances; we will discuss several in more depth later:

technique equationapproximate maximum

effective distance

radar ranging d = c * echo time / 2 Solar System
http://simbad.u-strasbg.fr/simbad/sim-fidhttp://antwrp.gsfc.nasa.gov/apod/ap090224.htmlhttp://www.seds.org/messier/more/oricloud.htmlhttp://kias.dyndns.org/astrophys/distances.html#ppvhttp://kias.dyndns.org/astrophys/populations.htmlhttp://kias.dyndns.org/astrophys/scopes.html


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stellar parallax dpc= 1000 /

parallaxmas

200 pc

H-R Diagram(main sequence spectral class determines absolute magnitude)dpc= 10

(mag - Mag +

5)/55000 pc

RR Lyrae / Cepheid Variables: Period/Luminosity relation, calibrated to

known distance to Cepheids in the Large Magellanic Cloud

Mag ~ 1.608 *

perioddays0.275 20 Mpc (~ Virgo Cluster)

Tully-Fisher Relation: absolute magnitude of a spiral galaxy (a and b depend

on morphological typeand wavelength)

Mag = a - b Log

(width of spectral line)100 Mpc

Type Ia Supernovae: C-O White Dwarfs explode with characteristic

luminosity as a function of their light curves

dpc

= 10(mag - Mag +

5)/5 1000 Mpc

Hubble Relation between distance and recessional velocity d = v / H0 z = 1

There are numerous variations on these themes, some involving very clever uses of statistics which are beyond the scope of this text.

All of the techniques based on luminosity measurement depend on our knowledge of the extinction: how interstellar and intergalactic dust and gas absorb light.

Note that these techniques must be calibrated to each other: radar ranging is necessary to accurately determine 1 AU, which is needed for stellar parallax,

which is used to calibrate the magnitude-distance relation, etc.

Each technique has limits to its accuracy, for some approaching 20%, and they should in principle all agree where they overlap. At present that agreement is

better than 10%. That it is not zero is a testament to the difficulty of consistently measuring many of these quantities.

The maximum distance for the Hubble Relation is listed as "z=1". This refers to the red shift, about which more later.

Table of Contents

References

Index


mailto:[email protected]://kias.dyndns.org/astrophys/index.htmlhttp://kias.dyndns.org/astrophys/refs.htmlhttp://kias.dyndns.org/astrophys/toc.htmlhttp://kias.dyndns.org/astrophys/expansion.htmlhttp://kias.dyndns.org/astrophys/spectra.html#extincthttp://kias.dyndns.org/astrophys/expansion.htmlhttp://kias.dyndns.org/astrophys/evolution.html#dwarfhttp://kias.dyndns.org/astrophys/spectra.htmlhttp://kias.dyndns.org/astrophys/waves.htmlhttp://kias.dyndns.org/astrophys/galaxies.htmlhttp://kias.dyndns.org/astrophys/populations.html#HR


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1/3/2016 Introduction to Physical Astronomy - Astronomical Observation

file:///E:/NSEA/Introduction%20to%20Physical%20Astronomy%20-%20Astronomical%20Observation.html 1/7

Astronomical Observation

As we have seen, we can only directly measure the angle between two objects, not their distances from us. But if we know

their distance from us, we can compute the distance between the two objects.More usually, we are measuring the size of a

single object from the angle it subtends:

size = distance * angular diameterradians

where a radianis 180/ degrees. Here are some examples of variation of angular diameter with distance:

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download

the Java VM (Virtual Machine)for your version of Windows at the download section at java.sun.com.

Perigeeis thepoint of closest approach during the orbit of a satellite about the Earth. Similarly, perihelionis

the point of closest approach during orbit of the Sun. Apogeeis the point of greatest distance from the Earth

during orbit, and aphelionis the point of greatest distance from the Sun during orbit.

By setting the angular diameter in the equation above to theresolutionof a telescope, we can compute the size of the

smallest object it can see at any given distance. The resolution is determined byinterference effectsand depends on the sizeof the optics (usually a mirror) and the wavelength being observed:

angular resolutionarcsec= .0025 * wavelengthAngstroms / mirror diametercm

For instance, the Hubble Space Telescope (below) has a mirror diameter of 2.4 meters, or 240 cm. At optical wavelengths

(for instance, 5600 Angstroms), its angular resolution would be

.0025 * 5600 / 240 = .0583 arc seconds,

times / (180 * 3600) radians in an arc second = 2.828 * 10-7radians.

Looking at Saturn at closest approach (8.004 AU, or 1.197 * 1012m), the Hubble could resolve an object whose

size = 1.197 * 1012* 2.828 * 10-7= 338.6 km wide.

The light gathering power (literally, how much electromagnetic radiation the instrument can gather in a given amount of time)

is proportional to the square of the mirror radius. This is important because intensitydecreases with the square of the

distance: if you move twice as far away, the intensity drops to one quarter of what it was at the original position. This is why

we distinguish between apparent magnitudeand absolute magnitude(M):

M = apparent magnitude + 5 - 5 * log10distancepc.

Absolute magnitude is the magnitude a star would have at a fixed distance of 10 parsecs; the apparent magnitude (m) will

be larger than M if the star is more than 10 parsecs distant, and less than M if it is closer. You can barely see a star of

apparent magnitude 6 with your eyes, if you are in a region of dark skies. Under the same conditions, binoculars takes you

to magnitude 10 and 8 inch telescopes to about magnitude 13. The Hubble telescope can just see objects of apparent

magnitude 30.

There are severe limits to which types of electromagnetic radiation can be observed from the Earth's surface. The Earth's

atmosphere is transparent to radio waves with wavelengths between about 10 meters and 1 cm, and to infrared and visible

wavelengths from 105Angstroms to the near ultraviolet (around 2900 Angstroms).

Turbulence in the atmosphere blurs point-like Betelgeuse into a "seeing disc" (1/10 speed) (source):
http://antwrp.gsfc.nasa.gov/apod/ap000725.htmlhttp://kias.dyndns.org/astrophys/imaging.htmlhttp://kias.dyndns.org/astrophys/waves.htmlhttp://kias.dyndns.org/astrophys/waves.htmlhttp://antwrp.gsfc.nasa.gov/apod/ap000725.htmlhttp://kias.dyndns.org/astrophys/imaging.htmlhttp://kias.dyndns.org/astrophys/waves.htmlhttp://kias.dyndns.org/astrophys/waves.html#interferometryhttp://java.com/en/download/index.jsphttp://kias.dyndns.org/astrophys/distances.html#orion


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The degree of the effect is referred to as "good" or "poor" seeing. For these reasons, many modern observatories are

based in space.

Much of what we observe requires extremely long exposure times.

This image of the Orion-Eridanus Superbubble required 40 hours of exposure time. (source)
http://www.skyandtelescope.com/skytel/beyondthepage/39942672.html


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Telescopes

One of the most common telescope designs in use today is the Ritchey-Chretien. (source)
http://hubblesite.org/the_telescope/hubble_essentials/image.php?image=light-path


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The Ritchey-Chretiendesign is a variation on the basic reflector telescope, and differs from theCassegrainreflector in

that the main mirror is shaped like a hyperbola instead of like a parabola, improving the image quality.

Some of the premier telescopes in recent use are:

The Hubble Space Telescopeorbits the Earth every 96 minutes at an altitude of 575 km. It is 13.2 m long and has a

mass of 11,110 kg. It is a Ritchey-Chretien design with a 2.4 m mirror and resolution of .05 as. It provides data at

the rate of approximately 120 GB/week. Hubble includes the following instruments:

The Advanced Camera for Surveys, has one 16 megapixel CCD (3500 to 11000 A) and two 1 megapixel

CCDs (1700 to 11000 A and 1150 to 1700 A), covering fields of view of 202x202, 26x29 and 31x35

arcseconds, respectively.

The Wide Field and Planetary Camera (3), has 48 filters, a 16 megapixel UV/visible CCD (2000 to 10000 A)

and a 1 megapixel near-IR detector (8000 to 17000 A), covering a field of view of 160x160 arcseconds.

The Cosmic Origins Spectrograph, sensitive to 1150 to 3000 A.

The Space Telescope Imaging Spectrograph, observing in the range 1150-10000 A with three 1 megapixel

detectors.

TheNear Infrared Camera and Multi-Object Spectrometer, observing in the range 8000-25000 A.

The Fine Guidance Sensors, sensitive to 4000-7000 A, are not primarily for observation but have been used

for precision location measurement.

Galex: the Galaxy Evolution Explorer, orbits the Earth every 90 minutes at an altitude of 690 km. It is 2 m long and

has a mass of 280 kg. It is a Ritchey-Chretien design with a .5 m mirror and resolution of 5 as. It provides data at the

rate of approximately 1 TB/month.

It has two instruments: NUV, observing in the range 1750-2800 A, and FUV, observing in the range 1350-1750 A;

both have 2 Mpixel detectors.

The Chandra X-Ray Observatory, orbits the Earth every 64 hrs. 18 min. in an eccentric orbit ranging from 10000-

140161 km. It is 13.8 m long and has a mass of 4800 kg. It features a High Resolution Mirror Assemblywith .84 m

optics and resolution of .5 as. It provides data at the rate of approximately 2.25 GB/week. Chandra includes thefollowing instruments:

The Advanced CCD Imaging Spectrometer, observing in the range .2-10 keV (1-62 A).

The High Resolution Camera.

The High Energy Transmission Grating, observing in the range .4-10 keV (1-30 A).

The Low Energy Transmission Grating, observing in the range 5-140 A.

The Spitzer Space Telescopetrails Earth around Sun. It is 4m long and has a mass of 865 kg. It is a Ritchey-

Chretien with .85 m optics and resolution of 1.5 as. Spitzer includes the following instruments:

The Infrared Array Camera, observing at 3.6, 4.5, 5.8 and 8 microns (1 micron = 104A). Each detector has65536 pixels, with resolution of 1.2 as/pixel.

The Infrared Spectrograph, observing at 5.2-14 (lo-res), 9.9-19.5 (hi-res), 14-38 (lo-res) and 19-37.2 (hi-

res) microns.

The Multiband Imaging Photometer, observing at 24 (2.5 as/pixel resolution), 70 (9.8 or 4.9 as/pixel), 160

microns (16 as/pixel), and measuring 52-97 micron spectra.

The SOHOobservatory has 12 instruments which continuously monitor the Sun, the solar corona and the solar wind.

The twin STEREOobservatories each have four instruments which continuously monitor the Sun and its corona.

The Green Bank Telescopeis a radio telescope with a diameter of 100 m and a mass of 7,300,000 kg. It features16 receivers covering frequencies from 342 MHz to 115 GHz.

The VLA: Very Large Arrayincludes 27 25 m dishes yielding a maximum resolution equivalent to a 36 km antenna,

with the sensitivity of a 130 m antenna. Each dish weighs 230 tons. The VLA has a resolution of .04 as at 43 GHz,
http://www.vla.nrao.edu/http://www.gb.nrao.edu/gbt/http://stereo.gsfc.nasa.gov/spacecraft.shtmlhttp://sohowww.nascom.nasa.gov/home.htmlhttp://www.spitzer.caltech.edu/mission/396-The-Multiband-Imaging-Photometer-MIPS-http://www.spitzer.caltech.edu/mission/394-The-Infrared-Spectrograph-IRS-http://www.spitzer.caltech.edu/mission/398-The-Infrared-Array-Camera-IRAC-http://www.spitzer.caltech.edu/spitzer/index.shtmlhttp://chandra.harvard.edu/about/science_instruments.htmlhttp://chandra.harvard.edu/about/telescope_system.htmlhttp://chandra.harvard.edu/http://www.galex.caltech.edu/http://hubblesite.org/the_telescope/nuts_.and._bolts/instruments/fgs/http://hubblesite.org/the_telescope/nuts_.and._bolts/instruments/nicmos/http://sm4.gsfc.nasa.gov/technology/sm4_stis.phphttp://sm4.gsfc.nasa.gov/technology/sm4_cos.phphttp://sm4.gsfc.nasa.gov/technology/sm4_wfc3.phphttp://sm4.gsfc.nasa.gov/technology/sm4_acs.phphttp://hubblesite.org/


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and features 8 receivers covering frequencies from 73 MHz to 50 GHz (at wavelengths of 400, 90, 20, 6, 3.6, 2, 1.3

and .7 cm).

The VLBA: Very Long Baseline Arrayincludes 10 25 m dishes, each weighing 240 tons. It features 10 receivers

covering frequencies from 312 MHz to 90 GHz (the central frequencies are .326, .611, 1.438/1.658, 2.275, 4.999,

8.425, 15.369, 22.236, 43.174 and 86.2 GHz; the wavelengths are 90, 50, 21/18, 13, 6, 4, 2, 1, .7, .3 cm, and the

resolutions are 22, 12, 5/4.3, 3.2, 1.4, 0.85, 0.47, 0.32, .17, .1 mas).

Here are sample images from these telescopes:



And here is a movie of M 20(1.74 Mb), taken by Spitzer's Multiband Imaging Photometer. (source).

(View Cosmos DVD 6, episode 10, dramatization of red shift discoveries at Mt. Wilson.)

Portfolio Exercise:Research 3 additional telescopes,each in a different region of the electromagnetic

spectrum.

Note that many telescopes, both ground-based and space-based, have multiple instruments. Be

specific about which instruments you are discussing.

For each, identify the range(s) of wavelengths it is sensitive to, and its resolution at those wavelengths. Use

published resolutions if you can find them; otherwise, compute the resolution from the equation above. What is

the smallest object it could discern at 1 parsec? 1000 parsecs? 1 million parsecs? For 1 and 1000 parsecs,

compute your answers in both parsecs and A.U.

For each telescope, include an image in representative colors taken by the telescope, and explain what

observational wavelengths correspond to each primary color.

Include references for wavelength and resolution information, and for the images.

Amateur Observing

So what can you expect to see through a reasonably good amateur telescope? Unfortunately, not as much as you might

expect. Here are sample images from an 8 inch Meade LX-90, using a 12.4 mm eyepiece:



These images were taken in suburban Cincinnati on a clear night, through the eyepiece with a Cannon G-1 and an Orion

SteadyPix camera mount. When taking photographs through the lens, alignment is a major headache. However, these

photos give a pretty good idea of what you see with your eye. While detail is lacking and the colors are somewhat washed

out, there is certainly something very exciting about seeing light from the planets with your own eyes, and no one fails to

express awe when they look at Saturn. But what about deep sky objects?

Looking through this telescope, M-31 (Andromeda) is a faint smear of dust. M-42 (the Orion Nebula) has a clear shape

but no color, and the LCD screen on the camera is not sensitive enough to focus properly at any rate. So why can't you see

what the Hubble sees? Even though you are on the ground, you'd think you could do better than that!

The whole problem is one of intensity. Your eye can't add up the light received over a long period, as a digital camera

might. When the intensity is so low, your color-sensitive cone cells are inactive, and so you only see in black and white. The

beautiful deep-sky photos shown by the Hubble were long exposures, with the light accumulated over minutes or hours; for

instance, thephoto of M-104took 10.2 hours. The deep-field photo above took over 48 hours.

And so amateur astronomers who want pictures like those taken by the professionals use CCD cameras specifically
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designed to fit the telescope in place of the eyepiece. They take black and white photos of the same object three times,

through red, green and blue filters, and thencompositethem into a color image. And they take many photographs a second,

using computer software to scan through the tens or hundreds of thousands of images, discarding those blurred by

momentary atmospheric turbulence, and then "stack" the images (literally adding the intensities) to produce the final product.

A stroll through the Astronomy Picture of the Day Archivewill show many examples of amateur photographs which rival

some of those taken professionally.

Cosmic Ray Astronomy

Cosmic raysare not radiation at all: they are high-energy atomic nuclei, mostly protons. Their energies range from 1 GeV

(109electron volts) up to (rarely) 1020eV. Those up to around 1015eV are thought to originate from within our galaxy,

while the more energetic cosmic rays are thought to originate outside of the galaxy. The energy density of cosmic rays in the

galaxy is around 10 MeV per cm3, maintained largely by exploding supernovae and stellar winds. Those cosmic rays

originating outside the galaxy come from within a radius of about 250 million light years. Above approximately 4 * 1019eV,

cosmic rays interact with the Cosmic Microwave Background Radiation; this limits the range of the most energetic cosmic

rays.

When cosmic rays hit the atmosphere they produce a shower of particles. It is this shower which is detected by cosmic rayobservatories such as the Pierre Auger Cosmic Ray Observatoryin western Argentina. Their goal is not to produce an

image of a cosmic ray source, but to simply identify the sources and measure the energies associated with cosmic rays. To

do this, the Auger Observatory has constructed 1600 detectors covering an area of about 3000 km2. Events with energies

over 1019eV have a flux of about 1 per km2per year.

Neutrino Astronomy

The purpose of neutrino astronomy is much the same as that of cosmic ray astronomy: to detect sources and measure

energies. Neutrinos are electrically neutral, almost massless, and interact so weakly that the flux of solar neutrinos through

the Earth of approximately 65 billion per cm3passes through the Earth each second with only a handful of interactions.

These facts makes this perhaps the most difficult astronomical undertaking besides the detection of gravitational waves.

The Kamioka Observatoryin Japan has been instrumental in confirming our understanding about supernova explosions, and

in determining that neutrinos indeed have mass. Its instrument, Super-Kamiokande, is comprised of 13027 photomultiplier

tubes in 50000 tons of pure water. The tubes detect Cherenkov Radiation: electromagnetic energy emitted by charged

particles whose speed is greater than the speed of light in water (about 2.25 * 108m/s). When a neutrino interacts with an

atom in the water, an electron or muon is created whose track the tubes can measure. The instrument typically detects less

than 14 solar neutrino events per day.

The latest high-energy neutrino observatory is currently under construction using 1 km3of Antarctic ice: the IceCubeNeutrino Observatory. It will focus on neutrinos entering the opposite side of the Earth so that the lower-energy neutrinos

associated with cosmic ray showers will not be confused with those of extraterrestrial origin.

Gravitational Wave Astronomy

In 1974, Taylor and Hulse found a binary system of neutron stars, one of which is a pulsar. After two decades of

observation, they determined that the change in the rate of spin of the pulsar matched the predictions of General Relativity

for such a system emitting gravitational waves:

The changing orbit of binary pulsar PSR 1913 + 16 meets General Relativity. (source)
http://www.ligo.caltech.edu/LIGO_web/seminars/pdf/surf06.pdfhttp://kias.dyndns.org/astrophys/evolution.html#neutronhttp://icecube.wisc.edu/http://www-sk.icrr.u-tokyo.ac.jp/sk/index-e.htmlhttp://www.auger.org/index.htmlhttp://kias.dyndns.org/astrophys/cmbr.htmlhttp://www.cfa.harvard.edu/news/2009/pr200921.htmlhttp://antwrp.gsfc.nasa.gov/apod/archivepix.htmlhttp://kias.dyndns.org/astrophys/imaging.html


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But no one has ever directly detected a gravitational wave. It is the purpose ofLIGO- the Laser Interferometer

Gravitational-wave Observatory - to change that.

LIGO consists of two L-shaped detectors, each 4 km long, one in Hanford, Washington, and the other in Livingston,

Louisiana. In each, laser light travels repeatedly from one end to the other, reflected by mirrors. A passing gravitational

wave will change the relative lengths of the two beams, and the change in the interference pattern will be registered by a

photodetector. The fifth science run (recently completed) achieved a sensitivity of one part in 1021from 70 Hz up, enabling

detection of binary inspiral of 1.4 solar mass neutron stars at a distance of 12 Mpc. No news yet on what if anything they

have seen.

There's a nice TED talk by Janna Levinwhich includes some auditory simulations of gravitational waves emitted byinspiraling black holes.

Table of Contents

References

Index

2012, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright

notice is included.

mailto:[email protected]://kias.dyndns.org/astrophys/index.htmlhttp://kias.dyndns.org/astrophys/refs.htmlhttp://kias.dyndns.org/astrophys/toc.htmlhttp://www.ted.com/talks/lang/en/janna_levin_the_sound_the_universe_makes.htmlhttp://www.ligo.caltech.edu/


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1/3/2016 Introduction to Physical Astronomy - Black Holes

fi le:///E:/NSEA/Introduction%20to%20Physical%20Astronomy%20-%20Black%20Holes.html 1/4

Black Holes

If the final mass of a collapsing star is greater than 3-3.2 solar masses, the remnant collapses behind the horizon of a black hole.

(View Cosmos DVD 6, episode 9, on Flatland and curved space.)

Note that since mass is a scalar (having no directionality), it is a constant in every frame of reference.

For a black hole of mass M and angular momentumL, the horizonis a spherical surface located at a distance

r = (G M2+ (G2M4- c2L2)1/2) / (M c2)

from the center of the black hole. This is a complicated function, so we will specialize for a moment to the (probably) unphysical

case of a static black hole, which does not spin. Its horizon is then at

r = 2 G M / c2

= 2953 meters * M / Msolar

Note that this implies that G / c

2

is a conversion factor for converting mass to length.

The escape velocitynecessary to escape the gravitational pull of a black hole gets larger as you get closer to the horizon. Using this

expression for r, the escape velocity at the horizon is

ev = (2 G M / r)1/2

= c

which is consistent with our notions

a. of nothing (particularly light) being able to escape from inside the horizon of a black hole, and

b. all light conesare tangent to the horizon of a black hole.

The surface gravityat the horizon is

g = c4/ (4 G M)

= 1.52 * 1013m/s2/ (M / Msolar)

For M = 2 Msolar, this is almost 2 milliontimes the surface gravity of Sirius B, and 4 times that of the neutron starin the center of

the Crab Nebula. But there is a caveat for the neutron star: it is apulsar, so we know it spins, and therefore using our simplistic

version of the equation for the horizon is not exactly a valid comparison. However, even though the pulsar is spinning 30 times each

second, the angular momentum term is less than 0.03% of the mass term, so this result is very close.

Consider now the tidal accelerationexperienced by a 2-meter object at the horizon:

G M / r2- G M / (r+2)2

= (c6/ (4 G M)) (c2+ 2 G M) / (c2+ G M)2

Since M is a multiple of Msolar, G M is much greater than c2, and this reduces to approximately

c6/ (2 G2M2)

= 2 * 1010

/ (M / Msolar)2

For M = 2 Msolar, this is about 5 * 109m/s2. This means that our 2-meter object experiences a tidal acceleration over 500 million

timesEarth's surface gravity! But for M = 106Msolar, the tidal acceleration is 0.02 m/s2: unnoticeable.
http://kias.dyndns.org/astrophys/kepler.html#tideshttp://kias.dyndns.org/astrophys/kepler.html#tideshttp://kias.dyndns.org/astrophys/kepler.html#tideshttp://kias.dyndns.org/astrophys/evolution.html#neutronhttp://kias.dyndns.org/astrophys/special.htmlhttp://kias.dyndns.org/astrophys/kepler.html#escvelhttp://kias.dyndns.org/astrophys/kepler.html#tideshttp://kias.dyndns.org/astrophys/evolution.html#neutronhttp://kias.dyndns.org/astrophys/evolution.html#neutronhttp://kias.dyndns.org/astrophys/evolution.html#dwarfhttp://kias.dyndns.org/astrophys/kepler.html#surfaceghttp://kias.dyndns.org/astrophys/special.htmlhttp://kias.dyndns.org/astrophys/kepler.html#escvelhttp://kias.dyndns.org/astrophys/kepler.html#angmomhttp://kias.dyndns.org/astrophys/special.htmlhttp://antwrp.gsfc.nasa.gov/apod/ap010119.html


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It is expected that many if not most galaxies harbor a supermassive black holein their cores, probably surrounded by an

accretion disc, whose matter is accelerated to relativistic speedsand radiates tremendous amounts of energy as it falls into the

horizon:

Accretion disc surrounding probable black hole in NGC 4261. (source)

Here is a movie of the crab pulsar(source). The disc-like disturbances around the pulsar and the accretion discs around the black

holes are related in that the curvature of spacetime is essentially the same (except in magnitude) around all spinning masses. It is

probable that most if not all of the violent events we see in the universe, from novaeto gamma ray bursts, are powered by either

stellar collapse,

the accretion of matter onto a massive compact object like a white dwarf, neutron star or black hole, or

mergers of same.

Portfolio Exercise:Find a white dwarf other thanSirius B and a neutron star other thanthe one at the heart of the

Crab Nebula, and compute the following: its density, the escape velocity at its surface, and its surface gravity. For the

white dwarf, you will need to know its radius and mass; you will have to find its mass (which means it will probably

have to be a binary companion), and you can compute its radius if you find its absolute magnitude and temperature.

For the neutron star, your source will have to provide its mass and radius.

Now compute the horizon radius for a black hole of mass equal to the masses of the white dwarf and neutron star you

found. Using that radius, compute the escape velocity and surface gravity of the "equivalent" black hole. Express all

escape velocities in terms of the speed of light, and all surface gravities in terms of Earth's surface gravity (9.8 m/s2).

Curvatureand Geodesics around a Black Hole

The hardest thing to conceptualize in General Relativityis how spacetime can be curved: how can something without substance
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have shape? With enough play time around a black hole, perhaps this can become clear, or at least clearer than it is now. Our black

hole is electrically neutral, so it is described by only two parameters: its mass and its angular momentum. A collapsing star must have

a mass "M" greater than (at least) 1.86 times the mass of the Sun to form a black hole, and its angular momentum "a" must be less

than or equal to "M" for the black hole to have a horizon.

In the following applet, you can choose "M" and "a" for the black hole. You can also choose the initial position (relative to the

horizon) and speed of a pair of probes, and their initial orbital direction: either azimuthal(around the "equator") or polar(along a

"great circle" through the "north pole"). The "Replot" button starts the computations. Please be patient: each plot requires evaluation

at over 3.5 millionpoints! The "Replot" button will be labeled with ellipsis while the evaluation process is taking place.

You need a Java-capable browser to be able to use the applets. If they do not work with your Windows system, download the

Java VM (Virtual Machine)for your version of Windows at the download section at java.sun.com.

The plot on the left is a 3-D plot showing the curvature of spacetime around the black hole, and the paths of the probes, which

follow geodesics . The Geodesic Equations describe the path of any object whose own mass is negligible compared to the mass of

the black hole (including light rays). The equations become very "stiff" near the horizon, so the last segment or two of the geodesic

plots may not be smooth. The curvature is measured by the Kretschmann Invariant. Spacetime is described by a metric, which

literally tells how the measurement of intervals varies from event to event. The Kretschmann Invariant is an algebraic function of the

metric and its derivatives, which measures the curvature in a way that does not depend on the coordinate system used to describe

the metric.

The 3-D plot is colored magenta where the Kretschmann Invariant is positive, and cyan where it is negative. Where the plot appears

blue or white, you are seeing positive regions behind negative ones, or vise versa. The axes on the three dimensional plot are not

drawn inside the horizon of the black hole. The region inside the horizon on the 3-D plot does not appear to be completely black

because you are seeing it through some nonzero values of the invariant. The plot scale automatically changes so that the width of the

plot is four times the radius of the horizon assuming "a" is 0. To zoom, turn the scroll wheel; to change the perspective, drag the

mouse across the window.

The applet also provides a two dimensional plot (on the right) of time vs. position of the geodesics. The axes menus allow you to

control the two dimensional plot. The origin of this plot is (0, 0) except when plotting radial distance, when it is (horizon radius, 0).

The coordinates of the upper right hand corner are determined by the maximum values begin plotted (given in the "Final conditions"

window at the bottom of the applet). For the polar and azimuthal angles, the right hand edge is at /2 and 2 , respectively. The

polar plot includes a yellow line which marks the value of the polar angle where the curvature is zero at the horizon.

Things to try...

Lower the initial speed of the probes to 50% of the speed of light. This is less than the escape velocity and so the probes

cross the horizon; but when? By default, the 2-D graph shows radial distance versus proper time (which is the time the

probes measure). You can see that the probes cross the horizon in a finite amount of time, and the "Final conditions" data

indicates that it is a very short time indeed. But if you choose "asymptotic time" for the 2-D vertical axis, a very different

graph appears. We see that from the point of view of an observer "at infinity", the probes never cross the horizon but only

approach it asymptotically. This is an eloquent indication that the coordinates we use to make measurements far from the

black hole do not have the expected meaning in the region near the horizon.

You can see that changing "M" is only interesting if "a" is nonzero; this is because the applet automatically changes scale with

"M". You can also see that "M" must be small and "a" must be a significant fraction of "M" before the plot changes

substantially. This is a physical consequence of the spacetime metric around the hole.

Start the probes in a polar orbit with "a" = 1 (an extremal black hole); observe that near the horizon, in the region called the

ergosphere, the angular momentum of the black hole "drags" the probes in the direction of the black hole's rotation. This is

called frame dragging.

Note that as "a" increases, regions of "negative curvature" appear at the poles. What can this mean physically? The paths of

the polar geodesics indicate that the regions of "negative curvature" correspond to centrifugal barriers.

Vary the initial position and speed to see how the escape velocity depends on the initial position. (You have found the escape

velocity when the 2-D radial distance plot for the inner probe is a vertical line, or leans just slightly to the right.) Do this first

for a = 0 and both large and small masses. Then set a = .9 M and do the same. Does the escape velocity depend on the

mass? Does it matter whether the probes follow an azimuthal or polar orbit?
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We found that the escape velocity at the horizon is the speed of light. Yet you may have noticed that even when

starting the probes from a distance, at almost the speed of light, sometimes they enter the horizon. While it is

true that the Newtonian escape velocity is the speed of light at the horizon, Einstein's General Relativity includes

additional effects which imply that there is a region around the black hole for which there are nocircular orbits.

Since our probes start in a direction tangent to a circle around the black hole, in that region they mustfall in!

We have really cheated a bit here for dramatic effect: we really don't need a black hole to see the same effects. The Kerr metric

used in this applet describes spacetime around anyisolated, compact rotating massive object. So the same effects, albeit much less

pronounced, can in principle be measured around our Sun, or even around the Earth or the Moon.

Portfolio Exercise:Using the applet, vary the initial position and speed to see how the escape velocity depends on

distance from the horizon. Do this first for a = 0 and masses of 2, 2000 and 2000000 M solar. Then set a = .9 M and

do the same. Does the escape velocity depend on the mass? Does it matter whether the probes follow an azimuthal or

polar orbit?

Falling in...

The surface of the future light coneis where a particle could be if it travels at the speed of light, and the interior of the cone is where

it could be if it travels more slowly. Therefore photons are destined to stay on the surface of their light cones and massive particlesare destined to stay in the interior of their light cones.

Contrary to what you might have heard, this means that you will indeed expire when you cross the horizon of a black hole.

Assuming you cross feet first, the future light cone of your feet is pointing into the center of the black hole, so no nerve impulses can

reach your head from there. When your heart crosses, no blood can flow from it to your head. And when your head crosses the

horizon, the parts of your brain cannot communicate with each other and your consciousness ceases.

Table of Contents

References

Index

2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is

included.

mailto:[email protected]://kias.dyndns.org/astrophys/index.htmlhttp://kias.dyndns.org/astrophys/refs.htmlhttp://kias.dyndns.org/astrophys/toc.htmlhttp://kias.dyndns.org/astrophys/special.html


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1/3/2016 Introduction to Physical Astronomy - Cosmic Microwave Background Radiation

file:///E:/NSEA/Introduction%20to%20Physical%20Astronomy%20-%20Cosmic%20Microwave%20Background%20Radiation.html 1/3

Cosmic Microwave Background Radiation

After collecting seven years of data from the Wilkinson Microwave Anisotropy Probe (WMAP), the WMAP Science Team released this image of the Cosmic

Microwave Background Radiation (CMBR):

7 year data from the Wilkinson Microwave Anisotropy Probe. (source)

This image is a weighted linear combination of data in five radio frequency bands (23, 33, 41, 61 and 94 GHz) which minimizes the foreground contamination from the

Milky Way. It is a snapshot of thephotosphereor last scattering surface: our view of the universe when it first became transparent to electromagnetic radiation. The

color scale in this image corresponds to temperatures of from 2 .7248 to 2.7252 K (blue to red). This represents a deviation from perfect isotropyof one part in 13625.

Note that the last scattering surface depends on both the time of decouplingand the place and time of observation. The expansion of the universe changes

the distance to the last scattering surface, and the passage of time increases our horizon, so we see more of the universe at decoupling as time passes.

The minute deviations from perfect isotropy in the CMBR tells us that there were small inhomogeneitiesin the plasma:

dark matterdensity fluctuations created small "pockets" of gravitational attraction into whichbaryonsfell;

opposing that gravitational infall was the radiation pressure, and these opposing forces caused the plasma to oscillate;

during the radiation-dominated era, the fluctuations grew with time until the length scale of the fluctuations exceeded the horizonsize (the distance light can travel

during "one" fluctuation);

during the matter-dominated era, the fluctuations grew more slowly;

at decoupling, fluctuations were damped at all scales less than about 10 Mpc (so dark matter is requiredfor galaxy formation);

the density fluctuations froze out when the universe became dominated by dark-energy.

These oscillations occurred at different length scales and left their imprint on the CMBR we observe today. Of course, those imprints have been modified by the

expanding universe, and by other factors we have yet to discuss.

By comparing the CMBR temperatures at different angles, we can construct the power spectrum: a measure of the correlations between temperature as a function ofangle.

The power spectrum which best fits the 7-year WMAP data. (source)
http://lambda.gsfc.nasa.gov/index.cfmhttp://lambda.gsfc.nasa.gov/index.cfmhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://kias.dyndns.org/astrophys/particles.htmlhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://antwrp.gsfc.nasa.gov/apod/ap990905.htmlhttp://kias.dyndns.org/astrophys/special.htmlhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://kias.dyndns.org/astrophys/cosmology.htmlhttp://kias.dyndns.org/astrophys/sun.htmlhttp://lambda.gsfc.nasa.gov/index.cfm


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The horizontal scale is the multipole moment, denoted l; the angular scale is actually /l, so larger values of ldenote smaller angles. The vertical scale is the temperature

correlation function Cl, multiplied by l(l+1)/2, and is measured in K2, or (10-6K)2. The blue region represents the range of data values within one standard deviation of

the fit line.

The peaks in the power spectrum are called acoustic peaks, and indicate the length scales of the oscillations in the plasma before the temperature fluctuations froze out

in the last scattering surface (at decoupling). The height and positioning of the peaks are influenced by a number of cosmological parameters. We will focus on the

following:

b- additional baryon mass provides additional gravitational instability and increases the amplitudes(sizes) of the acoustic peaks - if bis a larger fraction of

M, there is more inertia and the speed of sound in the plasma is smaller; this can make the sound horizonsmaller (the region reachable by a given oscillation)

and therefore the acoustic peaks occur at smaller scales

CDM- increases gravitational density fluctuations

vac- changes transition to dark energy-domination; at that time, density perturbations cease growing - if vacis larger, structures spread out more

optical- after the last scattering surface freezes out (optical= 1), matter structures begin to form in the early universe; when the first stars begin burning, much of

the universe is re-ionized (from around z=10.7 until about z=6; optical< 1); this is the optical depthat (time of) re-ionization- the re-ionization smooths out

temperature fluctuations (earlier re-ionization produces more smoothing)

In addition, any parameter which affects k (primarily the s) changes the angular scales we observe. Photons of the CMBR follow geodesics; the Geodesic Equations for

the FRW metrictell us that the rate an angle changes is inversely proportional to the square of the scale factor. From the graphs above, we can see that smaller values of

k cause the power spectrum to shift to higher values of l.

Note that the length scales corresponding to the acoustic peaks should correlate with the distances between large structures in the universe. Survey results have recently

begun to confirm that expectation.

Comparing CMBFAST Results

We can use CMBFASTto explore regions of the space of possible cosmological parameters. The following applet will allow an easy comparison of the effects of various

parameter values with the current best fit to the data. When you run CMBFAST, use the default parameter values for everythingexceptthe parameter(s) you have been

assigned. Using CMBFAST, we can investigate the following:

1. the effects of altering the ratio of bto CDMwithout changing M;

2. the effects of changing the ratio of vacto M;

3. the effects of making > 1 or < 1 without changing the ratio of bto CDMto vac, and

4. the effects of varying the optical depth.

After you run CMBFAST (which may take a few minutes), your results will be returned to you. Look for the number on the "Output Files" (ie., "02036736" in

"cmb_02036736.fcl"). Enter that number in the applet below and it will load the power spectrum data and plot it. Each time you enter a different number, it will be

plotted in a different color (from red to violet). The best fit plot is plotted in black.



We have ignored changes in the temperature anisotropy due to gravitational lensing. We have also ignored ionization from early hot clusters, and gravitational red shifting

from the galaxy foreground (between us and the last scattering surface). Finally, all of our deliberations are strictly with the temperature anisotropies; there are also

polarization anisotropies: deviations in the electric field and magnetic field directions in the CMBR. These promise to be important sources of information in future studies.
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Portfolio Exercise:Using CMBFAST and the comparison applet, perform the 4 investigations listed above the applet. Do at least 4 trials for each

investigation. Be sure that Omegabis greater than 0 for each trial.

Capture images of each of the comparison plots for the 4 investigations, and annotate them, describing which plots belong to which parameter values.

What is the relationship between the results of investigation number 3 and the geometry of the universe?

Include all 4 in your portfolio.

The Planck Collaboration has recently released datafrom their first 15.5 months which estimate the Hubble parameter (H0) at 67.15

km/s/Mpc, b

at 0.049, CDM

at .268 and vac

at .683. Run CMBFAST with this profile and compare it to the others. Include it in your

portfolio.

An Overview of Large-scale Structure Formation

This subject is relatively young, but we can build up what seems to be a reasonable picture as follows. Think of the formation of large-scale structures in the universe

(galactic clusters, voids, etc.) as being a result of the merging of dark matter halos:

expansion of the universe causes under-dense regions to grow, forming voids;

voids are separated by sheets;

filaments form where sheets meet;

nodes form where filaments intersect;

the nodes correspond to cluster halos(interesting note: these halos tend to be triaxial ellipsoids);

as the universe continues to expand, the process builds structure from the bottom up: halos merge, accrete.

At re-ionization, the speed of sound was about 10 km/s, so halos with escape speeds less than that (around 10 8Msolar) didn't form stars (the gas would not fall into the

halos).

Star formation drove gas out of the galactic halos (accounting for the presence of heavy elements in the intracluster medium); this process was aided by ram pressure as

the galaxies moved through the intracluster medium.

Table of Contents

References

Index


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1/3/2016 Introduction to Physical Astronomy - Cosmology

file:///E:/NSEA/Introduction%20to%20Physical%20Astronomy%20-%20Cosmology.html 1/9

Cosmology

History of the Universe

The average temperature of the universeis inversely related to the scale factor:

temperaturepast / temperaturenow= scale factornow/ scale factorpast

= red shift (z)+ 1

So as the universe expanded, the temperature dropped. We know that each particle has an energy associated with it through the equation

energy = mass * c2

Similarly, each of the fundamental forceshas an energy scale associated with it. By dividing each energy by Boltzmann's constant(1.381 * 10-23

J/K):

temperaturefreeze out= energy / kB

we find the temperature at which each forcebecomes effective, and at which each particle condenses from its constituent parts. For instance, above

1015K, the particles which mediate the weak force (W and Z bosons)are unstable to pair production(decay into an electron and apositron), andinteractions which change quark flavors(as in radioactive decay) are not possible. When the temperature drops below that associated with the mass of

the proton:

1.673 * 10-27kg * c2/ kB

= 1013K

the constituent quarks in the proton are cool enough to be bound together by the strong force:

event temperature (K) scale factornow/ scale factorthen time

strong forces freeze out 1027 3.7 * 1026 10-35s

weak forces freeze out 1015 3.7 * 1014 10-10s

protons, neutrons freeze out 1013 3.7 * 1012 0.0001 sneutrinosdecouple 3 *1010 1.1 * 1010 1 s

electrons freeze out 6 * 109 2.2 * 109 100 s

primordial 2H, 4He form 9 * 108 3.3 * 108 2-15 minutes

When the protons and neutrons froze out, the ratio of protons to neutrons was about 6:1 because of the mass difference between theneutron and proton (the neutron is slightly heavier). The large number of neutrons available, as well as the fact that neutron capture occursfaster than proton fusion, caused the nucleosynthesisreactions here to be somewhat different from those taking place in the Sun. Once

the universe cooled enough to allow Deuterium (2H) to exist, the ratio was 7:1 (from neutron decays) and the following reactionsoccurred:

1

H + n ->2

H + 2H + 2H -> 3He + n + 3He + n -> 4He +

This sequence lasted about 15 minutes. The final ratio of 4He to 1H was about 1:12, so that the universe was about 75% Hydrogen and25% Helium by mass. A small amount of Deuterium survived; since it does not survive in stars, what Deuterium we observe isprimordial. This is a sensitive indicator of the density of normal matter (not dark) in the universe, since a denser universe would havecontained more protons and produced more Deuterium during nucleosynthesis.

Heavier elements were not formed because the temperature and density were both dropping very quickly; in stars they do form becausethe temperature and density increase (slowly).

We now take up our history:

event temperature (K) scale factornow/ scale factorthen time

photons decouple, atoms form 3000 1091 377000 years

first stars 60 10.4 109years

today 2.73 1 1.378 * 1010years
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Decouplingmeans that those particles are no longer in thermal equilibrium with their environment. When neutrinos decoupled, theuniverse became transparent to them; similarly for photons.

The scale factors in the tables above were obtained by using Tnow= 2.725 K, the temperature of the Cosmic Microwave Background Radiation

(CMBR). Study of the CMBR has made cosmology an experimental science, as we shall soon see.

The temperatures in our history indicate that the early universe was filled with intense radiation. Even before the decoupling of photons, the density ofmatter became greater than the density of radiation (due to red-shifting, as we shall see). Wide field surveys indicate that the universe is now very closeto being a homogeneous "dust" of galaxy clusters. The pressure from the radiation has all but vanished. But the Type IA supernovae surveys we

discussed previouslyindicate that the expansion of the universe is accelerating. We do not know what causes this acceleration, and for now we simplygive it the commonly-used name dark energy. So the universe has passed through three distinct phases:

1. radiation-dominated phase(z > 3250),2. matter-dominated phase(3250 > z > 0.37), and now3. dark energy-dominated phase(z < 0.37):

Log-Log plot of temperature vs scale factor.

General Relativity

General Relativity (GR), which relates the geometric qualities of spacetimeto the matter and energy it is filled with, provides us with a mathematicalcontext for understanding the evolution of the universe. Spacetime is described by a metric: a rule for how to measure intervals. The usual procedure inGR is to find the most general metric which is consistent with the symmetries of the problem at hand, and to find the most general form of theexpressions describing the matter and energy. These are related by Einstein's Equations, which are then solved for relations between the free

parameters.

Given the wide field surveys and observations of the CMBR, we need the most general metric which is homogeneous and isotropic(the same in alldirections). This is the Friedmann-Robertson-Walker (FRW) metric, and it is described by two parameters. The first is "k", the curvatureconstant; if we choose a time "t" and take all the points in the spacetime which have the same value of t (called a spatial section),

k = 1 means the section is positively curved:cross sections in a fixed direction are circles;the universe is closed like a sphere;the sum of the interior angles in a triangle is more than 180 degrees;
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k = 0 means the section is not curved; it is flat space:cross sections in a fixed direction are straight lines;the sum of the interior angles in a triangle is 180 degrees;

k = -1 means the section is negatively curved:cross sections in a fixed direction are hyperbolas;the neighborhood of every point in the universe is shaped like a saddle;the sum of the interior angles in a triangle is less than 180 degrees:

Surfaces of constant curvature, and their triangles.

(Strictly speaking, what we have said about k, and the images above, are relevant to 2-dimensional surfaces. You have to use yourimagination to see how all this applies to 3 dimensions, but with a little practice it can be done.)

For nonpositive k, the universe can be either finite (although obviously verylarge!) or infinite. A finite universe need not have an edge: a flatclosed universe(finite, without boundary) could be like a cube, but with identifications: walking "out" one side is the same as walking "in" theopposite side. Similarly, a negatively curved space can have identifications, but these are much harder to visualize. An infinite universe is calledan open universe(without boundary). If k is positive, the universe cannot be open.

The other parameter is a function "a(t)"; this is the scale factor we mentioned earlier. It measures the "size" of the universe as a function of time. The

Big Bangoccurred when a(t) was zero, and the expansion of the universe meansthat a(t) increases as a function of time. The Hubble Parameterisdefined as the rate of change of a(t) divided by a(t). The rate of change of a(t) is denoted a'(t), and it must be positive as long as the universe isexpanding:

H(t) = a'(t) / a(t)

Our matter/energy expression must be able to describe our three act history of the universe: radiation-dominated, matter-dominated and dark energy-dominated. This can be done using a perfect fluid, which is described by its energy density"" and pressure "p" (perfect fluids do not have viscosityor convection). We will usually assume a simple (but reasonable) equation of state(which gives the pressure as a function of the density)

p = w

where "w" is a constant:

if w=0, the equation describes dust;if w=1/3 it describes radiation, andif w=-1 it describes the Cosmological Constant.

If the dark energy is not due to a Cosmological Constant, it is usually given the name quintessence, and it has a different equation of state. Currentdata is consistent with a Cosmological Constant, and we will assume that simple scenario in the following.

With these parameterizations, Einstein's Equations reduce to two simple equations:

a'2(t) ((t) / c- 1) = k c2,

and

a''(t) = - (4 G / 3 c2

) a(t) (3 p(t) + (t))

= - (3 w + 1) (4 G / 3 c2) a(t) (t)

where we have shown explicitly the dependence of the density and pressure on the time (since density and pressure both depend on volume andtherefore on the scale factor, which is a function of time). cis the critical density
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3 H2c2/ 8 G

= 8.2487 * 10-10J / m3,

equivalent to about 5.5 protons per cubic meter.

If = c, k must equal zero.

If > c, k must be positive, and

if < c, k must be negative.

Note that unless w < -1/3, the second of Einstein's Equations implies that the acceleration of the universe must slow down (since a''(t) 1, k must equal 1.

When the universe cooled so much that there was insufficient energy to ionize Hydrogen atoms, the universe became transparent to photons. Beforethen, it consisted of a dense plasma(electrically charged fluid) containing electrons,baryons, and photons. There was also dark matter: massive

particles (not yet understood as part of the Standard Model) which do not exchange photons, and so do not interact electromagnetically. Dark mattermay come in two forms: Cold Dark Matter (CDM)or Hot Dark Matter (HDM); HDM travels at speeds close to that of light, while CDM isnon-relativistic(speeds 50 km/s). There was also dark energy, but its influence appears to have been negligible in the early universe.

Since the baryons are roughly 2000 times more massive than electrons, they were the fundamental source of inertia(resistance to acceleration).

Baryons and dark matter were the fundamental sources of gravitational attraction.Photons were the fundamental source of pressure, which was therefore experienced by the electrons and baryons but not the dark matter.Neutrinos contributed to the radiation energy density because they are nearly massless and move at relativistic speeds, but because they areelectrically neutral they did not contribute to the pressure: they simply passed through the plasma unimpeded.

Because of their differing physical effects, the contributions of radiation, baryons, HDM, CDM and the dark energy to are distinguished bysubscripts:

= rad+ b+ HDM+ CDM+ vac

where "vac" denotes the dark energy contribution. Sometimes "" is used instead of "vac" when we are particularly interested in the cosmologicalconstant. In addition, we sometimes write

M= b+ HDM+ CDM

to denote the contribution of matter to .

Solving the Friedmann Equation

With a choice of k and w, we can solve the Friedmann Equation for radiation, matter or a Cosmological Constant:

Solutions of the Friedmann Equation for radiation (in red), dust (in green) and Cosmological Constant (in blue), for each value of k.
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The graph on the right shows the solutions for a Cosmological Constant; these solutions are exponential and must be fitted to the appropriate solutionfrom the graph on the left at the appropriate time. From these graphs we see that for smaller values of k, the universe expands more rapidly, and thatradiation tends to make the universe expand more rapidly than dust.

The universe of course has all three components: matter, radiation and Cosmological Constant. When all three are present, it is quite difficult to solvethe Friedmann Equation analytically, but it can be solved numerically. In order to do so, we must have values for the various s and k.

While our equation of state above implies that we can have either matter or radiation, but not both, the solutions to the conservation equation are valideven when both are present. Equating the energy densities as functions of the scale factor allows us to find the red shift at the transition from theradiation-dominated era to the matter-dominated era:

radiation matter

rad/ (aradM)4= M/ (aradM)

3

aradM= rad/ M

zradM= M/ rad- 1

Using M= 0.278, we can invert the equation to compute rad= 8.55 * 10-5, which includes contributions from both photons and neutrinos.

The energy density from photons alone can be found from theblack body distributionas

= 8 5(kB* TCMBR)4/ (15 (h c)3)

= 5.06 * 10-5c

We can perform a similar calculation, using matter, to find &Lambda.

Portfolio Exercise:Verify the computations of radand , and compute &Lambda. For &Lambda, use zM= 0.374397.

For our numerical solution, we have assumed values for H0, zradM, M, and k consistent with the WMAP7+BAO+SNSALT data set for the

CDM model. The numerical solution for the scale factor is shown below in blue; the left plot shows the past, and the right plot shows the future:

The scale factor up to the present (left) and in the future (right).

Up to the present day, the numerical scale factor is approximately

apast(t) = (t / tnow)2/3
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(left, in red), but in the distant future it increases exponentially:

afuture(t) = 4/3 ec t ( / 3)

(right, in red). apast(t) and afuture(t) are the solutions for the matter-dominated era and the Cosmological Constant-dominated eras, respectively. Since

they are in such good agreement with the complete numerical solution, we will use them in the following. Of course they do not quite match up, andthey neglect the fact that in the recent past, a''(t) becomes positive, as it must since we observe the expansion of the universe to be accelerating. Forthose shortcomings, they still are very good approximations, and will illustrate all of the qualitative points we wish to make.

There's a caveat here: for the past, we are using the solution for the matter-dominated universe, and in the early stages of its evolution, the

universe was dominated by radiation. The scale factor was essentially linear in t during that era, but we can't match the solutions easilybecause we have no distance information from those early times. So we will pretend this value is accurate, but remember that this is onlyan approximation.

Recalling our discussion of the Hubble relation, we know that the expansion speed of an object located at a distance r(t) is

vexp= H(t) * r(t)

= a'(t) * r(t) / a(t)

= a'(t) * r(tnow),

since r(t) = r(tnow) * a(t). Using apast(t) for a(t), we see that the Hubble parameter changes with time up to the present as

H(a) = 2 / (3 tnowa3/2)

The Hubble parameter / H0, from past to present as a function of scale factor.

But using a(t) = afuture(t) implies that in the future, the Hubble parameter approaches a constant: c (/3), or approximately 11.85 km/s / Mpc.

We have seen images ofproto-galaxies at z = 1 and beyond. Let us assume that an extraterrestrial named Bob lives on an early-developed planet inone of those protogalaxies (at z=1), and is not moving with respect to it. Using apast(t), it is possible to compute the current distance to Bob, even

though the light he emits now will not be seen by us for a long time. Our equation for v expis actually a differential equation:

dr(t)/dt = a'(t)/a(t) * r(t)

If we consider a light ray traveling toward us from the past, this equation describes the path of the ray as affected by the expansion of the universe:

dr(t)/dt = a'past(t)/apast(t) * r(t) - c

The expansion of the universe essentially modifies the speed of light, which is only guaranteed to be constant in inertial frames: coordinate systemsmoving at constant velocity. The solution to this equation is

rpast(t) = bpast * t2/3- 3 c t,
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where bpast is a constant to be determined by setting rpast(tnow) = 0, since we are measuring distances relative to our current position (where we see

the light from Bob).

Since Bob was at z = 1

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