Women in American Cosmology

Jack C. Straton © 2000

University Studies

Portland State University.

straton@pdx.edu

 

Day 2 (Week 24.2)- Cepheids

February 29, 2000

All text in black is from other sources, yellow-green is my commentary.

 

Reprise from Day 1

In 1900 Annie Jump Cannon, spectroscopist for the Harvard Observatory, undertook the classification of spectra from nearly 400,000 stars, published in the Henry Draper Memorial Catalog (Draper was the first astronomer to photograph the spectrum of a star)

She developed a classification scheme that is still in use today

Slide CO 16 Annie Jump Cannon_24b

Show spectra of stars

Slide 81a Spectral classification

Characteristics of Spectral Classes for Normal Stars

Type

Temperature

Color

Prominent Spectral Features

%

Examples

O

25,000-50,000 K

30,000 K

Blue

Lines of ionized helium; plus lines of multiply ionized [heavies] elements, such as O III, N III, C III, Si IV. Balmer lines of hydrogen rather weak

0

Mintaka,Meissa,

Alnitak,Naos

B

11,000-25,000 K

20,000 K

Blue

Lines of neutral helium; plus lines of [singly] ionized [heavies] elements, such as O II, N II, C II, Fe III. Balmer lines of hydrogen moderately strong.

0.1

Rigel,

Regulus,

Spica,

Bellatrix

A

7500-11,000 K

10,000 K

White

[hydrogen ] Balmer lines very strong; [singly ionized heavies] other features very weak or absent.

Vega, Sirius,

Altair, Deneb,

F

6000-7500 K

8,000 K

[hydrogen ] Balmer lines moderately strong [, singly ionized heavies,] plus lines of some ionized elements, such as Ca II, Ti II, Fe II. (Ca II, at 3933 Å is about as strong as Ha at 4340 Å.)

Polaris

Procyon A

G

5000-6000 K

6,000 K

Yellow-white

[hydrogen ] Balmer lines present but weaker than in hotter stars. [singly ionized heavies] Lines of neutral [metals] elements strong (e.g., Fe, Ti, Mg). Lines of easily ionized elements (e.g., Ca II) are strong.

Sun

a Cen A t Cet Capella

K

3500-5000 K

4,000 K

Red-orange

Lines of neutral [metals] elements strongest. Ca II still present but weaker.

14

Arcturus,

Aldebaran

Pollux

M

2000-3500 K

3,000 K

Red

[hydrogen ] Balmer lines [very] weak. Many lines of neutral elements. Spectrum dominated by molecular features, such as TiO, C2, and CH.

Betelgeuse

Antares

Mira

Bamard's star

Oh Be A Fine Girl, Kiss Me!

Only Boys Accepting Feminism Get Kissed Meaningfully

Cannon was considered for membership in the National Academy of Science because her work enabled Ejnar Hertzsprung and Henry Norris Russell to independently develop their diagram relating luminosity to temperature, the H-R Diagram. Anyone care to bet on whether or not she was appointed? She got a consolation prize of an honorary degree from Oxford.

Henrietta Swan Leavitt (1868-1921)

Slide CO 6 Henrietta Levitt poor res

http://www.physics.ucla.edu/~cwp/Phase2/Leavitt,_Henrietta_Swan@871234567.html

 

Born on July 4, 1868, she was the daughter of a Congregational minister. She graduated from Radcliffe College in 1892. In 1895 she accepted a position as a research assistant at Harvard College Observatory. During her time at Harvard, she worked with Annie Jump Cannon to measure the visual magnitudes of stars.

Leavitt's main research interest was photographic photometry, the problem of determining the brightness or magnitude of a star from a photographic image. She also investigated variable stars in the Magellanic Clouds and discovered 1,777 new variable stars.

Special thanks to the Microsoft Corporation for their contribution to this site. The following information came from Microsoft Encarta: http://www.netsrq.com/~dbois/leavitt.html

Henrietta Swan Leavitt

Leavitt, Henrietta Swan (1868-1921), American astronomer, whose work made possible the first accurate determination of extragalactic distances. While working at the Harvard College Observatory on a survey of Cepheid variable stars (stars the luminosity, or brightness, of which varies in an extremely regular manner) she discovered [in 1908] (1912) that the Cepheids having the greatest average brightness also had the longest periods of variation. When, in 1913, the Danish astronomer Ejnar Hertzsprung accurately estimated the distances of a few Cepheids, the distances of all Cepheids could be calculated from Leavitt's period-luminosity correlation. This method of distance determination greatly increased the scientific knowledge of the physical universe.

"Leavitt, Henrietta Swan" Microsoft(R) Encarta.
Copyright(c) 1995 Microsoft Corporation.

In 1908 Henrietta Levitt discovered a relationship between the period of the variation and the absolute luminosity of Cepheid variable stars. The Hipparcos Satellite revised this PL relation as [<Mv> = -2.81 log P - 1.43] a straight line from 300 Solar Luminosities (LSolar) for a one-day cycle to 30,000 LSolar for a 60 day cycle. Note the nonlinear scale on both axes of the graph.

 

[See http://131.176.13.132/Hipparcos]

Once you know the period, you have the absolute luminosity. Comparing to the apparent luminosity gives the distance. This was a major achievement for astronomy, because it provides an excellent next step on our cosmic distance ladder. (Henrietta Leavitt died in 1921.)

 

Divide the class of N students into small discussion groups on Cepheids (15 min) {answers in brackets}. Each discussion group does one of the problems. Each member of the group should know how to do their calculation when the group is done.

1. In 1784 John Goodricke, a deaf, mute, 19-year-old English Amateur Astronomer discovered that the star Delta Cephei (the 4th brightest star in the constellation Cephius) varied in brightness. Stars of this kind are now called (Type I) Cepheid Variable stars. From the attached light curve for Delta Cephei, , determine its period of oscillation. P = {5.3661 days}

2. For a Type I Cepheid Variable star with a period of 5.4 days, use the Period-Luminosity relation to find its luminosity in "Solar Luminosities," defined as how bright the sun looks from 10 parsecs away. (One parsec is 3.26 light years.) L@10pc pc= {I read about 2200 LSolar, and the relation the graph was derived from was MV = -2.81 log P - 1.43 = -3.48, which is used in 2.512[Solar absolute visual magnitude - MV] = 2.512[4.85 - (-3.48)] = 2149 LSolar. }

3. Delta Cephei appears, on average, 2 1/4 times brighter than the sun would if both were 10 pc away from us.{This is from Feast's ground-based value 3.954 for the absolute visual magnitude V, which he says is more accurate than the Hipparcos value of 4.07, we get 2.28 LSolar = 2.512[4.85 - 3.954]} If we know that it has a true luminosity of L@10pc = 2,150 LSolar, but it has an apparent luminosity of L@D = 2.28 LSolar, it must be further away than 10 pc. Use the inverse square law or to find how much farther than must it be away from us? D = {approximately Sqrt(1000) * 10 pc = 316 pc, or more exactly, Sqrt(2149/2.28) * 10 pc = 306 pc}

The distance to Delta Cephei as measured by Hipparcos was d=1000/3.32 = 301 pc

Harlow Shapley, Levitt’s advisor, studied a different kind of variable star, called RR Lyrae, after the prototype in the constellation Lyra. These are variable stars that have a shark’s tooth variation shape rather than the saw shape of the Cepheid’s wave. These stars all have the same period of about half a day and a luminosity of about 100. By 1915 he found a number of these in the 93 globe-shaped (globular) clusters that he studied outside of the milky-way band, and hence outside of obscuring dust, and determination that globular clusters appear to be centered on a point 8kpc away from the Earth.

Slide 105 Milky Way Galaxy layout

http://www.astro.virginia.edu/%7Eeww6n/astro/MilkyWayGalaxy.html

Our galaxy is 30 kpc (100,000 ly) in diameter, 0.3 kpc (2000 ly) thick in the disk at the distance of the sun, with a bulge about 5 kpc (15,000 ly) thick at the center. We are about 8 kpc (25,000 ly) from the galactic center, about 2/3 of the way to the edge.

Edwin Hubble's discovery of Cepheid variables in the Andromeda nebula

Slide 8 Andromeda Galaxy

[

http://antwrp.gsfc.nasa.gov/apod/image/andromeda_moo.gif

see his original image at http://antwrp.gsfc.nasa.gov/apod/ap960406.html]

led to the unambiguous conclusion that this object lies well beyond the limits of the Milky Way and must therefore be a separate galaxy. Hubble later made important discoveries about the properties of galaxies and what they tell us about the universe as a whole (see Chapter 19). (Niels Bohr Library, California Institute of Technology) http://universe.colorado.edu/universe/tango/figures.qry?function=number&number=18.01

This is but one galaxy in a cluster of near-by galaxies called the

local groupF18.17.jpg

http://universe.colorado.edu/universe/tango/figures.qry?function=number&number=18.17

If we go to a scale on 40 Mpc, we find that there is the huge Virgo cluster of some 2500 galaxies within 3 Mpc of each other. Dr. Wendy L. Freedman

B.Sc., 1979, M.Sc., 1980, Ph.D. (astronomy), 1984, University of Toronto

Cosmic distance scale; extragalactic astronomy; stellar populations of galaxies; cosmology

HST Key Project on the Extragalactic Distance Scale Team

Members

Principle Investigators

Wendy L. Freedman (Observatories of the Carnegie Institution of Washington, Pasadena, California)

Robert C. Kennicutt Jr. ( Steward Observatory, Univ. of Arizona)

Jeremy R. Mould (Mount Stromlo & Siding Springs Observatories, Australia)

Slide GH 8 M100 Color HST

JPEG M100 Color HST

in http://oposite.stsci.edu/pubinfo/pr/94/49.html

M100 (100th object in the Messier catalog of non-stellar objects) in the Virgo cluster is a majestic face-on spiral galaxy. What type?

Slide GH 11 M100Cepheid dummy Period

JPEG M100 Cepheid Variable HST

http://oposite.stsci.edu/pubinfo/pr/94/49.html

http://www.ipac.caltech.edu/H0kp/m100/m100vceph.data

Hubble's high resolution pinpoints a Cepheid, which is located in a starbirth region in one of the galaxy's spiral arms (bottom frame). The top three frames were taken on (from left to right) May 9, May 4, May 31, and they reveal that the star (in center of each box) changes brightness.

Rearrange the discussion groups (for N students) so that each new group has a representative from each of the original groups. Each group does the entire sequence on M100 Cepheid (30 min).

1. What is the period of oscillation for the C41 Cepheid in M100? P = {30.9± 1.5 days, [for dummy 51.3 days ]}

2. For the Type I Cepheid Variable star with the period you got above, use the Period-Luminosity relation to find its luminosity in "Solar Luminosities," defined as how bright the sun looks from 10 parsecs away. (One parsec is 3.26 light years.) L@10pc =

{For C41 I read 16000 for C31, and the relation the graph was derived from was MV =-2.81 log P - 1.43=-5.62, which is used in 2.512[Solar absolute visual magnitude - MV] = 2.512[4.85 - (-5.62)] = 15400 LSolar. For dummy I read about 26000 LSolar, or 2.512[4.85 - (-6.24)] = 27300 LSolar. }

3. C31 varies in brightness from 3.89 × 10-9 LSolar to 7.44 × 10-9 LSolar [for dummy 1.38 × 10-8 LSolar to 0.66 × 10-8 LSolar for an average of 1.02 × 10-8 LSolar]

{E.g., from a 24.5 magnitude star (1.38e-8 LSolar = 2.512[4.85 - 24.5]) to magnitude magnitude star to a 25.3 magnitude star. This is from Feast's ground-based value 3.954 for the absolute visual magnitude V, which he says is more accurate than the Hipparcos value of 4.07, we get [for C31 25.9 to 25.2] }.

Taking the average value for L@D = 5.60 × 10-9 LSolar, we have a star that appears, 1/100-millionth as bright as the sun would if both were 10 pc away from us. You calculated its true luminosity, but it has an apparent luminosity much smaller, 5.60 × 10-9 LSolar, so it must be much further away than 10 pc. Use the inverse square law or to find how much farther than must it be away from us? D =

{ Sqrt(15400/5.60 × 10-9) * 10 pc = Sqrt(2.75 × 10-12) * 10 pc = 1.66 × 10-6 * 10 pc = 16.6 Mpc LSolar.}[For dummy Sqrt(27300/1.02 × 10-8) * 10 pc = Sqrt(2.68 × 10-12) * 10 pc = 1.64 × 10-6 * 10 pc = 16.4 Mpc ]

4. What is M100’s distance in lyr? { 16.6 Mpc × 3.26 lyr/pc = 54.0 million lyr.}

The distance to M100 has been measured accurately as 56 million light-years (+/- 6 million light-years), [how did you do?] making it the farthest object where intergalactic distances have been determined precisely.

http://oposite.stsci.edu/pubinfo/press-releases/94-49.txt

CONTACT: Ray Villard, STScI EMBARGOED UNTIL: 2:00 P.M. EDT (410) 338-4514 Wednesday, October 26, 1994

Dr. Wendy L. Freedman PRESS RELEASE NO.: STScI-PR94-49 Carnegie Observatories (818) 304-0204

HUBBLE SPACE TELESCOPE MEASURES PRECISE DISTANCE TO THE MOST REMOTE GALAXY YET

An international team of astronomers using NASA's Hubble Space Telescope announced today the most accurate measurement yet of the distance of the remote galaxy M100, located in the Virgo cluster of galaxies.

This measurement will help provide a precise calculation of the expansion rate of the universe, called the Hubble Constant, which is crucial to determining the age and size of the universe.

"Although this is only the first step in a major systematic program to measure accurately the scale, size, and age of the universe," noted Dr. Wendy L. Freedman, of the Observatories of the Carnegie Institution of Washington, "a firm distance to the Virgo cluster is a critical milestone for the extragalactic distance scale, and it has major implications for the Hubble Constant."

HST's detection of Cepheid variable stars in the spiral galaxy M100, a member of the Virgo cluster, establishes the distance to the cluster as 56 million light-years (with an uncertainty of +/- 6 million light-years). M100 is now the most distant galaxy in which Cepheid variables have been measured accurately.

The precise measurement of this distance allows astronomers to calculate that the universe is expanding at the rate of 80 km/sec per megaparsec (+/- 17 km/sec). For example, a galaxy one million light-years away will appear to be moving away from us at approximately 60,000 miles per hour. If it is twice that distance, it will be seen to be moving at twice the speed, and so on. This rate of expansion is the Hubble Constant.

These results are being published in the October 27 issue of the journal Nature. The team of astronomers is jointly led by Freedman, Dr. Robert Kennicutt (Steward Observatory, University of Arizona), and Dr. Jeremy Mould (Mount Stromlo and Siding Spring Observatories, Australian National University).

Dr. Mould noted, "Those who pioneered the development of the Hubble Space Telescope in the 1960s and 1970s recognized its unique potential for finding the value of the Hubble Constant. Their foresight has been rewarded by the marvelous data that we have obtained for M100."

Using Hubble's Wide-Field and Planetary Camera (WFPC2), the team of astronomers repeatedly imaged a field where much star formation recently had taken place, and was, therefore, expected to be rich in Cepheids -- a class of pulsating stars used for determining distances. Twelve one-hour exposures, strategically placed in a two-month observing window, resulted in the discovery of 20 Cepheids. About 40,000 stars were measured in the search for these rare, but bright, variables. Once the periods and intrinsic brightness of these stars were established from the careful measurement of their pulsation rates, the researchers calculated a distance of 56 million light-years to the galaxy. (The team allowed for the dimming effects of distance as well as that due to dust and gas between Earth and M100.)

Many complementary projects are currently being carried out from the ground with the goal of providing values for the Hubble Constant. However, they are subject to many uncertainties which HST was designed and built to circumvent. For example, a team of astronomers using the Canada-France-Hawaii telescope at Mauna Kea recently have arrived at a distance to another galaxy in Virgo that is similar to that found for M100 using HST -- but their result is tentative because it is based on only three Cepheids in crowded star fields.

"Only Space Telescope can make these types of observations routinely," Freedman explained. "Typically, Cepheids are too faint and the resolution too poor, as seen from ground-based telescopes, to detect Cepheids clearly in a crowded region of a distant galaxy."

Although M100 is now the most distant galaxy in which Cepheid variables have been discovered, the Hubble team emphasized that the HST project must link into even more distant galaxies before a definitive number can be agreed on for the age and size of the universe. This is because the galaxies around the Virgo Cluster are perturbed by the large mass concentration of galaxies near the cluster. This influences their rate of expansion.

 

REFINING THE HUBBLE CONSTANT

These first HST results are a critical step in converging on the true value of the Hubble Constant, first developed by the American astronomer Edwin Hubble in 1929. Hubble found that the farther a galaxy is, the faster it is receding away from us. This "uniform expansion" effect is strong evidence the universe began in an event called the "Big Bang" and that it has been expanding ever since.

To calculate accurately the Hubble Constant, astronomers must have two key numbers: the recession velocities of galaxies and their distances as estimated by one or more cosmic "mileposts," such as Cepheids. The age of the universe can be estimated from the value of the Hubble Constant, but it is only as reliable as the accuracy of the distance measurements.

The Hubble constant is only one of several key numbers needed to estimate the universe's age. For example, the age also depends on the average density of matter in the universe, though to a lesser extent.

A simple interpretation of the large value of the Hubble Constant, as calculated from HST observations, implies an age of about 12 billion years for a low-density universe, and 8 billion years for a high-density universe. However, either value highlights a long-standing dilemma. These age estimates for the universe are shorter than the estimated ages of some of the oldest stars found in the Milky Way and in globular star clusters orbiting our Milky Way. Furthermore, small age values pose problems for current theories about the formation and development of the observed large-scale structure of the universe.

 

COSMIC MILEPOSTS

Cepheid variable stars rhythmically change in brightness over intervals of days (the prototype is the fourth brightest star in the circumpolar constellation Cepheus). For more than half a century, from the early work of the renowned astronomers Edwin Hubble, Henrietta Leavitt, Allan Sandage, and Walter Baade, it has been known that there is a direct link between a Cepheid's pulsation rate and its intrinsic brightness. Once a star's true brightness is known, its distance is a relatively straightforward calculation because the apparent intensity of light drops off at a geometrically predictable rate with distance. Although Cepheids are rare, once found, they provide a very reliable "standard candle" for estimating intergalactic distances, according to astronomers.

Besides being an ideal hunting ground for the Cepheids, M100 also contains other distance indicators that can in turn be calibrated with the Cepheid result. This majestic, face-on, spiral galaxy has been host to several supernovae, which are also excellent distance indicators. Individual supernovae (called Type II, massive exploding stars) can be seen to great distances, and, so, can be used to extend the cosmic distance scale well beyond Virgo.

As a crosscheck on the HST results, the distance to M100 has been estimated using the Tully-Fisher relation (a means of estimating distances to spiral galaxies using the maximum rate of rotation to predict the intrinsic brightness) and this independent measurement also agrees with both the Cepheid and supernova "yardsticks."

HST Key Projects are scientific programs that have been widely recognized as being of the highest priority for the Hubble Space Telescope and have been designated to receive a substantial amount of observing time on the telescope. The Extragalactic Distance Scale Key Project involves discovering Cepheids in a variety of important calibrating galaxies to determine their individual distances. These distances then will be used to establish an accurate value of the Hubble Constant.

----------------------------------------------------------------------

The Key Project Team on the Extragalactic Distance Scale consists of Sandra Faber, Garth Illingworth & Dan Kelson (Univ. of California, Santa Cruz), Laura Ferrarese & Holland Ford (Space Telescope Science Institute), Wendy Freedman, John Graham, Robert Hill & Randy Phelps (Carnegie Institution of Washington), James Gunn (Princeton University), John Hoessel & Mingsheng Han (University of Wisconsin), John Huchra (Harvard-Smithsonian Center for Astrophysics), Shaun Hughes (Royal Greenwich Observatory), Robert Kennicutt, Paul Harding, Anne Turner & Fabio Bresolin (Univ. of Arizona), Barry Madore & Nancy Silbermann (JPL, Caltech), Jeremy Mould (Mt. Stromlo, Australian National University), Abhijit Saha (Space Telescope Science Institute), and Peter Stetson (Dominion Astrophysical Observatory).

* * * * * * * * * * * *

The Space Telescope Science Institute is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) for NASA, under contract with the Goddard Space Flight Center, Greenbelt, MD. The Hubble Space Telescope is a project of international cooperation between NASA and the European Space Agency (ESA).

The Wide Field and Planetary Camera 2 was developed by the Jet Propulsion Laboratory (JPL) and is managed by the Goddard Space Flight Center for NASA's Office of Space Science.

From the new Cepheid distance measurements noted above, this cluster is 50 Mly from us (+- 8%) or 15.1 Mpc.

There are a number of small clusters along with our local group and the Virgo cluster, a conglomerate called a supercluster. 1015 Solar masses centered on the Virgo cluster.

Internet article placing the Virgo Cluster at 50 million ly from Earth, half the previous value. Age of universe then half of previous value or 7-11 Billion years. (see cluster age of 14 billion years on Day 15.)

Slide GH 23 NGC 4881 & Coma Cluster

JPEG: NGC4881 & Coma Cluster

http://oposite.stsci.edu/pubinfo/jpeg/NGC4881.jpg

The brightest object in this picture is NGC 4881, approximately centered here in the Planetary Camera (the small quadrant). It is a 13th-magnitude elliptical galaxy in the outskirts of the Coma Cluster, a great cluster of galaxies more than 5 times farther away than the Virgo Cluster. The radical velocity (redshift) of NGC 4881, based on the Doppler displacement of lines in its spectrum, is about 7000 km/sec. Except for a 16th-magnitude Coma spiral at the right and a few foreground stars of the Milky Way, nearly everything else in this field lies far beyond the Coma Cluster. There is a fascinating assortment of background galaxies, including an apparent galaxian merger in progress.

Purpose: This HST-WFPC2 observation was made to explore the use the globular star clusters surrounding NGC 4881 as distance indicators for inferring the distance to the Coma Cluster. They are barely visible point sources in this reproduction. The distance to the Coma Cluster is an important cosmic yardstick for scaling the over all size of the universe, because Coma (unlike Virgo) is far enough away that regional departures from a smooth expansion of the universe should not be a major source of uncertainty if Coma is used for estimating the age and rate of expansion (the Hubble Constant).

Discussion groups on Cepheids 15 min. Each discussion group does one of the problems. Each member of the group should know how to do their calculation when the group is done.

1. In 1784 John Goodricke, a deaf, mute, 19-year-old English Amateur Astronomer discovered that the star Delta Cephei (the 4th brightest star in the constellation Cephius) varied in brightness. Stars of this kind are now called (Type I) Cepheid Variable stars. From the attached light curve for Delta Cephei, determine its period of oscillation. P =

 

 

 

 

Discussion groups on Cepheids 15 min. Each discussion group does one of the problems. Each member of the group should know how to do their calculation when the group is done.

2. For a Type I Cepheid Variable star with a period of 5.4 days, use the Period-Luminosity relation to find its luminosity in "Solar Luminosities," defined as how bright the sun looks from 10 parsecs away. (One parsec is 3.26 light years.)

L@10pc =

 

 

 

 

Discussion groups on Cepheids 15 min. Each discussion group does one of the problems. Each member of the group should know how to do their calculation when the group is done.

3. Delta Cephei appears, on average, 2 1/4 times brighter than the sun would if both were 10 pc away from us. If we know that it has a true luminosity of L@10pc = 2,150 LSolar, but it has an apparent luminosity of L@D = 2.28 LSolar, it must be further away than 10 pc. Use the inverse square law or to find how much farther than must it be away from us? D =

 

Discussion groups on M100 Cepheid 30 min. Each group does the entire sequence.

1. What is the period of oscillation for the C41 Cepheid in M100? P =

 

2. For the Type I Cepheid Variable star with the period you got above, use the Period-Luminosity relation to find its luminosity in "Solar Luminosities," defined as how bright the sun looks from 10 parsecs away. (One parsec is 3.26 light years.) L@10pc =

3. C31 varies in brightness from 3.89 × 10-9 LSolar to 7.44 × 10-9 LSolar.Taking the average value for L@D = 5.60 × 10-9 LSolar, we have a star that appears, 1/100-millionth as bright as the sun would if both were 10 pc away from us. You calculated its true luminosity, but it has an apparent luminosity much smaller, 5.60 × 10-9 LSolar, so it must be much further away than 10 pc. Use the inverse square law or to find how much farther than must it be away from us? D =

4. What is M100’s distance in lyr? D =

 

 

Discussion groups on M100 Cepheid 30 min. Each group does the entire sequence.

1. What is the period of oscillation for the C41 Cepheid in M100? P = {

2. For the Type I Cepheid Variable star with the period you got above, use the Period-Luminosity relation to find its luminosity in "Solar Luminosities," defined as how bright the sun looks from 10 parsecs away. (One parsec is 3.26 light years.) L@10pc =

3. C31 varies in brightness from 3.89 × 10-9 LSolar to 7.44 × 10-9 LSolar.Taking the average value for L@D = 5.60 × 10-9 LSolar, we have a star that appears, 1/100-millionth as bright as the sun would if both were 10 pc away from us. You calculated its true luminosity, but it has an apparent luminosity much smaller, 5.60 × 10-9 LSolar, so it must be much further away than 10 pc. Use the inverse square law or to find how much farther than must it be away from us? D =

4. What is M100’s distance in lyr? D =