Deck 12: The Deaths and Remnants of Stars

Question 1

We have considered red dwarf stars that convert all their hydrogen to helium and then stop evolving.What is the maximum mass limit of a red dwarf star?

A) 0.4 M
B) 0.8 M
C) 2 M
D) 8 M

Answer 1

0.4 M

Question 2

In a star's evolutionary life,the asymptotic giant branch (AGB)is the:

A) helium core fusion phase.
B) pre-main-sequence core hydrogen fusion phase.
C) hydrogen shell fusion phase prior to helium ignition in the core.
D) helium shell fusion phase.

Answer 2

helium shell fusion phase.

Question 3

A star on the asymptotic giant branch (AGB)is a:

A) cool main-sequence star.
B) blue supergiant.
C) star in its first red giant phase.
D) red supergiant.

Answer 3

red supergiant.

Question 4

Consider a group of stars with masses up to eight times the mass of the Sun.Stars of which masses undergo a helium flash?

A) less than 0.4 M
B) 0.4 M to 2 M only
C) 2 M to 8 M only
D) all stars 0.4 M to 8 M

Question 5

Consider a group of stars with masses up to eight times the mass of the Sun.Stars of which masses will pass along the horizontal branch?

A) less than 0.4 M
B) 0.4 M to 2 M only
C) 2 M to 8 M only
D) all stars 0.4 M to 8 M

Question 6

A star ascending the red giant branch for the second time in the asymptotic giant branch phase will have:

A) no nuclear reactions in the core, but a helium-fusion shell outside the core, which itself is surrounded by a shell of hydrogen.
B) no fusion reactions; the star has used up all its nuclear fuel.
C) hydrogen-fusion reactions occurring in the core.
D) no nuclear reactions occurring in the core but hydrogen fusion in a shell outside the core.

Question 7

In this chapter,we are dealing with intermediate-mass stars.What are we using as the upper mass limit of this classification?

A) 0.4 M
B) 2.0 M
C) 8.0 M
D) 16.0 M

Question 8

The nuclear process in which helium fusion occurs in the deep interiors of red giant stars produces:

A) iron nuclei.
B) carbon and oxygen nuclei.
C) hydrogen nuclei by the splitting of helium nuclei.
D) pure energy from the nuclear mass.

Question 9

The characteristics of a red supergiant star are the brightness of _____ and a diameter of _____.

A) 10,000 Suns; about Mars' orbit
B) the Sun; Mercury's orbit
C) about 1 million Suns; the whole solar system
D) about 10,000 Suns; 1/10 that of the Sun

Question 10

What are the main products of helium nuclear fusion in red giant stars?

A) hydrogen nuclei by nuclear fission
B) energy from the complete transformation of the mass of helium to energy
C) iron nuclei
D) carbon and oxygen nuclei

Question 11

Helium nuclear reactions take place in a shell around the core of a low-mass star during its:

A) horizontal-branch phase.
B) first red giant phase.
C) main-sequence phase.
D) asymptotic giant branch phase.

Question 12

During which phase of a low-mass star's life does helium shell fusion occur?

A) main sequence
B) asymptotic giant branch
C) first red giant
D) horizontal branch

Question 13

Helium nuclear reactions (helium fusion)produce primarily:

A) carbon and oxygen.
B) carbon and silicon.
C) iron.
D) oxygen and neon.

Question 14

A low-mass giant on the horizontal branch fuses hydrogen into helium in its core.The core temperature is insufficient to fuse helium into carbon.So what nuclear reaction does happen next?

A) shell helium fusion
B) core oxygen fusion
C) shell beryllium fusion
D) core beryllium fusion

Question 15

How much brighter than its main-sequence luminosity will a Sun-like star become at the asymptotic giant branch (AGB)phase of its life?

A) 10 times brighter
B) 10⁴ times brighter
C) twice as bright
D) 10³ times brighter

Question 16

The structure of the deep interior of a low-mass star near the end of its life is a(n):

A) carbon-oxygen core, a shell around the core where helium nuclei are undergoing fusion, and a surrounding shell of hydrogen.
B) inactive hydrogen core and a helium shell undergoing nuclear fusion surrounded by a carbon-oxygen shell.
C) turbulent mixture of hydrogen, helium, carbon, and oxygen in which only helium continues to undergo nuclear fusion.
D) helium core surrounded by a thin hydrogen shell undergoing nuclear fusion with very small concentrations of heavier nuclei.

Question 17

Low-mass stars can ascend the H-R diagram in two evolutionary phases called giant phases.What is the difference between them?

A) In the first, the primary production of energy is from hydrogen burning in the core. In the second, the primary production of energy is from helium burning in the core.
B) In the first, the primary production of energy is from hydrogen burning in a shell around the core. In the second, the primary production of energy is from helium burning in a shell around the core.
C) In the first, the star's track on the Hertzsprung-Russell diagram lies along the red- giant branch. In the second, the track lies along the horizontal branch.
D) During the first red giant phase, the star moves up and to the right along the red giant branch. During the second red giant phase, the star's track is down and to the left along the same red giant branch.

Question 18

Consider a group of stars with masses up to eight times the mass of the Sun.Stars of which masses will end up as pure helium?

A) less than 0.4 M
B) 0.4 M to 2 M only
C) 2 M to 8 M only
D) all stars 0.4 M to 8 M

Question 19

Nuclear fusion reactions of helium produce primarily:

A) nitrogen and neon nuclei.
B) iron nuclei.
C) beryllium and lithium nuclei.
D) carbon and oxygen nuclei.

Question 20

Consider a group of stars with masses up to eight times the mass of the Sun.Stars of which masses will pass along the asymptotic giant branch?

A) less than 0.4 M
B) 0.4 M to 2 M only
C) 2 M to 8 M only
D) all stars 0.4 M to 8 M

Question 21

What is the difference between a helium flash and a helium shell flash?

A) A helium flash occurs when the core becomes supported by electron-degeneracy pressure; a helium shell flash occurs when the helium shell becomes supported by electron-degeneracy pressure.
B) All stars with mass less than eight times the mass of the Sun undergo a helium flash, but only those between two and eight times the mass of the Sun undergo a helium shell flash.
C) A helium flash occurs just once; a helium shell flash can repeat many times.
D) A helium flash results in a supernova; a helium shell flash results on a planetary nebula.

Question 22

Which important component does a planetary nebula contribute to the interstellar medium?

A) molecules such as NH₃ and CH₄, which contribute to giant molecular clouds
B) UV light that photoionizes hydrogen. The hydrogen, on recombination, produces the red Balmer α light by which we see interstellar emission nebulae.
C) rotational motion from the original star, which serves to concentrate interstellar matter into new stars and planetary systems
D) nuclei of moderately heavy elements, major components of planets such as our own

Question 23

A planetary nebula is a(n):

A) contracting spherical cloud of gas surrounding a newly formed star in which planets are forming.
B) expanding gas shell surrounding a hot, burned-out stellar core.
C) disk-shaped nebula of dust and gas around a relatively young star, from which planets will eventually form.
D) nebula caused by the supernova explosion of a massive star.

Question 24

The light from the expanding shell of gas in a planetary nebula consists of:

A) bright emission lines of hydrogen, carbon, nitrogen, and other elements.
B) thermal (blackbody) radiation with peak emission in the infrared.
C) the light of the central white dwarf star reflected and scattered by dust and gas in the shell.
D) thermal (blackbody) radiation with peak emission in the ultraviolet.

Question 25

The diameter of a typical planetary nebula,after 10,000 years of expansion,is:

A) about 1000 ly.
B) about 1 AU.
C) only about 3 to 5 stellar diameters.
D) a few light-years.

Question 26

A planetary nebula is:

A) a shell of ejected gases.
B) the formation stages of planets around stars.
C) a gas cloud surrounding a planet after its formation.
D) the spherical cloud of gas produced by a supernova explosion.

Question 27

In astronomical terms,planetary nebulae are:

A) very long-lived objects, having been in existence since just after the Big Bang at the beginning of the universe.
B) relatively short-lived, existing around the central white dwarf star for millions of years before slowly spreading into space.
C) relatively long-lived since they form when the original stars form and remain as slowly rotating shells for the whole of their lifetimes of several billion years.
D) very short-lived, with lifetimes of about 50,000 years.

Question 28

The shell of a planetary nebula is measured by the Doppler shift of emission lines to be expanding outward at a speed of 10⁴ m/s,while its radius is measured to be 1 ly,or about 10¹⁶ m.Roughly how long has the shell been expanding? (Hint: 1 year = 3.15 × 10⁷ sec.)

A) 30 years
B) 30,000 years
C) 30 million years
D) 10¹² years

Question 29

In the asymptotic giant branch (AGB)phase of their lives,stars like the Sun lose mass to space through an outflowing "stellar wind." Over a period of 1000 years,how much mass would such a star eject?

A) almost 1/10 solar mass
B) about 10-⁵ solar mass
C) about 1/100 solar mass
D) almost none since most of the mass flows back in at the star's poles

Question 30

What is the last nuclear fusion stage in the life of a low-mass star like the Sun?

A) fusion of silicon nuclei to form iron
B) fusion of oxygen nuclei to form sulfur
C) fusion of helium nuclei to form carbon and oxygen
D) fusion of hydrogen nuclei to form helium

Question 31

A planetary nebula is a:

A) gas shell, the atmosphere of a red giant star, slowly expanding away from the core of the star.
B) contracting spherical cloud of gas surrounding a newly formed star in which planets are forming.
C) nebula caused by the supernova explosion of a massive star.
D) disk-shaped nebula of dust and gas rotating around a relatively young star in which planets will eventually form.

Question 32

What happens to the surface of a low-mass star after the helium core and shell fusion stages are completed?

A) The star stabilizes at the size of a red giant star, radiation pressure from below balancing gravity from the core, and slowly cools for the rest of its life.
B) The star is spun off into space to make a spiral structure known as a spiral galaxy.
C) The star is propelled slowly away from the core to form a planetary nebula.
D) The star contracts back onto the core and becomes hot enough to undergo further hydrogen fusion, leading to a very hot and active white dwarf star.

Question 33

The event that follows the asymptotic giant branch (AGB)phase in the life of a low-mass star is:

A) the ejection of a planetary nebula.
B) core collapse and a supernova explosion.
C) helium flash and the start of helium fusion in the core.
D) the onset of hydrogen fusion in the core.

Question 34

What will be the mass of the Sun at the end of its asymptotic giant branch (AGB)phase,due to mass loss to space by its stellar wind?

A) still almost 1 solar mass since mass loss is negligible for a low-mass star like the Sun
B) between 0.1 and 0.2 solar mass
C) about 0.8 solar mass
D) about 0.5 solar mass

Question 35

In the process of helium shell fusion in a low-mass star near the end of its life,the star moves upward and to the right on the asymptotic giant branch of the Hertzsprung-Russell diagram.In this process,the star is:

A) contracting, cooling, and hence becoming less luminous.
B) expanding, heating up, and becoming more luminous.
C) contracting, becoming hotter, and becoming much less luminous.
D) expanding, cooling, and becoming more luminous.

Question 36

A planetary nebula is created:

A) over several hundred years, during mass transfer in a close binary star system.
B) over a few thousand years or more, in a slow expansion away from a low-mass star, driven by a series of thermal pulses from helium fusion.
C) in hours or less, during the explosion of a massive star.
D) in seconds, during the helium flash in a low-mass star.

Question 37

What physical process provides the energy for the ejection of a planetary nebula from a low-mass star?

A) transfer of hydrogen-rich material onto the surface of a white dwarf from its companion in a binary star system
B) helium shell flashes in the helium fusion shell
C) core collapse and the ensuing shock wave
D) collision with another star

Question 38

How much mass are planetary nebulae estimated to return to the interstellar medium each year over the Galaxy as a whole?

A) about 50,000 solar masses
B) about 5 × 10⁸ solar masses
C) about 5 solar masses
D) about 500 solar masses

Question 39

A planetary nebula is a:

A) cloud of gas surrounding a very young star in which planets are expected to form.
B) spherical, rapidly expanding cloud of gas produced by a supernova explosion.
C) gas cloud surrounding a planet after its formation.
D) shell of gases ejected from the surface of red giant star.

Question 40

The fraction of the mass of a low-mass star that is ejected in its evolutionary phases,up to and including the planetary nebula phase,is:

A) almost the entire star, more than 95%.
B) significant, up to 80%.
C) extremely small, less than 1 part in 10⁴, since it is only the star's atmosphere that has been ejected.
D) very small, close to 10%.

Question 41

How is it that white dwarfs,which are relatively small,can have surface temperatures of several tens of thousands of Kelvins?

A) They are actually very similar in size and temperature to small main sequence stars such as red dwarfs.
B) The nuclear fusion in the core of a white dwarf involves carbon and oxygen, and this produces more energy and heat than either hydrogen or helium fusion.
C) The surface of the white dwarf is actually the core since the cooler outer layers have been blown off.
D) Because white dwarfs are fully convective, the nuclear fusion takes place on the surface.

Question 42

The Sun will end its life by becoming a:

A) molecular cloud.
B) black hole.
C) white dwarf.
D) pulsar.

Question 43

A white dwarf is a(n):

A) object like Jupiter that was not quite massive enough to become a star.
B) small, very hot, low-mass star.
C) type of small protostar.
D) hot, main-sequence star.

Question 44

A white dwarf,the surviving core of a low-mass star toward the end of its life,can be found on the Hertzsprung-Russell diagram:

A) at the upper-left end of the main sequence since its surface temperature is extremely high.
B) at the bottom end of the main sequence, along which it has evolved throughout its life.
C) below and to the left of the main sequence.
D) above and to the right of the main sequence since it evolved there after its hydrogen-fusion phase.

Question 45

At which phase of its evolutionary life is a white dwarf?

A) post-supernova phase, the central remnant of the explosion
B) just at main-sequence, or hydrogen-fusion, phase
C) very late for small-mass stars, in the dying phase
D) in its early phases, soon after formation

Question 46

What percentage of all matter ejected into the interstellar medium in the Milky Way Galaxy each year by stars is contributed by planetary nebulae?

A) less than 1%
B) about 50%
C) between 10 and 20%
D) almost 100%

Question 47

What are thermal pulses?

A) They are the loops formed on the H-R diagram as the evolutionary tracks of low-mass stars move beyond the planetary nebula stage.
B) They are the pulses of radiation emitted during helium shell flashes.
C) This is another name for the high-luminosity pulses of radiation emitted periodically by variable stars.
D) They are the burst of radiation given off during a nova.

Question 48

The "star" that is seen at the center of a planetary nebula is:

A) a small, hot, and very dense white dwarf star.
B) composed almost entirely of neutrons and spinning rapidly.
C) the accretion disk around a black hole.
D) a planet in the process of formation.

Question 49

The two longest stages in the lifetime of a solar-mass star,each lasting billions of years,are:

A) protostar and main sequence.
B) main sequence and red giant.
C) red giant and white dwarf.
D) main sequence and white dwarf.

Question 50

A white dwarf is about the same size as

A) the Sun.
B) Earth.
C) the total solar system.
D) a major city.

Question 51

Each of the following statements about white dwarfs is true EXCEPT ONE.Which is the exception?

A) They generate energy by core fusion of carbon and hydrogen to produce oxygen.
B) Novae are generated by white dwarfs in close binary systems.
C) A white dwarf can be the source of more than one nova.
D) The Chandrasekhar limit restricts the maximum mass of a white dwarf.

Question 52

The interiors of white dwarfs are characteristically:

A) mainly carbon and oxygen nuclei supported by electron degeneracy pressure in a volume about the size of the Sun.
B) mostly hydrogen nuclei supported by normal gas pressure due to the very high gas temperature, in a volume about the size of the Earth.
C) mainly carbon and oxygen nuclei supported by electron degeneracy pressure in a volume about the size of the Earth.
D) mainly helium nuclei supported by electron degeneracy pressure in a volume with a radius about 11 times that of the Earth, about the volume of Jupiter.

Question 53

Planetary nebulae are so named because:

A) they were extended objects, often green-colored, that looked like planets when first seen by nineteenth-century observers through their telescopes.
B) the ejected material is rich in carbon and oxygen, necessary elements for the manufacture of planets in the nebulae surrounding stars.
C) they rotate slowly and condense into planetary objects around a central star.
D) their spectra appear to be similar to the spectra of the giant gas planets in the solar system.

Question 54

What is the name given to the type of planetary nebula in which a doughnut-shaped cloud of gas and dust in the plane of the equator channels the outflow in opposite directions toward the poles?

A) dumbbell nebula
B) axial planetary nebula
C) doughnut planetary nebula
D) bipolar planetary nebula

Question 55

Stars that have ejected a planetary nebula go on to become:

A) red giants.
B) supernovae.
C) protostars.
D) white dwarfs.

Question 56

In what manner does an isolated white dwarf generate energy?

A) hydrogen fusion
B) helium fusion
C) gravitational contraction
D) An isolated white dwarf does not generate energy.

Question 57

Usually,ideal gases increase their pressure and volume when heated and decrease their pressure and volume when cooled.Do these rules apply to stars?

A) No. Stars never follow the rules for ideal gases, even approximately.
B) Yes. Stars in all stages follow these rules quite closely.
C) No. Protostars have cores of degenerate matter in which the pressure is independent of the temperature.
D) No. White dwarfs are essentially degenerate matter in which the pressure is independent of the temperature.

Question 58

The energy-generation process inside a white dwarf is:

A) the combining of protons and electrons to form neutrons within its core.
B) hydrogen fusion.
C) nonexistent-a white dwarf is simply cooling by radiating its original heat.
D) the helium flash-very efficient and rapid helium fusion.

Question 59

The final remnant of the evolution of a red giant star that has ejected a planetary nebula is a:

A) protostar.
B) blue supergiant.
C) white dwarf.
D) supernova.

Question 60

A white dwarf is at what stage of its evolution?

A) protostar phase, just after formation, beginning to generate energy by nuclear fusion
B) main-sequence phase, "middle-aged," generating energy by fusion of hydrogen to helium
C) post-supernova stage, after the explosion of a star
D) very late phase of evolution, no longer generating energy

Question 61

As a white dwarf evolves,the direction of its motion on the Herzsprung-Russell diagram is from upper left to lower right,which means that:

A) its size or radius slowly increases as it cools until it ends up as a red giant star.
B) its size or radius remains constant as it cools and becomes less luminous.
C) it heats up as it shrinks because of the release of gravitational energy, ending up as a very hot but very small star.
D) it shrinks as it cools, eventually becoming a cold, black hole in space.

Question 62

The one characteristic shared by all solitary white dwarfs is that they:

A) have stopped generating thermonuclear energy but continue to shrink, thereby releasing gravitational energy as heat.
B) have never generated either thermonuclear or gravitational energy but are slowly cooling after their production in a supernova explosion.
C) are generating thermonuclear energy but are maintaining a constant radius and hence are not releasing gravitational energy.
D) have ceased to generate energy by thermonuclear processes or gravitational contraction and are slowly cooling down.

Question 63

When a solar-mass star is ejecting a planetary nebula,the temperature of its exposed core can reach 100,000 K.How does this temperature compare with the core temperature when the star is on the main sequence?

A) The exposed core is cooler simply because it is exposed to the cold regions of space.
B) The exposed core is cooler because it is at the end of its fuel supply.
C) The exposed core is hotter because it was heated by helium fusion rather than hydrogen fusion.
D) The exposed core is hotter because it was heated by carbon-oxygen fusion rather than hydrogen fusion.

Question 64

A nova is a sudden brightening of a star that occurs when:

A) material is transferred onto the surface of a white dwarf from a companion star in a binary system, then subsequently blasted into space by a runaway thermonuclear explosion (leaving the white dwarf intact to repeat the process).
B) material from a companion star is transferred onto the surface of a white dwarf star in a binary system, after which runaway carbon-fusion reactions cause the entire white dwarf to be destroyed in an explosion.
C) the electron degenerate iron core of a massive star collapses after its mass becomes greater than the Chandrasekhar mass limit.
D) material is transferred onto a neutron star from a companion star in a binary system, causing the neutron star to collapse into a black hole.

Question 65

Each of the following statements is true about novae EXCEPT ONE.Which is the exception?

A) Novae occur when two white dwarfs collide.
B) Novae are named after the constellation and the year in which they are discovered.
C) A white dwarf can be the origin of more than one nova.
D) The light curve for a typical nova shows a rapid rise followed by a gradual decline lasting a few months.

Question 66

One distinctive physical characteristic of matter inside a white dwarf star is that it is:

A) composed only of protons, with electrostatic repulsion preventing stellar collapse.
B) of extremely high density compared with ordinary stellar matter.
C) composed only of neutrons.
D) composed only of electrons in a degenerate state.

Question 67

Which type of star or stellar remnant can have a mass no larger than about 1.4 times the mass of the Sun,or else it will collapse under its own gravity?

A) a red giant
B) a black hole
C) a neutron star
D) a white dwarf

Question 68

The nova phenomenon,an occasional and sometimes repeated intense brightening of a star by a factor of about 10⁶,is caused by:

A) a beam of radiation from a nearby pulsar illuminating the surface of a red giant star and inducing rapid and intense heating.
B) the capture and rapid compression of matter by a black hole.
C) the explosion of a single massive star at the end of its thermonuclear fusion phases.
D) explosive hydrogen fusion on the surface of a white dwarf star after mass transfer from a companion star in a binary system.

Question 69

The stars that eventually become white dwarfs start life with solar masses less than:

A) 25.
B) 8.
C) 1.4.
D) 3.

Question 70

A white dwarf,as it evolves,undergoes which change?

A) Its temperature remains constant, but its radius and therefore its luminosity decrease.
B) Luminosity and size decrease, while its temperature remains constant.
C) It shrinks in size, the resulting release of gravitational energy keeping both luminosity and temperature constant.
D) Luminosity and temperature decrease.

Question 71

Are crystalline stars or crystalline remnants of stars possible? Why or why not?

A) No. Stars and stellar remnants are too hot to crystallize.
B) Yes. They are the likely outcome of the cooling of a white dwarf.
C) No. The forces needed to crystallize a star would actually cause the star to collapse gravitationally into a black hole.
D) Yes. They are the likely outcome of the creation of iron in the core of a massive star.

Question 72

A white dwarf is supported from collapse under gravity by:

A) pressure of the gas heated by nuclear fusion reactions in its core.
B) centrifugal force due to rapid rotation.
C) degenerate-electron pressure in the compact interior.
D) pressure of the gas heated by nuclear fusion reactions in a shell around its core.

Question 73

Recent observations reveal that the outer parts of novae are composed of:

A) smooth shells of expanding gas.
B) shells that originate from bipolar jets.
C) thousands of clumps of gas.
D) warped rings of gas and dust.

Question 74

The star Sirius (α Canis Majoris)is actually a binary star in which the brighter,more massive star (Sirius A)is an A-type main-sequence star and the fainter,less massive star (Sirius B)is a white dwarf.How is this system MOST likely to have formed?

A) Sirius A formed as a single star and later captured a passing white dwarf.
B) Sirius B formed first and evolved to become a white dwarf; capture of gas and dust from interstellar clouds then resulted in the formation of Sirius A.
C) Sirius B was initially more massive than Sirius A and evolved faster; it then became less massive due to mass loss to space and mass transfer to Sirius A.
D) Sirius A was always the more massive of the two and became a red giant; then mass transfer to Sirius B accelerated the evolution of Sirius B and caused it to become a white dwarf.

Question 75

When a typical nova explodes,it brightens in a few hours by a factor of:

A) 10⁸ to 10¹⁰.
B) 2 to 5.
C) 10⁴ to 10⁶.
D) 10 to 100.

Question 76

How does a white dwarf generate its energy?

A) It no longer generates energy but is slowly cooling as it radiates away its heat.
B) Nuclear fusion of hydrogen into helium is producing energy in its core.
C) Nuclear fission of heavy elements in the central core is releasing energy.
D) Gravitational potential energy is released as the star slowly contracts.

Question 77

White dwarfs are supported from gravitational collapse by:

A) centrifugal force due to rapid rotation.
B) degenerate-electron pressure.
C) nuclear fusion reactions in their cores.
D) nuclear fusion reactions in a shell around the core.

Question 78

The mechanism that gives rise to the phenomenon of the nova is:

A) the impact and subsequent explosion of a large comet nucleus on a star's surface.
B) material falling into a black hole and being condensed to the point where a thermonuclear explosion is produced.
C) the complete disintegration of a massive star due to a runaway thermonuclear explosion in the star's interior.
D) matter from a companion star falling onto a white dwarf in a close binary system, eventually causing a nuclear explosion on the dwarf's surface.

Question 79

What is it that keeps a white dwarf from collapsing inward on itself?

A) electron degeneracy, or "quantum crowding"
B) the physical size of the neutrons of which this star is composed
C) convection currents, or updrafts, from the nuclear furnace
D) normal gas pressure

Question 80

Which type of dwarf is largest?

A) white
B) red
C) brown
D) All are about the same size.