From Stars to Planets: Births and Deaths on Cosmic Scale

Planetary system development (artist’s impression)

Mov­ing along on our world build­ing quest, I’ll start talk­ing about plan­ets and grad­u­al­ly mov­ing towards ter­res­tri­al plan­ets and their prop­er­ties.

Plan­et hab­it­abil­i­ty depends on sev­er­al fac­tors: galac­tic envi­ron­ment of the plan­e­tary sys­tem (which includes the abun­dance of met­als), sta­bil­i­ty of the plan­e­tary sys­tem, evo­lu­tion, age and activ­i­ty of the star (or stars), atmos­phere, mag­ne­tos­phere, and dis­tance of a plan­et from its star. All this can make hab­it­able worlds extreme­ly rare. But we don’t take “no” for an answer, right?

Plan­e­tary sys­tem for­ma­tion

A good (if not the best) exam­ple of plan­e­tary sys­tem for­ma­tion and evo­lu­tion is our own Solar Sys­tem.

Stars form from clouds of gas, dust and ices. When a cloud of inter­stel­lar mat­ter cross­es the spi­ral arm of a galaxy, it begins to form clumps. The grav­i­ta­tion­al forces with­in the clumps cause them to con­tract, form­ing pro­to­stars. The cen­ter of a pro­to­star may reach a tem­per­a­ture of sev­er­al mil­lions of degrees Cel­sius. At this high tem­per­a­ture, a fusion reac­tion begins. The ener­gy released by this reac­tion pre­vents the pro­to­star from con­trac­tion. Accord­ing to the most con­ser­v­a­tive esti­mates it could take a hun­dred mil­lion years for a new sun to form (Mont­mer­le et al. 2006).

Plan­e­tary sys­tem for­ma­tion coin­cides with the process of star for­ma­tion, when a pro­to­plan­e­tary disc is formed around a young stel­lar object. Mass and metal­lic­i­ty of the star and pro­to­plan­e­tary disc impacts the type and size of plan­e­tary sys­tems they might pos­sess.

Hub­ble image of pro­to­plan­e­tary discs in the Ori­on Neb­u­la, a light-years-wide “stel­lar nurs­ery” prob­a­bly very sim­i­lar to the pri­mor­dial neb­u­la from which our Sun formed

For a start to pos­sess ter­res­tri­al planes it would have to have formed from a neb­u­la con­tain­ing suf­fi­cient heavy ele­ments. The star would have to be Pop­u­la­tion I and younger than the age of for­ma­tion of the galac­tic disc (~10 Gyr). Over this peri­od, the metal­lic­i­ty of the inter­stel­lar medi­um has risen due to the prod­ucts of nucle­osyn­the­sis from suc­ces­sive gen­er­a­tions of stars.

Nat­u­ral­ly, one might expect max­i­mum mass con­den­sa­tion with­in the pre-plan­e­tary neb­u­la to vary with stel­lar lumi­nos­i­ty. The cen­tral den­si­ty of neb­u­lar dust, the para­me­ter from which the mass of the neb­u­la is scaled, varies in direct pro­por­tion to the mass and metal­lic­i­ty of the cen­tral star (Fogg, 1992). For­mu­las for the radius and den­si­ty of neb­u­lar dust (the size of the pro­to­plan­e­tary disc and pos­si­ble plan­e­tary sys­tem scale) can be tak­en from the same paper. The ACCRETE algo­rithm, men­tioned in it, can be tak­en here. The best option from that list is the Star­form pro­gram (writ­ten in C) by Matt Bur­dick, 1988, which is an enhance­ment of the basic accre­tion code with more out­put options.

Plan­et for­ma­tion incor­po­rates four dis­tinct stages (Lis­sauer, 1993).

At the ini­tial stage grains con­dense and grow in the hot neb­u­lar disk, grad­u­al­ly set­tling to the mid-plane. The com­po­si­tion of the grains is deter­mined by the local tem­per­a­ture of the neb­u­la.

Then, dur­ing the ear­ly stage growth of grains to km-sized plan­etes­i­mals occurs. Plan­etes­i­mals ini­tial­ly have low eccen­tric­i­ties (e) and incli­na­tions (i) due to gas drag.

At the mid­dle stage (oli­garchic growth) “focused merg­ing” leads to agglom­er­a­tion of plan­etes­i­mals into Moon-to Mars-sized “plan­e­tary embryos.” Pos­si­ble run­away accre­tion and sub­se­quent dynam­i­cal fric­tion (loss of momen­tum and kinet­ic ener­gy of mov­ing bod­ies through a grav­i­ta­tion­al inter­ac­tion with sur­round­ing mat­ter in space) may lead to polar­iza­tion of the mass dis­tri­b­u­tion: a few large bod­ies with low e and i in a swarm of much small­er plan­etes­i­mals with high e and i. The timescale for this process cor­re­lates inverse­ly with helio­cen­tric dis­tance. Kokubo and Ida (2000) sug­gest that plan­e­tary embryos form in <1 Myr at 1 AU, in ∼ 40 Myr at 5 AU, and in > 300 Myr past 10 AU. The for­ma­tion timescale and mass­es of plan­e­tary embryos are sen­si­tive to the sur­face den­si­ty of the disc.

Dur­ing the late stage, once run­away accre­tion has ter­mi­nat­ed due to lack of slow mov­ing mate­r­i­al, plan­e­tary embryos and plan­etes­i­mals grad­u­al­ly evolve into cross­ing orbits as a result of cumu­la­tive grav­i­ta­tion­al per­tur­ba­tions. This leads to radi­al mix­ing and giant impacts until only a few sur­vivors remain, which are the nuclei of the system’s plan­ets. The timescale for this process is approx­i­mate­ly 108 yrs.

Planetary system development (artist’s impression)
Plan­e­tary sys­tem devel­op­ment (artist’s impres­sion)

Because of the high­er tem­per­a­tures in the inner stel­lar sys­tem, accre­tion of ice and gas is inhib­it­ed so the plan­etes­i­mals grow into what is known as the rocky ter­res­tri­al plan­ets. Plan­e­tary growth is slowed down sig­nif­i­cant­ly once a gap is cleared with­in its orbit.

But dur­ing their life­times plan­ets con­tin­ue to grow by small amounts as they sweep up microm­e­te­or dust par­ti­cles or are impact­ed every few mil­lion years by larg­er aster­oids or comets.

Plan­etes­i­mals that are mod­est in size but did not merge to form larg­er objects, become aster­oids and comets. The close prox­im­i­ty of Jov­ian grav­i­ta­tion­al pull might result in pre­ven­tion of plan­etes­i­mals grow­ing larg­er, as it hap­pened in the Solar Sys­tem, lead­ing to for­ma­tion of the aster­oid belt.

The the for­ma­tion of giant plan­ets can also occur via the disk insta­bil­i­ty (also see the papers here, here, here and here). How­ev­er, if a disc mass is too small, the abil­i­ty of disk insta­bil­i­ty to pro­duce viable, self-grav­i­tat­ing clumps is sign­f­i­cant­ly com­pro­mised. Thus, core accre­tion remains as the favored for­ma­tion mech­a­nism for giant plan­ets in such low­er mass disks.

March 9th 2012 Update — A new accre­tion mod­el has been offered by Anne Hofmeis­ter, PhD, research pro­fes­sor of earth and plan­e­tary sci­ences and Robert Criss, PhD, pro­fes­sor in earth and plan­e­tary sci­ences at Wash­ing­ton Uni­ver­si­ty in St.Louis.

Water con­tent

The water con­tent of plan­etes­i­mals in a giv­en plan­e­tary sys­tem depends in a com­plex way upon a range of fac­tors includ­ing the mass and evo­lu­tion­ary char­ac­ter­is­tics of the pro­to­plan­e­tary disk, over­all metal­lic­i­ty of the mol­e­c­u­lar cloud clump from which the star is form­ing, and the posi­tions, mass­es and tim­ings of for­ma­tion of the system’s giant plan­ets.

Cham­bers (2003) found that the water con­tent of ter­res­tri­al plan­ets depends strong­ly on the eccen­tric­i­ty, mass and for­ma­tion time of the giant plan­ets, with larg­er val­ues of e and M lead­ing to dri­er plan­ets, while larg­er val­ues of giants time for­ma­tion time led to more volatile-rich plan­ets. He also found that sys­tems with low­er mass giant plan­ets form the most life-sus­tain­ing plan­ets.

Anoth­er study shows as well that a Jov­ian plan­et of larg­er mass forms a small­er num­ber of ter­res­tri­al plan­ets than a low­er-mass body, but the water con­tent of the ter­res­tri­al plan­ets does not vary sig­nif­i­cant­ly with “Jupiter” mass.

August 27th 2013 Update — New study sheds light on plan­ets in the hab­it­able zone of red dwarfs. More recent work refresh­es the pos­si­bil­i­ty of water on these dis­tant worlds, pre­vi­ous­ly expect­ed to be dry.

A job for a Jupiter

The biggest giant of the plan­e­tary sys­tem is usu­al­ly referred to as Jupiter (or a Jov­ian plan­et), giv­ing cred­it the Jupiter of the Solar Sys­tem.

It has been shown that an eccen­tric Jupiter pref­er­en­tial­ly ejects much of the water-rich mate­r­i­al beyond 2.5 AU, which caus­es the ter­res­tri­al plan­ets to be dry (Cham­bers and Cassen 2002, Ray­mond et al., 2004). It has also been shown that, for water-rich ter­res­tri­al plan­ets to form in the hab­it­able zone, a Jupiter-mass giant plan­et must be at least 3.5 AU from the star and much far­ther if its eccen­tric­i­ty is nonze­ro (Ray­mond 2006). A Jupiter-mass giant plan­et at 5 AU, even on a cir­cu­lar orbit, plays a neg­a­tive role in the water deliv­ery process, eject­ing more water-rich mate­r­i­al than it scat­ters inward (Ray­mond et al., 2005a).

Sys­tems with eJ > 0 tend to form ter­res­tri­al plan­ets with slight­ly high­er eccen­tric­i­ties than those with eJ = 0, and the total mass in ter­res­tri­al plan­ets is less for sys­tems with eccen­tric Jupiters. Dur­ing plan­e­tary for­ma­tion an eccen­tric Jupiter clears out the aster­oid region much more quick­ly than a low eccen­tric­i­ty Jupiter (eJ < 0.1), both by increased ejec­tion effi­cien­cy and, more sig­nif­i­cant­ly, a large increase in the num­ber of objects which col­lide with the Sun, as expect­ed from the results of Cham­bers and Wether­ill (2001). The result of this is that eccen­tric giant plan­ets tend to form volatile-poor ter­res­tri­al plan­ets (Ray­mond et al., 2004).

In our Solar sys­tem Jupiter also played a key role in the for­ma­tion of oth­er giants and is believed to be impor­tant to life on Earth. It helps to sta­bi­lize the orbits of the inner plan­ets, which in turn helps to sta­bi­lize Earth’s cli­mate. And it keeps the inner solar sys­tem rel­a­tive­ly free of comets and aster­oids that could cause dev­as­tat­ing impacts.

How­ev­er, if Jupiter was not in orbit around the Sun and Earth were the only plan­et orbit­ing our star, the eccen­tric­i­ty of its orbit would not vary over time. The Earth’s eccen­tric­i­ty varies pri­mar­i­ly due to inter­ac­tions with the grav­i­ta­tion­al fields of Jupiter and Sat­urn.

More recent sim­u­la­tions show that the fre­quent for­ma­tion of plan­e­tary-mass objects in the disk sug­gests the pos­si­bil­i­ty of con­struct­ing a hybrid plan­et for­ma­tion sce­nario, where the rocky plan­ets form lat­er under the influ­ence of the giant plan­ets in the pro­to­plan­e­tary disk (Shu-ichi­ro Inut­su­ka et al. 2010).

The snow line

In astro­physics the term refers to a par­tic­u­lar dis­tance in the solar neb­u­la from the cen­tral pro­to­sun where it is cool enough for hydro­gen com­pounds such as water, ammo­nia, and methane to con­dense into sol­id ice grains. Depend­ing on den­si­ty, that tem­per­a­ture is esti­mat­ed to be about 150K170K. A den­si­ty increase imme­di­ate­ly past the snow line is expect­ed due to the “cold trap” effect (Steven­son and Lunine, 1988). Thus, the low­er tem­per­a­ture in the neb­u­la beyond the frost line makes many more sol­id grains avail­able for accre­tion into plan­etes­i­mals and even­tu­al­ly plan­ets. The frost line there­fore sep­a­rates ter­res­tri­al plan­ets from Jov­ian plan­ets.

There is a large uncer­tain­ty in the posi­tion of the snow line in the solar neb­u­la. The stan­dard notion of a snow line around 4–5 AU can explain the rapid for­ma­tion of Jupiter in a high den­si­ty envi­ron­ment imme­di­ate­ly past the snow line. How­ev­er, volatile-rich class­es of aster­oids are found as close as 2–2.5 AU, and are pre­sum­ably a fos­sil record of ice-bear­ing mate­r­i­al. Mod­els of pro­to­plan­e­tary disks around T Tau­ri stars by Sas­selov and Lecar (2000) result in snow lines as close as 1 AU to the cen­tral stars, depend­ing pri­mar­i­ly on the stel­lar lumi­nos­i­ty and the rate of accre­tion­al heat­ing with­in the disk. As these quan­ti­ties evolve with time, so might the posi­tion of the snow line migrate with time.

Cur­rent­ly, the snow line of our solar sys­tem is around 2.7 AU, near the mid­dle of the aster­oid belt.

Snow line calc for­mu­la: SL =2.7*(Mstar/Msun)^2

It is pos­si­ble to have gas giants (or mini gas giants) inside the frost line. Close-in giant plan­ets (e.g. “hot Jupiters”, “hot Sat­urns”, “hot Nep­tunes” and Wet Giants) are thought to form far from their host stars and migrate inward, through the ter­res­tri­al plan­et zone, via torques with a mas­sive gaseous disk. Sev­er­al-Earth-mass plan­ets also form inte­ri­or to the migrat­ing Jov­ian plan­et, anal­o­gous to recent­ly dis­cov­ered “hot Earths”. Very-water-rich, Earth-mass plan­ets form from sur­viv­ing mate­r­i­al out­side the giant planet’s orbit, often in the hab­it­able zone and with low orbital eccen­tric­i­ties (Ray­mond et al, 2006).

Metal­lic­i­ty

High­er metal­lic­i­ty means that (for a fixed total pro­to­plan­e­tary disc mass) the amount of sol­id mate­r­i­al will be high­er. The abun­dance of raw mate­ri­als in a met­al-rich pro­to­plan­e­tary disc increas­es the sur­face den­si­ty and so accel­er­ates the build-up of gas giant cores in the inner 10 AU. Pol­lack et al. (1996) found that increas­ing the sur­face den­si­ty of solids by 50 per cent (equiv­a­lent to just +0.18 in [M/H]) reduced the time to form Jupiter from 8 to 2 Myr.

When sub­stan­tial cores can form while the disc is still in its ear­ly gas-rich phase (~10 Myr), they can accu­mu­late thick gaseous envelopes and also migrate inwards due to the vis­cous drag of the gas. This can pro­duce inner gas giants as observed. The gen­er­al effect of high­er sol­id abun­dance is to speed up core growth, and so there is much more time for giant plan­ets to form and migrate before the disc dis­ap­pears.

While the occur­rence of gas giant plan­ets is a sen­si­tive func­tion of stel­lar metal­lic­i­ty, the occur­rence of debris discs does not have this same depen­dence. This sug­gests that con­struc­tion of small­er plan­etes­i­mal bod­ies, such as those found in the Kuiper Belt, does not require enhanced metal­lic­i­ty. How­ev­er, core growth times are much longer in the out­er disc, at sev­er­al tens of AU. If it can take 3 Gyr for a Plu­to-sized core to form out at 100 AU (Keny­on & Brom­ley 2004), the gas would have dis­ap­peared much ear­li­er and so the plan­et could not have added an atmos­phere (Greaves 2005).

Plan­e­tary sys­tem death and (pos­si­ble) “life after death”

It is gen­er­al­ly believed that our Sun was cre­at­ed with­in a neb­u­lar cloud pro­duced by a super­no­va near­ly five bil­lion years ago. How­ev­er, plan­ets, includ­ing Earth, may have been rem­nants eject­ed from the dying solar sys­tem by a super­no­va.

Using our own solar sys­tem as an exam­ple (Schroder & Smith 2008) when the par­ent star became a red giant, the accel­er­at­ing pow­er of its solar winds would have blown away the life-sus­tain­ing atmos­pheres of its plan­ets which includ­ed air­borne microbes, cre­at­ing a neb­u­lar cloud at the far edges of the dying solar sys­tem.

The par­ent star may have lost between 40% to 80% of its mass before explod­ing (Kali­rai, et al. 2007; Liebert et al. 2005; Wachter et al. 2008) and its plan­ets would have sig­nif­i­cant­ly increased their orbital dis­tances and may have been eject­ed from its solar sys­tem even pri­or to super­no­va. Thus the super­no­va may have shat­tered but prob­a­bly did not atom­ize all its plan­ets.

A super­no­va cre­ates tremen­dous shock waves, shat­ter­ing plan­ets, and expelling most of the star and remain­ing plan­e­tary debris into the sur­round­ing inter­stel­lar medi­um. This debris even­tu­al­ly becomes part of the sur­round­ing neb­u­lar ring cre­at­ed by the solar winds, plan­e­tary atmos­pheres, and expelled mass of the dead star (Greaves 2005, van Dishoeck 2006).

There is also a pos­si­bil­i­ty that when a star goes super­no­va, it ejects molten iron into these neb­u­lar clouds. There­fore, plan­ets begin to form when debris comes into con­tact with and then sticks to the hot iron which becomes a plan­e­tary core (Joseph and Schild 2010a). Plan­e­tary cores there­fore, may be com­prised of the remains of the shat­tered plan­ets which had been expelled from the dead sys­tem. There­fore, some solar sys­tems may acquire ful­ly formed or bro­ken and shat­tered plan­ets which grow by accre­tion after they are cap­tured by the new pro­to­star.

Giv­en the pauci­ty of evi­dence for near­by stars the same age as the sun, it could be assumed only a few pro­to­stars may have been pro­duced by the super­no­va of the par­ent star. Thus, the par­ent star may have been only a few solar mass­es larg­er than the sun. This assump­tion is sup­port­ed by iso­topic analy­sis of the Murchi­son mete­orite. Mea­sur­ments of sil­i­con car­bide (Wern­er et al. 1994; Nit­tler & Hoppe 2005) and preso­lar SiC grains (Sav­ina et al. 2003) from the Murchi­son indi­cates that the grains and sil­i­con are most like­ly the residue of or were pro­duced sec­ondary to a super­no­va of a car­bon rich inter­me­di­ate mass star that was between 1.5 to 3 solar mass­es (Sav­ina et al. 2003). Thus, the Murchi­son may be a rem­nant of the par­ent star’s solar sys­tem, though this can’t be deter­mined at this time.

As only the esti­mat­ed mass of that star is avail­able and there is no infor­ma­tion on near­by stars at the time of super­no­va, a Hertzsprung-Rus­sell dia­gram can­not be applied to deter­mine the age of the par­ent star at the time of super­no­va. How­ev­er, based on the esti­mat­ed ages and life­times of oth­er inter­me­di­ate mass stars (Pil­lit­teri and Fava­ta 2008) it can be esti­mat­ed that a par­ent star of between 1.5 and 3 solar mass­es was at least 1 bil­lion to 3 bil­lion years in age before it entered the red giant phase.

Jeno Marz
JENO MARZ is a science fiction writer from Latvia, Northern Europe, with background in electronics engineering and computer science. She is the author of two serial novels, Falaha’s Journey: A Spacegirl’s Account in Three Movements and Falaha’s Journey into Pleasure. Marz is current at work on a new SF trilogy. All her fiction is aimed at an adult audience.

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