Set Your Timer: The Star

Stars are amaz­ing. Lots of things depend on them. So, fig­u­ra­tive­ly speak­ing, they are your local cen­ters of the uni­verse.

A star is a mas­sive, lumi­nous, self-grav­i­tat­ing ball of plas­ma. And the force that trig­gers a stel­lar timer is grav­i­ty. So, once it is on, things start to hap­pen. Dur­ing its life­time a star under­goes a sequence of changes. The­se changes affect every­thing in the vicin­i­ty of a star; and may­be a lit­tle fur­ther than that. Stel­lar evo­lu­tion is stud­ied by observ­ing numer­ous stars at the var­i­ous points of their life, and by sim­u­lat­ing stel­lar struc­ture with com­put­er mod­els.

Before choos­ing a star (or a mul­ti­ple star) for your sys­tem, you might con­sid­er some options here: life as we know it; life as we don’t know it, or no life at all. And if the lat­ter, what next? Will there be some­one arriv­ing or is it just a dead world?

In this arti­cle I will stick to the life as we know it sce­nar­io.

This leaves me with a lim­it­ed choice of suit­able stel­lar types from the main sequence range between a late F and an early/mid K. Because the­se are the ones that are more or less suit­able hav­ing an earth­like world (be it a plan­et or a moon) in terms of hab­it­abil­i­ty accord­ing to the UV con­strains and oth­er accept­ed cri­te­ria of hab­it­abil­i­ty (liq­uid water on planet’s sur­face, com­pa­ra­ble sur­face inven­to­ries of car­bon diox­ide, water, dini­tro­gen and oth­er bio­genic ele­ments, an ear­ly his­to­ry allow­ing chem­i­cal evo­lu­tion that leads to life, and sub­se­quent cli­mat­ic sta­bil­i­ty for sev­er­al bil­lions of years).

Stars ear­lier than F0 have very short (2 Gyr) main sequence life­times and, hence, have a low prob­a­bil­i­ty of har­bor­ing plan­ets with com­plex life. Their hab­it­able zones migrate out­wards rapid­ly, so even micro­bial life might not have time to devel­op in the­se sys­tems. Plan­ets orbit­ing stars lat­er than K5 are like­ly to become tidal­ly locked, which may be a prob­lem for hab­it­abil­i­ty. Or may­be not, but it is a dif­fer­ent case, though no less inter­est­ing.

Main sequence stars of spec­tral class F8V to K2V (or 0.50 to 1.00 in B−V) are sim­i­lar to the Sun in mass and evo­lu­tion­ary state, and are usu­al­ly called solar-like stars.

Cir­cum­stel­lar hab­it­able zones

The hab­it­able zones of main sequence stars have tra­di­tion­al­ly been defined as the range of orbits that inter­cept the appro­pri­ate amount of stel­lar flux to per­mit sur­face water on a plan­et. The inner HZ bound­ary is deter­mined by the loss of water via pho­tol­y­sis and hydro­gen escape. The out­er HZ bound­ary is deter­mined by the con­den­sa­tion of car­bon diox­ide crys­tals out of the atmos­phere.

How­ev­er, in the case of life as we know it, this is not the only fac­tor to con­sid­er.

Ultra­vi­o­let radi­a­tion is known to inhibit pho­to­syn­the­sis, induce DNA destruc­tion and cause dam­age to a wide vari­ety of pro­teins and lipids. In par­tic­u­lar, UV radi­a­tion between 200–300 nm becomes ener­get­i­cal­ly very dam­ag­ing to most of the ter­res­tri­al bio­log­i­cal sys­tems. On the oth­er hand, UV radi­a­tion is usu­al­ly one of the most impor­tant ener­gy sources on the prim­i­tive Earth for the syn­the­sis of many bio­chem­i­cal com­pounds and, there­fore, essen­tial for sev­er­al bio­gen­e­sis process­es (Buc­ci­no et al. 2006, 2007).

Chro­mos­pher­ic UV radi­a­tion is increased in young stars in regard to all stel­lar spec­tral types. Com­pelling obser­va­tion­al evi­dence (Gudel et al. 1997) shows that zero-age main sequence (ZAMS) solar-type stars rotate over 10 times faster than today’s Sun. As a con­se­quence of this, young solar-type stars, includ­ing the young Sun, have vig­or­ous mag­net­ic dynamos and cor­re­spond­ing­ly strong high ener­gy emis­sions.

Flare activ­i­ty (an impor­tant agent for the deliv­ery of high­ly ener­get­ic radi­a­tion, espe­cial­ly UVC) is most pro­nounced in K and M-type stars, which also has the poten­tial of strip­ping the plan­e­tary atmos­pheres of close-in plan­ets, includ­ing plan­ets locat­ed in the stel­lar hab­it­able zone. The amount of chro­mos­pher­ic radi­a­tion is, in a sta­tis­ti­cal sense, direct­ly cou­pled to the stel­lar age as well as the pres­ence of sig­nif­i­cant stel­lar mag­net­ic fields and dynamo activ­i­ty.

Stud­ies have shown that chro­mos­pher­i­cal­ly induced bio­log­i­cal dam­age for plan­ets host­ed by F and G-type stars will be insignif­i­cant. The sit­u­a­tion is, how­ev­er, deci­sive­ly dif­fer­ent for K and M dwarfs. Any of the­se stars, includ­ing inac­tive stars, show notice­able chro­mos­pher­ic emis­sion. For stars with basal chro­mos­pher­ic emis­sion, chro­mos­phere induced bio­log­i­cal dam­age only occurs for stars of spec­tral type mid-K and lat­er, where­as for stars with rel­a­tive­ly high chro­mos­pher­ic emis­sion, chro­mos­phere-induced bio­log­i­cal dam­age can also be found in the envi­ron­ments of very late G-type and ear­ly K-type stars (Cuntz et al., 2010).

How­ev­er, photochemical/radiative–convective mod­el­ing shows that plan­ets around K2V and F2V stars both exhibit bet­ter UV pro­tec­tion than does Earth. See “Ozone con­cen­tra­tions and ultra­vi­o­let flux­es on Earth-Like plan­ets around oth­er stars”, Segu­ra et al, Astro­bi­ol­o­gy, Vol­ume 3, Num­ber 4, 2003.

So, in order to set your world in a right place of your solar sys­tem, you need to con­sid­er two fac­tors – liq­uid water HZ and UV HZ.

Both are impor­tant fac­tors to deter­mine the loca­tion and the size of cir­cum­stel­lar hab­it­able zone.

For life sys­tems to evolve, the plan­et should be in the hab­it­able zone con­tin­u­ous­ly dur­ing a cer­tain time. A com­mon choice for this time is 4 Gyr, the time that was need­ed on Earth for intel­li­gent life to emerge and evolve into a tech­no­log­i­cal civ­i­liza­tion. Hen­ry et al. (1995) and Turn­bull and Tarter (2003a) con­sid­ered 3 Gyr, while Schopf (1993) used the time required for micro­bial life to emerge 1 Gyr in his def­i­n­i­tion of the CHZ.

Because main sequence stars become brighter as they age and con­vert hydro­gen into heli­um and heav­ier ele­ments, hab­it­able zones tend to migrate out­ward with time. In order to ana­lyze the evo­lu­tion of the hab­it­able zones, it is assumed that the UV radi­a­tion fol­lows the same pat­tern as the change in lumi­nosi­ties of F, G and K main sequence stars.

Until an atmos­pher­ic pro­tec­tion is built, a plan­e­tary sur­face would be exposed to larg­er amounts of UV radi­a­tion, which could act as one of the main source in the syn­the­sis of bio­prod­ucts and, in a cer­tain wave­length, could be dam­ag­ing for DNA. Both con­cepts rep­re­sent the UV bound­aries for the UV hab­zone. To obtain the exact AUs of this “safe cir­cle”, you might con­sid­er using for­mu­las for UV hab­it­able zones around host stars pre­sent­ed by Guo et al, 2010.

For tra­di­tion­al lumi­nos­i­ty-water hab­it­able zone cal­cu­la­tions see Kast­ing et al.,1993.

An example of liquid water and UV HZs calc
An exam­ple of liq­uid water and UV HZs calc

The tra­di­tion­al and the UV HZ must at least par­tial­ly over­lap for a con­sid­er­able amount of time in order to host a hab­it­able plan­et in it.

An example of HZ calculus output in MS Excel
An exam­ple of HZ cal­cu­lus out­put in MS Excel

Things you’ll need to get start­ed

As I men­tioned before, stars evolve. You need evo­lu­tion­ary tracks of the star if you are inter­est­ed in the long term evo­lu­tion­ary path of your world and its inhab­i­tants, what­ev­er those might be.

First of all, decide on a mass and effec­tive tem­per­a­ture of your star. Those usu­al­ly cor­re­spond to the spec­tral class (F8VK2V or lat­er). You might actu­al­ly want to use an exist­ing star from a cat­a­logue to get all the para­me­ters nec­es­sary. And don’t for­get to look up star’s actu­al age. It will be your anchor.

In order to obtain evo­lu­tion­ary tracks of any star you might choose, you don’t have to derive any for­mu­las. It has already been done. You sim­ply can use stel­lar mod­el grids. Per­son­al­ly, I like to use Stel­lar mod­els grids I. Z=0.02, M=0.8 to 125 Msol by Claret, 2004, which present stel­lar mod­els suit­able for the mean solar neigh­bor­hood, i.e. for Z=0.02 (metal­lic­i­ty) and X=0.70 (hydro­gen). The cov­ered mass range is from 0.8 up to 125M­sol and the mod­els are fol­lowed until the exhaus­tion of car­bon in the core, for the more mas­sive ones. In addi­tion, the effec­tive tem­per­a­tures of the more mas­sive mod­els are cor­rect­ed for the effects of stel­lar winds, while mod­els with low­er effec­tive tem­per­a­tures are com­put­ed using a spe­cial treat­ment of the equa­tion of state. You can read a more detailed descrip­tion here and see the grids here.

The grid mod­el has time steps in years and you can com­pare it with your select­ed star’s data (i.e. in lumi­nos­i­ty, effec­tive tem­per­a­ture and oth­er things accord­ing to age, which is your anchor).

Try to exper­i­ment with dif­fer­ent grids for oth­er ele­ment abun­dance ratios. They can be found here. (E.g. Grids of stel­lar mod­els. VIII. From 0.4 to 1.0 Msun at Z=0.020 and Z=0.001, Char­bon­nel+ 1999, descrip­tion).

When you’re done, you’ll have a full table of stel­lar life­time para­me­ters, which lat­er can be used as a basis for all of your cal­cu­la­tions. The­se include mass, lumi­nos­i­ty, effec­tive tem­per­a­ture, cen­tral den­si­ty and tem­per­a­ture, ele­ment abun­dan­cies and some oth­er stuff like frac­tion­al gyra­tion radius at sev­er­al age steps.

Have fun, and more excit­ing stuff to fol­low.

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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