Gamma Ray Burst engine activity within the quark nova scenario: Prompt emission, X-ray Plateau, and sharp drop-off
aa r X i v : . [ a s t r o - ph ] N ov Draft version November 13, 2018
Preprint typeset using L A TEX style emulateapj v. 08/22/09
GAMMA RAY BURST ENGINE ACTIVITY WITHIN THE QUARK NOVA SCENARIO:PROMPT EMISSION, X-RAY PLATEAU, AND SHARP DROP-OFF
Jan Staff
Department of Physics, Purdue University, 525 Northwestern Avenue, West Lafayette, IN 47907-2036
Brian Niebergal and Rachid Ouyed
Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, AB T2N 1N4, Canada
Draft version November 13, 2018
ABSTRACTWe present a three-stage model for a long GRB inner engine to explain the prompt gamma rayemission, and interpret recent Swift satellite observations of early X-ray afterglow plateaus followedby a sharp drop off or a shallow power law decay. The three stages involves a neutron star phase, aquark star (QS) and a black hole phase as described in Staff et al. (2007). We find that the QS stageallows for more energy to be extracted from neutron star to QS conversion as well as from ensuingaccretion onto the QS. The QS accretion phase naturally extends the engine activity and can accountfor both the prompt emission and irregular early X-ray afterglow activity. Following the accretionphase, the QS can spin-down by emission of a baryon-free outflow. The magnetar-like magnetic fieldstrengths resulting from the NS to QS transition provide enough spin-down energy, for the correctamount of time, to account for the plateau in the X-ray afterglow. In our model, a sharp drop-offfollowing the plateau occurs when the QS collapses to a BH during the spin-down, thus shutting-offthe secondary outflow. We applied our model to GRB 070110 and GRB 060607A and found that wecan consistently account for the energetics and duration during the prompt and plateau phases.
Subject headings: gamma rays: bursts, stars: evolution INTRODUCTION
Observations of Gamma ray bursts (GRBs) by theSWIFT satellite (Gehrels et al. 2004) have revealed thatmany GRBs show a flat segment in their early X-ray af-terglow. This flat segment is often observed to start afterabout 10 seconds, and lasts up to 10 seconds. Follow-ing the plateau, some afterglows decay following a powerlaw with a modest power of about − −
2. However,in some cases a very sharp drop-off succeeds the plateau.In the literature, there are mainly two different ex-planations for the flattening that have been proposed:(i) the refreshed shocks explanation (Rees & M´esz´aros1998), where slower shells ejected during the prompt en-gine phase catch up with the external shock and refreshit. The plateau is then followed by a shallow decay ofpower index − − Electronic address: jstaff@purdue.edu paper (Staff et al. 2007, hereafter SOB07), a three stagemodel for long GRBs was suggested, involving a neutronstar (NS) phase, followed by an accreting QS phase anda plausible third stage that occurs when the QS accretesenough material to become a BH. The advantages of ourmodel is that, by including a QS phase, we can accountfor both energy and duration of the prompt emission, theflattening, the sharp drop-off or shallow decay, and theX-ray flaring (see SOB07).The secondary outflow is a pair wind due to spin-downfrom magnetic braking of the QS (Niebergal et al. 2006).Here we suggest that the rotational energy of a rapidlyrotating QS can be used to explain the flattening. Thispaper is organized as follows: In section 2 we briefly de-scribe the framework of our model. In section 3 we dis-cuss how the rotational energy released as the QS spinsdown due to magnetic braking can give rise to flatten-ing in the X-ray afterglow. Also, the sharp drop-off isdiscussed as a signature of the QS turning into a BH. Insection 4 we apply our model to GRB 070110 and GRB060607A. We summarize and conclude in section 5. THE THREE STAGES
The three stages of the GRB engine described inSOB07 are as follows. Stage 1 is a (proto-) NS phase, theNS being born in the collapse of the iron core in an ini-tially massive star. This NS can collapse to a QS, eitherby spin-down (Staff et al. 2006) or through accreting ma-terial, thereby increasing its central density sufficientlythat it can form strange quark matter. We suggested thatthis stage could lead to a delay between the core collapseand the GRB. The collapse into a QS, in a quark nova(QN; Ouyed et al. 2002; Ker¨anen et al. 2005), releases up Staff et al.to 10 ergs that might help power the explosion of thestar. This can possibly explain why GRBs associated su-pernovae are often very energetic (see Ouyed et al. 2007;Leahy&Ouyed 2007). If a QS is formed directly in thecore collapse, stage 1 will be bypassed and the processstarts from stage 2.Stage 2 is accretion onto the QS from the surroundinghyperaccreting debris disk, which is formed from mate-rial left over from the collapse of the progenitor. Thislaunches a highly variable ultra-relativistic jet, in whichinternal shocks can give rise to the gamma radiation seenin a GRB (Ouyed et al. 2005). This jet will eventually in-teract with the surrounding medium creating an externalshock that gives rise to the GRB afterglow. The after-glow light curve would follow a powerlaw F ν ∼ t − (1 − (Sari et al. 1998). However, slower shells can catch upwith the external shock at later times and refresh it. Thiscan lead to a flatter segment in the X-ray afterglow (e.g.Rees & M´esz´aros 1998) which is commonly seen in GRBafterglows (O’Brien et al. 2006; Liang et al. 2007).Stage 3, which occurs if the QS accreted sufficientlythat it collapsed to a BH, is accretion onto the BH whichlaunches another ultra-relativistic jet, as described inDe Villiers, Staff, & Ouyed (2005). Interaction betweenthis jet and the QS jet or internal shocks in the BH jetitself can give rise to flaring commonly seen in the X-rayafterglow of GRBs. The BH jet has the potential to bevery powerful, so if it catches up with the external shocka bump might be seen in the light curve. The relevantfeatures and emission have been discussed in details inSOB07. Alternatively, if the QS did not collapse to aBH, continued accretion onto the QS after the promptphase might also be able to explain X-ray flaring. PROMPT EMISSION, X-RAY PLATEAU, AND SHARPDROP-OFF
In our model the prompt emission is produced by inter-nal shocks in a QS jet launched by hyperaccretion ontoa QS (Ouyed et al. 2005). In this section we will first ex-plain that for the accreting material to be channeled tothe polar cap region, this requires a very high magneticfield. If the QS survives the accretion and is rapidly ro-tating, this magnetic field can then spin the QS down.We will show that a similarly strong magnetic field iswhat is needed to get the right spin-down time to ex-plain the observed flattening.
Prompt Emission
The prompt gamma ray emission corresponds to syn-chrotron emission by electrons accelerated in internalshocks in the QS jet. This jet forms an external shockupon interacting with the surrounding medium, and syn-chrotron emission from this external shock is responsiblefor the afterglow.In order to explain the energy observed in the promptgamma radiation, SOB07 found that the accretion rateonto the QS must be of the order ˙ M ∼ − − − M ⊙ / s.In order to create a jet, the accretion has to be channeledonto the polar cap. This can occur if the magnetic ra-dius is at least twice the radius of the star. With the be-fore mentioned accretion rate, a magnetic field of the or-der B ∼ − G (see Ouyed, Ker¨anen, & Maalampi 2005) is required. It should be noted that this QS jetis much different than the typical MHD disk wind jets.A QS jet is created as the accreting material reaches thesurface of the QS, it is converted into CFL quark mat-ter, resulting in the creation of a hot spot due to therelease of excess binding energy. This region cools byemitting photons, which collide with subsequent accret-ing material, resulting in the ejection of material withhigh Lorentz factors (for details, see Ouyed et al. 2005).Given that the prompt emission requires such highmagnetic fields (because of the high accretion rates), onehas to reconcile this with the plateaus observed in somelight curves at later times.A very high magnetic field and a high accretion ratecan make the QS find itself in the propeller regime if it isalso spinning very fast ( P . Flattening
Panaitescu (2007) suggested that an outflow, ejectedby the engine after the initial blast, can scatter theforward-shock synchrotron emission and thereby produceflux that will outshine the primary one, especially if theoutflow is nearly baryon free and highly relativistic .This reflected flux can produce certain light-curve fea-tures such as flares, plateaus, and chromatic breaks. Forthis to occur, the duration of this scattering outflow hasto last as long as these observed features (modulo cos-mological time-dilation).We next show that by using the rotational energy lostfrom a QS spinning down, assuming a magnetic field of10 G, a spin-period of ∼ - 10 seconds is obtained. Theobserved flattening in the light-curves of certain GRBscan last for several times 10 s and fits well with theduration from the QS spin-down.Following the birth of a CFL QS, due the to onsetof color superconductivity the magnetic flux inside thestar is forced into a vortex lattice that is aligned withthe rotation axis. This subsequently forces the mag-netic field outside the star to re-structure itself into adipole configuration that is aligned with the rotation axis(Ouyed et al. 2006). Such an aligned rotator will spindown by magnetospheric currents escaping through thelight cylinder. Pair production from magnetic reconnec-tion supplies these currents (Niebergal et al. 2006) with acorresponding luminosity given by (Shapiro & Teukolsky1983): L = − ˙ E rot ∼ B Ω ( n +1) R c , (1)where B is the magnetic field at the pole, R is the radiusof the star, Ω is the angular rotational frequency of the Recent work shows that 10 G magnetic fields can readily beobtained during QS formation due to the response of quarks to thespontaneous magnetization of the gluons (e.g. Iwazaki 2005, andreferences therein). An alternative model for generating the radiation is magneticreconnection or dissipation processes in a highly magnetized out-flow which was proposed by Usov (1994, for the prompt emission)and Gao & Fan (2006, for the afterglow). rompt emission and X-ray plateau 3star, c is the speed of light, n is the magnetic brakingindex.For an aligned rotator without field decay, the brakingindex is roughly n ∼
3, however due to magnetic fluxexpulsion from a CFL QS, the magnetic field decays asprescribed by Niebergal et al. (2006). This results in anevolution of the luminosity due to spin-down, which isexpressed by the relation, L ∼ . × erg s − (cid:18) B G (cid:19) (cid:18) P (cid:19) (cid:18) tτ (cid:19) − / , (2)where the characteristic spin-down time (in seconds) is, τ = 3 . × s (cid:18) G B (cid:19) (cid:18) P (cid:19) (cid:18) M QS . M ⊙ (cid:19) (cid:18) R QS (cid:19) . (3)In the above equations, M QS is the QS mass, P is theinitial spin period, and B is the initial magnetic fieldstrength.From Eq. 2 one can see that the luminosity, due torotational energy extracted from spin-down of a QS, hasa natural break at time τ . Thus, if there was a oneto one relationship between spin-down luminosity andobserved emission, then the power law decay of the ob-served light-curve should change from zero to − / e + e − wind. Thus, it shouldbe mostly baryon free, since the QS becomes bare imme-diately following its birth as it enters the CFL phase (seeNiebergal et al. 2006). As in the case of a pulsar, spin-down energy extracted from a QS is mainly in the equato-rial plane. Bucciantini et al. (2007) performed numericalsimulations where they showed that it is still possible tocollimate such equatorial flows into a jet.A relativistic outflow from the spin-down of a highly-magnetized neutron star has been suggested beforeas a mechanism to produce plateaus (for instance inTroja et al. 2007), however they did not propose a uni-fied model explaining both the prompt emission and theafterglow features. We have here proposed a model thatcan explain both the prompt GRB emission and the ob-served X-ray afterglow features. Sharp vs. Gradual decay
Eq. 2 naturally gives a break in the engine luminos-ity at t = τ . The engine will also remain active afterthis break, but the engine luminosity will gradually de-cay (with a power law ∼ − /
3; which is not necessarilythe power law decay in the observed emission). In someinstances however, it is possible that the QS reaches anunstable configuration, such that the QS stage is onlytemporary before the collapse to a BH.If the QS collapses to a BH during spin-down, theengine will likely be shut off. Although the BH islikely to be rapidly rotating, a disk is necessary in or-der to extract the rotational energy of a BH through theBlandford-Znajek mechanism (BZ; Blandford & Znajek1977). Only if a disk has remained around the QS dur-ing spin-down or if it is formed after the formation of theBH, can the BZ mechanism play a role. If this does not
TABLE 1Observed quantities in GRB 070110 and GRB 060607A.
GRB 070110 ref GRB 060607A refredshift ( z ) 2.352 † † E iso,X . × ergs † . × ergs † T break (engine frame) 6000 s ‡ ‡ L Obs ., iso (during plateau) 10 erg/s ♣ × erg/s ♠ L Eng ., (during plateau) 1 . × erg/s ♦ × erg/s ♦ T / (1 + z ) 25.4 s ‡ ‡ E γ, iso × ergs † . × ergs † E γ, . × ergs 2 . × ergsReferences: † : Liang et al. (2007) ‡ : Calculated using redshift and duration from Liang et al. (2007) ♣ : Troja et al. (2007) ♠ : Calculated using E iso , X , z, and T break from Liang et al. (2007) ♦ : Observed luminosity corrected for redshift, assuming 10degrees opening angle occur, the observed light curve will be generated by theexternal shock only after this stage. A sharp drop off willbe seen as the light curve drops from the level given bythe spin-down outflow to the level given by the externalshock.We suggest that in GRB light curves exhibitingplateaus, those possessing a gradual decay following theplateau are either due to refreshed shocks as discussedin SOB07 or from spin-down of QSs that have not col-lapsed to BHs. If the secondary outflow is responsiblefor the X-ray afterglow, then the external shock can pro-duce the optical afterglow. This scenario might explainwhy the optical and X-ray afterglows behave different insome GRBs. CASE STUDY
In this section we will apply our model to two GRBs,GRB 070110 and GRB 060607A, that both show a flat-tening followed by a sharp drop off which is difficult toexplain with the external shock. Some observed proper-ties of both GRBs are summarized in Table 1.Based on observations of the duration of the X-rayflattening, we use Eq. 3 to estimate the correspondingmagnetic field strength. We then use Eq. 2 to find thespin-down luminosity. Both the magnetic field and thespin-down luminosity found this way are listed in Ta-ble 2 which is then compared to observed values (Ta-ble 1). Furthermore, now that we have an estimate forthe magnetic field of the QS, this gives us an estimatefor the accretion rate that can be channeled to the polarcap. We assume a jet opening angle of about 10 degrees.The observed prompt GRB emission is then calculatedby assuming that a combination of accretion efficiencyand radiative efficiency leads to ∼
1% of the total grav-itational energy of the accreted material is converted toprompt radiation. As shown below, for both GRB 070110and GRB 060607A we find that the magnetic field foundbased on the duration of the X-ray flattening consistentlyand simultaneously explains the energy of both the GRBitself and the X-ray flattening.In our model we know the time at which the QS col-lapses to a BH (the time of the steep decay). The calcu-lations above assumed that this occurred at t collapse = τ .However, it could also occur at t collapse < τ , which im- Staff et al. TABLE 2Derived quantities for GRB 070110 and GRB 060607A.
GRB 070110 GRB 060607AMaximum magnetic field 6 . × G 1 . × GSpin-down luminosity 1 . × erg/s 3 . × erg/s˙ m acc ., max . . × − M ⊙ / s 1 . × − M ⊙ / s E γ, ,max . × ergs 7 . × ergs E γ, iso , max . × ergs 1 . × ergsThe maximum magnetic field is calculated using Eq. 3 assumingthat the QS collapsed to a BH at t = τ and an initial spin periodof 2 ms. The other quantities in this table is calculated based onthis maximum magnetic field. plies that the magnetic field is weaker than found above.Hence, the magnetic field found above is the maximumpossible magnetic field, and therefore the spin-down lu-minosity, accretion rate and prompt gamma ray energyare also maximum. GRB 060607A and 070110
The QS magnetic field needed to explain the flatteningobserved in GRB 070110 is B = 6 . × G (see Ta-ble 2). The corresponding spin-down luminosity is foundto be 1 . × erg/s. We can compare this to the ob-served engine luminosity assuming an opening angle of10 degrees for this outflow. If we assume an efficiencyof 10% in converting kinetic energy to photons we seethat we have an order of magnitude more energy thanneeded. Comparing the observed prompt gamma ray en-ergy to what we find from the jet launched by the QS,we again find that the jet energy is higher (by a factor4) than the observed gamma ray energy.The QS magnetic field needed to explain the flatteningobserved in GRB 060607A is B=1 × G (see Table 2).The corresponding spin-down luminosity is found to be3 . × erg/s. Assuming 10% efficiency in producingX-ray photons, we find (as for GRB 070110) that theestimated luminosity is higher than the observed. Thegamma ray energy released during the prompt phase isalso higher than the observed gamma ray energy.The higher luminosities can be because the estimate forthe magnetic field is too high, meaning that τ is largerand that the QS collapsed to a BH before t = τ . A lowermagnetic field implies that the accretion rate is lower.Alternatively, we have overestimated the efficiencies, orthe opening angle of the outflow is larger.In GRB06067A there are several X-ray flares observeduntil about 300 seconds (about 75 seconds when cor-rected for redshift). If we explain these flares by accretiononto the QS as well, that means that the accretion pro-cess lasts for about 75 seconds. The derived accretionrates imply the necessity of a debris disk with a mass of the order of ∼ − M ⊙ , which is reasonable since the QNgoes off inside a collapsar, where such a large fall-backdisk is in principle allowed. SUMMARY & CONCLUSION
We have presented a model to explain the flatteningand occasional sharp drop-off seen in X-ray afterglowsof some GRBs. Our model borrows the framework ofthe 3 stage model presented in SOB07 which makes useof an intermediate QS stage between the NS and theBH. By appealing to a secondary outflow, from the QSspin-down due to magnetic braking, our model seemsto explain the GRB itself (i.e. prompt emission), theobserved flat segment (i.e. plateau), and the subsequentsharp or gradual decay following the plateau. The sharpor gradual decay depends on whether the QS collapsesto a BH or not during spin-down. During spin-down, abreak will be seen after a characteristic time τ given byEq. 3 followed by a power law with power of − / − ergs released in a few seconds (Ouyed et al. 2006). Assuch, the QS phase extends the engine activity and socan account for both the prompt emission and irregularX-ray afterglow activity; (ii) a natural amplification ofthe NS magnetic field to 10 -10 G during the tran-sition to the QS (Iwazaki 2005). Such high strengthsgives the correct spin down time to for the plateau; (iii)since QS in the CFL phase might not have a crust, thespin down energy will most likely be extracted as an e + e − fireball with very little baryon contamination (see discus-sion in Niebergal et al. 2006). Panaitescu (2007) favorsa baryon free secondary outflow to explain the plateau.We thank Y. Fan and D. Xu for comments. REFERENCESBlandford, R. D. & Znajek, R. 1977, MNRAS, 179, 433Bucciantini, N., Quataert, E., Arons, J., Metzger, B. D., &Thompson, T. A., 2007, arXiv:0707.2100v1De Villiers, J.-P., Staff, J., & Ouyed, R., 2005, astro-ph/0502225Gao, W. H, Fan, Y. Z. 2006, Chin. J. Astron. Astrophys, 6, 513Gehrels, N., et al. 2004, ApJ, 611, 1005Iwazaki, A. 2005, PhRvD, 72, 114003Ker¨anen, P., Ouyed, R., & Jaikumar, P. 2005, ApJ, 618, 485Leahy, D. & Ouyed, R., 2007, arXiv:0708.1787 Liang, E-W., Zhang, B-B., & Zhang, B., 2007, arXiv:0705.1373Niebergal, B., Ouyed, R., & Leahy, D. ApJ, 646, L17O’Brien, et al., 2006a, ApJ, 647, 1213Ouyed, R., Dey, J., & Dey, M. 2002, A&A, 390, 39Ouyed, R., Rapp, R., & Vogt, C. 2005, ApJ, 632, 1001Ouyed, R., Ker¨anen, P., & Maalampi, J., 2005, ApJ, 626, 389Ouyed, R., Niebergal, B., Dobler, W., & Leahy, D. 2006, ApJ,653, 558 rompt emission and X-ray plateau 5rompt emission and X-ray plateau 5