The Cause of the Difference in the Propagation Distances between Compact and Transient Jets in Black Hole X-Ray Binaries

Accreting black hole binaries change their properties during evolution, passing through two main luminous states, dominated by either hard or soft X-rays. In the hard state, steady compact jets emitting multiwavelength radiation are present. Those jets are usually observed in radio, and when resolved, their extent is ≲1015 cm. Then, during hard-to-soft transitions, powerful ejecta in the form of blobs appear. They are observed up to distances of ∼1018 cm, which are ≳1000 times larger than the extent of hard-state jets. On the other hand, estimates of the accretion rates during most luminous hard states and the hard-to-soft transitions are very similar, implying that maximum achievable powers of both types of jets are similar and cannot cause a huge difference in their propagation. Instead, we explain the difference in the propagation length by postulating that the ejecta consist of electron-ion plasmas, whereas the hard-state jets consist mostly of electron–positron pairs. The inertia of the ejecta are then much higher than those of compact jets, and the former are not readily stopped by ambient media. A related result is that the accretion flow during the hard state is of standard and normal evolution, while it is a magnetically arrested disk during transient ejections. The pairs in hard-state jets can be produced by collisions of photons of the hard spectrum emitted by hot accretion flows within the jet base. On the other hand, the X-ray spectra during the state transitions are relatively soft, and the same process produces much fewer pairs.


INTRODUCTION
Most of accreting black-hole (BH) X-ray binaries (XRBs) are transient, having outbursts observed from radio to X-rays separated by years of quiescence.Almost all of transient BH XRBs have low-mass donors, with the mass 1M ⊙ , while several with either massive or undetermined donors are persistent, see Corral-Santana et al. (2016).BH XRBs show two main luminous X-ray spectral states, hard and soft, see Done et al. (2007) for a review of their X-ray properties.In radio, they show two main types of activity: compact steady jets in the hard state, and transient, discrete, jets appearing occasionally during transitions from the hard intermediate state (i.e., the softest part of the hard state, with the X-ray energy index α > 1, defined by F ν ∝ ν −α ) to the soft state, while there is usually no or very weak radio emission during the soft state itself, see Fender et al. (2004) for a review.
A striking difference between the two types of jets is in the distances to which they are observed to propagate.Compact jets appear always relatively small, in spite of the duration of their launching from the BH spanning from weeks to even years.In most cases they remain unresolved in radio.Currently, compact jets in only four BH XRBs have been resolved in radio.Three of them are MAXI J1820+070 with the deprojected jet elongation of ℓ max ≈ 3 × 10 13 cm at 15 GHz (Tetarenko et al. 2021), Cyg X-1 with ℓ max ≈ 10 15 cm at 8 GHz (Stirling et al. 2001), and GRS 1915+105 (assuming the distance of D ≈ 8 kpc; Reid et al. 2014) with ℓ max ≈ 3×10 15 (1 GHz/ν) (Dhawan et al. 2000).Then, MAXI J1836-194 has an only rough (due to the distance and inclination of this source being uncertain) estimate of the length of ℓ max ∼ 10 16 cm at 2.3 GHz (Russell et al. 2015), which was obtained in only one out of several VLBA observations after subtracting the point source.Theoretically, we expect ℓ max ∝ ∼ ν −1 (Blandford & Königl 1979).Then, not a single discrete extension of a hard-state jet was detected moving at large distances from the core.
On the other hand, transient jets are observed as discrete moving ejecta at much larger distances, up to ∼ 10 17 -10 18 cm, in spite of the duration of their launching being of the order of a day (e.g., Carotenuto et al. 2021Carotenuto et al. , 2024)).Often both the approaching and the receding components are seen (e.g., Mirabel & Rodríguez 1994;Fender et al. 1999;Bright et al. 2020), and they are sometimes detected even at distances > 10 18 cm (Carotenuto et al. 2021(Carotenuto et al. , 2024)).Both types of jets often appear during the same observational campaigns, e.g., for MAXI J1820+070 and MAXI J1348-630.The cause of the difference in the propagation distances has remained unexplained.So far, this type of activity has been detected only from transient sources (i.e., showing outbursts separated by years of quiescence), and not from persistent sources.
We need to mention another small class of BH XRBs that show parsec-scale persistent radio jets.We know two such sources, 1E 1740.7-2942(Mirabel et al. 1992;Luque-Escamilla et al. 2015) and GRS 1758-258 (Rodriguez et al. 1992;Martí et al. 2002Martí et al. , 2017)).Both are persistent X-ray sources.Then, the jet in the persistent source Cyg X-1 may power an interstellar shell distant by ∼10 pc (Gallo et al. 2005), though it remains uncertain (Sell et al. 2015), and the hypothetical large-scale jet connecting to the shell is invisible.Then, there is yet another case of the per-sistent source, namely Cyg X-3, which has major radio outbursts in its soft state (e.g., Koljonen et al. 2010).Here, we will not consider those cases, and we will concentrate on the differences between compact and transient jets in transient BH XRBs only.
Another difference between the two types of jets is in their radio spectra.The radio emission of the compact jets is flat or inverted (Fender 2001), with α 0, which is well explained by the partially synchrotron self-absorbed jet model of Blandford & Königl (1979), see, e.g., Tetarenko et al. (2021), Zdziarski et al. (2022b), while that of the transient jets is steep, α ∼ 0.5 (e.g., Rodriguez et al. 1995;Carotenuto et al. 2021), characteristic of optically thin synchrotron emission by power-law electrons.The emitting regions of compact jets are continuously replenished and stay optically thick up to some wavelength-dependent distances, while transient ejecta rapidly expand to large lateral sizes (e.g., Mirabel & Rodríguez 1994;Rushton et al. 2017), causing the self-absorption optical depth to be low.
Also, existing estimates of the powers, P j , of the compact and transient jets are relatively similar.A theoretical upper limit on P j is ∼ Ṁaccr c 2 , where Ṁaccr is the accretion rate (Davis & Tchekhovskoy 2020 and references therein).The accretion luminosities, L, of the hard state before the state transition and during it are quite similar, and the accretion efficiency, ǫ, is theoretically predicted to increase from the hard state to the soft one (Yuan & Narayan 2014).Then Ṁaccr = L/(ǫc 2 ) is unlikely to substantially increase at the hard-tosoft transition.For compact jets, published estimates are mostly in the P j ∼ 10 37−39 erg/s range, e.g., Zdziarski et al. (2022b).In the case of transient jets, there were some estimates of extreme powers, P j ∼ 10 41 erg/s, in particular those of Mirabel & Rodríguez (1994) and Carotenuto et al. (2022).However, these values were revised and found much lower by Zdziarski (2014) and Zdziarski et al. (2023).In the recent study of Carotenuto et al. (2024), the kinetic energy of three transient jets were calculated, and they also imply a P j ∼ 10 37−39 erg/s range.
In a recent work, Sikora & Zdziarski (2023) proposed that the jets produced during the hard-to-soft state transitions are transient because of an increase of the accretion rate, Ṁaccr , associated with the transitions.If the jet before the transition was launched from a magnetically-arrested accretion disk (MAD; McKinney et al. 2012) and the accumulated magnetic flux remains constant during the transition (see fig. 1 in Sikora & Zdziarski 2023), the system can cease to be in the MAD state above certain Ṁaccr , which, in turn, can decollimate the outflow and stop the jet production.The discrete ejection would correspond then to a part of the compact jet produced just before the decollimation.This picture implies that the transient jets are similar to the compact ones except for a shorter launching time.This, however, does not explain the dramatic difference in the propagation distances between the compact and transient jets, which thus is still unknown.In this work, we attempt to explain this difference.We concentrate our study on the case of MAXI J1820+070, whose detailed observations allow relatively reliable estimates of the jet parameters for both the compact jet and the transient ones.

Measurements and estimates
The deprojected elongation of the jet resolved at 15 GHz by VLBA on MJD 58193 (5 days after the source discovery in X-rays, Kawamuro et al. 2018) for the distance of D ≈ 3.0 ± 0.3 kpc (as measured by Atri et al. 2020) and the inclination of 64 (Tetarenko et al. 2021).Extrapolating it to MJD 58220 based on the radio flux (with a model based on Blandford & Königl 1979), the estimated length for that day was ℓ max ≈ 4 × 10 13 cm (Zdziarski et al. 2022b).This also approximately agrees with the time-lag estimates of Zdziarski et al. (2022b), see their fig.7, as well as with the estimates based on the breaks in the power spectra (Tetarenko et al. 2021;Zdziarski et al. 2022b).Then, the size estimates based on the method of core shift are still lower by a factor of several (Prabu et al. 2023).
On the other hand, the main approaching ejection in that source, launched during the hard-to-soft state transition (around MJD 58306; Wood et al. 2021) was detected in Xrays at the distances from the compact object as large as ≈ 6 × 10 17 cm (Espinasse et al. 2020), which is >4 orders of magnitude longer than the measured length of the hard-state jet.This is in spite of the similar jet Lorentz factors, see below, and in spite both types of jets apparently launched in the same directions.
The Lorentz factor of the compact jet was estimated as Γ ≈1.5-4 (Zdziarski et al. 2022b).Then, Carotenuto et al. (2024) estimated the initial Lorentz factor as Γ 0 ≈ 2.6 +0.5 −0.4 for the main transient ejection.Thus, there is no indication on which of the jets has the higher Γ.
The main method for estimating the jet power in steady, compact, jets is to use the observed synchrotron flux to calculate the flux of the emitting electrons and positrons (e ± ).By assuming the ratio of the energy densities in the e ± to that in the magnetic field (the equipartition parameter), we can calculate the power in the e ± and the field, P Be .Another component is the power in ions, P i , which depends on the fraction of e ± pairs and on the number of non-emitting electrons at low energies.In the case of MAXI J1820+070 at the absence of non-emitting electrons, Observational estimates of the jet power can be compared to theoretical predictions for the jet power.The most efficient such model known as yet is that based on the extraction of the rotation power of the BH (Blandford & Znajek 1977).In this model, where k is a constant (Tchekhovskoy 2015), a * is the BH spin parameter, and Φ BH is the magnetic flux threading the BH.Then, the maximum possible Φ BH ≡ Φ MAD corresponds to the balance between the magnetic pressure and the ram pressure of the accreting matter, i.e., a Magnetically Arrested Disk (MAD; Bisnovatyi-Kogan & Ruzmaikin 1974; Narayan et al. 2003).Based on numerical simulations of jets (Tchekhovskoy et al. 2011;Davis & Tchekhovskoy 2020), it has been found to correspond to (for both the jet and counterjet) which gives the upper limit on the possible jet power, P j ≤ P MAD .Assuming isotropy, we estimate where F accr is the bolometric accretion flux, and ǫ is the accretion efficiency.Shidatsu et al. (2019) found the unabsorbed 1-100 keV flux in the luminous hard state to be between ≈0.5 and ≈ 1.4 × 10 −7 erg cm −2 s −1 .The 0.1-200 keV flux as observed by XMM and INTEGRAL in the luminous hard state on MJD 58220 (for which the hard-state jet power was estimated above) was ≈ 1.1 × 10 −7 erg cm −2 s −1 (J.Rodi, private communication; Rodi et al. 2021).We find the estimated bolometric flux of ≈ 1.2 × 10 −7 erg cm −2 s −1 , corresponding to L bol ≈ 1.3(D/3 kpc) 2 10 38 erg s −1 .For the BH mass of M = 6.8M ⊙ (Torres et al. 2020;Mikołajewska et al. 2022) and for the H mass fraction of X = 0.7, this L bol represents 13% of the Eddington luminosity.It implies Ṁaccr c 2 ≈ 1.3×10 39 (D/3 kpc) 2 (ǫ/0.1)−1 erg s −1 .The initial estimates of a * using the continuum method were a * ≈ 0.2 +0.2 −0.3 (Guan et al. 2021) and a * ≈ 0.14 ± 0.09 (Zhao et al. 2021), or even a * < 0 (Fabian et al. 2020) at the binary inclination of ≈66-81 • (Torres et al. 2020).On the other hand, Bhargava et al. (2021) obtained a * ≈ 0.8 from timing using the relativistic  (Shidatsu et al. 2019), which spectrum approximately consists of a disk blackbody followed by a steep power law with α > 1.The 0.1-78 keV flux on MJD 58306 was measured as ≈ 1.62 × 10 −7 erg cm −2 s −1 (Fabian et al. 2020), which, given the shape of the spectrum is only slightly lower than the estimated bolometric flux, ≈ 1.7 × 10 −7 erg cm −2 s −1 .The bolometric luminosity is then L bol ≈ 1.8(D/3 kpc) 2 10 38 erg s −1 (which is 18% of the Eddington luminosity), and P MAD,transient ≈ 1.5(a * /0.8) 2 (ǫ/0.1)−1 10 39 erg s −1 , (5) similar to P MAD,compact , Equation (4).The intermediate state has a stronger disk component than the hard state, indicating the disc inner radius, R in , is closer to the innermost stable circular orbit than in the hard state.Since the efficiency of thin disks is ≈ R g /(2R in ) (Shakura & Sunyaev 1973) and the efficiency of hot flows is generally lower than that (Yuan & Narayan 2014), ǫ is expected to be higher in the intermediate state than in the hard state.Then, the estimated Ṁaccr c 2 and P MAD,transient can be even more similar to that for the hard state.Table 1 compares the accretion luminosity, the jet properties and the maximum distance travelled for the two types of jet launching.

Implications
The energy content of transient jets can be estimated from modelling their motion in the surrounding medium (e.g., Wang et al. 2003;Steiner & McClintock 2012;Steiner et al. 2012;Zdziarski et al. 2023;Carotenuto et al. 2024), which can be converted to the jet power if the duration of the ejection event can be estimated.However, those estimates scale with the unknown density of the surrounding medium, which appears much lower than the density of a warm ISM, n ≪ 1 cm −3 , if the jet power is limited from above by Ṁaccr c 2 (Heinz 2002).Since the densities of the surrounding media remain unknown, we can only place upper limits on the jet power, equal to that of Equation ( 2).
Taking P j,transient = P MAD,transient ≈ 1.5 × 10 39 erg s −1 , Equation ( 5), the kinetic energy of the one-sided ejection of MAXI J1820+070 estimated using the ejection duration of 7 h (as in Carotenuto et al. 2024) becomes E 0 ≈ 2 × 10 43 erg, which, given the Lorentz factor estimated by Carotenuto et al. (2024), gives the single mass of E 0 /[(Γ 0 − 1)c 2 ] ≈ 1.4 × 10 22 g.If the ejection mass were dominated by low-energy e ± , there would 1.4 × 10 49 pairs in both ejecta.For the 7 h ejection duration, this requires the total pair production rate of N + ≈ 6 × 10 44 s −1 .This is more than four orders of magnitude larger than Ṅ+ ∼ 2 × 10 40 s −1 estimated for the hard state of this source by considering pair production by accretion photons (γγ → e + e − ) within the base of the compact jet (Zdziarski et al. 2022b).Furthermore, the Xray spectrum of that intermediate state (Fabian et al. 2020) was much softer than that of the hard state, and the number of photons available for pair production was correspondingly much lower.Thus, we conclude that the ejection composition was dominated by ions, similar to the case of MAXI J1348-630 (Zdziarski et al. 2023).
On the other hand, if the composition of compact jets were dominated by ions, its power would be at the MAD limit, compare Equations ( 1) and ( 4), which would in turn leave the huge difference between the propagation lengths of the compact and transient jets unexplained.However, Zdziarski et al. (2022b) showed that the rate of pair production in the hard state (see the paragraph above) approximately equals the rate of the flow of the synchrotron-emitting leptons.Thus, the jet in that state can easily be dominated by relativistic e ± pairs, with only few ions.The same conclusion was reached for Cyg X-1 (Zdziarski & Egron 2022) and the radio galaxy 3C 120 (Zdziarski et al. 2022a).Then, the hard-state jet power based on the synchrotron emission and assuming pair dominance is P j,compact ≪ P MAD,compact .This, in turn, implies that the hard-state accretion flow contains a magnetic flux much lower than that of the MAD, Φ ≪ Φ MAD , and thus it is of the Standard and Normal Evolution (SANE) type (Narayan et al. 2012).The differences in both the jet composition and the power can then explain the difference in the jet propagation length, see Section 3 below.This conclusion also agrees with that of Fragile et al. (2023), based on theoretical modelling of quasi-periodic oscillations, that the luminous hard state cannot be MAD.
Summarizing the above, we find that the jet Lorentz factors, Ṁaccr c 2 , and the maximum possible jet powers, P MAD , are similar for both kinds of jets, see Table 1.Furthermore, if the compact jets were dominated by ions, their powers would be similar to P MAD,compact , which is unlikely.The power of transient jets cannot be uniquely determined, but given their large propagation distances, it is much higher than that of the compact jets, and likely at the MAD limit.
Thus, considering possible differences between the two kinds of jets that would explain the difference in their propagation, we postulate they lie in both the composition and the jet power.Transient jets are clearly dominated by normal plasma with at most few pairs, and their power appears to be at the MAD limit.In contrast, compact jets are very likely dominated by pairs, though this is not proven by their modelling.Their power is then low and much below the MAD limit since it is dominated by the component due to relativistic pairs and magnetic field (with an at most small contribution from ions, cf.Equation 1).Consequently, the magnetic flux threading the BH in the hard state has to be well below the MAD limit.This, in turn, can explain the very limited distances they propagate, see Section 3.
The power of the transient jet is, as discussed above, uncertain since it scales with the unknown density of the surrounding medium.However, given their very long propagation distances, it is likely that their power is at the MAD limit, with P MAD,transient ≈ 1.5(a * /0.8) 2 10 39 erg s −1 in the case of MAXI J1820+070.For a * = 0.8, is two orders of magnitude larger than the P j,compact for the jet dominated by pairs.
We also mention a possible mechanism (Thomas et al. 2022) of the ejections of transient jets, which happen on the time scale of a day or less, much shorter than the duration of the launching of compact jets.An accumulating magnetic field flux can stop the accretion at some radius.Then, matter accumulates outside this radius, and finally breaks through it, causing the advected magnetic field to accumulate on the BH, reaching the MAD state, during which the infalling matter gets ejected.
Finally, we consider correspondence to jets in radio loud AGNs.Those jets have two main types, FR I and FR II (Fanaroff & Riley 1974).FR I sources show jets whose luminosity decreases as the distance from the central BH and have lower radio luminosity than FR II jets, suggesting they are counterparts of the compact jets in XRBs.While their total spectra are steep, their core spectra are flat on average, with α ≈ 0 (Yuan et al. 2018).Then, FR II jets are edgebrightened, with luminous radio lobes, and could be associated with the transient jets in XRBs.However, their radio spectra are typically flat, unlike those of the transient ejecta.Furthermore, Sikora et al. (2020) have shown that the FR II jet composition appears to be dominated by e ± pairs, again unlike the case of the transient ejecta.Also, both types of AGN jets are long-lasting, different from the transient XRB ejections.Thus, there seems to be no simple correspondence between the two FR types in AGNs and the two types of jets in XRBs.

PROPAGATION OF JETS
The propagation of transient jets appears to be well described by the widely-used formalism of Wang et al. (2003), which then requires the density of the surrounding medium to be very low.Within that formalism, we have derived the density of (similar to, but more accurate than eq. 5 of Heinz 2002) where l k is the distance at which the Lorentz factor of the ejection is reduced to kΓ 0 (1/Γ 0 < k < 1), φ is the halfopening angle, s ≈ 0.7 (Wang et al. 2003), and m p is the proton mass.In the derivation, we made a simplifying assumption that the Lorentz factor of the shock front equals that of the ejection.The stopping length is then For E 0 = 2 × 10 43 erg s −1 (see Section 2), k = 0.5, Γ 0 = 2.6 and n 10 −3 cm −3 (Carotenuto et al. 2024), we obtain l 1/2 4 × 10 17 cm, which agrees well with the observations.In the case of compact jets dominated by e ± , the pairs in the jet may first lose most of their energy, strongly reducing the mass.This may provide the required reduction of the kinetic energy.Indeed, Zdziarski et al. (2022b) found that the synchrotron power of MAXI J1820+070 is very similar to P Be .If P j ≈ P Be (i.e., the bulk kinetic power of ions can be neglected), the e ± will indeed lose most of their internal energy during the propagation.We will then have a dark jet, possibly propagating to large distances.In the presence of both synchrotron and adiabatic losses, the relativistic electrons lose all their energy.In the absence of adiabatic losses, they reach a terminal Lorentz factor > 1 (Kaiser 2006).
Then (for the case of adiabatic losses) the jet power will be equal to that of the energy flow of the cold pairs and the magnetic field.For MAXI J1820+070, it can be estimated as ≈ 4 × 10 34 erg s −1 (Zdziarski et al. 2022b) provided the magnetic field is effectively dissipated, maintaining the equipartition.In order to find the jet kinetic energy, we need to estimate the characteristic time this power operates before the jet is slowed down.The maximum estimate of this time is l k /c, k ∼ 1/2.Inserting E 0 = (1/2)P j l k /c into Equation (7) gives For P j = 4 × 10 34 erg s −1 , k = 0.5, Γ 0 = 2.6 and n = 10 −3 cm −3 , we still find a large l 1/2 ≈ 5 × 10 16 cm.Thus, the jet made of cold pairs would still be stopped at a large distance from the BH, and we need some additional processes to efficiently stop it.However, the main uncertainty in this estimate is in the assumption of the time the jet kinetic energy effectively accumulates of E 0 = (1/2)P j l k /c.If the effective E 0 is much lower, the jet will stop at a much closer distance.An additional effect increasing the efficiency of the jet stopping is its lateral expansion, increasing φ.The jet stopping process will be considered in detail in Heinz et al. (in preparation).
4. CONCLUSIONS We have confirmed that the accretion rate during launching of compact jets during the luminous hard state is very similar to that in the case of transient jet launching, which in turn, happens during transitions from the hard state to the soft one.This implies that the maximum possible jet powers, achieved during the MAD, are very similar.We used a specific example of the very well-studied BH XRB, MAXI J1820+070.The estimated/measured bulk Lorentz factors of both the compact and transient jets also appear similar.Furthermore, the compact jet power estimated from its synchrotron emission assuming the absence of e ± pairs would be at the MAD limit.
This would then leave unexplained the striking difference between the two types of jets, with transient jets propagating to much larger distances than the compact ones.We postulate here that compact jets consist mostly of e ± pairs, which strongly reduces both their powers and inertia estimated from their synchrotron emission.A sufficient number of pairs can be produced by photon-photon collisions of hard X-rays/soft γ-rays emitted by the accretion flow (as found in earlier works).Then, the lower jet power together with a high accretion rate imply that the hard-state luminous accretion flow has the magnetic flux much below the MAD limit, and it is consequently of the SANE type.This confirms the conclusion of Fragile et al. (2023) that the hard state is not MAD.
Compact jets then propagate and lose their internal energy, further reducing their power.This can then explain the compact jets propagating to much shorter distances than the transient jets.Propagation of compact jets in BH XRBs will be studied in detail in Heinz et al. (in preparation).

Table 1 .
Wood et al. 2021) source properties during the compact and transient jet launching in MAXI J1820+070 = 3 kpc is assumed, and ℓ max for the compact jet is based on the radio imaging at 15 GHz.We see that while both the accretion and jet properties appear similar, the maximum distances travelled are very different.precessionmodel.Similarly, Banerjee et al. (2024) obtained a * = 0.77 ± 0.21.Scaling the power to a * = 0.8 givesP MAD,compact ≈ 1.0(a * /0.8) 2 (ǫ/0.1)−1 10 39 erg s −1 .(4)Thus, the estimate for the jet compact power based on the synchrotron emission of Equation (1) in the absence of pairs is approximately equal to P MAD,compact at a * ≈ 0.8.On the other hand, P j,compact ≪ P MAD,compact for the same estimate if the jet composition is dominated by pairs.Just before and during the main transient ejection from MAXI J1820+070 (estimated to occur on MJD 58306, 2018-07-07;Wood et al. 2021), the source was in the intermediate state