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Radio jets from young stellar objects

  • Guillem Anglada
  • Luis F. Rodríguez
  • Carlos Carrasco-González
Open Access
Review Article

Abstract

Jets and outflows are ubiquitous in the process of formation of stars since outflow is intimately associated with accretion. Free–free (thermal) radio continuum emission in the centimeter domain is associated with these jets. The emission is relatively weak and compact, and sensitive radio interferometers of high angular resolution are required to detect and study it. One of the key problems in the study of outflows is to determine how they are accelerated and collimated. Observations in the cm range are most useful to trace the base of the ionized jets, close to the young central object and the inner parts of its accretion disk, where optical or near-IR imaging is made difficult by the high extinction present. Radio recombination lines in jets (in combination with proper motions) should provide their 3D kinematics at very small scale (near their origin). Future instruments such as the Square Kilometre Array (SKA) and the Next Generation Very Large Array (ngVLA) will be crucial to perform this kind of sensitive observations. Thermal jets are associated with both high and low mass protostars and possibly even with objects in the substellar domain. The ionizing mechanism of these radio jets appears to be related to shocks in the associated outflows, as suggested by the observed correlation between the centimeter luminosity and the outflow momentum rate. From this correlation and that of the centimeter luminosity with the bolometric luminosity of the system it will be possible to discriminate between unresolved HII regions and jets, and to infer additional physical properties of the embedded objects. Some jets associated with young stellar objects (YSOs) show indications of non-thermal emission (negative spectral indices) in part of their lobes. Linearly polarized synchrotron emission has been found in the jet of HH 80–81, allowing one to measure the direction and intensity of the jet magnetic field, a key ingredient to determine the collimation and ejection mechanisms. As only a fraction of the emission is polarized, very sensitive observations such as those that will be feasible with the interferometers previously mentioned are required to perform studies in a large sample of sources. Jets are present in many kinds of astrophysical scenarios. Characterizing radio jets in YSOs, where thermal emission allows one to determine their physical conditions in a reliable way, would also be useful in understanding acceleration and collimation mechanisms in all kinds of astrophysical jets, such as those associated with stellar and supermassive black holes and planetary nebulae.

Keywords

Radiation mechanisms: non-thermal Radiation mechanisms: thermal Stars: pre-main sequence ISM: Herbig–Haro objects Radio lines: stars 

1 Introduction

Until around 1980, the process of star formation was believed to be dominated by infall motions from an ambient cloud that made the forming star at its center grow in mass. Several papers published at that time indicated that powerful bipolar ejections of high-velocity molecular (Snell et al. 1980; Rodriguez et al. 1980a) and ionized (Herbig and Jones 1981) gas were also present. The star formation paradigm changed from one of pure infall to one in which infall and outflow coexisted. As a matter of fact, both processes have a symbiotic relation: the rotating disk by which the star accretes provides the energy for the outflow, while this latter process removes the excess of angular momentum that otherwise will impede further accretion.

Early studies of centimeter radio continuum from visible T Tau stars made mostly with the Very Large Array (VLA) showed that emission was sometimes detected in them (e.g., Cohen et al. 1982). Later studies made evident that in these more evolved stars the emission could have a thermal (free–free) origin but that most frequently the emission was dominated by a nonthermal (gyrosynchrotron) process (Feigelson and Montmerle 1985) produced in the active magnetospheres of the stars. These non-thermal radio stars are frequently time-variable (e.g., Rivilla et al. 2015) and its compact radio size makes them ideal for the determination of accurate parallaxes using Very Long Baseline Interferometry (VLBI) observations (e.g., Kounkel et al. 2017).

In contrast, the youngest low-mass stars, the so-called Class 0 and I objects (Lada 1991; Andre et al. 1993) frequently exhibit free–free emission at weak but detectable levels (Anglada et al. 1992). In the best studied cases, the sources are resolved angularly at the sub-arcsec scale and found to be elongated in the direction of the large-scale tracers of the outflow (e.g., Rodriguez et al. 1990; Anglada 1996), indicating that they trace the region, very close to the exciting star, where the outflow phenomenon originates. The spectral index at centimeter wavelengths \(\alpha \) (defined as \(S_\nu \propto \nu ^\alpha \)), usually rises slowly with frequency and can be understood with the free–free jet models of Reynolds (1986). Given its morphology and spectrum, these radio sources are sometimes referred to as “thermal radio jets”. It should be noted that there are a few Class I objects where the emission seems to be dominantly gyrosynchrotron (Feigelson et al. 1998; Dzib et al. 2013). These cases might be due to a favorable geometry (that is, the protostar is seen nearly pole-on or nearly edge-on, where the free–free opacity might be reduced; Forbrich et al. 2007), or to clearing of circumstellar material by tidal forces in a tight binary system (Dzib et al. 2010)

In the last years it has become clear that the radio jets are present in young stars across the stellar spectrum, from O-type protostars (Garay et al. 2003) and possibly to brown dwarfs (Palau et al. 2014), suggesting that the disk–jet scenario that explains the formation of solar-type stars extends to all stars and even into the sub-stellar regime. The observed centimeter radio luminosities (taken to be \(S_\nu d^2\), with d being the distance) go from \(\sim \) 100 mJy kpc\(^2\) for massive young stars to \(\sim 3 \times 10^{-3}\) mJy kpc\(^2\) for young brown dwarfs.

High sensitivity studies of Herbig–Haro systems revealed that a large fraction of them showed the presence of central centimeter continuum sources (Rodriguez and Reipurth 1998). With the extraordinary sensitivity of the Jansky VLA (JVLA) and planed future instrumentation it is expected that all nearby (a few kpc) young stellar objects (YSOs) known to be associated with outflows, both molecular and/or optical/infrared, will be detectable as centimeter sources (Anglada et al. 2015).

The topic of radio jets from young stars has been reviewed by Anglada (1996), Anglada et al. (2015) and Rodríguez (1997, 2011). The more general theme of multifrequency jets and outflows from young stars has been extensively reviewed in the literature, with the most recent contributions being Frank et al. (2014) and Bally (2016). In this review we concentrate on radio results obtained over the last two decades, emphasizing possible lines of study feasible with the improved capabilities of current and future radio interferometers.

2 Information from radio jets

The study of radio jets associated with young stars has several astronomical uses. Given the large obscuration present towards the very young stars, the detection of the radio jet provides so far the best way to obtain their accurate positions. These observations also provide information on the direction and collimation of the gas ejected by the young system in the last few years and allow a comparison with the gas in the molecular outflows and optical/infrared HH jets, that trace the ejection over timescales one to two orders of magnitude larger. This comparison allows to make evident changes in the ejection direction possibly resulting from precession or orbital motions in binary systems (Rodríguez et al. 2010; Masqué et al. 2012).

In some sources it has been possible to establish the proper motions of the core of the jet and to confirm its association with the region studied (Loinard et al. 2002; Rodríguez et al. 2003a; Lim and Takakuwa 2006; Carrasco-González et al. 2008a; Loinard et al. 2010; Rodríguez et al. 2012a, b). In the case of the binary jet systems L1551 IRS5 and YLW 15, the determination of its orbital motions (Lim and Takakuwa 2006; Curiel et al. 2004) allows one to confirm that they are solar-mass systems and that they are very overluminous with respect to the corresponding main sequence luminosity, as expected for objects that are accreting strongly.

The free–free radio emission at cm wavelengths has been used for a long time to estimate important physical properties of YSO jets (see below). Recently, the observation of the radio emission from jets has reached much lower frequencies, as in the recent Low Frequency ARray (LOFAR) observations at 149 GHz (2 m) of T Tau (Coughlan et al. 2017). These observations have revealed the low-frequency turnover of the free–free spectrum, a result that has allowed the degeneracy between emission measure and electron density to be broken.
Fig. 1

Images of selected radio jets. From left to right, and top to bottom: HH 1–2 (Rodríguez et al. 2000); L1551-IRS5 (Rodríguez et al. 2003b); HH 111 (Gómez et al. 2013); DG Tau (Rodríguez et al. 2012b); NGC2071-IRS3 (Carrasco-González et al. 2012a); W75N (Carrasco-González et al. 2010a); IRAS 16547−4247 (Rodríguez et al. 2005); IRAS 20126+4104 (Hofner et al. 2007); Cep A HW2 (Rodriguez et al. 1994b). Jets from low- and intermediate-mass protostars are shown in the top and middle panels, while those from high-mass protostars are shown in the bottom panels

3 Observed properties of radio jets

3.1 Properties of currently known angularly resolved radio jets

Table 1

Properties of selected angularly resolved radio jets in YSOs

Source

\(L_{\mathrm{bol}}\) (\(L_\odot \))

\(M_\star \) (\(M_\odot \))

d (kpc)

\(S_\nu \) (mJy)

\(\alpha \)

\(\theta _0\) (deg)

Size (au)

\(v_j\) (\(\text {km s}^{-1}\))

\(t_{\mathrm{dyn}}\) (year)

\(\epsilon \)

\(\dot{M}_{\textit{ion}}\) (\(M_\odot \) year\(^{-1}\))

\(r_0\) (au)

Refs.

HH 1–2 VLA1

20

\(\sim \) 1

0.4

1

0.3

19

200

270

2

0.7

\(1 \times 10^{-8}\)

\(\le \) 11

1, 2, 3, 4

NGC 2071-IRS3

\(\sim \) 500

4

0.4

3

0.6

40

200

400\(^\mathrm{a}\)

1

1.0

\(2 \times 10^{-7}\)

\(\le \) 18

5, 6, 2, 7

Cep A HW2

\(1\times 10^4\)

15

0.7

10

0.7

14

400

460

2

0.9

\(5 \times 10^{-7}\)

\(\le \) 60

8, 9, 10, 11, 12

HH 80–81

\(2\times 10^4\)

15

1.7

5

0.2

34

1500

1000

4

0.6

\(1 \times 10^{-6}\)

\(\le \) 25

13, 14, 15, 16, 17, 18

IRAS 16547-4247

\(6\times 10^4\)

20

2.9

11

0.5

25

3000

900\(^\mathrm{a}\)

8

0.9

\(8 \times 10^{-6}\)

\(\le \) 310

19, 20, 21, 22

Serpens

300

3

0.42

2.8

0.2

< 34

280

300

2

0.6

\(3 \times 10^{-8}\)

\(\le \) 9

23, 24, 25, 26, 27

AB Aur

38

2.4

0.14

0.14

1.1

< 39

24

300\(^\mathrm{a}\)

0.2

3.5

\(2 \times 10^{-8}\)

\(\le \) 3

28, 29, 30

L1551 IRS5\(^\mathrm{b}\)

20

0.6

0.14

0.8

0.1

36

39

150\(^\mathrm{a}\)

0.6

0.6

\(1 \times 10^{-9}\)

\(\le \) 1

31, 32, 33

HH 111\(^\mathrm{c}\)

25

1.3

0.4

0.8

\(\sim \) 1

< 79

110

400

0.7

2.3

\(2 \times 10^{-7}\)

\(\le \) 12

34, 35, 36, 37, 38

HL Tau

7

1.3

0.14

0.3

\(\sim \) 0.3

69

27

230\(^\mathrm{a}\)

0.3

0.7

\(2 \times 10^{-9}\)

\(\sim \) 1.5

39, 40, 41

IC 348-SMM2E

0.1

0.03

0.24

0.02

\(\sim \) 0.4

45\(^\mathrm{d}\)

< 100

\(\sim \) 50\(^\mathrm{a}\)

< 2

0.8

\(2 \times 10^{-10}\)

\(\le \) 1

42, 43, 44

W75N VLA3

750

6\(^\mathrm{d}\)

2.0

4.0

0.6

37

420

220

4.6

1.0

\(6 \times 10^{-7}\)

\(\le \) 70

45, 46

OMC2 VLA11

360

4\(^\mathrm{d}\)

0.42

2.2

0.3

10

200

100

4.6

1.0

\(6 \times 10^{-7}\)

\(\le \) 70

2, 47, 48

Re50N

250

4\(^\mathrm{d}\)

0.42

1.1

0.7

33

450

400

2.7

1.2

\(8 \times 10^{-8}\)

\(\le \) 13

2, 49, 50

References: (1) Fischer et al. (2010; 2) Menten et al. (2007; 3) Rodriguez et al. (1990; 4) Rodríguez et al. (2000; 5) Butner et al. (1990; 6) Carrasco-González et al. (2012a; 7) Torrelles et al. (1998; 8) Hughes et al. (1995; 9) Patel et al. (2005; 10) Dzib et al. (2011; 11) Curiel et al. (2006; 12) Rodriguez et al. (1994b; 13) Aspin and Geballe (1992); (14) Fernández-López et al. (2011; 15) Rodríguez et al. (1980b); (16) Marti et al. (1995; 17) Marti et al. (1993; 18) Carrasco-González et al. (2012b; 19) Zapata et al. (2015b; 20) Garay et al. (2003; 21) Rodríguez et al. (2008; 22) Rodríguez et al. (2005; 23) Dzib et al. (2010; 24) Rodriguez et al. (1989a; 25) Harvey et al. (1984; 26) Curiel et al. (1993; 27) Rodríguez-Kamenetzky et al. (2016; 28) DeWarf et al. (2003; 29) van den Ancker et al. (1997; 30) Rodríguez et al. (2014a; 31) Liseau (2005; 32) Rodríguez et al. (2003b; 33) Rodríguez et al. (1998; 34) Reipurth (1989; 35) Lee (2010; 36) Gómez et al. (2013; 37) Rodriguez and Reipurth (1994; 38) Cernicharo and Reipurth (1996; 39) Cohen (1983; 40) ALMA Partnership (2015; 41) A. M. Lumbreras et al., in preparation (42) Palau et al. (2014; 43) Forbrich et al. (2015; 44) Rodríguez et al. (2014b; 45) Persi et al. (2006; 46) Carrasco-González et al. (2010a; 47) Adams et al. (2012; 48) Osorio et al. (2017; 49) Chiang et al. (2015; 50) L. F. Rodríguez et al., in preparation

\(^\mathrm{a}\) Calculated using Eq. (12)

\(^{\mathrm{b}}\) Binary twin jet system. The values listed are the mean value of the two jets

\(^{\mathrm{c}}\) Binary jet system. The values listed are for the dominant east-west jet

\(^{\mathrm{d}}\) Assumed

In Table 1 we present the parameters of selected radio jets that have been angularly resolved. Several trends can be outlined. The spectral index, \(\alpha \), is moderately positive, going from values of 0.1 to \(\sim \) 1, with a median of 0.45. The opening angle of the radio jet near its origin, \(\theta _0\), is typically in the few tens of degrees. In contrast, if we consider the HH objects or knots located relatively far from the star, an opening angle an order of magnitude smaller is derived. This result has been taken to suggest that there is recollimation at scales of tens to hundreds of au. The jet velocity is typically in the 100 to 1000 km s\(^{-1}\) range. The ionized mass loss rate, \(\dot{M}_{\textit{ion}}\), is found to be typically an order of magnitude smaller than that determined from the large-scale molecular outflow, and as derived from atomic emission lines, a result that has been taken to imply that the radio jet is only partially ionized (\(\sim \) 1–10%; Rodriguez et al. 1990; Hartigan et al. 1994; Bacciotti et al. 1995) and that the mass loss rates determined from them are only lower limits. In Fig. 1 we show images of several selected radio jets.

3.2 Proper motions in the jet

As noted above, comparing observations taken with years of separation it has been possible in a few cases to determine the proper motions of the core of the jet, whose centroid is believed to coincide within a few au’s with the young star (e.g., Curiel et al. 2003; Chandler et al. 2005; Rodríguez et al. 2012b, a). These proper motions are consistent with those of other stars in the region.

It is also possible to follow the birth and proper motions of new radio knots ejected by the star (Marti et al. 1995; Curiel et al. 2006; Pech et al. 2010; Carrasco-González et al. 2010a, 2012a; Gómez et al. 2013; Rodríguez-Kamenetzky et al. 2016; Osorio et al. 2017). When radio knots are detected very near the protostar, these are most probably due to internal shocks in the jet resulting from changes in the velocity of the material with time. These shocks are weak, and the emission mechanism seems to be free–free emission from (partially) ionized gas. Their proper motions are directly related to the velocity of the jet material as it arises from the protostar. The observed proper motions of these internal shocks suggest velocities of the jet that go from \(\sim 100\,\hbox {km}\,\hbox {s}^{-1}\) in the low mass stars up to \(\sim 1000\,\hbox {km}\,\hbox {s}^{-1}\) in the most massive objects. So far, in some sources there is also evidence of deceleration far from the protostar. The radio knots observed by Marti et al. (1995) close to the star in the HH 80–81 system move at velocities of \(\sim \) 1000 km s\(^{-1}\) in the plane of the sky, while the more distant optical HH objects show velocities of order \(350\,\hbox {km}\,\hbox {s}^{-1}\) (Heathcote et al. 1998; Masqué et al. 2015). A similar case has been observed in the triple source in Serpens, where knots near the protostar appear to be ejected at very high velocities (\(\sim 500\,\hbox {km}\,\hbox {s}^{-1}\)), while radio knots far from the protostar move at slower velocities (\(\sim 200\,\hbox {km}\,\hbox {s}^{-1}\); Rodríguez-Kamenetzky et al. 2016). These results suggest that radio knots far from the star are then most probably tracing the shocks of the jet against the ambient medium. In some cases, when the velocity of the jet is high, the emission of these outer knots seems to be of synchrotron nature (negative spectral indices), implying that a mechanism of particle acceleration can take place at these termination shocks. This topic is discussed in more detail below (Sect. 6).

3.3 Variability

Since thermal radio jets are typically detected over scales of \(\sim \) 100 au and have velocities in the order of 300 km s\(^{-1}\), one expects that if variations are present they will be detectable on timescales of the order of the travel time (\(\sim \) a few years) or longer.

The first attempts to detect time variability suggested that modest variations, of order 10–20%, could be present in some sources (Martí et al. 1998; Rodríguez et al. 1999, 2000).

However, over time a few examples of more extreme variability were detected. The 3.5 cm flux density of the radio source powering the HH 119 flow in B335 was \(0.21\pm 0.03\) mJy in 1990 (Anglada et al. 1992), dropping to \(\le 0.08\pm 0.02\) mJy in 1994 (Avila et al. 2001), and finally increasing to \(0.39\pm 0.02\) mJy in 2001 (Reipurth et al. 2002). C. Carrasco-González et al. (in preparation) report a factor of two increase in the 1.0 cm flux density of the southern component of XZ Tau over a few months. This increase in radio flux density has been related by these authors to an optical/infrared outburst (Krist et al. 2008) attributed to the periastron passage in a close binary system.

The radio source associated with DG Tau A presented an important increase in its 3.5 cm flux density, that was \(0.41\pm 0.04\) mJy in 1994 to \(0.84\pm 0.05\) mJy in 1996 (Rodríguez et al. 2012b). The radio source associated with DG Tau B decreased from a total 3.5 cm flux density of \(0.56\pm 0.07\) mJy in 1994 to \(0.32\pm 0.05\) mJy in 1996 (Rodríguez et al. 2012a). In the source IRAS 16293–2422A2, Pech et al. (2010) observed an increase in the 3.5 cm flux density from \(1.35\pm 0.08\) mJy in 2003 to > 2.2 mJy en 2009. In these last three sources the observed variations were clearly associated with the appearance or disappearance of bright radio knots in the systems.

Despite these remarkable cases, most of the radio jets that have been monitored show no evidence of variability above the 10–20% level (e.g., Rodríguez et al. 2008; Loinard et al. 2010; Carrasco-González et al. 2012a, 2015; Rodríguez et al. 2014a; see Fig. 2). If ejections are present in these systems, they are not as bright as the cases discussed in the previous paragraph.
Fig. 2

Monitoring of the deconvolved size of the major axis (a), position angle (b), peak intensity (c), and flux density (d) of NGC2071 IRS 3 at 3.6 cm. Image reproduced with permission from Carrasco-González et al. (2012a), copyright by AAS

Given that accretion and outflow are believed to be correlated, the variations in the radio continuum emission (tracing the ionized outflow) and in the compact infrared and millimeter continuum emissions (tracing the accretion to the star) are expected to present some degree of temporal correlation. The correlation of the [OI] jet brightness with the mid-infrared excess from the inner disk and with the optical excess from the hot accretion layer has been considered as evidence that jets are powered by accretion (Cabrit 2007 and references therein; see also the recent work by Nisini et al. 2018). Also the correlation between the radio and bolometric luminosities (see Sect. 8.1) in very young objects supports this hypothesis. In these objects this correlation is expected since most of the luminosity comes from accretion, while the radio continuum traces the outflow.

However, temporal correlations between the variations in the bolometric luminosity and the radio continuum have not been clearly observed. For example, the infrared source HOPS 383 in Orion was reported to have a large bolometric luminosity increase between 2004 and 2008 (Safron et al. 2015), while the radio continuum monitoring at several epochs before and after the outburst (from 1998 to 2014) shows no significant variation in the flux density (Galván-Madrid et al. 2015). Ellerbroek et al. (2014) could not establish a relation between outflow and accretion variability in the Herbig Ae/Be star HD 163296, the former being measured from proper motions and radial velocities of the jet knots, whereas the latter was measured from near-infrared photometric and Br\(\gamma \) variability. Similarly, Connelley and Greene (2014) monitored a sample of 19 embedded (class I) YSOs with near-IR spectroscopy and found that, on average, accretion tracers such as Br\(\gamma \) are not correlated in time to wind tracers such as the H\(_2\) and [Fe II] lines. The infrared source LRLL 54361 shows a periodic variation in its infrared luminosity, increasing by a factor of 10 over roughly 1 week every 25.34 days. However, the sensitive JVLA observations of Forbrich et al. (2015) show no correlation with the infrared variations.

3.4 Outflow rotation

At the scale of the molecular outflows, several cases have been found that show a suggestion of rotation, with a small velocity gradient perpendicular to the major axis of the outflow (e.g., Chrysostomou et al. 2008; Launhardt et al. 2009; Lee et al. 2009; Zapata et al. 2010; Choi et al. 2011; Pech et al. 2012; Hara et al. 2013; Chen et al. 2016; Bjerkeli et al. 2016). Evidence of outflow rotation has also been found in optical/IR microjets from T Tauri stars (e.g., Bacciotti et al. 2002; Anderson et al. 2003; Pesenti et al. 2004; Coffey et al. 2004, 2007). The observed velocity difference across the minor axis of the molecular outflow is typically a few km s\(^{-1}\), while in the case of optical/IR microjets (that trace the inner, more collimated component) it can reach a few tens of km s\(^{-1}\). These signatures of jet rotation about its symmetry axis are very important because they represent the best way to test the hypothesis that jets extract angular momentum from the star-disk systems. However, there is considerable debate on the actual nature and origin of these gradients (Frank et al. 2014; De Colle et al. 2016). The presence of precession, asymmetric shocks or multiple sources could also produce apparent jet rotation. Also, it is possible that most of the angular momentum could be stored in magnetic form, rather than in rotation of matter (Coffey et al. 2015). To ensure that the true jet rotation is being probed it should be checked that rotation signatures are consistent at different positions along the jet, and that the jet gradient goes in the same direction as that of the disk. This kind of tests have been carried out only in very few objects (see Coffey et al. 2015) with disparate results. In the case of the rotating outflow associated with HH 797 (Pech et al. 2012) a double radio source with angular separation of \(\sim 3''\) is found at its core (Forbrich et al. 2015), suggesting an explanation in terms of a binary jet system.

It is important that the jet is observed as close as possible to the star, where any evidence of angular momentum transfer is still preserved, since far from the star the interaction with the environment can hide and confuse rotation signatures. Therefore, high angular resolution observations of radio recombination lines from radio jets, reaching the region closer to the star, could help to solve these problems. In principle, it could be possible to observe the jet near its launch region and compare the velocity gradients with those observed al larger scales. However, these observations are very difficult and can be feasible only with new instruments such as the Atacama Large Millimeter/submillimeter Array (ALMA) and in the future the Next Generation Very Large Array (ngVLA) and the Square Kilometre Array (SKA).

4 Free–free continuum emission from radio jets

4.1 Frequency dependences

Reynolds (1986) modeled the free–free emission from an ionized jet. He assumed that the ionized flow begins at an injection radius \(r_0\) with a circular cross section with initial half-width \(w_0\). He adopted power-law dependences with radius r, so that the half-width of the jet is given by
$$\begin{aligned} w = w_0 \left( {{r} \over {r_0}}\right) ^\epsilon . \end{aligned}$$
(1)
The case of \(\epsilon =1\) corresponds to a conical (constant opening angle) jet. The electron temperature, velocity, density, and ionized fraction were taken to vary as \(r/r_0\) to the powers \(q_T\), \(q_v\), \(q_n\), and \(q_x\), respectively. In general. the jets are optically thick close to the origin and optically thin at large r. The jet axis is assumed to have an inclination angle i with respect to the line of sight. In consequence, the optical depth along a line of sight through the jet follows a power law with index:
$$\begin{aligned} q_\tau = \epsilon + 2 q_x + 2 q_n - 1.35 q_T. \end{aligned}$$
(2)
Assuming flux continuity
$$\begin{aligned} q_\tau = -3 \epsilon + 2 q_x - 2 q_v - 1.35 q_T. \end{aligned}$$
(3)
Assuming the case of an isothermal jet with constant velocity and ionization fraction (\(q_T = q_v = q_x\) = 0), the flux density increases with frequency as
$$\begin{aligned} S_\nu \propto \nu ^\alpha , \end{aligned}$$
(4)
where the spectral index \(\alpha \) is given by
$$\begin{aligned} \alpha = 1.3 - {{0.7} \over {\epsilon }}. \end{aligned}$$
(5)
The angular size of the major axis of the jet decreases with frequency as
$$\begin{aligned} \theta _\nu \propto \nu ^{-0.7/\epsilon } = \nu ^{\alpha - 1.3}. \end{aligned}$$
(6)
The previous discussion is valid for frequencies below the turnover frequency \(\nu _m\), which is related to the injection radius \(r_0\). At high enough frequencies, \(\nu > \nu _m\), the whole jet becomes optically thin and the spectral index becomes − 0.1.

4.2 Physical parameters from radio continuum emission

Following Reynolds (1986) the injection radius and ionized mass loss rate are given by:
$$\begin{aligned}&\left( \frac{r_0}{\mathrm{au}}\right) = 26 \left[ \frac{(2-\alpha ) (0.1+\alpha )}{1.3-\alpha }\right] ^{0.5} \left[ {\left( \frac{S_\nu }{\mathrm{mJy}}\right) \left( \frac{\nu }{10~\mathrm{GHz}}\right) ^{-\alpha }}\right] ^{0.5} \left( \frac{\nu _m}{10~\mathrm{GHz}}\right) ^{0.5 \alpha - 1} \nonumber \\&\quad \times \left( \frac{\theta _0 \sin i}{\mathrm{rad}}\right) ^{-0.5} \left( \frac{d}{\mathrm{kpc}}\right) \left( \frac{T}{10^4~\mathrm{K}}\right) ^{-0.5}, \end{aligned}$$
(7)
$$\begin{aligned}&\left( \frac{\dot{M}_{\mathrm{ion}}}{10^{-6}~M_\odot ~{{\mathrm {year}}^{-1}}}\right) = 0.108 \left[ \frac{(2-\alpha ) (0.1+\alpha )}{1.3-\alpha }\right] ^{0.75} \left[ {\left( \frac{S_\nu }{\mathrm{mJy}}\right) \left( \frac{\nu }{\mathrm{10~GHz}}\right) ^{-\alpha }}\right] ^{0.75} \nonumber \\&\quad \times \left( \frac{v_{j}}{200~{\mathrm{km~s}}^{-1}}\right) \left( \frac{\nu _m}{\mathrm{10~GHz}}\right) ^{0.75 \alpha - 0.45} \left( \frac{\theta _0}{\mathrm{rad}}\right) ^{0.75} \left( {\sin i}\right) ^{-0.25} \nonumber \\&\quad \times \left( \frac{d}{{\mathrm{kpc}}}\right) ^{1.5} \left( \frac{T}{10^4~\mathrm{K}}\right) ^{-0.075}, \end{aligned}$$
(8)
where \(\theta _0 = 2 w_0/r_0\) is the injection opening angle of the jet, that usually is roughly estimated using
$$\begin{aligned} \theta _0 = 2~\arctan (\theta _{\mathrm{min}}/\theta _{\mathrm{maj}}), \end{aligned}$$
(9)
where \(\theta _{\mathrm{min}}\) and \(\theta _{\mathrm{maj}}\) are the deconvolved minor and major axes of the jet. We note that the dimensions of the jet are very compact, comparable or smaller than the beam and as a consequence the value of \(\theta _0\) is uncertain. The opening angle determined on larger scales (for example using Herbig–Haro knots along the flow away from the jet core) is usually smaller and at present it is not known if this is the result of recollimation or of an overestimate in the measurement of \(\theta _0\).
In the case of a conical (\(\alpha = 0.6\)) jet, Eqs. (7) and (8) simplify to:
$$\begin{aligned} \left( \frac{r_0}{\mathrm{au}}\right)= & {} 31\left[ {\left( \frac{S_\nu }{\mathrm{mJy}}\right) \left( \frac{\nu }{\mathrm{10~GHz}}\right) ^{-0.6}}\right] ^{0.5} \left( \frac{\nu _m}{\mathrm{10~GHz}}\right) ^{-0.7} \nonumber \\&\times \left( \frac{\theta _0 \sin i}{\mathrm{rad}}\right) ^{-0.5} \left( \frac{d}{\mathrm{kpc}}\right) \left( \frac{T}{\mathrm{10^4~K}}\right) ^{-0.5}, \end{aligned}$$
(10)
$$\begin{aligned} \left( \frac{\dot{M}_{\mathrm{ion}}}{10^{-6}~M_\odot ~{\mathrm{year}}^{-1}}\right)= & {} 0.139 \left[ {\left( \frac{S_\nu }{\mathrm{mJy}}\right) \left( \frac{\nu }{\mathrm{10~GHz}}\right) ^{-0.6}}\right] ^{0.75} \nonumber \\&\times \left( \frac{v_{j}}{200~{\mathrm{km~s}^{-1}}}\right) \left( \frac{\theta _0}{\mathrm{rad}}\right) ^{0.75} \left( {\sin i}\right) ^{-0.25} \nonumber \\&\times \left( \frac{d}{\mathrm{kpc}}\right) ^{1.5} \left( \frac{T}{\mathrm{10^4~K}}\right) ^{-0.075}, \end{aligned}$$
(11)
Usually a value of \(T = 10^4\) K is adopted. In a few cases there is information on the jet velocity, but in general one has to assume a velocity typically in the range from 100 km s\(^{-1}\) to 1000 km s\(^{-1}\), depending on the mass of the young star. Following Panoglou et al. (2012) and assuming a launch radius of about 0.5 au (Estalella et al. 2012), the jet velocity can be crudely estimated from
$$\begin{aligned} \left( {{v_j} \over {\mathrm{km~s^{-1}}}}\right) \simeq 140 \left( {{M_*} \over {0.5~M_\odot }}\right) ^{1/2}. \end{aligned}$$
(12)
Until recently, the turnover frequency has not been determined directly from observations and is estimated that it will appear above 40 GHz. Only in the case of HL Tau, the detailed multifrequency observations and modeling suggest a value of \(\sim \) 1.5 au (A.M. Lumbreras et al., in preparation). Determining \(\nu _m\) is difficult because at high frequencies dust emission from the associated disk starts to become dominant. Future observations at high frequencies made with high angular resolution should allow to separate the compact free–free emission from the base of the jet to that of the more extended dust emission in the disk and give more determinations of \(\nu _m\) and of the morphology and size of the gap between the star and the injection radius of the jet. Anyhow, the dependence of \(r_0\) on \(\nu _m\) is not critical, that is, in order to change \(r_0\) one order of magnitude, the turnover frequency should typically change a factor of \(\sim \) 30. Assuming a lower limit of \(\sim \) 10 GHz for the turnover frequency, upper limits of \(\sim \) 10 au have been obtained for \(r_0\) (Anglada et al. 1998; Beltrán et al. 2001).

In the case of \(\dot{M}_{\mathrm{ion}}\) the dependence on \(\nu _m\) is almost negligible and disappears for the case of a conical jet \((\alpha = 0.6).\) Using this technique, ionized mass loss rates in the range of \(10^{-10}~M_\odot \) year\(^{-1}\) (low-mass objects) to \(10^{-5}~M_\odot \) year\(^{-1}\) (high-mass objects) have been determined (Rodriguez et al. 1994b; Beltrán et al. 2001; Guzmán et al. 2016, 2012; see Table 1).

5 Radio recombination lines from radio jets

5.1 LTE formulation

Following Reynolds (1986), the flux density at frequency \(\nu \), \(S_\nu \), from a jet is given by
$$\begin{aligned} S_\nu = \int _0^\infty B_\nu (T) (1 - \exp [-\tau _\nu ])\,\mathrm{d} \varOmega , \end{aligned}$$
(13)
where \(B_\nu (T)\) is the source function (taken to be Planck’s function since we are assuming LTE), \(\tau _\nu \) is the optical depth along a line of sight through the jet, and \(\mathrm{d} \varOmega \) is the differential of solid angle.
Since
$$\begin{aligned} \mathrm{d} \varOmega = {{2 w(r)} \over {d^2}}\,\mathrm{d}y, \end{aligned}$$
(14)
where d is the distance to the source and \(y = r \sin i\) is the projected distance in the plane of the sky. Assuming an isothermal jet, the continuum emission is given by
$$\begin{aligned} S_{\mathrm{C}} = B_\nu (T) \int _0^\infty {{2 w(r)} \over {d^2}} (1 - \exp [-\tau _{\mathrm{C}}])\,\mathrm{d}y, \end{aligned}$$
(15)
while the line plus continuum emission will be given by
$$\begin{aligned} S_{\mathrm{L}+\mathrm{C}} = B_\nu (T) \int _0^\infty {{2 w(r)} \over {d^2}} (1 - \exp [-\tau _{\mathrm{L}+\mathrm{C}}])\,\mathrm{d}y. \end{aligned}$$
(16)
The line-to-continuum ratio will be given by
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = {{S_{\mathrm{L}+\mathrm{C}}} \over {S_{\mathrm{C}}}} -1. \end{aligned}$$
(17)
Using the power law dependences of the variables and noting that the line and the continuum opacities have the same radial dependence, we obtain
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = {{\int _0^\infty y^{\epsilon } (1 - \exp [-\tau _{\mathrm{L}+\mathrm{C}}(r_0) y^{\epsilon + 2 q_x + 2 q_n}/ \sin i])\,\mathrm{d}y} \over {\int _0^\infty y^{\epsilon } (1 - \exp [-\tau _{\mathrm{C}}(r_0) y^{\epsilon + 2 q_x + 2 q_n}/ \sin i])\,\mathrm{d}y}} - 1. \end{aligned}$$
(18)
Using the definite integral (Gradshteyn and Ryzhik 1994)
$$\begin{aligned} \int _0^\infty [1- \exp (-\mu x^{p})]~x^{t-1}~\mathrm{d}x = - {{1} \over {|p|}}~ \mu ^{-{{t} \over {p}}}~ \varGamma \left( {{t} \over {p}}\right) , \end{aligned}$$
(19)
valid for \(0< t < -p\) for \(p < 0\) and with \(\varGamma \) being the Gamma function.
We then obtain
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = \left[ {{\tau _{\mathrm{L}+\mathrm{C}}(r_0)} \over {\tau _{\mathrm{C}}(r_0)}} \right] ^{-(\epsilon +1)/(\epsilon + 2 q_x + 2 q_n)} - 1. \end{aligned}$$
(20)
Finally,
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = \left[ {{\kappa _{\mathrm{L}}} \over {\kappa _{\mathrm{C}}}} + 1 \right] ^{-(\epsilon +1)/(\epsilon + 2 q_x + 2 q_n)} - 1, \end{aligned}$$
(21)
where \(\kappa _{\mathrm{L}}\) and \(\kappa _{\mathrm{C}}\) are the line and continuum absorption coefficients at the frequency of observation, respectively. Substituting the LTE ratio of these coefficients (Mezger and Hoglund 1967; Gordon 1969; Quireza et al. 2006), we obtain:
$$\begin{aligned}&{{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}}=\left[ 0.28 {\left( {\nu _{\mathrm{L}}\over {\mathrm{GHz}}}\right) ^{1.1}} {\left( {{T}\over {\mathrm{10^4\,K}}}\right) ^{-1.1}}{\left( \frac{\varDelta v}{\mathrm{km\,s^{-1}}}\right) ^{-1}}{(1 + Y^+)^{-1}}+1\right] ^{-(\epsilon +1)/(\epsilon + 2 q_x + 2 q_n)} -1,\nonumber \\ \end{aligned}$$
(22)
where \(\nu _{\mathrm{L}}\) is the frequency of the line, \(\varDelta v\) the full width at half maximum of the line, and \(Y^+\) is the ionized helium to ionized hydrogen ratio.
For a standard biconical jet with constant velocity and ionized fraction, the equation becomes
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = \left[ 0.28 \left( {{\nu _{\mathrm{L}}} \over {\mathrm{GHz}}} \right) ^{1.1} \left( {{T} \over {\mathrm{10^4~K}}} \right) ^{-1.1} \left( {{\varDelta v} \over {\mathrm{km~s^{-1}}}}\right) ^{-1} (1 + Y^+)^{-1} + 1 \right] ^{2/3} - 1.\nonumber \\ \end{aligned}$$
(23)
In the centimeter regime, the first term inside the brackets is smaller than 1 and using a Taylor expansion the equation can be approximated by
$$\begin{aligned} {{S_{\mathrm{L}}} \over {S_{\mathrm{C}}}} = 0.19 \left( {{\nu _{\mathrm{L}}} \over {\mathrm{GHz}}} \right) ^{1.1} \left( {{T} \over {\mathrm{10^4~K}}} \right) ^{-1.1} \left( {{\varDelta v} \over {\mathrm{km~s^{-1}}}}\right) ^{-1} (1 + Y^+)^{-1}. \end{aligned}$$
(24)
Are these relatively weak RRLs detectable with the next generation of radio interferometers? Let us assume that we attempt to observe the H86\(\alpha \) line at 10.2 GHz and adopt an electron temperature of \(10^4\) K and an ionized helium to ionized hydrogen ratio of 0.1. The line width expected for these lines is poorly known. If the jet is highly collimated, the line width could be a few tens of km s\(^{-1}\), similar to those observed in HII regions and dominated by the microscopic velocity dispersion of the gas. Under these circumstances, we expect to see two relatively narrow lines separated by the projected difference in radial velocity of the two sides of the jet. However, if the jet is highly turbulent and/or has a large opening angle we expect a single line with a width of a few hundreds of km s\(^{-1}\). Since for a constant area under the line it is easier to detect narrow lines (the signal-to-noise ratio improves as \(\varDelta v^{-1/2}\)), we will conservatively (perhaps pessimistically) assume a line width of 200 km s\(^{-1}\).

Using Eq. (24) we obtain that the line-to-continuum ratio will be \(S_{\mathrm{L}}/S_{\mathrm{C}} = 0.011.\) The brightest thermal jets (see Table 1) have continuum flux densities of about 5 mJy, so we expect a peak line flux density of 55 \(\upmu \)Jy. These are indeed weak lines. However, the modern wide-band receivers allow the simultaneous detection of many recombination lines. For example, in the X band (8–12 GHz) there are 11 \(\alpha \) lines (from the H92\(\alpha \) at 8.3 GHz to the H82\(\alpha \) at 11.7 GHz). Stacking N different lines will improve the signal-to-noise ratio by \(N^{1/2}\), so we expect a gain of a factor of 3.3 from this averaging.

At present, the Jansky VLA will give, for a frequency of 10.2 GHz, a channel width of 100 km s\(^{-1}\) and, with an on-source integration time of \(\sim \) 45 h, an rms noise of \(\sim \) 11 \(\upmu \)Jy beam\(^{-1}\), sufficient to detect the H86\(\alpha \) emission at the 5\(\sigma \) level from a handful of bright jets. Line stacking will improve this signal-to-noise ratio by 3.3. In contrast, the ngVLA is expected to be 10 times as sensitive as the Jansky VLA, which means that a similar sensitivity will be achieved with 1/100 of the time, that is about 0.5 h. For an on-source integration time of about 14 hours the ngVLA will have an rms noise of \(\sim \) 2 \(\upmu \)Jy beam\(^{-1}\) in the line mode previously described and will be able to detect the RRLs from the more typical 1 mJy continuum jet at the 5\(\sigma \) level. Line stacking will increase this detection to a very robust \(\sim \) 16\(\sigma \). This will allow to start resolving the jets into at least a few pixels and start studying the detailed kinematics of the jet. Then, a program of a few hundred hours with the ngVLA will characterize the RRL emission from a wide sample of thermal jets. Similar on-source integration times would be required with the expected sensitivity of the SKA (see Anglada et al. 2015).

5.2 Stark broadening

The collisions between the electrons and the atoms produce a line broadening, known as Stark or pressure broadening, that depends strongly on the electron density of the medium and in particular on the level of the transition. For an RRL with principal quantum number n, quantum number decrement \(\varDelta n\) in a medium with electron density \(N_{\mathrm{e}}\) and electron temperature \(T_{\mathrm{e}}\), the Stark broadening is given by (Walmsley 1990):
$$\begin{aligned} \left( \delta _S \over {\mathrm{km ~s}}^{-1} \right) = 2.72 \left( {n \over 42} \right) ^{7.5} \varDelta n^{-1} \left( {N_{\mathrm{e}} \over 10^7 ~{\mathrm{cm}}^{-3}} \right) \left( {T_{\mathrm{e}} \over 10^4 ~{\mathrm{K}}} \right) ^{-0.1}. \end{aligned}$$
(25)
Stark broadening has been detected in the case of HII regions (e.g., Smirnov et al. 1984; Alexander and Gulyaev 2016) and slow ionized winds (e.g., Guzmán et al. 2014). Would it be an important effect in the case of RRLs from ionized jets? In contrast with HII regions, where a uniform electron density can approximately describe the object, thermal jets are characterized by steep gradients in the electron density, that is expected to decrease typically as the distance to the star squared (see discussion above). On the other hand, the inner parts of a thermal jet are optically thick in the continuum and do not contribute to the recombination line emission. All the line emission comes from radii external to the line of sight where the free–free continuum opacity, \(\tau _{\mathrm{C}}\), is \(\sim \) 1.
The length of the jets along its major axis is of the order of twice the radius at which \(\tau _{\mathrm{C}} \simeq 1\). From Table 1 we estimate that at cm wavelengths the distance from the star where \(\tau _{\mathrm{C}} \simeq 1\) is in the range of 100 to 500 au. Assuming a typical opening angle of \(30^\circ \) we find that the physical depth of the jet, 2w, at this position ranges from 50 to 250 au. The free–free opacity is given approximately by (Mezger et al. 1967):
$$\begin{aligned} \tau _{\mathrm{C}} \simeq 1.59 \times 10^{-10} \left( {T_{\mathrm{e}} \over 10^4 ~{\mathrm{K}}} \right) ^{-1.35} \left( {\nu \over {\mathrm{GHz}}}\right) ^{-2.1} \left( {N_{\mathrm{e}} \over {\mathrm{cm}}^{-3}}\right) ^{2} \left( {2 w \over 100 ~{\mathrm{au}}}\right) . \end{aligned}$$
(26)
Adopting \(T_{\mathrm{e}} = 10^4\) K, \(\nu = 10.2\) GHz (the H86\(\alpha \) line) and \(\tau _{\mathrm{C}} = 1,\) we find that the electron density at this position will be in the range of \(5.7 \times 10^5\) cm\(^{-3}\) to \(1.3 \times 10^6\) cm\(^{-3}\). The recombination line emission will be coming from regions with electron densities equal or smaller than these values. Finally, using the equation for the Stark broadening given above, we find that the broadening will be in the range of 33–167 km s\(^{-1}\). We then conclude that Stark broadening will be important in the case that the line widths are of the order of the microscopic velocity dispersion (tens of km s\(^{-1}\)), but it will not be dominant in the case that the line widths have a value similar to that of the jet speed.

5.3 Non-LTE radio recombination lines

The treatment presented here assumes that the recombination line emission is in LTE, which seems to be a reasonable approach. There are, however, cases where the LTE treatment is clearly insufficient and a detailed modeling of the line transfer is required. The more clear case is that of MWC 349A, a photoevaporating disk located some 1.2 kpc away (Gordon 1994). Even when this source is not a jet properly but a photoevaporated wind, we discuss it briefly since it is the best case known of non-LTE radio recombination lines.

At centimeter wavelengths, the line emission from MWC 349A is consistent with LTE conditions (Rodriguez and Bastian 1994). However, at the millimeter wavelengths, below 3 mm, this source presents strong, double-peaked hydrogen recombination lines (Martin-Pintado et al. 1989). These spectra arise from a dense Keplerian-rotating disk, that is observed nearly edge-on (Weintroub et al. 2008; Báez-Rubio et al. 2014). The flux density of these features is an order or magnitude larger than expected from the LTE assumption and the inference that maser emission is at work seems well justified. However, the nature of MWC 349A remains controversial, with some groups considering it a young object, while others attribute to it an evolved nature (Strelnitski et al. 2013).

Extremely broad millimeter recombination lines of a possible maser nature have been reported from the high-velocity ionized jet Cep A HW2 (Jiménez-Serra et al. 2011). In this case, the difference between the LTE and non-LTE models is less than a factor of two and in some of the transitions it is necessary to multiply the non-LTE model intensities by a factor of several to agree with the observations. The source Mon R2-IRS2 could be a case of weakly amplified radio recombination lines in a young massive star. Jiménez-Serra et al. (2013) report toward this source a double-peaked spectrum. with the peaks separated by about 40 km s\(^{-1}\). However, the line intensity is only \(\sim \) 50% larger than expected from LTE. Jiménez-Serra et al. (2013) propose that the radio recombination lines arise from a dense and collimated jet embedded in a cylindrical ionized wind, oriented nearly along the line of sight. In the case of LkH\(\alpha \)101, Thum et al. (2013) find the millimeter RRLs to be close to LTE and to show non-Gaussian wings that can be used to infer the velocity of the wind, in this case 55 km s\(^{-1}\). Finally, Guzmán et al. (2014) detect millimeter recombination lines from the high-mass young stellar object G345.4938+01.4677. The hydrogen recombination lines exhibit Voigt profiles, which is a strong signature of Stark broadening. The continuum and line emissions can be successfully reproduced with a simple model of a slow ionized wind in LTE.

6 Non-thermal emission from radio jets

As commented above, jets from YSOs have been long studied at radio wavelengths through their thermal free–free emission which traces the base of the ionized jet, and shows a characteristic positive spectral index (the intensity of the emission increases with the frequency, e.g., Rodriguez 1995, 1996; Anglada 1996). However, in the early 1990s, sensitive observations started to reveal that non-thermal emission at centimeter wavelengths might be also present in several YSO jets (e.g., Rodriguez et al. 1989a; Rodríguez et al. 2005; Marti et al. 1993; Garay et al. 1996; Wilner et al. 1999). This non-thermal emission is usually found in relatively strong radio knots, away from the core, showing negative spectral indices at centimeter wavelengths (see Fig. 3). Oftentimes, these non-thermal radio knots appear in pairs, moving away from the central protostar at velocities of several hundred kilometers per second (e.g., the triple source in Serpens; Curiel et al. 1993). Because of these characteristics, it was proposed that these knots could be tracing strong shocks of the jet against dense material in the surrounding molecular cloud where the protostar is forming. Their non-thermal nature was interpreted as synchrotron emission from a small population of relativistic particles that would be accelerated in the ensuing strong shocks. This scenario is supported by several theoretical studies, showing the feasibility of strong shocks in protostellar jets as efficient particle accelerators (e.g., Araudo et al. 2007; Bosch-Ramon et al. 2010; Padovani et al. 2015, 2016; Cécere et al. 2016).
Fig. 3

Image of the non-thermal radio jet in Serpens. The radio continuum image is shown in contours and was made by combining the data from the S, C, and X bands. This image is superposed on the spectral index image (color contours). Image reproduced with permission from Rodríguez-Kamenetzky et al. (2016), copyright by AAS

The possibility of protostellar jets as efficient particle accelerators has been confirmed only recently, with the detection and mapping of linearly polarized emission from the YSO jet in HH 80–81 (Carrasco-González et al. 2010b; see Fig. 4). This result provided for the first time conclusive evidence for the presence of synchrotron emission in a jet from a YSO, and then, the presence of relativistic particles.
Fig. 4

Images of the non-thermal HH 80–81 radio jet. The left panel (a) shows in color scale the total intensity at 6 cm extending from the central source to the HH objects. The upper right panel (b) shows a close-up of the central region with the total intensity in contours and the linearly polarized emission in colors. The white bars indicate the direction of the polarization. The bottom right panel (c) shows the direction of the magnetic field. Image reproduced with permission from Carrasco-González et al. (2010b), copyright by AAAS

At centimeter wavelengths, where most of the radio jet studies have been carried out, the emission of the non-thermal lobes is usually weaker than that of the thermal core of the jet. Consequently, most of the early detections of non-thermal radio knots were obtained through very sensitive observations resulting from unusually long projects, mainly carried out at the VLA. After the confirmation in 2010 of synchrotron emission in the HH 80–81 radio jet, the improvement in sensitivity of radio interferometers has facilitated higher sensitivity observations at multiple wavelengths of star forming regions, and new non-thermal protostellar jet candidates are emerging (e.g., Purser et al. 2016; Osorio et al. 2017; Hunter et al. 2018; Tychoniec et al. 2018; see Fig. 5). It is then expected that the next generation of ultra-sensitive radio interferometers (LOFAR, SKA, ngVLA) will produce very detailed studies on the nature of non-thermal emission in protostellar jets.
Fig. 5

The non-thermal radio jet from the intermediate-mass YSO FIR3 (VLA 11) in OMC-2. The left panel shows the 3 cm continuum emission (angular resolution \(\sim 2''\)) of the thermal core (VLA 11) and the non-thermal lobe (VLA 12N, 12C, 12S) of the FIR3 radio jet. Insets show the 5 cm emission at higher angular resolution (\(\sim 0.3''\)) of the thermal core of the FIR3 radio jet and of the Class 0 protostar HOPS 108. The right panels show the spectra of the radio sources. Image adapted from Osorio et al. (2017)

It is worth noting that, even when non-thermal emission is brighter at lower frequencies, most of the proposed detections have been performed at relatively high frequencies, typically in the 4–10 GHz range. One reason is that studies of radio jets have been focused preferentially on the detection of thermal emission, which is dominant at higher frequencies. Another reason is the lack of sensitivity at low frequencies, specially below 1 GHz, in most of the available interferometers. However, despite the small number of sensitive observations performed at low frequencies, they have produced very interesting results. For example, the only non-thermal radio jet candidate associated with a low-mass protostar known so far has been identified through Giant Metrewave Radio Telescope (GMRT) observations of DG Tau in the 300–700 MHz range (Ainsworth et al. 2014; see Fig. 6). Very recent GMRT observations of HH 80–81 (Vig et al. 2018) at 325 and 610 MHz found negative spectral indices steeper than previous studies at higher frequencies. This has been interpreted as indicating that an important free–free contribution is present at high frequencies even in the non-thermal radio knots. We should then expect more interesting results from low-frequency observations using the next generation of low-frequency interferometers, such as the Low Wavelength Array (LWA), and the aforementioned LOFAR and SKA.
Fig. 6

GMRT image at 325 MHz (dashed contours) and 610 MHz (solid contours) overlaid on a composite RGB image (I, H\(\alpha \) and [SII]) of the DG Tau jet. The VLA positions of the bow shock at 5.4 and 8.5 GHz are shown as a plus (+) and a cross (\(\times \)), respectively. The optical stellar position is shown as an asterisk (\(*\)) and the optical jet axis and bow shock are shown as solid black lines. Image reproduced with permission from Ainsworth et al. (2014), copyright by AAS

At present, the best studied cases of particle acceleration in protostellar jets are the triple source in Serpens and HH 80–81 (Rodríguez-Kamenetzky et al. 2016, 2017). These sources were observed very recently with the VLA combining high angular resolution and very high sensitivity in the 1–10 GHz frequency range. These observations resolve both jets at all observed frequencies, allowing to study the different emission mechanisms present in the jet in a spatially resolved way. In both cases, strong non-thermal emission is detected at the termination points of the jets, which is consistent with particle acceleration in strong shocks against a very dense ambient medium. Additionally, in the case of HH 80–81, non-thermal emission is observed at several positions along the very well collimated radio jet, suggesting that this object is able to accelerate particles also in internal shocks (Rodríguez-Kamenetzky et al. 2017). Overall, these studies have found that the necessary conditions to accelerate particles in a protostellar jet are high velocities (\(\gtrsim \) 500 km s\(^{-1}\)) and an ambient medium denser than the jet. These conditions are probably well satisfied in the case of very young protostellar jets, which are still deeply embedded in their parental cloud.

The discovery of linearly polarized emission in the HH 80–81 radio jet by Carrasco-González et al. (2010b) opened the interesting possibility of studying magnetic fields in protostellar jets. Detection of linearly polarized emission at several wavelengths would allow one to infer the properties of the magnetic field in these jets in a way similar to that commonly employed in AGN jets. The magnetic field strength can be estimated from the spectral energy distribution at cm wavelengths (e.g., Pacholczyk 1970; Beck and Krause 2005), while the magnetic field morphology can be obtained from the properties of the linear polarization (polarization angle, polarization degree and Faraday rotation). For non-relativistic jets, the apparent magnetic field (magnetic field averaged along the line-of-sight) is perpendicular to the direction of the linear polarization. Moreover, theoretical models of helical magnetic fields predict gradients of the polarization degree and Faraday rotation measurements along and across the jet (Lyutikov et al. 2005). Thus, by comparing the observational results with theoretical models, the 3D morphology of the magnetic field can be inferred.

Mapping the polarization in a set of YSO jets in combination with detailed theoretical modeling may lead to a deeper understanding of the overall jet phenomenon. However, radio synchrotron emission in YSO jets seems to be intrinsically much weaker and difficult to study than in relativistic jets (e.g., AGN and microquasar jets). So far, only in the case of HH 80–81, one of the brightest and most powerful YSO jets known, it has been possible to obtain enough sensitivity to detect and study its linear polarization, which is only a fraction of the total continuum emission. Subsequent higher sensitivity studies (Rodríguez-Kamenetzky et al. 2016, 2017) have not been able to detect polarization in YSO jets. One of the reasons of this is that, due to the presence of thermal electrons mixed with the relativistic particles, we expect strong Faraday rotation. At the moment, high sensitivities in radio interferometers are obtained by averaging data in large bandwidths. Within these bandwidths, we expect large rotations of the polarization angle, resulting in strong depolarization when the emission is averaged. Then, it is still necessary to observe using long integration times in order to obtain enough sensitivity to detect polarization in smaller frequency ranges. Note that using the Faraday RM-Synthesis tool (Brentjens and Bruyn 2005) to determine the rotation measure to account for this effect is also hampered by the poor signal-to-noise ratio over narrow frequency ranges in these weak sources. At the moment, probably HH 80–81 is the only object bright enough to perform a study of polarization at several wavelengths; and even in this object, polarization would be detected only after observations of several tens of hours long. Therefore, we will probably have to wait for new ultra-sensitive interferometers in order to perform a polarization study in a large sample of protostellar jets.
Fig. 7

a Distribution and proper motions of H\(_2\)O masers showing a very compact (\(\sim \) 180 au), short-lived (\(\sim \) 40 year), bipolar jet from a very embedded protostar of unknown nature in the LkH\(\alpha \) 234 star-forming region (Torrelles et al. 2014). b Micro-bow shock traced by water masers in AFGL2591 VLA 3-N. Arrows indicate the measured proper motions (Trinidad et al. 2013). c Maser microstructures tracing a low-collimation outflow around the radio jet associated with the massive protostar Cep A HW2 (Torrelles et al. 2011). d Magnetic field structure around the protostar–disk–jet system of Cep A HW2. Spheres indicate the \(\hbox {CH}_3\hbox {OH}\) masers and black vectors the magnetic field direction. Image adapted from Vlemmings et al. (2010)

7 Masers as tracers of jets

Molecular maser emission at cm wavelengths (e.g., \(\hbox {H}_2\hbox {O}\), \(\hbox {CH}_3\hbox {OH}\), OH) is often found in the early evolutionary stages of massive protostars. Such maser emission is usually very compact and strong, with brightness temperatures exceeding in some cases 10\(^{10}\) K, allowing the observation of outflows at milliarcsecond (mas) scales (1 mas = 1 au at a distance of 1 kpc) using Very Long Baseline Interferometry (VLBI). Sensitive VLBI observations show, in some sources, thousands of maser spots forming microstructures that reveal the 3D kinematics of outflows and disks at small scale (e.g., Sanna et al. 2015). This kind of observations have given a number of interesting results: the discovery of short-lived, episodic non-collimated outflow events (e.g., Torrelles et al. 2001, 2003; Surcis et al. 2014); detection of infall motions in accretion disks around massive protostars (Sanna et al. 2017); the imaging of young (\(< 100\) year) small-scale (a few 100 au) bipolar jets of masers (Sanna et al. 2012, Torrelles et al. 2014; Fig. 7a), and even allowed to analyze the small-scale (1–20 au) structure of the micro bow-shocks (Uscanga et al. 2005; Trinidad et al. 2013; Fig. 7b); the simultaneous presence of a wide-angle outflow and a collimated jet in a massive protostar (Torrelles et al. 2011; see Fig. 7c); and polarization studies have determined the distribution and strength of the magnetic field very close to protostars allowing to better understand its role in the star formation processes (Surcis et al. 2009; Vlemmings et al. 2010; Sanna et al. 2015; Fig. 7d).

In particular, the combination of continuum and maser studies in Cep A HW2 has been useful to provide one of the best examples of the two-wind model for outflows from massive protostars (Torrelles et al. 2011; Fig. 7c). In this source the water masers trace the presence of a relatively slow (\(\sim \) 10–70 km s\(^{-1}\)) wide-angle outflow (opening angle of \(\sim 102^\circ \)), while the thermal jet traces a fast (\(\sim \) 500 km s\(^{-1}\)) highly collimated radio jet (opening angle of \(\sim 18^\circ \)). This two-wind phenomenon had been previously imaged only in low mass protostars such as L1551-IRS5 (Itoh et al. 2000, Pyo et al. 2005), HH 46/47 (Velusamy et al. 2007), HH 211 (Gueth and Guilloteau 1999, Hirano et al. 2006) and IRAS 04166+2706 (Santiago-García et al. 2009). An extensive study of the connection between high-velocity collimated jets and slow un-collimated winds in a large sample of low-mass class II objects has been carried out recently by Nisini et al. (2018); this work has been performed from the analysis of [OI]6300 Å line profiles under the working hypothesis that the low velocity component traces a wide wind and the high-velocity component a collimated jet.

8 Nature of the centimeter continuum emission in thermal radio jets

8.1 Observational properties: radio to bolometric luminosity correlation

Photoionization does not appear to be the ionizing mechanism of radio jets since, in the sources associated with low-luminosity objects, the rate of ionizing UV photons (\(\lambda <912\) Å) from the star is clearly insufficient to produce the ionization required to account for the observed radio continuum emission (e.g., Rodriguez et al. 1989b; Anglada 1995). For low-luminosity objects (\(1 \lesssim L_{\mathrm{bol}} \lesssim 1000~L_\odot \)), the observed flux densities at cm wavelengths are several orders of magnitude higher than those expected by photoionization (see Fig. 8 and left panel in Fig. 5 of Anglada 1995). Ionization by shocks in a strong stellar wind or in the jet itself has been proposed as the most likely possibility (Torrelles et al. 1985; Curiel et al. 1987, 1989; Anglada et al. 1992; see below). Detailed simulations of the two-shock internal working surfaces traveling down the jet flow, and the expected emission of the ionized material at shorter wavelengths have been performed (e.g., the H\(\alpha \) and [OI]6300 Å line emission of a radiative jet model with a variable ejection velocity by Raga et al. 2007).
Fig. 8

Empirical correlation between the bolometric luminosity and the radio continuum luminosity at cm wavelengths. Data are taken from Table 2. Triangles correspond to high luminosity objects (\(L_{\mathrm{bol}} > 1000~L_\odot \)), dots correspond to low-luminosity objects (\(1 \le L_{\mathrm{bol}} \le 1000~L_\odot \)), and squares to very low-luminosity objects (\(L_{\mathrm{bol}} < 1~L_\odot \)). The dashed line is a least-squares fit to all the data points and the grey area indicates the residual standard deviation of the fit. The solid line is a fit to the low-luminosity objects alone. The dot-dashed line corresponds to the expected radio luminosity of an optically thin region photoionized by the Lyman continuum of the star

In Fig. 8 we plot the observed cm luminosity (\(S_\nu d^2\)) as a function of the bolometric luminosity for the sources listed in Table 2 (squares, dots, and triangles correspond, respectively, to very low, low, and high luminosity objects). For most of the sources in this plot, \(S_\nu \) is the flux density at 3.6 cm, but some data at 6, 2, and 1.3 cm are included to construct a larger sample; these data points are used to estimate the 3.6 cm luminosity using the spectral index, when known, or assuming a value of \(\sim \) 0.5. As can be seen in Fig. 8, the observed cm luminosity (data points) is uncorrelated with the cm luminosity expected from photoionization (dot-dashed line), further indicating that this is not the ionizing mechanism. However, as the figure shows, the observed cm luminosity is indeed correlated with the bolometric luminosity (\(L_{\mathrm{bol}}\)). A fit to the 48 data points with \(1~L_\odot \lesssim L_{\mathrm{bol}} \lesssim 1000~L_\odot \) (dots) gives:
$$\begin{aligned} {\left( \frac{S_\nu d^2}{\mathrm{mJy~kpc^2}}\right) } = 10^{-1.93\pm 0.14} \left( \frac{L_{\mathrm{bol}}}{L_\odot }\right) ^{0.54\pm 0.08}. \end{aligned}$$
(27)
As can be seen in the figure, the correlation also holds for both the most luminous (triangles) and the very low luminosity (squares) objects, suggesting that the mechanism that relates the bolometric and cm luminosities is shared by all the YSOs. A fit to all the 81 data points (\(10^{-2}~L_\odot \lesssim L_{\mathrm{bol}} \lesssim 10^6~L_\odot \)) gives a better fit, with a similar result,
$$\begin{aligned} {\left( \frac{S_\nu d^2}{\mathrm{mJy~kpc^2}}\right) } = 10^{-1.90\pm 0.07} \left( \frac{L_{\mathrm{bol}}}{L_\odot }\right) ^{0.59\pm 0.03}. \end{aligned}$$
(28)
Table 2

Sample of YSOs associated with outflows and radio continuum emission

Source

d (kpc)

\(L_{\mathrm{bol}}\) (\(L_\odot \))

\(S_\nu \) (mJy)

\(\dot{P}\) (\(M_\odot \,{\mathrm{year^{-1}\,km~s^{-1}}}\))

Refs.

J041757

0.140

0.003

0.14

\(\cdots \)

79, 83, 84

J041836

0.140

0.0033

0.13

\(\cdots \)

84

J041847

0.140

0.0041

0.10

\(\cdots \)

84

J041938

0.140

0.0062

0.10

\(\cdots \)

84

IRAM04191

0.140

0.05

0.14

\(1.5\times 10^{-5}\)

70, 71, 72

L1014IRS

0.260

0.15

0.11

\(1.3\times 10^{-7}\)

70, 73, 74, 75

L1148-IRS

0.140

0.13

0.080

\(1.0\times 10^{-7}\)

70, 76, 77

L1521F-IRS

0.140

0.04

0.07

\(1.1\times 10^{-6}\)

77, 78, 79

IC348-SMM2E

0.240

0.06

0.027

\(1.1\times 10^{-7}\)

79, 80, 81, 82

HH30

0.140

0.42

0.042

\(7.5\times 10^{-7}\)

85, 86, 87

L1262

0.2

1.0

0.33

\(4.0\times 10^{-5}\)

47, 50, 51, 142, 46

VLA1623

0.16

1.5

0.6

\(4.5\times 10^{-4}\)

16, 35

L723

0.3

2.4

0.4

\(3.2\times 10^{-4}\)

10, 11, 33, 28, 132, 155

L1489

0.14

4.4

0.5

\(2.0\times 10^{-7}\)

3, 4, 24, 137

B335

0.25

4

0.2

\(2.0\times 10^{-5}\)

10, 12, 24, 22, 58, 140, 142

NGC2264G

0.8

5

0.3

\(3.0\times 10^{-3}\)

17, 18, 36

AS353A

0.3

8.4

0.1

\(4.5\times 10^{-4}\)

1, 23, 52, 12

L1448C

0.35

9

0.1

\(4.5\times 10^{-4}\)

14, 15, 34

L1448N(A)

0.35

10

0.9

\(1.2\times 10^{-4}\)

14, 15, 35, 129, 130, 140

RNO43

0.4

12

0.5

\(2.1\times 10^{-4}\)

12, 22, 39

L483

0.2

14

0.31

\(1.5\times 10^{-5}\)

47, 45, 24

L1251B

0.2

14

1.2

\(4.9\times 10^{-5}\)

48, 142, 49

TTAU

0.14

17

5.8

\(4.1\times 10^{-5}\)

5, 6, 25, 26, 19, 1, 27

HH111

0.46

24

0.9

\(5.0\times 10^{-5}\)

20, 21, 23

IRAS16293

0.16

27

2.9

\(1.6\times 10^{-3}\)

8, 9, 30, 31, 32

L1251A

0.3

27

0.47

\(8.6\times 10^{-5}\)

48, 45, 49

HARO4-255FIR

0.48

28

0.2

\(1.3\times 10^{-4}\)

12, 19, 37, 38

L1551-IRS5

0.14

20

0.8

\(1.0\times 10^{-4}\)

1, 6, 28, 101, 102, 103

HLTAU

0.16

44

0.3

\(1.4\times 10^{-6}\)

5, 19, 1, 29, 23, 7, 119

L1228

0.20

7

0.15

\(5.4\times 10^{-6}\)

53, 94, 198

PVCEP

0.5

80

0.2

\(1.0\times 10^{-4}\)

12, 13, 19, 27

L1641N

0.42

170

0.6

\(9.0\times 10^{-4}\)

43, 37, 44, 142

FIRSSE101

0.45

123

1.1

\(2.0\times 10^{-3}\)

37, 40, 41

HH7-11 VLA3

0.35

150

0.8

\(1.1\times 10^{-3}\)

1, 2, 23, 69

RE50

0.46

295

0.84

\(3.0\times 10^{-4}\)

42, 37, 40, 23, 41, 116

SERPENS

0.415

98

2.0

\(5.3\times 10^{-4}\)

110, 111, 112, 156, 92, 93

IRAS22198

1.3

1240

0.57

\(2.3\times 10^{-4}\)

88, 89

NGC2071-IRS3

0.39

520

2.9

\(1.5\times 10^{-2}\)

54, 90, 91, 136

HH34

0.42

15

0.160

\(3.0\times 10^{-6}\)

59, 94, 95

AF5142 CM1

2.14

10 000

1.3

\(2.4\times 10^{-3}\)

96, 108

AF5142 CM2

2.14

1000

0.35

\(2.4\times 10^{-3}\)

96, 108

CepAHW2

0.725

10 000

6.9

\(5.4\times 10^{-3}\)

104, 105, 106, 107

IRAS20126

1.7

13 000

0.2

\(6.0\times 10^{-3}\)

152, 153, 199

HH80–81

1.7

20 000

5.0

\(1.0\times 10^{-3}\)

98, 113, 114, 115

V645Cyg

3.5

40 000

0.6

\(7.0\times 10^{-4}\)

122, 129, 137

IRAS16547

2.9

60 000

8.7

\(4.0\times 10^{-1}\)

149, 150, 151

IRAS18566 B

6.7

80 000

0.077

\(7.2\times 10^{-3}\)

99, 100, 167

IRAS04579

2.5

3910

0.15

\(9.0\times 10^{-4}\)

88, 148, 194

GGD14-VLA7

0.9

1000

0.18

\(1.6\times 10^{-3}\)

55, 65, 66, 67, 68, 97

IRAS23139

4.8

20 000

0.53

\(8.0\times 10^{-4}\)

123, 124, 125

N7538-IRS9

2.8

40 000

3.8

\(2.1\times 10^{-2}\)

88, 126, 127

N7538-IRS9 A1

2.8

40 000

1.4

\(3.0\times 10^{-2}\)

88, 126, 127

IRAS16562

1.6

70 000

21.1

\(3.0\times 10^{-2}\)

131, 133

I18264-1152 F

3.5

10 000

0.28

\(1.4\times 10^{-2}\)

99, 100, 123

G31.41

7.9

200 000

0.32

\(6.0\times 10^{-2}\)

134, 135, 143, 147

AF2591-VLA3

3.3

230 000

1.52

\(7.7\times 10^{-3}\)

121, 172, 195

I18182-1433b

4.5

20 000

0.6

\(2.8\times 10^{-3}\)

99, 196

I18089-1732(1)a

3.6

32 000

1.1

\(\cdots \)

196

G28S-JVLA1

4.8

100

0.02

\(\cdots \)

197

G28N-JVLA2N

4.8

1000

0.06

\(\cdots \)

197

G28N-JVLA2S

4.8

1000

0.03

\(\cdots \)

197

L1287

0.85

1000

0.5

\(3.3\times 10^{-4}\)

192, 193, 116, 118

DG Tau B

0.15

0.9

0.31

\(6.0\times 10^{-6}\)

60, 61, 157, 158

Z CMa

1.15

3000

1.74

\(1.0\times 10^{-4}\)

122, 159, 160

W3IRS5(d)

1.83

200 000

1.5

\(3.0\times 10^{-2}\)

128, 161, 162

YLW 16A

0.16

13

0.78

\(3.4\times 10^{-6}\)

137, 163

YLW 15 VLA1

0.12

1

1.5

\(1.1\times 10^{-5}\)

138, 164, 165, 166

L778

0.25

0.93

0.69

\(1.9\times 10^{-6}\)

4, 137, 168

W75N(B)VLA1

1.3

19 000

4.0

\(1.2\times 10^{-2}\)

139, 169, 170, 171, 172, 154

NGC1333 VLA2

0.235

1.5

2.5

\(4.9\times 10^{-4}\)

140, 141, 173, 174, 175

NGC1333 IRAS4A1

0.235

8

0.32

\(1.5\times 10^{-4}\)

140, 173, 176, 177, 178

NGC1333 IRAS4B

0.235

1.1

0.33

\(4.1\times 10^{-5}\)

140, 173, 177, 178

L1551 NE-A

0.14

4.0

0.39

\(1.5\times 10^{-5}\)

140, 179, 180, 181, 61, 62

Haro 6-10 VLA1

0.14

0.5

1.1

\(9.4\times 10^{-6}\)

146, 12, 182, 183, 184

L1527 VLA1

0.14

1.9

1.1

\(1.6\times 10^{-4}\)

144, 145, 146, 179, 184

OMC 2/3 VLA4

0.414

40

0.83

\(5.2\times 10^{-4}\)

146, 185

HH1–2 VLA1

0.414

23

1.2

\(4.6\times 10^{-5}\)

186, 187, 188, 109

HH1–2 VLA3

0.414

84

0.40

\(5.7\times 10^{-4}\)

186, 187, 188

OMC2 VLA11

0.414

360

2.16

\(3.2\times 10^{-3}\)

189, 190, 191

HH46/47

0.45

12

1.8

\(2.0\times 10^{-4}\)

23, 56, 57, 117, 120

IRAS20050

0.7

260

1.4

\(5.0\times 10^{-3}\)

63, 64

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(2017); (168) Rodriguez et al. (1989b); (169) Hunter et al. (1994); (170) Shepherd et al. (2003); (171) Carrasco-González et al. (2010a); (172) Rygl et al. (2012); (173) Plunkett et al. (2013); (174) Sadavoy et al. (2014); (175) Downes and Cabrit (2007); (176) Dunham et al. (2014); (177) Ching et al. (2016); (178) Yıldız et al. (2012); (179) Froebrich (2005); (180) Lim et al. (2016); (181) Takakuwa et al. (2017); (182) Doppmann et al. (2008); (183) Roccatagliata et al. (2011); (184) Hogerheijde et al. (1998); (185) Yu et al. (2000); (186) Fischer et al. (2010); (187) Rodríguez et al. (2000); (188) Correia et al. (1997); (189) Furlan et al. (2016); (190) Osorio et al. (2017); (191) Takahashi et al. (2008); (192) Yang et al. (1991); (193) Wu et al. (2010); (194) Xu et al. (2012); (195) Johnston et al. (2013); (196) Zapata et al. (2006); (197) C. Carrasco-González et al., in preparation; (198) Skinner et al. (2014; 199) Shepherd et al. (2000)

A correlation between bolometric and cm luminosities was noted by Cabrit and Bertout (1992) from a set of \(\sim \) 25 outflow sources, quoting a slope of \(\sim \) 0.8 in a log-log plot. Skinner et al. (1993) suggested a correlation between the 3.6 cm luminosity and the bolometric luminosity with a slope of 0.9 by fitting a sample of Herbig Ae/Be stars and candidates with 11 detections and 7 upper limits. The fit to the 29 outflow sources presented in Anglada (1995) gives a slope of 0.6 (after updating some distances and flux densities; a slope of 0.7 was obtained with the values originally listed in Table 1 of that paper), similar to the value given in Eq. (28). Shirley et al. (2007) obtained separate fits for the 3.6 cm and for the 6 cm data, obtaining slopes of 0.7 and 0.9, respectively (although these fits are probably affected by a few outliers with anomalously high values of the flux density, taken from the compilation of Furuya et al. 2003). Because radio jets have positive spectral indices with typical values around \(\sim 0.4\), it is expected that the 3.6 cm flux densities are \(\sim \) 20% higher than the 6 cm flux densities, but the slopes of the luminosity correlations are expected to be similar, provided the scattering in the values of the spectral index is small. L. Tychoniec et al. (in preparation) analyze a large homogeneous sample of low-mass protostars in Perseus, obtaining similar slopes of \(\sim \) 0.7 for data at 4.1 and 6.4 cm. These authors note, however, that the correlations are weak for these sources that cover a relatively small range of luminosities. These results suggest that there is a general trend over a wide range of luminosities, but with an intrinsic dispersion.

Recently, Moscadelli et al. (2016) derived a slope of 0.5 from a small sample (8 sources) of high luminosity objects with outflows traced by masers. Also, recent surveys targeted towards high-mass protostellar candidates (but without a confirmed association with an outflow) also show radio continuum to bolometric luminosity correlations with similar slopes of \(\sim \) 0.7 (Purser et al. 2016). Recently, Tanaka et al. (2016) modeled the evolution of a massive protostar and its associated jet as it is being photoionized by the protostar, making predictions for the free–free continuum and RRL emissions. These authors find global properties of the continuum emission similar to those of radio jets. The radio continuum luminosities of the photoionized outflows predicted by the models are somewhat higher than those obtained from the empirical correlations for jets but much lower than those expected for optically thin HII regions. When including an estimate of the ionization of the ambient clump by photons that escape along the outflow cavity the predicted properties get closer to those of the observed UC/HC HII regions. Photoevaporation has not been included. This kind of models, including additional effects such as the photoevaporation, are a promising tool to investigate the transition from jets to HII regions in massive protostars. Purser et al. (2016) found a number of objects with radio luminosities intermediate between optically thin HII regions and radio jets that these authors interpret as optically thick HII regions. We note that this kind of objects could be in an evolutionary stage intermediate between the jet and the HII region phases, and their properties could be predicted by models similar to those of Tanaka et al. (2016).

From a sample of outflow sources of low and very low bolometric luminosity, but using low angular resolution data (\(\sim 30''\)) at 1.8 cm, a correlation between the cm luminosity and the internal luminosity1 with a slope of either 0.5 or 0.6 was found (AMI Consortium et al. 2011a, b), depending, respectively, on the use of either the bolometric luminosity or the IR luminosity as an estimate of the internal luminosity. Morata et al. (2015) report cm emission from four proposed proto-brown dwarf (proto-BD) candidates, that appear to follow the general trend of the luminosity correlation but showing some excess of radio emission. Further observations are required to confirm the nature of these objects as proto-BDs, to better determine their properties such as distance and intrinsic luminosity, as well as their radio jet morphology. If confirmed as bona fide proto-BDs that follow the correlation, this would suggest that the same mechanisms are at work for YSOs and proto-BDs, supporting the idea that the intrinsic properties of proto-BDs are a continuation to smaller masses of the properties of low-mass YSOs. It is interesting that the only two bona fide young brown dwarfs detected in the radio continuum fall well in this correlation (Rodríguez et al. 2017).

Recently, it has been realized that young stars in more advanced stages, such as those surrounded by transitional disks2 are also associated with radio jets that have become detectable with the improved sensitivity of the JVLA (Rodríguez et al. 2014a; Macías et al. 2016). In these objects, accretion is very low but high enough to produce outflow activity detectable through the associated radio emission at a level of \(\lesssim \) 0.1 mJy. These radio jets follow the general trend of the luminosity correlation but appear to be radio underluminous with respect to the correlation that was established from data corresponding to younger objects. This fact has been interpreted as indicating that it is the accretion component of the luminosity that is correlated with the outflow (and, thus, with the radio flux of the jet). Accretion luminosity is dominant in the youngest objects, from which the correlation was derived, while in more evolved objects the stellar contribution (which is not expected to be correlated with the radio emission) to the total luminosity becomes more important. Thus, it is expected that in more evolved objects the observed radio luminosity is correlated with only a fraction of the bolometric luminosity.

In summary, the radio luminosity (\(S_\nu d^2\)) of thermal jets associated with very young stellar objects is correlated with their bolometric luminosity (\(L_{\mathrm{bol}}\)). This correlation is valid for objects of a wide range of luminosities, from high to very low luminosity objects, and likely even for proto-BDs. This suggests that accretion and outflow processes work in a similar way for objects of a wide range of masses and luminosities. Accretion appears to be correlated with outflow (which is traced by the radio luminosity). As the young star evolves, accretion decreases and so does the radio luminosity. However, for these more evolved objects the accretion luminosity represents a smaller fraction of the bolometric luminosity (the luminosity of the star becomes more important) and they become radio underluminous with respect to the empirical correlation, which was derived for younger objects.

8.2 Observational properties: radio luminosity to outflow momentum rate correlation

The radio luminosity of thermal radio jets is also correlated with the properties of the associated outflows. A correlation between the momentum rate (force) in the outflow, \(\dot{P}\), derived from observations, and the observed radio continuum luminosity at centimeter wavelengths, \(S_{\nu }d^2\), was first noted by Anglada et al. (1992) and by Cabrit and Bertout (1992). Anglada et al. (1992) considered a sample of 16 sources of low bolometric luminosity (to avoid a contribution from photoionization) and found a correlation \((S_\nu d^2/{\mathrm{mJy~kpc^2}}) = 10^{2.4\pm 1.0}\,(\dot{P}/M_{\odot }~{\mathrm{year^{-1}}})^{0.9\pm 0.3}\). Since the outflow momentum rate estimates have considerable uncertainties (more than one order of magnitude, typically), \(\dot{P}\) was fitted (in the log-log space) taking \(S_{\nu }d^2\) as the independent variable, as it was considered to be less affected by observational uncertainties. The correlation was confirmed with fits to larger samples (Anglada 1995, 1996; Anglada et al. 1998; Shirley et al. 2007; AMI Consortium et al. 2011a, b, 2012). The best fit to the low-luminosity sources (\(1 \lesssim L_{{\mathrm{bol}}} \lesssim 1000~L_\odot \)) presented in Table 2 gives (see also Fig. 9):
$$\begin{aligned} {\left( \frac{S_\nu d^2}{\mathrm{mJy~kpc^2}}\right) } = 10^{2.22\pm 0.46} \left( \frac{\dot{P}}{M_\odot ~\mathrm{{ year^{-1}~km~s^{-1}}}}\right) ^{0.89\pm 0.16}. \end{aligned}$$
(29)
Fig. 9

Empirical correlation between the outflow momentum rate and the radio continuum luminosity at cm wavelengths. Data are taken from Table 2. Triangles correspond to high luminosity objects (\(L_{\mathrm{bol}} > 1000~L_\odot \)), dots correspond to low-luminosity objects (\(1 \le L_{\mathrm{bol}} \le 1000~L_\odot \)), and squares to very low-luminosity objects (\(L_{\mathrm{bol}} < 1~L_\odot \)). The dashed line is a least-squares fit to all the data points and the grey area indicates the residual standard deviation of the fit. The solid line is a fit to the low-luminosity objects alone. The dot-dashed line corresponds to the radio luminosity predicted by the models of Curiel et al. (1987, 1989)

This correlation between the outflow momentum rate and the radio luminosity has been interpreted as evidence that shocks are the ionizing mechanism of jets. Curiel et al. (1987, 1989) modeled the scenario in which a neutral stellar wind is ionized as a result of a shock against the surrounding high-density material, assuming a plane-parallel shock. From the results obtained in this model, ignoring further details about the radiative transfer and geometry of the emitting region, and assuming that the free–free emission is optically thin, a relationship between the momentum rate in the outflow and the centimeter luminosity can be obtained (see Anglada 1996; Anglada et al. 1998):
$$\begin{aligned} \left( \frac{S_{\nu }d^2}{\mathrm{mJy~kpc^2}}\right) = 10^{3.5}\,\eta \left( \frac{\dot{P}}{M_{\odot }~{\mathrm{year^{-1}}}~\text {km s}^{-1}} \right) , \end{aligned}$$
(30)
where \(\eta = \varOmega /{4\pi }\) is an efficiency factor that can be taken to equal the fraction of the stellar wind that is shocked and produces the observed radio continuum emission. Despite the limitations of the model, and the simplicity of the assumptions used to derive Eq. (30), its predictions agree quite well with the results obtained from a large number of observations (Eq. 29), for an efficiency \(\eta \simeq 0.1\). González and Cantó (2002) present a model in which the ionization is produced by internal shocks in a wind, resulting of periodic variations of the velocity of the wind at injection.
Cabrit and Bertout (1992) and Rodríguez et al. (2008) noted that high-mass protostars driving molecular outflows appear to follow the same radio luminosity to outflow momentum rate correlation as the sources of low luminosity. As can be seen in Fig. 9, high luminosity objects fall close to the fit determined by the low luminosity objects. Actually, a fit including all the sources in the sample of Table 2, including both low and high luminosity objects, gives a quite similar result,
$$\begin{aligned} {\left( \frac{S_\nu d^2}{\mathrm {mJy~kpc^2}}\right) } = 10^{2.97\pm 0.27} \left( \frac{\dot{P}}{M_\odot ~{\mathrm {year^{-1}~km~s^{-1}}}} \right) ^{1.02\pm 0.08}, \end{aligned}$$
(31)
as it was also the case for the bolometric luminosity correlation (Fig. 8). Thus, radio jets in massive protostars appear to be ionized by a mechanism similar to that acting in low luminosity objects. Radio jets would represent a stage in massive star formation previous to the onset of photoionization and the development of an HII region. Actually, the correlations can be used as a diagnostic tool to discriminate between photoionized (HII regions) versus shock-ionized (jets) sources (see Tanaka et al. 2016 and the previous discussion in Sect. 8.1).

As in the radio to bolometric luminosity correlation, the very low luminosity objects also fall in the outflow momentum rate correlation. These results are interpreted as indicating that the mechanisms for accretion, ejection and ionization of outflows are very similar for all kind of YSOs, from very low to high luminosity protostars.

A direct measure of the outflow momentum rate is difficult for objects in the last stages of the star formation process, when accretion has decreased to very small values and outflows are hard to detect. For these objects, the weak radio continuum emission can be used as a tracer of the outflow. Recent results obtained for sources associated with transitional disks (Rodríguez et al. 2014a; Macías et al. 2016) indicate that the observed radio luminosities are consistent with the outflow momentum rate to radio luminosity correlation being valid and the ratio between accretion, and outflow being similar in these low accretion objects than in younger protostars.

8.3 On the origin of the correlations

As has been shown above, the observable properties of the cm continuum outflow sources indicate that these sources trace thermal free–free emission from ionized collimated outflows (jets). Both theoretical and observational results suggest that the ionization in thermal jets is only partial (\(\sim \) 1–10%; Rodriguez et al. 1990; Hartigan et al. 1994; Bacciotti et al. 1995). The mechanism that is able to produce the required ionization, even at these relatively low levels, is still not fully understood. As photoionization cannot account for the observed radio continuum emission of low-luminosity objects (see above), shock ionization has been proposed as a viable alternative mechanism (Curiel et al. 1987; González and Cantó 2002).

The correlations described in Sects. 8.1 and 8.2 are related to the well-known correlation between the momentum rate observed in molecular outflows and the bolometric luminosity of the driving sources, first noted by Rodriguez et al. (1982). More recent determinations of this correlation give \((\dot{P}/M_{\odot }~{\mathrm {year^{-1}~km~s^{-1}}}) = 10^{-4.36\pm 0.12}\) \((L_{\mathrm{bol}}/L_\odot )^{0.69\pm 0.05}\) (Cabrit and Bertout 1992) or \((\dot{P}/M_{\odot }~{\mathrm {year^{-1}~km~s^{-1}}}) = 10^{-4.24\pm 0.32}\) \((L_{\mathrm{bol}}/L_\odot )^{0.67\pm 0.13}\) (Maud et al. 2015, for a sample of massive protostars). The empirical correlations with cm emission described by Eqs. 28 and 31 result in an expected correlation \((\dot{P}/M_{\odot }~{{\mathrm {year^{-1}~km~s^{-1}}}})\) = \(10^{-4.77\pm 0.14}\) \((L_{\mathrm{bol}}/L_\odot )^{0.58\pm 0.08}\), which is in agreement with the results obtained directly from the observations. We interpreted the correlation of the outflow momentum rate with the radio luminosity (Eq. 31) as a consequence of the shock ionization mechanism working in radio jets, and the correlation of the bolometric and radio luminosities (Eq. 28) as a consequence of the accretion and outflow relationship. In this context, the well-known correlation between the momentum rate of molecular outflows and the bolometric luminosity of their driving sources can be interpreted as a natural consequence of the other two correlations.

9 Additional topics

9.1 Fossil outflows

In the case of regions of massive star formation there are also clear examples of jets that show the morphology and spectral index characteristic of this type of sources. Furthermore, these massive jets fall in the correlations previously discussed.

However, there is a significant number of molecular outflows in regions of massive star formation where it has not been possible to detect the jet. Instead, ultracompact HII regions are found near the center of these outflows (e.g., G5.89−0.39, Zijlstra et al. 1990; G25.65+1.05 and G240.31+0.07, Shepherd and Churchwell 1996; G45.12+0.13 and G45.07+0.13, Hunter et al. 1997; G192.16−3.82, Devine et al. 1999; G213.880−11.837, Qin et al. 2008; G10.6−0.4, Liu et al. 2010; G24.78+0.08, Codella et al. 2013; G35.58−0.03, Zhang et al. 2014).

We can think of two explanations for this result. One is that the central source has evolved and the jet has been replaced by an ultracompact HII region. From momentum conservation the outflow will continue coasting for a large period of time, becoming a fossil outflow in the sense that it now lacks an exciting source of energy. The alternative explanation is that a centimeter jet is present in the region but that the much brighter HII region makes it difficult to detect it. This is a problem that requires further research.

It should also be noted that in two of the best studied cases, G25.65+1.05 and G240.31+0.07, high angular resolution radio observations (Kurtz et al. 1994; Chen 2007; Trinidad 2011) have revealed fainter sources in the region that could be the true energizing sources of the molecular outflows. If this is the case, the outflows cannot be considered as fossil since they would have an associated active jet.

9.2 Jets or ionized disks?

The presence in star forming regions of an elongated centimeter source is usually interpreted as indicating the presence of a thermal jet. This interpretation is typically confirmed by showing that the outflow traced at larger scales by molecular outflows and/or optical/IR HH objects aligns with the small-scale radio jet. In the sources where the true dust disk is detected and resolved, it is found to align perpendicular to the outflow axis. However, in a few massive objects there is evidence that the elongated centimeter source actually traces a photoionized disk (S106IR: Hoare et al. 1994; S140-IRS: Hoare 2006; Orion Source I: Reid et al. 2007; see Fig. 10). These objects show a similar centimeter spectral index to that of jets and one cannot discriminate using this criterion. There is also the case of NGC 7538 IRS1, a source that has been interpreted as an ionized jet (Sandell et al. 2009) or modeled as a photoionized accretion disk (Lugo et al. 2004), although it is usually referred to as an ultracompact HII region (Zhu et al. 2013).
Fig. 10

The radio sources associated with S140 IRS1 and with source I in Orion. These sources of radio continuum emission are believed to trace photoionized disks and not jets. Image reproduced with permission from [left] Hoare (2006), copyright by AAS; and [right] based on Reid et al. (2007)

A possible way to favor one of the interpretations is to locate the object in a radio luminosity versus bolometric luminosity diagram as has been discussed above. It is expected that a photoionized disk will fall in between the regions of thermal jets and UC HII regions in such a diagram. Another test to discriminate between thermal jets and photoionized disks would be to eventually detect radio recombination lines from the source. In the case of photoionized disks lines with widths of tens of km s\(^{-1}\) are expected, while in the case of thermal jets the lines could exhibit widths an order of magnitude larger. It should be noted, however, that in the case of very collimated jets the velocity dispersion and, thus, the observed line widths, will be narrow.

The possibility of an ionized disk is also present in the case of low mass protostars. The high resolution images of GM Aur presented by Macías et al. (2016) show that, after subtracting the expected dust emission from the disk, the centimeter emission from this source is composed of an ionized radio jet and a photoevaporative wind arising from the disk perpendicular to the jet (see Fig. 11). It is believed that extreme-UV (EUV) radiation from the star is the main ionizing mechanism of the disk surface. Dust emission at cm wavelengths is supposed to arise mainly from grains that have grown up to reach pebble sizes (e.g., Guzmán et al. 2016).
Fig. 11

Decomposition of the emission of GM Aur at cm wavelengths. The free–free emission at 3 cm of the radio jet is shown in white contours and that of the photoevaporative wind from the disk is shown in black contours. The dust emission from the disk at 7 mm is shown in color scale. The free–free emission of the two ionized components was separated by fitting two Gaussians to the 3 cm image after subtraction of the contribution at 3 cm of the dust of the disk, estimated by scaling the 7 mm image with the dust spectral index obtained from a fit to the spectral energy distribution. Image reproduced with permission from Macías et al. (2016), copyright by AAS

10 Conclusions

The study of jets associated with young stars has contributed in an important manner to our understanding of the process of star formation. We list below the main conclusions that arise from these studies:
  1. 1.

    Free–free radio jets are typically found in association with the forming stars that can also power optical or molecular large-scale outflows. While the jets trace the outflow over the last few years, the optical and molecular outflows integrate in time over centuries or even millenia.

     
  2. 2.

    The radio jets provide a means to determine accurately the position and proper motions of the stellar system in regions of extremely high obscuration.

     
  3. 3.

    The core of these jets emits as a partially optically thick free–free source. However, in knots along the jet (notably in the more massive protostars) optically thin synchrotron emission could be present. Studies of this non-thermal emission will provide important information on the role of magnetic fields in these jets.

     
  4. 4.

    At present there are only tentative detections of radio recombination lines from the jets. Future instruments such as SKA and the ngVLA will allow a new avenue of research using this observational tool.

     
  5. 5.

    The radio luminosity of the jets is well correlated both with the bolometric luminosity and the outflow momentum rate of the optical or molecular outflow. This is a result that can be understood theoretically for sources that derive most of its luminosity from accretion and where the ionization of the jet is due to shocks with the ambient medium. These correlations extend from massive young stars to the sub-stellar domain, suggesting a common formation mechanism for all stars.

     

Footnotes

  1. 1.

    The internal luminosity is the luminosity in excess of that supplied by the interstellar radiation field.

  2. 2.

    Transitional disks are accretion disks with central cavities or gaps in the dust distribution that are attributed to disk clearing by still forming planets.

Notes

Acknowledgements

GA acknowledges support from MINECO (Spain) AYA2014-57369-C3-3-P and AYA2017-84390-C2-1-R grants (co-funded by FEDER). LFR acknowledges support from CONACyT, Mexico and DGAPA, UNAM. CC-G acknowledges support from UNAM-DGAPA-PAPIIT grant numbers IA102816 and IN108218. We thank an anonymous referee for his/her useful comments and suggestions.

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Authors and Affiliations

  1. 1.Instituto de Astrofísica de Andalucía, CSICGranadaSpain
  2. 2.Instituto de Radioastronomía y Astrofísica, UNAMMoreliaMexico

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