Voyager 1 Electron Densities in the Very Local Interstellar Medium to beyond 160 au

The two Voyager spacecraft have been exploring the interstellar medium beyond the heliopause since 2012 (Voyager 1) and 2018 (Voyager 2). Electron plasma oscillations and a quasi-thermal noise line at the electron plasma frequency have enabled the determination of the electron density in this region, revealing a radial density gradient convolved with shocks and pressure fronts. Voyager 1 has a functioning wideband receiver that provides high-spectral-resolution observations allowing the detection of the quasi-thermal noise line and has now provided electron densities to 161.4 au. Since a pressure pulse observed in 2020 around day 146 at about 149 au, the density has remained relatively constant at 0.147 cm−3 based on the most recent observations from 2023, suggesting that Voyager 1 has reached a broad density peak and possibly a new regime.


Introduction
Voyager 1 crossed the heliopause and entered the very local interstellar medium (VLISM) on 2012 August 25 (Gurnett et al. 2013;Krimigis et al. 2013;Stone et al. 2013) at about 121.6 au.Voyager 2 followed on 2018 November 5 at 119 au (Burlaga et al. 2019;Gurnett & Kurth 2019;Krimigis et al. 2019;Richardson et al. 2019;Stone et al. 2019).These spacecraft have provided the first in situ observations of the magnetic field, energetic charged particles, cosmic rays, and plasma waves in this region.In particular, plasma wave observations have revealed electron plasma oscillations at the local electron plasma frequency f pe (Gurnett et al. 2013;Gurnett & Kurth 2019;Kurth & Gurnett 2020) and, more recently, the detection of a quasithermal noise line at f pe (Burlaga et al. 2021;Gurnett et al. 2021;Ocker et al. 2021;Meyer-Vernet et al. 2022;Kurth et al. 2023;Meyer-Vernet et al. 2023), both of which allow the local electron density to be determined by n f 8980.
where frequency is in Hz and density is in cm −3 .
An overview of the Voyager 1 plasma wave and electron density observations since the heliopause crossing are given in Figure 1.The bottom panel shows the plasma wave spectrum from the Voyager wideband receiver between 1.8 and 4.0 kHz using an extreme stretch of the gray amplitude scale to highlight the narrow line at f pe after about 2017.The result is that intense plasma oscillations (labeled epo) are saturated.The plasma oscillations occur at frequencies as low as about 2.1 kHz in late 2012, which is shortly after the heliopause crossing.These occur approximately annually at increasingly higher frequencies through 2019.The more recent plasma oscillation events are brief and are not clearly visible in this presentation, but are shown more clearly in Figure 3 of Gurnett & Kurth (2019).In that paper, there is a correspondence shown between two of the plasma oscillation events and shocks detected in the magnetometer data.However, Gurnett et al. (2021) argue the other events are likely associated with distant shocks that were too weak to be observed in situ by Voyager 1. Burlaga et al. (2021) show two pressure fronts, pf1 and pf2, as identified in the magnetometer data that are not accompanied by plasma oscillations.It is thought these are pressure waves that have not yet steepened into shocks.Nevertheless, the increase in magnetic field intensity across the pressure front as expressed as B 2 /B 1 is the same as the increase in plasma density as determined by the quasi-thermal line at f pe and expressed as n 2 /n 1 to within the uncertainties.In each case the subscript 2 refers to the parameter measured after the pressure front and 1 to the parameter measured before crossing the front.
The observations presented herein are from the Voyager Plasma Wave Science instrument (Scarf & Gurnett 1977).The instrument detects radio and plasma waves with two receivers.One is a stepped-frequency receiver having 16 log-spaced channels with center frequencies from 10 Hz to 56.2 kHz and ∼15% bandwidth.This spacing gives four channels per decade in frequency.For the Voyager Interstellar Mission, each channel provides an average of four measurements of the electric field acquired every 16 s.The second receiver is a wideband receiver with a bandpass of 50 Hz to ∼12 kHz.The voltage at the input is sampled at a rate of 28,800 s −1 with 4-bit precision.There is an automatic gain control amplifier to keep the signal within an optimum range for the 4-b analog-to-digital converter, but there is no telemetry channel for the gain; hence the wideband data do not have an absolute calibration.The Appendix of Kurth et al. (2023) describes the processing of the wideband data used for the spectrogram in the bottom panel of Figure 1.The Voyager 2 wideband receiver ceased returning usable data in 2002.
The purpose of this paper is to update the Voyager 1 densities through late 2023.We show that the electron density has remained remarkably constant since the pressure front in 2020 and we suggest this represents the end of the heliospheric boundary layer (Pogorelov et al. 2017;Gurnett & Kurth 2019) characterized by a radial gradient in the electron density and the beginning of a broad region of relatively constant density, possibly related to the broad maximum predicted by heliospheric models.Of course, only continued observations of the density by Voyager 1 will be able to identify an actual peak.

New Observations
Figure 2 expands the timescale for the last five years shown in Figure 1.This covers the interval from before pf2 through the most recent data.It should be noted that the digital wideband waveforms are recorded on board Voyager at a rate of 115 kbps whereas the maximum downlink rate from Voyager at its great distance is 1.4 kbps.Hence, extraordinary measures are required to return these data.Only tens of seconds of these data are acquired per week.And, since the data are played back only a few times per year and they are periodically overwritten on the onboard digital tape recorder, gaps can occur if there is a loss of data during downlink due to weather or other issues; this accounts for the gaps in Figures 1 and 2. Furthermore, even using most of the resources at a Deep Space Network complex (i.e., an array of one 70 m and four 34 m antennas) the received signal-to-noise ratio on the ground is minimal, which can translate into bit errors in the telemetry stream.While some despiking can be performed on the received data to minimize the effect of these errors, the resulting spectrogram can have a high noise background such as during mid-2022.
Figure 2 shows that the electron density has been relatively stable since pf2, averaging 0.1484 ± 0.0028 cm −3 .This period includes a modest rise centered on 2021 when Burlaga et al. (2023)  reported a "hump" in the magnetic field and a somewhat smaller rise in 2023.After both of these time-limited rises, the density returned to what appears to be a nominal value of ∼0.147 cm −3 .After the hump, from 2022 through the end of the available data, the average density was 0.1469 ±0.0014 cm −3 .The latter is a less than 1% variation.Further, the post-2022 average density is virtually the same as the post-pf2/pre-hump value of 0.147 cm −3 .We have added a dashed red line at a density of 0.147 cm −3 to show that both before and after the two density rises in this time period, the background density seems to return to this value.
The post-2022 average density of 0.1469 cm −3 corresponds to a plasma frequency of 3.44 kHz.Strikingly, this is very close to the maximum frequency of heliospheric radio emissions reported by Kurth et al. (1984Kurth et al. ( , 1987) ) and Gurnett et al. (1993).They suggested the radio emissions were generated in a plasma whose plasma frequency matched the frequency of the radio emissions.Voyager 1 has apparently reached this VLISM density.To avoid confusion, however, given the recent lack of electron plasma oscillations as evidence of shocks, Kurth et al. (2023) suggested that either due to the recent minimum in the solar cycle or the increasing distance of Voyager 1, one might conclude that shocks simply do not propagate beyond about 145 au.And, should very strong shocks associated with the current solar maximum be able to propagate much farther, these would likely not reach Voyager 1 until 2036.Hence, we do not suggest Voyager 1 is currently in the radio emission source region, just that the radio emissions' maximum frequency argue for a VLISM density similar to what Voyager 1 observed in 2023.

Discussion
Voyager 1 has reached a region whose plasma density corresponds to the source of the highest-frequency heliospheric radio emissions observed by the Voyagers in the 1980s and 1990s.However, it remains to be seen whether this is a maximum of the expected VLISM density, prior to the rollover in the density predicted, for example, by simulations such as in Pogorelov et al. (2017) and Sokół et al. (2022).Alternately, this could be a transient feature due to an extended increase in the solar wind dynamic pressure related to a solar cycle effect as described by Burlaga et al. (2023).
Voyager 1 is likely more than several hundred astronomical units from reaching an interstellar medium unaffected by the Sun and its heliosphere (see, Pogorelov et al. 2017).A heliospheric bow shock existing at a distance of order 250 au was discounted by McComas et al. (2012).However, this issue has been reconsidered (Ben-Jaffel et al. 2013;Scherer & Fichtner 2014;Pogorelov et al. 2017;Mostafavi et al. 2022) and may exist as far as 400 au (Zank et al. 2013).And Lyα measurements (see, Linsky & Wood 1996) and simulations have shown a hydrogen wall extending hundreds of astronomical units upstream from the heliosphere (Zank et al. 2013;Figure 3. (Top) Daily averages of the magnetic field magnitude from 2012 through April 2022.Notations sh1, sh2, pf1, and pf2 are shocks and pressure fronts described in (Burlaga et al. 2021).(Bottom) Electron densities from the Voyager 1 plasma wave instrument's observations of electron plasma oscillations (epo) and detection of a quasi-thermal line at the electron plasma frequency f pe .Taken from (Kurth et al. 2023).Pogorelov et al. 2017).Hence, Voyager is still well within the very local interstellar medium defined as being subject to the influence of the Sun and heliosphere.Nevertheless, Voyager 1 has not observed electron plasma oscillations, an indicator of a shock, since 2019 near 145 au (Kurth et al. 2023) and the observations presented herein show a nearly constant plasma density extending for ∼10 au and more than 3 yr since pf2.Such a broad local maximum is given in simulations (see Pogorelov et al. 2017).This appears to be an evolution into a new (for Voyager) region still influenced by the nearby heliosphere, and characterized by minimal density gradients.Burlaga et al. (2023) have shown that since the 2020 pressure front, Voyager 1 has observed generally high magnetic field intensities.This is in contrast to earlier shock and pressure front crossings characterized by jumps in |B| followed by ramps during which the field intensity decreases.These authors point to an ∼2 yr interval between 2015 and 2017 during the declining phase of the solar cycle when the solar wind dynamic pressure was unusually high at 1 au.This high-pressure region, then, would propagate through the heliosphere and result in a pressure wave upon colliding with the heliopause.The pressure wave would eventually arrive at Voyager's location in 2020, about 5 yr after it was observed near Earth.In this regard, the large electron densities observed after pf2 could be considered an aspect of this solar cycle effect.We point out, though, that while the jump in n e matched the jump in B at the second shock and two pressure fronts discussed by Burlaga et al. (2021), the density and |B| follow different general trends between these events.Figure 3 from (Kurth et al. 2023) shows the large-scale variations in |B| and n e .The top panel in Figure 3 makes the point that after the jump in |B| at the two shocks and pf1, there is a downward ramp.This was not the case after pf2, the "hump" feature.The electron densities do not show the jump-ramp variation seen in the magnetic field.In general, there is a general increase in density through about 2018, which is not seen in the field.Only after pf2 do both parameters show a jump and remain high through 2021.That both the density and field strength have remained high since pf2, therefore, stands as a difference with the previous interval.And, recently (Burlaga et al. 2024) reported that the magnetic field in 2022 displays no intermittency, something not observed elsewhere in the VLISM.Data from 2023 were not analyzed in that work.

Conclusion
It is apparent that Voyager 1 has entered a new regime beyond the heliospheric boundary layer in the VLISM.This regime is characterized by sustained high plasma densities of ∼0.147 cm −3 and magnetic fields of ∼0.5 nT (at least through 2022).The plasma densites show very small variations, of the order 0.3% or half that outside of two modest density increases lasting several months to a year.Further, they approximately correspond in plasma frequency to the maximum heliospheric radio emission frequencies observed by the Voyagers in the 1980s and 1990s coming from beyond the heliopause.What is not understood is whether this region is the result of a solar cycle variation in solar wind dynamic pressure (Burlaga et al. 2023), or a more stable region, possibly an indication of a broad density maximum beyond the heliopause as given in a number of models.Continued Voyager observations may resolve this.

Figure 1 .
Figure 1.(Top) Electron densities determined from electron plasma oscillations (in red) and a quasi-thermal line at the electron plasma frequency f pe (in black) shown in the bottom panel.Noted in green are the times of two shocks, sh1 and sh2, and two pressure fronts, pf1 and pf2, reported by Burlaga et al. (2021).(Bottom) A frequency-time spectrogram showing plasma wave phenomena as a function of frequency and time.Noted are electron plasma oscillation events (epo) that are highly saturated due to the extreme grayscale stretch.In the last half of the plotted interval, a thin line at the electron plasma frequency can be seen.

Figure 2 .
Figure 2. Similar in format to Figure 1, this figure focuses on the interval from just before pressure front 2 through the end of available data.The dashed red line at about 0.147 cm −3 represents a recurring density observed in the post-pf2 regime.