Tiny-scale Structure Discovered toward PSR B1557$-$50

Tiny-scale atomic structures (TSAS) with spatial scales spanning from a few to hundreds of astronomical units have been studied for over four decades in the interstellar medium (ISM). Compared to the traditional definitions of the atomic medium in thermal equilibrium states—the cold neutral medium (CNM) and the warm neutral medium (WNM)—TSAS are overdense and overpressured, with densities and pressures several orders of magnitude higher than the theoretical values based on the heating and cooling balance (Stanimirović & Zweibel, 2018). TSAS has been probed mainly through three methods: (1) spatial and temporal $\rm H\textsc{i}$ absorption variability from high-resolution maps against extragalactic compact and resolved radio continuum sources (e.g. Diamond et al., 1989; Deshpande et al., 2000; Lazio et al., 2009; Roy et al., 2012; Rybarczyk et al., 2020); (2) temporal variability of $\rm H\textsc{i}$ absorption against pulsars (e.g. Frail et al., 1994; Johnston et al., 2003; Minter et al., 2005; Stanimirović et al., 2010); (3) spatial and temporal absorption variability of optical and ultraviolet lines (e.g. Na i, Ca i) toward stars in binary, multiple stellar systems, and globular clusters over a period of years (e.g. Meyer, 1990; Meyer & Blades, 1996; Lauroesch & Meyer, 2003).

Several mechanisms have been proposed to form TSAS, although there is no consensus yet. These mechanisms include TSAS being the tail-end of the turbulent spectrum(Deshpande et al., 2000), discrete elongated disk or cylinder clouds passing across the line of sight (Heiles, 1997), isolated events, such as fragmentation of the Local Bubble wall through hydrodynamic instabilities (Stanimirović et al., 2010), and structures related to planet-building gas materials (Ray & Loeb, 2017; Stanimirović & Zweibel, 2018). If TSAS represents the tail-end of turbulent dissipation processes, then a power-law relation between the spatial scales of TSAS and the optical depth variation is expected (Deshpande, 2000). Alternatively, Koyama & Inutsuka (2002) and Hennebelle & Audit (2007) modeled TSAS creation by shocks and colliding WNM flows in shocked regions.

Pulsars are particularly useful background sources because: (1) on- and off-source measurements can be obtained without position switching; (2) the relative high-velocity motion of the Earth and a pulsar over time allows us to sample a slightly different line-of-sight(LOS) through the ISM, therefore probing small structures in the ISM; (3) Hi absorption spectra of low-latitude pulsars can be used to estimate the pulsar kinematic distance (Weisberg et al., 2008);

TSAS may contain ionized gas. For example, assuming shielding is not too high, a high fraction of the carbon in TSAS clouds may be ionized by the interstellar radiation field (Heiles 1997; Stanimirović & Zweibel 2018). Ionization of hydrogen may also be instigated by local stellar objects, to produce fully ionized tiny-scale structures. McCullough & Benjamin (2001) detected an extremely narrow ionized filament, which can be attributed to the effect of photoionization from a star or compact object. Tiny-scale inhomogeneities in the ionized ISM can also be discerned through scintillation and/or extreme scattering events (Stanimirović & Zweibel, 2018). For example, Basu et al. (2016), Coles et al. (2015), and Hill et al. (2005) detected tiny-scale ionized structure with spatial scales of a few to hundreds of astronomical units through extreme scattering events and substructure in scintillation arcs toward pulsars.

PSR B1557$-$50 (J1600$-$5044) was the first pulsar against which Hi absorption variations were detected in the southern sky (Deshpande et al., 1992). In observations spaced around five years apart, these authors found an overpressured TSAS with a spatial scale of 1000 au, at a velocity of $-$40 km s^-1 with $\Delta\tau$ of 1.1. Johnston et al. (2003) confirmed similar Hi absorption variation at $-$40 km s^-1 as well as another two components at $-$110 and $-$80 km s^-1 toward this pulsar using Parkes, in two observational epochs spaced 14 yr apart. They concluded that the component at $-$110 km s^-1 is related to a TSAS of 1000 au, with a density of 2.6$\times$10⁴ cm^-3, and $\Delta\tau$ of 0.15. The sight line toward PSR B1557$-$50 traverses substantial distances, and has previously been monitored at such long cadences that multiple TSAS components could have passed across the source between observations. We focus here on monitoring PSR B1557$-$50 over a much shorter time baseline: $\sim$0.36 yr.

This Letter is organized as follows: Section 2 describes the observing and data processing strategies. In Section 3, we decompose the optical depth profile and study the properties of the CNM. Meanwhile, we analyze the variations of Hi optical depth profiles and the properties of the changes in the observed Hi gas at different epochs. We discuss our results and their implications in Section 4. We conclude in Section 5.

We used the Parkes ultra-wide-bandwidth, low-frequency receiver (‘UWL’) and the MEDUSA signal processing system (Hobbs et al., 2020), to observe the 21cm Hi line towards PSR B1557$-$50 at two epochs, referred to below as E1(2019.42) and E2(2019.78). The UTC dates at the beginning of the observations are 2019 May 26 and 2019 September 11, respectively. The integration time for each epoch was 379 and 382 minutes, respectively.

We recorded voltage data streams covering frequencies from 1344 to 1472 MHz. We injected a calibration signal (CAL) every 1 hr for a duration of 3 minutes in order to calibrate the antenna temperature. We used the DSPSR package (van Straten & Bailes, 2011) to process the baseband data to get spectra with a velocity resolution of $\sim$0.1 km s^-1. The data were folded synchronously with the pulsar period for an integration time of 10 s with 64 phase bins.

The final calibrated antenna temperature of the $\rm H\textsc{i}$ emission spectrum, $T_{\rm HI}(v)$, is required to compute the frequency-dependent noise spectrum (see §3.2). $T_{\rm HI}(v)$ was obtained by removing the baseline of $I^{\rm off}(v)$ using a third-order polynomial. To obtain the brightness temperature-calibrated $T^{\rm off}(v)$, which is required to derive $T_{\rm s}$ (see Appendix B), we scaled $T_{\rm HI}(v)$ to match the Parkes Galactic All-Sky Survey (GASS) intensity scale (McClure-Griffiths et al., 2009).

The absorption spectra are affected by on-source ripples, especially for E2. We identified the Fourier components of the ripples. Among these there are two baseline ripples with lag times of 0.175 and 0.35 $\mu$s (the second harmonic ripple) corresponding to the periods of standing waves formed by the reflections between the vertex and the focal plane. We did not attempt to diagnose formation mechanisms for any other ripples. All ripples were reduced in $I(v)$ by fitting for and removing sinusoidal functions with the same Fourier components.

The Hi emission and absorption spectra from E1 and E2 are shown in the first and second panels of Figure 1, respectively. There are clear differences in the absorption features between the two epochs, which we discuss further below.

Below the spectra, we display the distance versus radial velocity curve, which was derived for the Galactic coordinates of PSR B1557$-$50 ($l=$330.690^∘, $b=$1.631^∘) using a linear rotation curve (Mróz et al., 2019). A detailed description of the derivation is given in Appendix A. The lower distance limit $D_{l}$=$5.6\pm 0.3$ kpc for PSR B1557$-$50 is set by the velocity center of the most distant absorption feature. The upper distance limit $D_{u}=16.6\pm 0.8$ kpc is given by the distance of the nearest significant emission component (brightness temperature above 35 K; Weisberg et al., 1979) not seen in absorption. We adopted the method described in Verbiest et al. (2012) to translate these lower and upper limits into actual distance using a likelihood analysis. The updated pulsar distance $D_{\rm updated}$ is $6.0^{1.8}_{0.6}$ kpc. This is lower than the distance from the Australia Telescope National Facility (ATNF) pulsar catalog $D_{\rm psrcat}=6.9^{1.9}_{0.9}$ kpc, which was estimated by Verbiest et al. (2012) based on Hi distance limits from Johnston et al. (2001) with a flat rotation curve (Fich et al., 1989), while higher than the distance determined from recent electron density models, which give $D_{\rm DM}$=5.1 kpc (Yao et al., 2017).

If the tentative TSAS is a spherical cloud with diameter of $L_{\perp}$, the derived Hi volume density and thermal pressure are larger than $\sim 10^{4}$ cm^-3 and $\sim 10^{6}$ K cm^-3, respectively. These values are consistent with previous TSAS studies (assuming similar geometry), with TSAS showing densities and thermal pressures two to three orders of magnitude larger than typical ISM values (Heiles, 1997; Stanimirović et al., 2010; Stanimirović & Zweibel, 2018).

When the dynamical time $t_{dyn}$ is larger than the cooling time $t_{cool}$, clouds may reach a thermal equilibrium, even if they are overpressured. The column density $N_{\rm min,c}$ for a cloud at the balance of cooling and expanding can be calculated. As estimated by Stanimirović & Zweibel (2018),

where $R$ is the size of the cloud, $T$ is the kinetic temperature, and $\Lambda$ is the radiative loss function assuming the Cii fine structure line is the main source of cooling, with a carbon depletion factor of 0.35. Clouds with a column density larger than $N_{\rm min,c}$ would cool radiatively faster than they expand and reach thermal equilibrium. We use the Hi spin temperature as an approximation of the kinetic temperature (Lauroesch & Meyer, 2003) to estimate $N_{\rm min,c}$. We found that our tentative TSAS component has $N{(\rm HI)}_{\rm TSAS}$ significantly larger than $N_{\rm min,c}$, suggesting that it may be overpressured and in thermal equilibrium with the ambient ISM.

To alleviate the problem of overpressurization, Heiles (1997) proposed a model in which TSAS represents discrete features in the shape of cylinders and disks that are homogeneously and isotropically distributed within CNM clouds. The volume density of TSAS depends both on the spatial scale across the LOS, $L_{\perp}$, and the path length along the LOS $L_{\parallel}$. Following Heiles (1997), we define the geometric elongation factor $\mathscr{G}$ = $L_{\parallel}/$$L_{\perp}$ and use the standard CNM thermal pressure of 4000 $\rm\,cm^{-3}\,K$. Based on our measured spin temperature and column density, the elongation factor $\mathscr{G}$ required for our tentative TSAS to match the CNM pressure is $\sim 5000$. Such extremely filamentary structure is out of the range predicted by Heiles (1997), who found $\mathscr{G}$ larger than 1 and less than 10. This is a result of the large variation of optical depth and the small spatial scale of the tentative TSAS that we detected.

Hennebelle & Audit (2007) found that CNM clouds can be generated from thermally unstable regions in colliding WNM flows based on simulations with resolutions of 400 and 4000 au (larger than the typical spatial scales of observed TSAS). The supersonic collisions of CNM clouds form transient shocked regions with large temperature variations at the boundaries, showing similar properties to TSAS. Such temperature variations could induce line width and optical depth variations in the observed Hi absorption spectrum. From Figure 1 and Table 1 it can be seen that, in addition to apparent optical depth variations, the spin temperatures and line widths of the CNM components detected in this work do exhibit differences between the two epochs. While much of this variation lies below strict $3\sigma$ limits, it may still be indicative of the variations predicted by colliding flows models, possibly suggesting that our tentative TSAS cloud could have formed from such colliding WNM flows. However, better evidence of variability in the data, together with detailed descriptions of the properties of TSAS from higher-resolution simulations (<100 au) are needed to make firm quantitative comparisons.

We have obtained Hi absorption spectra in two epochs 0.36 yr apart toward PSR B1557$-$50 with the Parkes telescope. We have detected one component with marginally significant absorption variations, which probes astronomical-unit-scale atomic structure in the Milky Way. Our main results are summarized as follows:

1. One TSAS component at $\sim$$-$54 km s^-1 was marginally detected with an S/N of 3.2 after carefully reducing artifacts on the difference spectrum.

2. The characteristic plane-of-sky spatial scale of the TSAS component is 17 au, with an inferred volume density (assuming a spherical cloud) of $2.7\times 10^{5}$ cm^-3, and thermal pressure of $2.1\times 10^{7}\rm\,cm^{-3}$ K, suggesting that the TSAS is overdense and overpressured by two to three orders of magnitude.

3. The inferred overpressured TSAS has sufficiently high column density to be in thermal equilibrium with the ambient ISM, while still being overpressured.

4. The elongation factor of the TSAS cloud would need to be $\sim$5000 in order for it to be in pressure equilibrium with a canonical CNM. This is much larger than expected from disks or cylinders (Heiles, 1997), and than the aspect ratio of observed ISM filaments.

5. In addition to optical depth variations, there is some evidence of line width and temperature variations in the CNM components observed at the two epochs. This may hint at a possible formation mechanism involving WNM collisions.

6. We consider a scenario in which the TSAS represents the tail-end of a turbulent cascade, and find that the turbulent line width would be insufficient to confine such an overpressured cloud.

Further monitoring of this pulsar, as well as other pulsars with previous Hi absorption measurements using single-dish telescopes (e.g. Parkes, FAST), would enable us to detect a larger population of TSAS, and with sensitivity to a wide range of spatial scales, which may be critical in better probing the role of turbulence in TSAS formation. More generally, future high-resolution, interferometric observations (e.g. with the VLA, ALMA) of atomic and molecular lines (e.g. Hi, CO, Ci, Cii, SiO) toward TSAS associated with a larger range of spin temperature estimates are necessary to better constrain TSAS cooling and heating mechanisms, and shed crucial light onto TSAS formation.