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The Galactic distribution of pulsar scattering and the 𝜏 − DM relation

Speaker: Qiuyi He

Supervisor: Xun Shi

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CONTENT

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scintillation studies

scattering time

flux variations (dynamic spectra)

complementary

Probe ISM on sub-AU scales using individual pulsars

Probe ISM on the Galactic scale using a large sample of pulsars

1. Introduction

the method we use

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1. Introduction

Cordes et al., 2016

Our results

2-population picture

Sutton 1971; Ramachandran et al. 1997; Bhat et al. 2004; Krishnakumar et al. 2015; Cordes et al. 2016 …

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2. Data collection

ATNF ++

single frequency: 224 pulsars

multi-frequency: 229 pulsars

Frequency information

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3. The reduced scattering intensity

reduced scattering strength

Physically, the dispersion measure represents the integrated free electron density in the pulsar line of sight. Accordingly, the scattering time is proportional to the integrated electron density fluctuation, where D is the distance to the pulsar. In both quantities, there is a degeneracy between distance and electron density/density fluctuation. In an effort to overcome this degeneracy and to focus on the scattering, we introduce a combined quantity -- reduced scattering strength. It is not directly affected by the pulsar distance and the average electron number density in the path. This reduced scattering directly reflects the reduced electron density fluctuation and can be related to the fluctuation parameter in Galactic scattering models.

Fig.1 shows the distribution of 𝝉 ̃ for both low-frequency and high-frequency observations in our sample. Regardless of the observing frequency, the number of measurements around 𝝉 ̃ = 10^{-5.1} is relatively small, separating two distinct populations at lower and higher 𝝉 ̃ values.

the negative five point one power of ten

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3. The reduced scattering intensity

Local (red pulsar)

Inner (blue pulsar)

Galactic distribution of reduced scattering strength

Confirmation of 2-population

The Galactic distribution of 𝝉 ̃ confirms the existence of two main pulsar populations underlying the current scattering data. It is worth noting that we have corrected the Galactic 3D positions of some of the pulsar distances in our sample by means of publicly available data on the Pulsar Parallaxes website, thus correcting the Galactic 3D positions of this fraction of the pulsars. Fig.2 shows the distribution of the `Galactic-plane‘ pulsars superimposed on the mid-plane Galactic electron number density distribution given by the YMW16 model. We can clearly see that the pulsars with different reduced scattering intensities are clustering in different locations in the Galaxy. While pulsars with smaller 𝜏 ̃ is red and form a local population in the vicinity of Earth, pulsars with larger 𝜏 ̃ shows blue points and reside on spiral arms, a region in the inner Galaxy referred to as the `inner thin disk’ in the electron density models. Note that, according to our definition of the reduced scattering intensity 𝝉 ̃, there is no apparent distance dependence in it. It implies that the fractional electron density fluctuations in our local environment are much smaller than those in the inner Galaxy.

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5. Scattering scale height of the inner disk

scattering

interstellar structure

corrugated plasma reconnection sheets

HII regions

superbubble shells

supernova remnants

ionized skins of molecular clumps

filaments ionized by hot stars

Stinebring et al. 2000 …

Stinebring et al. 2022 …

Ocker et al. 2020; Yao et al. 2021 …

Walker et al. 2017 …

corrugated plasma reconnection sheets

Pen & King 2012; Pen & Levin 2014; Liu et al. 2016; Simard & Pen 2018 …

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5. Scattering scale height of the inner disk

We have found that we have a sufficient sample of pulsars in the direction toward the inner Galaxy to carry out this study. To obtain a homogeneous sample for such analysis, we plot the r-Z distribution of 𝝉 ̃ of our pulsar sample, where r is the distance from the pulsar to the center of the galaxy. We find that the 𝝉 ̃ in the inner disk region at r from 3 to 5.5 kpc is relatively(ruai勒踢vly) independent of r. Within this radial range, we select pulsars in a compact region between us and the Galactic Center as our sample for analyzing the vertical scattering structure of the inner disk, which is the red fan-like region in Fig. We further limit the analysis to the absolute(爱b瑟录t) value of r is less than 1 kpc, where the distributions above and below the Galactic plane are symmetric(see迈取k) and well-sampled.

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5. Scattering scale height of the inner disk

Our result

Scattering 0.28kpc

HI disk 0.1 kpc

molecular gas 0.05kpc

OB stars 0.05kpc

“thin” stellar disk 0.3kpc

In this topic, I have so far come to the following conclusions.

There is a relationship between 𝜏 and DM, with 𝜏 increasing with DM, while low and high DM pulsars show different slopes with 𝜏, with the slope of high DM pulsars being significantly steeper.

𝜏 –DM relation may be systematically frequency dependent.

The reason for the change of slope in the 𝜏 -DM relation is the different galactic position of the pulsar.

We refitted a curve with the new sample.

The effect of thin disks in the range of r from 3 to 5.5 kpc on the pulsar scattering effect in height can be further analyzed.

在这个课题中，我到目前为止已经得出了以下结论。

𝜏与DM之间存在着一种关系，𝜏随着DM的增加而增加，而低和高DM脉冲星与𝜏的斜率不同，高DM脉冲星的斜率明显更陡峭。

𝜏-DM的关系可能是系统地依赖于频率的。

𝜏-DM关系中斜率变化的原因是脉冲星的银河系位置不同。

我们用新的样本重新拟合了一条曲线。

可以进一步分析在3到5.5kpc范围内的薄盘对脉冲星高度散射效应的影响。

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6. Effect of observing frequency

The scattering time tau is highly dependent on the observing frequency, the relationship between them is usually exponential, where the scattering index 𝜸 has been obtained from several observational measurements in general agreement with the predicted value of the Kolmogorov turbulence spectrum, which means,𝜸= 4, but still with uncertainties. In our study, we used $\gamma = 4.0$ to normalize all pulsar scattering measurements to 1 GHz. This extrapolation could, in principle, give rise to large errors in the scattering data of some pulsars. Therefore, we examine the influence of this normalization on our results by splitting the data into sub-samples of low-frequency and high-frequency observations.

The above line of figures shows the tau-DM relations for the two sub-samples. Low-frequency and high-frequency observations occupy different regions on the tau-DM fig: the high-frequency data clearly form two populations. It is thus the high-frequency data that dictated the separation of the pulsar scattering data into local and inner-Galactic populations.

This is confirmed by the following line of figures which shows the Galactic distribution of the scattering data. For the high-frequency data, we can clearly see that the blue and red parts belong to the inner-Galactic and local. But for the low-frequency data, the boundary between the local and inner-Galactic populations is less clear.

These apparently different distributions of the low- and high-frequency data arise primarily from an observational selection effect, so, it is still hard to tell whether the underlying distributions of low- and high-frequency data of the same pulsar population are different.

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7. Conclusions

scale height of the inner Galactic disk

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T H A N K S