Year1 Astrophysics Laboratory Phy-10021/23 Al-3

YEAR1 ASTROPHYSICS LABORATORY PHY-10021/23

PHY-10023 Laboratory Report Example R. D. Jeﬀries Last Updated 24th February 2015 (RDJ)

1 Abstract

Measurements from a UK Schmidt telescope photographic negative of the Vela supernova remnant were used to ﬁnd that the radius of the supernova shell is 21.5±0.2 pc. A simple theoretical description of the supernova expansion lead to estimates that the remnant is (56.7 ± 0.5) × 103 years old and is expanding into an interstellar medium of density of (1.9 ± 0.1) × 10−21 kg m−3. Comparing the present position of the Vela pulsar with an estimate of the shell centre position, it is found that the pulsar recoil velocity is 107 ± 4 km s−1. It is likely that these errors are under-estimates, because they depend on assumed values for the initial supernova explosion energy and current remnant shock temperature. The pulsar recoil is likely due to an asymmetric supernova explosion. These measurements suggest that the remnant is slightly asymmetric but this might be due to inhomogeneities in the interstellar medium.

2 Introduction

Supernova explosions mark the ends of the nuclear burning lifetimes of massive stars. These extraordinarily energetic events are caused when a star runs out of nuclear fuel and collapses. Supernovae are important for many reasons. The ejected matter and energy can stir up the interstellar medium (ISM) and trigger star formation, they are the major means of returning processed heavy elements to the ISM and the stellar corpses that they leave behind, namely black holes or neutron stars, are among the most exotic in the universe. When a supernova occurs, a large quantity of energy is deposited into a very small volume of space. The gas in this small volume becomes very hot and expands. A shock wave develops, separating the hot material from the cooler material of the external ISM. The shock propagates spherically outwards, sweeping up the ISM as it does so in the form of a shell. As the expansion, slows the shock temperature decreases, until the shell becomes visible in optical emission lines, forming a visible supernova remnant (SNR). The Vela SNR, at a distance of 500 pc, is among the most frequently photographed of southern hemisphere extended objects. Its filamentary structure is several degrees across. It is an important object because it is one of the few supernova remnants where the associated neutron star has been identified within it as a radio pulsar. It is thought that most young neutron stars AL-3 2 suffer a large recoil impulse during the supernova explosion and become dissociated from their supernova remnants on astronomically short timescales. The Vela SNR and pulsar offer a rare opportunity to measure this recoil velocity as well as study the dynamics of the interaction between the supernova shock wave and the ISM. This report outlines how measurements of the Vela SNR from photographic material along with a simple theoretical model of the SNR expansion lead to the age of the SNR, recoil velocity of the pulsar and density of the ambient ISM.

3 Theory

In this experiment a simple model for the SNR expansion was used. It can be shown that one quarter of the initial supernova energy, E, is deposited as kinetic energy in the expanding shell. Thus for a shell of mass M and radius R, expanding at a speed v we have

Mv2 E = (1) 2 4 Assuming that the temperature behind the expanding shock front, T , is given by

3mv2 T = , (2) 16k where m is the mass per particle in the ISM (assumed to be mainly hydrogen atoms) and k is the Boltzmann constant. Rewriting equation 1 in terms of the mean interstellar density ρ, it is found that 3E v = (3) 8πρR3 Integrating and substituting for E from equation 1, it follows that the age of the remnant, τ, is given by 2R τ = (4) 5v

4 Method

The main source of data was a photographic plate negative (Hα 1355) taken with the UK Schmidt telescope. The plate centre was at RA 08h 40m, Dec −44◦ 470 and the plate scale was 67.2 arcsec/mm. The plate was viewed using a light box and several measurements of the approximate diameter of the supernova shell were taken (see Figure 1). Five points on the shell circumference were marked and the largest angular distance across to the other side of the shell was used as an estimate for the diameter. These estimates are far more uncertain than the measurement errors, due to diﬃculty in deciding where the edge of the shell was. The standard deviation of the shell diameters was used as an estimate of the error. The ﬁve bisecting points of these chords across the SNR were marked and their coordinates with respect to the plate centre were measured. The average of these coordinates was used as an estimate of the physical centre of the SNR, presumably where the supernova explosion took place. AL-3 3

Figure 1: A schematic of the Vela SNR showing where our diameters were measured and our estimated positions of the SNR centre and current pulsar position

It was assumed that the initial supernova energy was E = 1044 Joules and that the temperature behind the shock was T = 5 × 105 K. Equation 2 was used to ﬁnd the present SNR expansion velocity and this was substituted into equations 3 and 4 to ﬁnd the mean density of the external ISM and the age of the SNR. By comparing the present position of the Vela pulsar with our estimate of the SNR centre, the SNR age could be used to estimate the component of the pulsar recoil velocity tangential to our line of sight.

5 Results

The ﬁve diameters and bisection coordinates (with respect to the plate centre) are given in Table 1. The mean diameter of the shell is 26.4 ± 0.2 cm, which, for an assumed SNR distance of 500 pc and plate scale of 67.2 arcsec/mm leads to a SNR radius of 21.5 ± 0.2 pc. The mean x and y coordinates of the SNR centre are 2.0 ± 0.4 cm, −0.4 ± 0.2 cm (where x is positive to the west of the plate centre and y is positive to the north of the plate centre – see Figure 1). The coordinates have been converted to oﬀsets in RA and Dec, leading to astronomical coordinates of the SNR centre of RA 08h 37m 34s ±25s, Dec -44◦ 510 2900 ±13400 . From these measurements the following quantities are calculated according to the methods outlined in the last section. The current SNR expansion velocity, v = 150 kms (from assumed values for m and T in equation 2). From equation 3, the mean ISM density, ρ = (1.9 ± 0.1) × 10−21 kg m−3. From equation 4 the age of the SNR, τ = (56.7 ± 0.5) × 103 years. The current position of the Vela pulsar is RA 08h 33m 39s, Dec -45◦ 000 10“. Comparing this AL-3 4

Table 1: Diameters and diameter bisection coordinates taken at ﬁve points around the SNR circumference (see Figure 1).

Measurement Diameter (cm) Bisection Coordinates (cm) (±0.1) x (±0.1) y (±0.1)

1 27.2 +2.2 -0.6 2 25.8 +2.6 +0.2 3 26.4 +3.0 -0.1 4 26.8 +1.7 -0.7 5 26.0 +0.6 -0.9

with our estimate of the SNR centre, it is found that the pulsar has moved 6.22 ± 0.24 pc in τ years, in a direction making an angle of (102.5 ± 2.9)◦ measured west from north (see Figure 1). The pulsar recoil velocity tangential to the line of sight is therefore 107 ± 4 km s−1.

6 Discussion and Conclusions

The accuracy of the estimates for the SNR age, ISM density and pulsar recoil velocity are likely to be poorer than estimated here, because these values depend on rather uncertain assumed values for the initial supernova explosion energy and present SNR shock temperature. The age of the SNR may also have been overestimated because the radiative energy losses from the shock has been ignored in our simple theoretical treatment of the expansion. The value obtained for the ISM density is rather typical for regions within the galactic disk (∼ 10−21 kg m−3 – Zombeck 1990), giving some conﬁdence that the estimated parameters are at least of the right order of magnitude. 40 The size of the pulsar recoil velocity and kinetic energy (∼ 10 Joules for a 1 M¯ neutron star), suggests that only a 0.01 percent asymmetry in the supernova explosion would be required to explain it. The measurements for the diameter of the supernova shell in Table 1 (and see Figure 1) also suggest a slight asymmetry in the SNR shape. While this might be attributed to an asymmetric explosion, it is far more likely to result from density inhomogeneity in the ISM and in any case, the individual diameter measurements are compromised by diﬃculties in deciding where the edge of the SNR lies.

7 Bibliography

Zombeck, M. V., 1990, Handbook of Space Astronomy and Astrophysics, 2nd ed., (Cambridge: CUP)