# Pulsars and neutron stars/The pulsar population
## The globular cluster population

Globular clusters are bound collections of stars in the halo of a galaxy. There are approximately 150 globular clusters in our Galaxy. Globular clusters are often searched for pulsars as 1) they contain a high fraction of millisecond pulsars and 2) their angular size is small allowing for a single, long observation. As globular clusters have a very high star density, close interactions are common. It is thought that the millisecond pulsars arise from such interactions.

### Particular globular cluster pulsars of interest

PSR B1620-26 is within the globular cluster M4. This pulsar system contains planetary mass bodies.

### Determining the population of globular cluster pulsars

Turk & Lorimer (2013) described a Bayesian method that can be applied to studying the pulsar population in a globular cluster. The number of pulsars in any given cluster depends upon the parameters of the globular cluster. In particular Hui et al. (2010) proposed a relationship between the pulsar abundance in a particular cluster and the stellar encounter rate, $\Gamma$.
The best fit model from the Turk & Lorimer (2013) paper suggested that the number of pulsars in a specific globular cluster, $N_{\rm {psr}}$ is
$\log _{e}N_{\rm {psr}}=-1.1+1.5\log _{10}\Gamma$
The number of pulsars expected to be detectable in any given survey is then given by:
$N_{\rm {expected}}={\frac {N_{\rm {psr}}}{2}}{\rm {erfc}}\left({\frac {\log _{10}L_{\rm {min}}-\mu }{{\sqrt {2}}\sigma }}\right)$
where $\mu =-1.1$ and $\sigma =0.9$ are reasonable values and $L_{\rm {min}}$ is the extrapolated luminosity sensitivity at an observing frequency of 1400 MHz (note that $L_{\rm {min}}=S_{\rm {min}}D^{2}$ where $D$ is the distance to the globular cluster).
A list of close-by globular clusters is given below:
| Cluster | Right ascension | Declination | Distance (kpc) | $\Gamma$ | $N_{\rm {known}}$ |
| Terzan 5 | 17:48:05 | -24:46:48 | 6.9 | 6800 | 34 |
| NGC 7078, M15 | 21:29:58.33 | +12:10:01.2 | 10.4 | 4510 | 8 |
| Terzan 6 | | | 6.8 | 2470 | |
| NGC 6441 | | | 11.6 | 2300 | 4 |
| NGC 6266, M62 | 17:01:12.60 | -30:06:44.5 | 6.8 | 1670 | 6 |
| NGC 1851 | 05:14:06.76 | -40:02:47.6 | 12.1 | 1530 | 1 |
| NGC 6440 | | | 8.5 | 1400 | 6 |
| NGC 6624 | 18:23:41 | -30:21:39 | 7.9 | 1150 | 6 |
| NGC 6681, M70 | 18:43:12.76 | -32:17:31.6 | 9.0 | 1040 | |
| 47 Tucanae, NGC 104 | 00:24:05.67 | -72:04:52.6 | 4.5 | 1000 | 23 |
| Pal 2 | 04:46:05.91 | +31:22:53.4 | 27.2 | 929 | 0 |
| |NGC 2808 | 09:23:03.10 | -64:51:48.6 | 9.6 | 923 | |
| NGC 6388 | 17:36:17.461 | -44:44:08.34 | 9.9 | 899 | |
| NGC 6293 | 17:10:10.4 | -26:34:54 | 9.5 | 847 | |
| NGC 6652 | | | 10.0 | 700 | 1 |
| NGC 6284 | 17:04:28.7 | -24:45:52 | 15.3 | 666 | |
| NGC 6626, M28 | 18:24:32.89 | -24:52:11.4 | 5.5 | 648 | 12 |
| M80 | 16:17:02.42 | -22:58:33.9 | 10.0 | 532 | |
| NGC 7089, M2 | 21:33:27.02 | -00:49:23.7 | 11.5 | 518 | |
| NGC 5286 | 13:46:26.81 | -51:22:27.3 | 11.7 | 458 | |
| NGC 6517 | 18:01:50.52 | -08:57:31.6 | 10.6 | | 4 |
| NGC 6539 | 18:04:49.68 | -07:35:09.1 | 7.8 | | 1 |
| NGC 6760 | 19:11:12.01 | +01:01:49.7 | 7.4 | | 2 |
| NGC 5904, M5 | 15:18:33.22 | +02:04:51.7 | 7.5 | | 5 |
| NGC 5024, M53 | 13:12:55.25 | +18:10:05.4 | 17.9 | | 1 |
| NGC 6838, M71 | 19:53:46.49 | +18:46:45.1 | 4 | | 1 |
| NGC 5272, M3 | 13:42:11.62 | +28:22:38.2 | 10.2 | | 4 |
| NGC 6205, M13 | 16:41:41.24 | +36:27:35.5 | 7.1 | | 5 |
| NGC 5986 | 15:46:03.00 | -37:47:11.1 | 10.4 | | 1 |
| M4, NGC 6121 | 16:23:35.22 | -26:31:32.7 | 2.2 | | 1 |
| NGC 6342 | | | | | 1 |
| NGC 6397 | 17:40:42.09 | -53:40:27.6 | 2.2 | | 1 |
| NGC 6522 | | | | | 3 |
| NGC 6544 | | | | | 2 |
| NGC 6656, M22 | 18:36:23.94 | -23:54:17.1 | 3 | | 2 |
| NGC 6749 | | | | | 1 |
| NGC 6752 | 19:10:52.11 | -59:59:04.4 | 4.0 | | 5 |
| NGC 7099, M30 | 21:40:22.12 | -23:10:47.5 | 8.3 | | 2 |
| Omega Centuari, NGC 5139 | 13:26:47.28 | -47:28:46.1 | 4.84 | | |

## The extra-Galactic population
### The Magellanic Clouds

The following pulsars are currently known in the small Magellanic cloud (SMC):
| Name | Period (s) | Dispersion measure (cm$^{-3}$pc) |
| J0045-7042 | 0.632 | 70 |
| J0045-7319 | 0.926 | 105.4 |
| J0100-7211 | 8.02 | - (XRS) |
| J0111-7131 | 0.689 | 76 |
| J0113-7220 | 0.326 | 125.49 |
| J0131-7310 | 0.348 | 205.2 |
The following pulsars are currently known in the small Magellanic cloud (LMC):
| Name | Period (s) | Dispersion measure (cm$^{-3}$pc) |
| J0449-7031 | 0.479 | 65.83 |
| J0451-67 | 0.245 | 45 |
| J0455-6951, B0456-69 | 0.320 | 94.89 |
| J0456-69 | 0.117 | 103 |
| J0456-7031 | 0.800 | 100.3 |
| J0457-69 | 0.231 | 91 |
| J0458-67 | 1.134 | 97 |
| J0502-6617, B0502-66 | 0.691 | 68.9 |
| J0519-6932 | 0.263 | 119.4 |
| J0521-68 | 0.433 | 136 |
| J0522-6847 | 0.675 | 126.45 |
| J0529-6652, B0529-66 | 0.976 | 103.2 |
| J0532-6639 | 0.642 | 69.3 |
| J0534-6703 | 1.818 | 94.7 |
| J0535-66 | 0.211 | 75 |
| J0535-6935 | 0.201 | 93.7 |
| J0537-69 | 0.113 | 273 |
| J0537-6910 | 0.016 | - |
| J0540-6919, B0540-69 | 0.050 | 146.5 |
| J0542-68 | 0.425 | 114 |
| J0543-6851 | 0.709 | 131 |
| J0555-7056 | 0.828 | 73.4 |

### Distant galaxies

McLaughlin et al. (2003) carried out a large-scale search for giant pulses coming from extragalactic pulsars, but did not make any convincing detections. As described below Rubio-Herrera et al. (2013) used Westerbork to search for pulsars in M31. Kondratiev et al. (2013) used the Green Bank and Arecibo telescopes to search for pulsars in nearby galaxies.

#### M31

Rubio-Herrera et al. (2013) used the Westerbork Synthesis Radio Telescope (WSRT) to search for radio pulsars and fast transients in M31. This search did not find any periodic sources, but they tentatively found some burst events with a dispersion measure of 55cm$^{-3}$pc which, they argued, placed these objects outside of our Galaxy. These burst signals have not been redetected.

#### Dwarf galaxies

Dwarf spheroidal galaxies (dSph) are low luminosity galaxies that are companions to our Galaxy (and to M31).
Rubio-Herrera & Maccarone (2012) searched for pulsars in dwarf spheroidal satellite galaxies of the Milky Way using the Green Bank telescope. No unambiguous detections were made.
The following table contains a list of dwarf galaxies that have been searched:
| Galaxy | Right ascension | Declination | Distance (kpc) | Reference |
| Ursa Minoris | 15:09:08.04 | +67:13:21.36 | 60 | Rubio-Herrera & Maccarone (2012) |
| Draco | 17:20:12.12 | +57:54:55.80 | 80 | Rubio-Herrera & Maccarone (2012) |
| Leo I | 10:08:27.00 | +12:18:27.36 | 250 | Rubio-Herrera & Maccarone (2012) |