Milky Way Accelerometry via Millisecond Pulsar Timing

The temporal stability of millisecond pulsars is remarkable, rivaling even some terrestrial atomic clocks at long timescales. Using this property, we show that millisecond pulsars distributed in the galactic neighborhood form an ensemble of accelerometers from which we can directly extract the local galactic acceleration. From pulsar spin period measurements, we demonstrate acceleration sensitivity with about $1\sigma$ precision using 117 pulsars. We also present a complementary analysis using orbital periods of 13 binary pulsar systems that eliminates the systematics associated with pulsar braking and results in a local acceleration of $(1.7\pm 0.5)\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$ in good agreement with expectations. This work is a first step toward dynamically measuring acceleration gradients that will eventually inform us about the dark matter density distribution in the Milky Way galaxy.

Figure 1

(a) Apparent pulsar acceleration ($c\dot{P}/P$) distribution vs spin period $P$. We plot $c\dot{P}/P$ uncorrected for proper motion and visualize the entire pulsar catalog. The pulsars selected for this work are in black in the bottom left of the plot. (b) Spatial distribution of selected pulsars across the galactic midplane, color coded by acceleration. The GC is marked with a cross ($+$). Pulsar distance uncertainties are suppressed for clarity. Inset: galactic rotation curve with data from Ref. [80].

Figure 2

Local galactic acceleration extracted from pulsar spin periods for selected pulsars. The abscissa $f(D,l,b)$ is a function of pulsar distance $D$, galactic longitude $l$, and latitude $b$ [Eq. (3a)]. Each dot represents an individual pulsar, and the ellipse around the dot represents the observational covariance matrix for that pulsar. The points are color coded by the degree of certainty that a particular point is an outlier [62]. The thick violet line is the best-fit estimate given by the relationship $a={\widehat{a}}_{0}f+\widehat{\lambda }$, where ${\widehat{a}}_0=(5.2\pm 1.6)\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$ and $\widehat{\lambda }=(5.7\pm 0.4)\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$. The fainter violet lines around the thick violet represent the distribution of fitted accelerations [62]. Lastly, the dashed black line has the slope $2.2\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$, which is the nominal value for the SSB assuming a circular velocity of $233\mathrm{km}/\mathrm{s}$ [83] and galactocentric distance of 8.1 kpc [83]. Inset: recovered braking distribution—in black, the distribution described by $\widehat{\lambda }$ is plotted over a histogram of $a$ values for pulsars within the green region $|f|<0.3$ in (a) that have an outlier score $<0.5$. In this region, the braking effect dominates over the galactic component.

Figure 3

Local galactic acceleration extracted from binary millisecond pulsar orbital periods given in Table II of Ref. [62]. The abscissa $f(D,l,b)$ is a function of pulsar distance $D$, galactic longitude $l$, and latitude $b$. Each dot represents an individual binary pulsar system, and the ellipse around the dot represents the observational covariance matrix for that system. The thick violet line is the best-fit estimate given by the relationship $a_b={\widehat{a}}_{0}f$, where ${\widehat{a}}_0=(1.73_{-0.37}^{+0.50})\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$. The fainter violet lines around the thick violet represent the distribution of fitted accelerations [62]. Finally, the dashed black line has the slope $2.2\times {10}^{-10}{\mathrm{m}/\mathrm{s}}^2$, which is the nominal value for the SSB assuming a circular velocity of $233\mathrm{km}/\mathrm{s}$ [83] and galactocentric distance of 8.1 kpc [83].