We present an analysis of the substructure revealed by RR Lyraes in Sloan Digital Sky Survey ( SDSS ) Stripe 82 , which covers 2 \aas@@fstack { \circ } 5 in declination on the celestial equator over the right ascension range \alpha = 20.7 ^ { \mbox { \small h } } to 3.3 ^ { \mbox { \small h } } .
We use the new public archive of light-motion curves in Stripe 82 , published by Bramich et al .
in 2008 , to identify a set of high-quality RR Lyrae candidates .
Period estimates are determined to high accuracy using a string-length method .
A subset of 178 RR Lyraes with spectrally derived metallicities are employed to derive metallicity-period-amplitude relations , which are then used , together with archive magnitude data and lightcurve Fourier decomposition , to estimate metallicities and hence distances for the entire sample .
The RR Lyraes lie 5–115 kpc from the Galactic center , with distance estimates accurate to \sim 8 per cent .
The RR Lyraes are further divided into subsets of 316 RRab types and 91 RRc types based on their period , colour and metallicity .

We fit a smooth density law to the distribution as a simple representation of the data .
For Galactocentric radii 5–25 kpc the number density of RR Lyraes falls as r ^ { -2.4 } , but beyond 25 kpc , the number density falls much more steeply , as r ^ { -4.5 } .
However , we stress that in practice the density distribution is not smooth , but dominated by clumps and substructure .
Samples of 55 and 237 RR Lyraes associated with the Sagittarius Stream and the Hercules-Aquila Cloud respectively are identified .
Hence , \sim 70 per cent of the RR Lyraes in Stripe 82 belong to known substructure , and the sharp break in the density law reflects the fact that the dominant substructure in Stripe 82 – the Hercules-Aquila Cloud and the Sagittarius Stream – lie within 40 kpc .
In fact , almost 60 per cent of all the RR Lyraes in Stripe 82 are associated with the Hercules-Aquila Cloud alone , which emphasises the Cloud ’ s pre-eminence .
Additionally , evidence of a new and distant substructure – the Pisces Overdensity – is found , consisting of 28 faint RR Lyraes centered on Galactic coordinates ( \ell \approx 80 ^ { \circ } ,b \approx - 55 ^ { \circ } ) , with distances of \sim 80 kpc .
The total stellar mass in the Pisces Overdensity is \sim 10 ^ { 4 } M _ { \odot } and its metallicity is [ Fe/H ] \sim - 1.5 .